ELECTROLYTIC DISSOCIATION THE THEORY . OF ELECTROLYTIC DISSOCIATION AND SOME OF ITS APPLICATIONS BY HARRY C. JONES ASSOCIATE PROFESSOR OF PHYSICAL CHEMISTRY IN JOHNS HOPKINS UNIVERSITY Neto gork THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., Ltd. 1904 All rights reserved Copyright, 1900, By THE MACMILLAN COMPANY. Set up and electrotyped. Published January, 1900. Reprinted June, 1904. NottoooD JPrras J. S. Cushing & Co. - Berwick & Smith Co. Norwood, Mass., U.S.A. PREFACE TO SECOND EDITION When this little volume was first written, the Theory of Electrolytic Dissociation was well established, but was much less known than at present. During the past few years it has become the household word of practically every scientific chemist, and is now recognized to be indispensable to the development of chemical science. Indeed, it has become of such fundamental importance that it is now introduced into the very early stages of the teaching of chemistry, and the chemistry of atoms and molecules is rapidly giving place to the chemistry of ions. The Theory of Electrolytic Dissociation has thus ac- quired a new interest, and will doubtless ingraft itself more and more deeply into general chemistry. A number of minor changes have been made, but the plan of the second edition of this book is essentially the same as the first; the reception with which the work has met having led to the conviction that serious changes might injure rather than improve the work. H. C. J. PREFACE During the last few years the writer has been frequently asked, directly and by letter: Where can an account of the newer developments in physical chemistry be obtained ? Where can we learn something about the relation between osmotic pressure and gas pressure, and about the origin and significance of the theory of electrolytic dissociation ? The most satisfactory reply which could be made was, read certain original papers. But these were not always accessible, and, in some cases, not quite adapted to the state of development of the reader. While it is true that certain chapters in some of the text-books on physical chemistry are helpful in the direction indicated, yet no one of them seemed to meet entirely the demands of a large number of students. This little volume has been written with the hope of supplying students of chemistry, physics, and physical chemistry with at least a part of the information which they desire. It aims to give an account of the origin and significance of these newer developments. A student who has a fair knowledge of the origin of the theory of electrolytic dissociation, of the evidence upon which it rests, and of its applications, has already acquired an ele- mentary conception of many of the fundamental principles which underlie modern physical chemistry. In order that the relation between the newer and the older physical chemistry may be the better understood, a V VI PREFACE chapter is devoted to the latter. A few typical pieces of work in the earlier period are considered very briefly, and some of the conclusions reached are pointed out. It is hoped, in this way, to show clearly the nature of the problems solved, the methods employed, and some of the results obtained. The origin and development of the theory are then taken up. This is followed by an examination of some of the more important lines of evidence bearing upon the theory; and, finally, some applications of the theory in chemistry, physics, and biology are considered. The attempt is made to answer, in part, the questions: What was physical chemistry before the theory of electro- lytic dissociation arose ? How did the theory arise ? Is it true ? What is its scientific use ? It is believed that a closer acquaintance with the facts will but serve to increase the interest in physical chemistry, which is already manifesting itself in so many directions. I wish to express my indebtedness to my friend Dr. S. H. King, for valuable assistance in reading the proof of this volume. HARRY C. JONES. Johns Hopkins University, October, 1899. CONTENTS CHAPTER I THE EARLIER PHYSICAL CHEMISTRY PAGE Relations between Properties and Composition, and Properties and Constitution i Introduction ......... I The Boiling-Points of Liquids 4 Specific Heat of Liquids . 8 Atomic and Molecular Volumes 11 Viscosity 14 Refraction of Light 16 Rotation of the Plane of Polarization 21 Magnetic Rotation of the Plane of Polarization ... 27 Conclusion from the Preceding Work 29 The Study of Solutions ....... 30 Other Lines of Work 31 The Development of Thermochemistry .... 32 Work of Hess ......... 32 Favre and Silbermann ........ 33 Work of Berthelot ........ 34 Work of Julius Thomsen 35 Thermochemical Results . 36 The Development of Electrochemistry .... 39 Davy's Electrochemical Theory 40 Berzelius's Electrochemical Theory 40 Faraday's Law 44 Electrolysis .• 45 Theories of Electrolysis ....... 46 Clausius's Theory of Electrolysis 48 VII VIII CONTENTS PAGE Williamson's Theory of Electrolysis 50 Hittorf's Work on the Migration Velocity of Ions . . 52 Kohlrausch's Work on the Conductivity of Solutions . . 52 The Development of Chemical Dynamics and Chemical Statics 53 Wilhelmy's Discovery of the Law of Reaction Velocity . 56 Work of Berthelot and Pean de St. Gilles .... 58 Guldberg and Waage's Law of Mass Action ... 60 The Application of Thermodynamics to Chemical Processes 64 Methods of Measuring Affinity ...... 67 Conclusions from the Earlier Physical Chemical Work . . 68 CHAPTER II THE ORIGIN OF THE THEORY OF ELECTROLYTIC DISS O CIA TION Pfeffer's Osmotic Investigations 71 Introduction . . . . . . . . .71 Pfeffer's Method of Measuring Osmotic Pressure ... 72 Some of Pfeffer's Results 75 Relations between Osmotic Pressure and Gas Pressure discovered by van't Hoff 76 Historical 76 Boyle's Law for Dilute Solutions ...... 82 Gay Lussac's Law for Dilute Solutions 84 Experimental Evidence in Favor of both the Laws of Boyle and Gay Lussac for Solutions ...... 85 Avogadro's Law for Dilute Solutions 87 General Expression of the Laws of Boyle, Gay Lussac, and Avogadro for Solutions and Gases 89 Exceptions to the General Applicability of the Gas Laws to Osmotic Pressure . . . . . . . . 91 On the Dissociation of Substances Dissolved in Water. By Svante Arrhenius 93 Summary 101 CONTENTS IX CHAPTER III EVIDENCE BEARING UPON THE THEORY OF ELEC- TROLYTIC DISSOCIATION PAGE The Physical Properties of Completely Dissociated Solutions should be Additive 104 Specific Gravity of Salt Solutions ..... 105 Change of Volume in Neutralization . . . . 107 Specific Refractive Power of Salt Solutions . . . .108 Rotatory Power of Salt Solutions . . . . .110 The Color of Salt Solutions . . . . . . .110 A Demonstration of the Dissociating Action of Water . . 113 Conductivity is Additive. The Law of Kohlrausch . .116 Properties of Completely Dissociated and of Undisso- ciated Mixtures 117 Mixtures of Two Completely Dissociated Compounds . . 117 Mixtures of Two Completely Undissociated Compounds . 118 Heat of Neutralization in Dilute Solutions . . .119 Strong Acids and Bases' 121 Weak Acids and Strong Base 121 Hess's Law of the Thermoneutrality of Salt Solutions . .122 Osmotic Pressure - Lowering of Freezing-point-Rise in Boiling-point - Conductivity . . . .123 Relation between Osmotic Pressure and Lowering of Freezing- point 126 Relation between Osmotic Pressure and Lowering of Vapor- tension. Rise in Boiling-point . . . . .127 Relation between Osmotic Pressure and Conductivity . .128 Relation between Lowering of Freezing-point and Rise in Boiling-point 129 Relation between Lowering of Freezing-point and Conductivity 129 Connection between Osmotic Pressure and Lowering of Freez- ing-point, established by Thermodynamics . . . 131 Relation between Osmotic Pressure and Lowering of Vapor- tension (Rise in Boiling-point). Theoretical Demon- stration .......... 134 CONTENTS X PAGE Experiment to show the Presence of Free Ions . -137 Illustration of a Solution charged Electrostatically . .138 Experiment of Ostwald and Nernst . . . . . 139 The Ostwald Dilution Law 142 Ostwald's Deduction 143 Rudolphi's Dilution Law 147 Effect of an Excess of One of the Products of Disso- ciation 149 Further Relation between Dissociation by Heat and Electro- lytic Dissociation . . . . . . . 149 Determination of Electrolytic Dissociation by Change in Solubility 151 Agreement between Dissociation determined by Conductivity, Freezing-point Lowering, and Solubility . . . .152 The Relation between the Two Kinds of Dissociation an Analogy 153 Dissociation and Chemical Activity 154 Conductivity and Reaction Velocity . . . . . 155 Dissociation measured by Chemical Activity . . . 157 Chemical Reactions usually take Place between Ions . . 158 Dissociating Power of Different Solvents . . . .160 Effect of Water on Chemical Activity . . . .160 Action of Dry Chlorine on Metals 161 Comparative Inactivity of Dry Oxygen .... 162 Dry Hydrochloric Acid does not decompose Carbonates . 163 Dry Acids exert no Action on Litmus and do not form Salts 165 Dry Hydrochloric Acid does not precipitate Silver Nitrate in Ether or Benzene 165 Comparative Inactivity of Dry Hydrogen Sulphide . . 165 Other Reactions which do not take Place without Water . 168 Dry Hydrochloric Acid does not act on Dry Ammonia . .168 Dry Sulphuric Acid does not act on Dry Metallic Sodium . 169 Conclusion . . . . . . . . . .170 CONTENTS XI CHAPTER IV SOME APPLICATIONS OF THE THEORY OF ELECTRO- LYTIC DISSOCIATION PAGE Application of the Theory of Electrolytic Dissocia- tion to Chemical Problems 171 The Theory of Electrolytic Dissociation as applied to Solutions 172 Osmotic Pressure . . . . . . . . 173 Diffusion 174 Lowering of Freezing-point 176 Lowering of Vapor-tension, Rise in Boiling-point . . . 178 The Theory of Electrolytic Dissociation as applied to Electro- chemistry . . . . . . . . .182 Electrolysis 183 Modes of Ion Formation 189 Velocity of Ions 191 Relative Velocity of Ions . . . . . . .192 Kohlrausch's Law of the Independent Migration Velocity of Ions 197 The Absolute Velocity of Ions 198 The Conductivity of Solutions 201 Specific Conductivity ........ 202 Method of Measuring the Conductivity of Solutions . . 203 Carrying out a Conductivity Measurement .... 206 Conductivity of Water ........ 207 Calculation of Dissociation 209 The Conductivity of Solutions in the Different Solvents varies very greatly . . . . . . . . .211 Thomson's Theory . . . . . . . .213 Conductivity at Elevated Temperatures . . . .215 Electromotive Force 216 Strength of Acids and Bases . . . . . .216 Relations between Acidity and Composition and Constitution 219 Bases 223 Application of the Theory of Electrolytic Dissocia- tion to a Physical Problem 226 XII CONTENTS PAGE The Seat of the Electromotive Force in Primary Cells 226 Calculation of Electromotive Force from Osmotic Pressure . 227 Electrolytic Solution-tension . . . . . .231 Constancy of Solution-tension ...... 236 Calculation of the Difference in Potential between Metal and Solution 237 Types of Cells 238 Concentration Elements of the First Type .... 239 Concentration Elements of the Second Type . . . 243 Liquid Elements 247 Theory of the Liquid Element ...... 247 Sources of Potential in a Concentration Element . . .252 The Electromotive Force of the Daniell Element . . . 254 The Gas-battery ......... 256 Chemical Action at a Distance ...... 261 Experiment to demonstrate Chemical Action at a Distance . 262 Conclusion .......... 267 Application of the Theory of Electrolytic Dissocia- tion to BioloCjICal Problems 268 Toxic Action and Electrolytic Dissociation .... 268 Toxic Action of the Phenols and their Dissociation . . 272 Dissociation and Disinfecting Action ..... 273 Toxic Action of Substances on Certain Fungi . . . 275 Application of the Dissociation Theory to Animal Physiology 276 Physical Chemical Methods applied to Animal Physiology . 278 Application of Osmotic Pressure and Dissociation to the Mechanics of Secretion . . . . . . .281 Conclusion .......... 282 ELECTROLYTIC DISSOCIATION ELECTROLYTIC DISSOCIATION CHAPTER I THE EARLIER PHYSICAL CHEMISTRY RELATIONS BETWEEN PROPERTIES AND COMPOSITION, AND PROPERTIES AND CONSTITUTION Introduction. - Such marked advances have been made in physical chemistry during the last few years, that it is sometimes thought that this is distinctively a new branch of science. Indeed, the beginning of physical chemistry is often regarded as contemporaneous with the origin of the theory of electrolytic dissociation. While it is true that the new physical chemistry, which has revolutionized so many of our chemical conceptions, has grown up around the theory of electrolytic dissocia- tion, nevertheless, we must not forget that the newer is built upon, and incorporates, the entire work of the cen- tury. Indeed, the theory of electrolytic dissociation itself had its beginning, as we shall see, about the middle of the century. What was termed physical chemistry, prior to 1885, was largely a study of the physical properties of chemical substances, and work of this kind is in progress up to the present. At first, the physical properties of the ele- 1 2 ELECTROLYTIC DISSOCIATION ments, and of compounds, attracted attention, with the result, that the laws of gases, liquids, and solids were dis- covered. The earlier workers in this field, however, were not content with a disjointed knowledge of the properties of substances; they began to look for, and discover, rela- tions ; for the highest aim of scientific investigation is to find out relations between apparently disconnected facts - to discover generalizations. The first point which would naturally be taken up was the relation between properties and chemical composition. How would the introduction of an oxygen or a chlorine atom into a compound affect the physical properties of the compound; or the intro- duction of a CH2 group into organic compounds alter their properties ? The study of this relation was com- paratively simple. It was only necessary to prepare a compound, study its properties, then introduce an oxygen or chlorine atom, or a CH2 group, and study the properties of the new compound formed. By applying this process to a large number of substances, relations between composition and properties could be discovered, and much valuable work was done along this line. But it was well known that there are many chemical compounds which have the same composition, but very different physical properties. Isomeric substances in gen- eral have different physical properties. Isomeric sub- stances have the same kind of atoms in the molecule; but there is the possibility that the molecule of one isomeric substance may be the simplest possible, and the molecule of the other isomeric substance may be an aggregate of the simplest molecules; and this might account for the difference in properties of isomeric substances. THE EARLIER PHYSICAL CHEMISTRY 3 .There are also other substances, called metameric, which have not only the same kind of atoms in the molecule, but the same number of the same kind of atoms; and yet have different physical properties. The composition of the molecules in the two cases is exactly the same, so that the difference in properties, in such cases, cannot be attributed to a difference either in the kind or number of atoms in the molecule. To what then is the difference in properties in such cases to be attributed ? If it is due neither to the kind, nor to the number of atoms in the molecule, it must be due to the way in which the atoms are combined with one another in the molecule. This brings us to the second problem which was investigated by the earlier physical chemists, the relation between properties and constitution. In investigating this point, such questions arose as what would be the effect on the physical properties, produced by oxygen in the carbonyl condition (CO), with respect to oxygen in the hydroxyl condition (OH) ? Or how would /C\ carbon atoms combined as in ethylene differ in their effect on the physical properties of the compound, from /C\ carbon atoms combined as in ethane By using metameric compounds such questions could be, and in a number of cases have been, answered. Work of this earlier kind had to do with gases, liquids, and solids, but we will confine ourselves to that which has been done upon liquids; since relations have been more fully developed here than for either gases or solids. 4 ELECTROLYTIC DISSOCIATION The Boiling-points of Liquids. - A relation between the boiling-points- of liquids and their composition was first pointed out by Kopp,1 in 1842. An elaborate investigation on the boiling-points of a large number of organic com- pounds was published in 185 5,2 the result of which was to show that his earlier generalization was, in the main, cor- rect. The following are a few of the data obtained by Kopp, and these will suffice to bring out the relation be- tween composition and boiling-point discovered by him : - Substance Boiling-point Methyl alcohol, CH4O 65° Ethyl alcohol, C2H6O 78°^ \i8° Propyl alcohol, C3H8O 9 6°/ x^0 Butyl alcohol, C4H10O IO9 \ /230 Amyl alcohol, C5H12O 1320' Ethyl formate, C3H6O2 55°\ >9° Ethyl acetate, C4H8O2 74° ^>22° Ethyl propionate, C5H10O2 96°' Formic acid, CH2O2 105° XI2° Acetic acid, C2H4O2 117^ Z25° Propionic acid, C3H6O2 142°^ >4° Butyric acid, C4H8O2 156°^ ^>20° Valeric acid, C5H10O2 i76O// 1 Liebig's Ann., 41, 86, 169 (1842). 2Ibid., 96, 1 (1858). THE EARLIER PHYSICAL CHEMISTRY 5 Take succeeding members of any of the above three groups of compounds; they differ in composition by one carbon atom and two hydrogen atoms,-by the group CH2, - and there is, in every case, an approximately constant dif- ference between the boiling-points of succeeding members. This relation between composition and boiling-point, Kopp formulated from data obtained much earlier, as follows : Equal differences in the chemical composition of organic compounds correspond to equal differences in the boiling- points. It is obvious from the above data that this relation holds only approximately. If the above relation held rigidly, then isomeric sub- stances having the same composition must have the same boiling-point. The following data will serve, in part, to show the validity of this conclusion: - Substance Boiling-point (Methyl acetate 56° [ Ethyl formate 55° j Methyl butyrate 950 | Ethyl propionate 96° Methyl valerate 1150 ■ Amyl formate 1160 Ethyl butyrate 1150 We might conclude from the above data, that isomeric compounds have the same, or very nearly the same, boiling- point. It should be observed, however, that the above isomeric compounds have similar constitution. As soon as isomeric compounds which have different constitution 6 ELECTROLYTIC DISSOCIATION were compared, it was found that they have very different boiling-points; which shows that boiling-point is con- ditioned not simply by the number and kind of atoms in the molecule, but also by the way in which these atoms are combined with one another. Subsequent work has shown that these relations, pointed out by Kopp, are only rough approximations. Dittmar1 has proved that metameric compounds, such as methyl acetate and ethyl formate, do not have the same boiling-point, and more accurate work on the boiling- points of homologous series of compounds has shown that the difference between the boiling-points of succeeding members is not constant, but usually decreases as the com- pounds become more complex. This is illustrated by the following data, taken from the work of Schorlemmer :2- Substance Boiling-point C4H1o i° /37° C5H12 38°( /32° CeH14 7o°/ /29° C7H16 99P\ /25° C8H18 125 C2H5C1 12.5° /33-9° • C3H7C1 46.4°/ /3x-2° C4H9C1 77.6°/ >28.0° C5HuC1 105.6°/ 1 Liebig's Ann. Suppl., 6, 313 (1868). 2 Liebig's Ann., 161, 281. THE EARLIER PHYSICAL CHEMISTRY 7 Substance Boiling-point C2H5Br 39.0° 732.0° C3H7Br 71.07 729.4° C4H9Br 100.40/ \28.3° C5HnBr 12 8.7°/ Some interesting facts in connection with the relation be- tween constitution and boiling-point have been discovered. Take the benzene hydrocarbons, and compare those in which one hydrogen has been replaced by a group, with those having two hydrogen atoms replaced; and these, in turn, with those having three hydrogen atoms replaced. Compounds with One Hydrogen Atom Replaced Boiling-point C6H5C2H5 134° C6H5C3H7 152° C6H3C4H9 (172° calculated) C6H5C5Hu 193° Compounds with Two Hydrogen Atoms Replaced C6H4(CH3)2 139-140° /CH3 C6hZ i 59-160° xc2H5 /CH3 c6hZ 175-178° \c3H7 C6H4(C2H5)2 178-179O Boiling-point Compounds with Three Hydrogen Atoms Replaced C6H3(CH3)3 165-166° /(CH3), c6h3< 183-184° \c2H5 Boiling-point 8 ELECTROLYTIC DISSOCIATION By comparing these three classes of substances, we see that the second boils higher than the first, and the third higher than the second. Between the first and second there is almost a constant difference of about 6°, and between the second and third the difference is just about 6°, and is nearly constant. The study of a number of classes of primary and secondary compounds has established the fact, that the same difference in constitution produces approximately the same difference in boiling-point. Specific Heat of Liquids. - The specific heat of a liquid is different at different temperatures. In determining specific heats it is, therefore, necessary to choose some temperature for making the measurements, in order that the results may be comparable. Reis1 took the mean specific heats between 20° and the boiling-points of the substances investigated. That speci- fic heats may be comparable, it is necessary to refer them to comparable quantities of substances. Molecular quanti- ties are taken, and the molecular heats are compared, to bring out any relations which might exist. A few results for homologous series of alcohols, acids, and hydrocarbons, will serve to bring out any relation between composition and this property. Substance Molecular Heat Methyl alcohol, CH4O 21.0 /9-3 Ethyl alcohol, C2H6O 30.3/ >10.2 Propyl alcohol, C3H8O 4°-5\ /IO.4 Butyl alcohol, C4H10O 5°-9\ /9-6 Amyl alcohol, C5H12O , 60.5' 1 Wied. Ann., 13, 447, THE EARLIER PHYSICAL CHEMISTRY 9 Substance Molecular Heat Formic acid, CH2O2 24.2 /7-4 Acetic acid, C2H4O2 3i.6x /2 x 7-9 Butyric acid, C4H8O2 47-4\ \8.6 Isovaleric acid, C5H10O2 56.0^ 29-6 Caproic acid, C6H12O6 65.6Z Benzene, C6H6 33.8 28-0 Toluene, C7H8 41.8( 27-° Ethyl benzene, C8H10 48.8X 28.0 Mesitylene, CaH12 56.8X The difference between the molecular heats of any two members of a series is nearly constant. This difference corresponds to a difference in composition of CH2, in each series of compounds; yet its value varies somewhat from one series to another. The effect of constitution on molecular heat can be seen from the following examples of isomeric substances : - Substance Molecular Heat J Propyl aldehyde, C3H6O 32.6 [Acetone, C3H6O 32.6 f Butyric acid, C4H8O2 47.4 [ Isobutyric acid, C4H8O2 47.6 [Allyl alcohol, C3H6O 38.1 [ Propyl aldehyde, C3H6O 32.6 Isomeric compounds, having similar constitution, have very nearly the same molecular heats ; but if the constitu- 10 ELECTROLYTIC DISSOCIATION tions are markedly different, as in the last example, then the molecular heats differ widely from one another. This conclusion has been, in the main, confirmed by the work of de Heen.1 Schiff2 found the further relation between specific heat and composition; that the specific heat is nearly the same for large groups of closely related substances. If we represent the specific heat at t degrees, by St, we have the following results : - Substance Specific Heat Methyl benzoate St = 0.3630 + 0.00075 Ethyl benzoate St = 0.3740 + 0.00075 Propyl benzoate St = 0.3830 + 0.00075 * Benzene St= 0.3834 + 0.001043 Toluene St= 0.3834 + 0.001043 t JZ-Xylene St= 0.3834 + 0.001043 /'-Xylene 5/= 0.3834 + 0.001043 / Acetic acid St= 0.444 +0.001418/ Propionic acid St= 0.444 +0,001418/ Butyric acid St= 0.444 +0.001418/ This relation can be generalized as follows: - The specific heat of homologous compounds is represented by the formula c - a + bt, in which b always has the same value for the different members, and a often has the same, but sometimes slightly different values for the different members. Later work by Schiff 3 confirmed his earlier results. Considerable work has been done on the specific heats 1 Essai de phys. comp., Brussels, 1883. 2 Liebig's Ann., 234, 300. ' 3 Ztschr. phys. Chern., 1, 376. THE EARLIER PHYSICAL CHEMISTRY 11 of aqueous solutions. That of Marignac1 is to be espe- cially mentioned. He carried out an elaborate investiga- tion of closely related compounds, as chlorides, bromides, iodides, sulphates, nitrates, acetates, etc., with the object of discovering any relations which might exist. The molec- ular heats of solutions of a number of substances were found to be the sum of two parts; the one depending upon the acid, the other upon the base - they belong to that class of properties which are known as additive. But a large number of substances did not show this regularity, so that no comprehensive generalization was reached. Atomic and Molecular Volumes. - Here, again, to find relations we must use comparable quantities of substances, and it is most convenient to use molecular quantities. If g is the specific gravity, - is the specific volume. If m g is the molecular weight, - is the molecular volume. A number of relations were pointed out by Kopp.2 For closely allied compounds, the same difference in composition corresponds to the same difference in molec- ular volume. This is seen from the following examples :- Substance Molecular Volume CH4O 42.1 ^>20.1 C2H6O 62.2^ C2H4O 56.5 \20.1 C3H6O 77.5/ 1 Ann. Chim. Phys. [5], 8, 410. 2 Liebig's Ann., 4!, 79; 96, 153, 303. 12 ELECTROLYTIC DISSOCIATION Substance Molecular Volume CH2O2 4i-4 /22-3 C2H4O2 63.7/ \21.7 C3HgO2 85-4^ \21.7 C4H8O2 107.1/ The following generalization was also reached by Kopp : When two atoms of hydrogen are replaced by one of oxygen, the molecular volume is only slightly changed. Thus: - Substance Molecular Volume Methyl alcohol, CH4O 42.1 Formic acid, CH2O2 41.4 Ethyl alcohol, C2H6O 62.2 Acetic acid, C2H4O2 63.7 The relation between molecular volume and constitution was also worked out. A few results for isomeric sub- stances will serve to bring out the conclusion reached. Substance Molecular Volume f Acetic acid, C2H4O 63.7 | Methyl formate, C2H4O 63.4 f Methyl valerate, C6H12O2 149.2 | Ethyl butyrate, C6H12O2 149.3 f Propionic acid, C3H6O2 85.4 | Ethyl formate, C3H6O2 85.3 Isomeric liquids have the same molecular volumes. Kopp found, also, that the atomic volumes were not constants, independent of the nature of the atoms with THE EARLIER PHYSICAL CHEMISTRY 13 which any given atom is combined, but varied somewhat. Thus, oxygen in hydroxyl has a different atomic volume from oxygen in carbonyl. Similarly, carbon and nitrogen in their different forms of combination have different atomic volumes. Yet the molecular volumes are, in gen- eral, approximately the sum of the atomic volumes. The following atomic volumes, - Atomic Volume P 25-5 As 26.4 Sb 32.3 Sn 40.2 show the relation which was pointed out by Kopp, that the atomic volumes of the elements are nearly multiples of a constant, the value of the constant lying between 5.1 and 5.9. The more recent work of Thorpe1 has shown that isomeric liquids, at their boiling-points, do not always have exactly the same molecular volume, though the dif- ference is not great. While Schiff found that isomeric liquids, in general, have somewhat different molecular vol- umes, the differences corresponding to the law, that the higher the boiling-point of the substance the higher its molecular volume. W. Lessen2 concluded, from a number of pieces of work carried out by his pupils, that we cannot say, in general, that the molecular volume is additive - that it is the sum of the atomic volumes of its constituents. The molecular volume depends not simply on the kind of 1 Journ. Chem. Soc., 141, 327 (1880). 2 Liebig's Ann., 254, 42, 1889. 14 ELECTROLYTIC DISSOCIATION atoms in the molecule, but also on the way in which the atoms are combined in the molecule. It may, however, be stated, that while the molecular volumes of liquids at the boiling-point, are not exactly the sum of the constant atomic volumes, yet they are approxi- mately so; and molecular volume is approximately an additive property. Viscosity. -Some interesting relations between the vis- cosity of liquids, and their composition and constitution, have been recently pointed out by Thorpe and Rodger,1 in their elaborate investigation along this line. Although this work has been done very recently, yet it is typical of the earlier work, and, therefore, belongs in this place. The viscosities were measured by the time required for a liquid to flow through a capillary tube. To calculate the viscosity coefficient, the formula of Slotte was used, - c V = , (i + bt) n in which is the coefficient of viscosity, in dynes per square centimetre, c, b, and n are constants, varying with the nature of the liquid. To test the influence of com- position and constitution on viscosity, this property of some seventy liquids was determined in absolute measure, at all temperatures from o° to the boiling-points of the liquids. To compare viscosity coefficients, we must use compara- ble temperatures, and we will use first the boiling-points of the liquids. As we ascend a homologous series of com- 1 Thorpe and Rodger, Proceed. Royal Soc., 1894; Bakerian Lecture, Royal Soc. Chem. News, 69,123,135 ; Journ. Chem. Soc., 71,360 ; Ztschr. phys. Chem., 14,361. THE EARLIER PHYSICAL CHEMISTRY 15 pounds, the coefficient generally decreases; in a few cases it remains the same, and in one series increases. If we compare corresponding compounds, we find that the one with the highest molecular weight has the highest coeffi- cient. The effect of increase in molecular weight, however, may be more than counterbalanced by constitution. Iso- compounds have, in general, a larger coefficient than normal compounds. The degree of symmetry of the molecule can have a marked influence on the size of the coefficient. The following relations between the molecular viscosi- ties at the boiling-point, were established by Thorpe and Rodger. An increment of CH2 in compounds, with the exception of the alcohols, dibromides, and lowest members of the homologous series, corresponds to an increase in the molecular viscosity. The compound having the highest molecular weight, with the exception of the compounds mentioned above, has the highest molecular viscosity. The differences in the molecular viscosities, between corresponding members of two correlated series, are fairly constant. An attempt was made to calculate the viscosity constants of a number of atoms and groups, but since constitution comes so largely into play, it is evident that these con- stants are only approximations. Yet, the molecular vis- cosity of forty-five liquids, calculated from these constants, differs in few cases more than 5 per cent from those found. There are, however, many exceptions to this rule. The above relations were all obtained by comparing the viscosities of liquids at their boiling-points. But another method of comparison was also used. 16 ELECTROLYTIC DISSOCIATION The general shape of the viscosity curves, toward the boiling-point, was practically the same. If tangents are drawn to the curves at points corresponding to the boiling- points of liquids, the inclinations of the tangents to the axis, i.e. the slopes of the curves, varied but little. Curves for the alcohols, etc., were an exception. The temperatures of equal slope of curves were then taken for comparison. At this point, the effect of tem- perature would be the same for different substances. It was found that at the temperature of equal slope, there were more definite relations between the viscosity coefficients and the chemical nature of the compounds. At this temperature a CH2 group exerts a positive influence on the coefficient, which decreases as the series ascends. Exceptions are the alcohols, acids, and dichlorides. Of corresponding compounds, that with the highest molecular weight has the highest coefficient. Iso-compounds invari- ably have a larger coefficient than normal compounds; while for other isomeric substances a branching of the atomic chain has an influence on the magnitude of the coefficient. The molecular viscosity at constant slope can be calcu- lated from the fundamental constants for the constituents, but here, again, water and the alcohols are exceptions. It is evident from the above, that the relations found, thus far, between viscosity and composition and consti- tution, are, at best, only approximately correct, and apply only to a limited number of cases. Refraction of Light. - A number of attempts have been made to formulate a relation between the power of sub- stances to refract light and their densities. Of these, that THE EARLIER PHYSICAL CHEMISTRY 17 proposed by Dale and Gladstone1 is probably the most general. If we represent the index of refraction by n, and the density by d, 72 - I = constant. d They showed that this relation holds for a large number of liquids, within very wide ranges of temperature. Landolt2 tested this relation very accurately, for a small range of temperature, and found almost exactly a constant for a number of substances. Others3 have, however, obtained results to which the above expression did not accurately apply, the value --- either increasing or de- creasing with the temperature. The formula of Dale and Gladstone is far more accurate 722 j than the expression , which was proposed earlier, d and it is preferable to that of Lorenz-Lorentz,4 which is:- o I n ~ 1 d rd + 2 Recently, Edwards 5 has tested the formula - 77 - I nd and has shown that it holds for a number of substances, over a considerable range of temperature. None of these expressions, however, are perfectly gen- eral, and without the introduction of specific constants, they do not show an exact relation between refractivity 1 Phil. Trans. (1858), 887. Ibid,., 1863. 3 Ibid., 132, 202; 133, I. 2 Pogg. Ann., 123, 595. 4 Wied. Ann., 11, 70; 9, 641. 5 Amer. Chem. Journ., 16, 625; 17, 473. 18 ELECTROLYTIC DISSOCIATION and density. Indeed, it is not at all certain that such a relation exists. Relations between refractivity, and composition and con- stitution, have, however, been worked out, and a few of these will now be considered. Dale and Gladstone1 found that isomeres of similar con- stitution have very nearly the same specific refractivity. In homologous series this quantity increases regularly. They drew the general conclusion, that " every liquid has a specific refractivity, composed of the specific refractivities of the elements in the compound, modified by the kind of union." Landolt2 compared the "refraction equivalents" of sub- stances, calculating them from the formula - m{n - i) d ' in which m is the molecular weight of the substance, and the other symbols have the same significance as in the Dale-Gladstone expression. The relation between composition and refraction equiva- lents was worked out, and it was found that equal differ- ences in composition correspond to equal differences in refraction equivalents. Landolt showed, also, that the refraction equivalent of a compound is approximately the sum of the refraction equivalents of its parts. He investigated, further, the relation between constitu- tion and refraction equivalents, by studying metameric substances. A few results are given: - 1 Phil. Trans., 1863. 2 Pogg. Ann., 117, 353; 122,545; 123,595. THE EARLIER PHYSICAL CHEMISTRY 19 Substance Refraction Equivalent Propionic acid, C3H6O2 28.57 Methyl acetate, C3H6O2 29.36 Ethyl formate, C3H6O2 29.18 Valeric acid, C5H10O2 44-05 Methyl butyrate, C5H10O2 43-97 Butyl alcohol, C4H10O 36.11 Ethyl ether, C4H10O 36.26 Isomeric substances are thus seen to have the same refraction equivalents. J. W. Bruhl has carried out elaborate investigations, since the year 1880,1 on the refractive power of liquids. His work, which has now extended over nearly twenty years, has brought to light many interesting and important rela- tions. He took up the effect of carbon, in its different forms of combination, upon refractive power, and showed that doubly united carbon exerted a different influence from carbon united by single bonds. Each double union in a compound increases the refraction equivalent about two units. He thus showed the influence of constitution on refractivity. He also found that oxygen, in its different forms of combination, had different effects on refractivity. The question of the effect of symmetry on refractive power has also been studied. Two isomeric compounds, the one symmetrical, the other asymmetrical, have been studied with the following results : - Substance Refraction Equivalent j Ethylene chloride 20.95 [ Ethylidene chloride 21.08 J Ethylene bromide 26.84 { Ethylidene bromide 27.31 1 Liebig's Ann., 200, 139. 20 ELECTROLYTIC DISSOCIATION The unsymmetrical compound has a larger refraction equivalent than the symmetrical. The refraction values of a number of elements have been worked out, and also the differences in the refraction values of certain elements in different forms of combina- tion. Refractivity, therefore, can be and has been used to throw light on the question of constitution. Bruhl has applied the method of refractivity to the problem of the constitution of benzene. How are the carbon atoms united in benzene ? If by a single bond, they will have a different refractive power than if they were doubly united. From the power of benzene to refract, Bruhl was led to the conclusion that there are three single and three double bonds in the molecule, which is expressed thus: - CH Hc/Z^CH CH This is the well-known benzene formula of Kekule. It should be stated, that it is not safe to place unlimited confidence in a method like the above for determining the constitution of chemical compounds. The same problem has been attacked by Julius Thomsen, with very differ- ent result, using a thermochemical method. Thomsen's method is based upon the principle, that when a compound is burned a different amount of heat is liberated if the carbon atoms are united by single or double bonds, than if they are united by triple bonds. He determined the heat of combustion of benzene, and found that it cor- THE EARLIER PHYSICAL CHEMISTRY 21 responds to nine single bonds between the carbon atoms,J which would be expressed thus : - MCis- -tiCh c[h Hcl^--^JcH CH This is the well-known prism formula of benzene, sug- gested and defended by Ladenburg. This apparent di- gression is made, to show the caution which is necessary in accepting conclusions based upon work such as that above described. Rotation of the Plane of Polarization. - When a beam of polarized light is passed through certain liquids, the plane of polarization is changed. Sometimes it is turned in the one direction, sometimes in the other. This property is not confined to liquids, but is possessed also by solids and gases. Substances which have this property are said to be optically active. According as the substance rotates the plane of polarization in the one or in the other direc- tion, it is termed dextro- or laevo-rotatory. The direction and amount of rotation depend chiefly upon the nature of the substance. The rotation depends, also, upon the thickness of the layer, the wave-length of light, and the temperature. Comparable results can, therefore, be obtained only by keeping all of the con- ditions constant, and then studying the kind and amount of rotation which different compounds produce. 1 Ber. d. chem. Gesell., 13, 1808. 22 ELECTROLYTIC DISSOCIATION The specific rotatory power of a liquid has been defined by Biot, as the rotation produced by a layer one decimetre in length. But since different liquids have different den- sities, this would contain different amounts of substance. The specific rotatory power r is obtained by dividing the angle a, through which a column of liquid of length I, and density d, rotates the plane of polarization, by Id. a r - - Id In order to compare the rotatory power of liquids we must deal with comparable quantities, and most conveniently with molecular quantities. If m is the molecular weight of the substance, this must be multiplied into the above expression. The molecular rotatory power mr would then be:- ma mr = Id This unit is usually divided by one hundred. Some exceedingly interesting relations between rotatory power, and composition and constitution, have been worked out. There is quite a large number of substances which exist in different forms, one rotating the plane of polariza- tion to the right, the other to the left. Pasteur1 pointed this out in connection with the tartaric acids. There is a dextro-rotatory tartaric acid, and a laevo-rotatory tartaric acid, and inactive racemic acid. The latter is produced by mixing solutions of the dextro- and laevo-varieties, and, on the other hand, racemic acid can be separated into dextro- and laevo-tartaric acids. This separation is accomplished 1 Ann. China. Phys., 28, 56 (1850). THE EARLIER PHYSICAL CHEMISTRY 23 by preparing the sodium-ammonium salt of racemic acid, and allowing it to crystallize. Salts of dextro- and laevo- tartaric acids will separate, and can be distinguished by the difference in crystal forms. Certain right-handed hemihedral planes appear on the salt of the dextro-acid, and left-handed planes on the salt of the laevo-acid. There is also a fourth tartaric acid, which is inactive, but this can be transformed into the other modifications. There are several other examples known of a substance existing in a dextro- and laevo-modification, and also in an inactive form; and by combining the active modifications, the inactive is formed, and from the inactive form the active may be obtained. A direct study of the relation between optical activity, and composition and constitution, will be considered more in detail. We will deal with the compounds of carbon. It was observed by the French chemist, Le Bel,1 and a little later by van't Hoff,2 that every carbon compound which is optically active can be represented as containing a car- bon atom in combination with four different atoms or groups. Take the simplest case, that of lactic acid. We have : - CH3 I H - C - COOH OH Le Bel ascribed optical activity to the asymmetrical nature of such an arrangement, but van't Hoff went much far- 1 Bull. Soc. Chim. [2], 22, 337 (1874). 2 Ibid., 23, 295 (1875). 24 ELECTROLYTIC DISSOCIATION ther, and tried to show how the atoms are actually ar- ranged in space. He represented the central carbon atom of the system, as placed at the centre of a regular tetrahe- dron, with its four bonds acting in the directions of the solid angles. At those angles are placed the four atoms, or groups, in combination with the central carbon atom. If these atoms, or groups, are the same, we would have a perfectly symmetrical arrangement, and every atom would bear the same relation to the molecule as every other atom. Take the case of marsh gas, the four hydrogen atoms should each bear the same relation to the molecule, and such has been shown to be the case by the elaborate work of Henry. If either two of the atoms, or groups, at the corners of the tetrahedron are the same, then it is im- possible to so arrange them that two tetrahedra, contain- ing the same four groups at the corners, could not be completely superimposed. But if all four atoms, or groups, are different, then two tetrahedra containing these at the corners can never be superimposed, but bear the relation to one another of an object and its image in a mirror. If this asymmetrical arrangement is the cause of optical activity, then only those carbon compounds could be opti- cally active which have four different atoms, or groups, combined with the central carbon atom. Of all the cases of optical activity known among carbon compounds, there is only one possible exception. Baeyer1 has described a dipentene, which he thinks does not contain an asymmetric carbon atom, and which is, however, optically active. But this cannot be cited as a positive exception, since the con- stitution of this substance is not definitely established. 1 Ber. d. chem. Gesell., 27, 454. THE EARLIER PHYSICAL CHEMISTRY 25 Another consequence of the van't Hoff theory is, that whenever a dextro-rotatory substance appears, a laevo must also be formed, and such is the fact. Of the large number of cases known, there is no exception to this rule. If optical activity is due to the presence of an asymmet- ric carbon atom, then, whenever we have such a carbon atom present, we ought to have optical activity. There are, however, many compounds known, which contain an asymmetric carbon atom, yet do not show optical activity. This is explained by assuming that there are present an equal number of dextro- and laevo-molecules, and optical inactivity is the result. Similarly, if there are two asym- metric carbon atoms in the same molecule, these may exactly neutralize each other's influence on polarized light, as in the case of the fourth variety of tartaric acid. It is difficult to overestimate the importance of these suggestions by Le Bel and van't Hoff. They underlie all that has been done along the line of stereochemistry, and this is certainly one of the most important advances which has been made in organic chemistry in the last quarter of a century. This suggestion of the tetrahedron as the spatial ar- rangement in carbon compounds has been developed much farther by Wislicenus1 than was done by van't Hoff. The former has shown how this arrangement is capable of accounting satisfactorily for the transformations of maleic and fumaric acids; of the malic acids; and, what is even more interesting, it furnishes a beautiful explanation of 1 Monograph, Ueber die raumliche Anordnung der Atome in organischen Molekiilen, Leipzig. 26 ELECTROLYTIC DISSOCIATION the optical behavior of the four tartaric acids; facts which hitherto had been empirically established, but whose significance was entirely unknown. While space will not permit us to enter into a discussion of this monograph by Wislicenus, yet we should again call attention to its unus- ual interest and importance for all who are interested in the philosophy of organic chemistry. The suggestion by van't Hoff to account for optical activity has been further extended by Guye.1 If optical activity is due to the groups being different at the four corners of the tetrahedron, - to an asymmetrical arrange- ment, - then by changing the degree of asymmetry, the degree of optical activity ought also to be changed. If we have a carbon atom surrounded by four different atoms or groups, the centre of gravity of the system will lie off of the planes of symmetry. If now we replace one of the atoms or groups by one having a greater weight, the centre of gravity of the system will be moved toward the heavier substituent. By changing the masses of the atoms or groups, the centre of gravity of the system can be changed, first in one and then in another direction. Guye has shown, in a large number of cases, that as the centre of gravity of the system is changed, by intro- ducing lighter or heavier groups, the optical activity of the substance changes, and in the way that would be ex- pected. As the asymmetry was increased, optical activity in general increased. By introducing groups of the weights desired, the centre of gravity could often be changed from one side of the molecule to the other, and in a number of such cases the 1 Compt. rend., no, 714. THE EARLIER PHYSICAL CHEMISTRY 27 nature of the rotation was changed - a dextro-rotatory- substance becoming laevo-rotatory, and the reverse. There are some cases known which cannot be entirely reconciled with the views of Guye. Work of this kind is undoubtedly of the very highest importance, since it throws light on the inner arrangement of the atoms and groups in the molecule. Another outcome of the stereochemical conception of van't Hoff, with respect to carbon, is the recent work which has been done on the stereochemistry of nitrogen. Hantzsch and Werner1 have shown, that if we represent the nitrogen atom as being placed at one of the angles of a tetrahedron, we can explain the differences in constitu- tion which undoubtedly exist between many of the isomeric substances containing nitrogen; differences for which it is impossible to account, in many cases, by the ordinary methods of representing constitution, which do not take into account spatial relations. Although the work of Wislicenus, Guye, and Hantzsch and Werner was done in the last few years, yet it is the direct outcome of the suggestion made by van't Hoff in 1875, which is more than ten years before the newer de- velopments in physical chemistry began. It, therefore, seems not to be entirely out of place to refer to this recent work under the head of the earlier physical chemistry, of which it is the direct consequence. Magnetic Rotation of the Plane of Polarization. - It was discovered by Faraday,2 that substances in general have the power to rotate the plane of polarization of light, when placed in a suitable position in a magnetic field. An electro- 1 Ber. d. chem. Gesell., 23, 11,1243, 2764, 2769. 2 Pogg. Ann., 68, 105. 28 ELECTROLYTIC DISSOCIATION magnetic field is the most convenient, the current flowing in a plane at right angles to the direction in which the ray of light moves. The amount of rotation depends on the strength of the magnetic field, length of layer of substance, the temperature, and the nature of the substance. To dis- cover any relations between magnetic rotation and compo- sition, every one of the above conditions must be kept constant, from one substance to another. The work of Becquerel1 brought out some relations, such as that the rotatory power of the alcohols increased with increase in molecular weight; but by far the most elaborate investigation of this phenomenon we owe to W. H. Perkin.2 He chose as his unit the molecular rota- tion of water, and compared other substances with it. A few examples are given : - Substance Molecular Rotation Methyl alcohol, CH4O 1.640 /i-i4 Ethyl alcohol, C2HGO 2.780/ \0.988 Propyl alcohol, C3H8O 3.768/ Formic acid, H2CO2 1.617 yo.908 Acetic acid, C2H4O2 2.525/ /°-937 Propionic acid, C3HGO2 3.462^ yi.oio Butyric acid, C4H8O2 4.472/ These results, taken from a large number, show, for a homologous series, a constant difference in the magnetic 1 Ann. Chim. Phys. [4], 22, 5. 2 Journ. prakt. Chem. [2], 31, 481; 32, 523. THE EARLIER PHYSICAL CHEMISTRY 29 rotation produced by the constant difference in composi- tion of CH2. The effect of constitution on magnetic rota- tion can be seen by comparing isomeric compounds. Substance Magnetic Rotation [ Propyl alcohol, C3HbO 3.768 ^Isopropyl alcohol, C3H8O 4.019 | Ethylene chloride, C2H4C12 5-485 [Ethylidene chloride, C2H4C12 5-335 These examples suffice to bring out the fact, that isomeric substances have different magnetic rotation, showing the effect of constitution on this property. Perkin has continued his work on magnetic rotation up to the present, and some of his more important com- munications are referred to below.1 J. W. Rodger and W. Watson2 have published an inves- tigation on magnetic rotation, where a stronger magnetic field was used, and, consequently, the amount of rotation to be measured was greater. Their paper is devoted mainly to a description of their apparatus, and contains too few results to warrant any generalization. It is to be hoped that this work will be continued, using the stronger mag- netic field. Conclusion from the Preceding Work. - On examining the work thus far described, we are impressed by the large number of relations which have been pointed out between physical properties, and composition and constitution. But we are also impressed by the fact that these relations 1 Chem. News, 60,253 ; 62,255; 64,19; 65, 284; 66,277; 67,143 ; 68, 302; 69, 224; 71,123; 73,301. Journ. Chem. Soc., 59, 981; 61,287; 61,800; 65,815; 69, 1025. Ztschr. phys. Chem., 21, 451; 21, 671. 2 Ztschr. phys. Chem., 19, 323. 30 ELECTROLYTIC DISSOCIATION are only approximations; they are not sharply defined and rigorous. A relation was often discovered, which, at first, seemed to be fairly exact, but as the experimental work became more refined, a larger number of exceptions appeared. Thus, in many cases, what seemed to be a quantitative relation was merely a qualitative one. We feel, throughout this entire work, the purely empir- ical nature of the generalizations reached, and that they are very incomplete expressions of the truth. There is a lack of any definite, mathematical conception, in terms of which this earlier work can be interpreted. The Study of Solutions. - The physical properties of substances may be studied when they are isolated, or when they are mixed with other substances. Under the latter condition, one substance is said to be dissolved in the other, and we have to do with solutions. A number of the prop- erties of solutions were early investigated. Graham1 studied the phenomenon of diffusion, and Fick2 pointed out that diffusion depends upon, and is proportional to, the difference in concentration of the solutions. Blagden3 discovered, more than a hundred years ago, that the lower- ing of the freezing-point of water by a dissolved substance is proportional to the amount of substance present. The same fact was rediscovered by Riidorff,4 and, later, Coppet5 showed that the molecular lowering of the freezing-point, produced by closely allied substances, is very nearly con- stant. Raoult6 studied the freezing-point lowering of solutions 1 Liebig's Ann., 77, 56, 129; 80, 197. 3 Phil. Trans., 78, 277. 2 Pogg. Ann., 94, 59. 4 Pogg. Ann., 114, 63 ; 116, 55 ; 145, 599. 5 Ann. Chim. Phys. [4], 23, 366; 25, 502; 26, 98. 6 Compt. rend., 94, 1517; 95, 188, 1030; Ann. Chim. Phys. [6], 2, 66. THE EARLIER PHYSICAL CHEMISTRY 31 in solvents other than water, and arrived at the generali- zation, that a molecule of any substance, in one hundred molecules of a solvent, lowers the freezing-point of the solvent by a nearly constant amount. These investigations by Raoult on freezing-point lowering were very elaborate, including a large number of solutions in acetic acid, formic acid, benzene, nitrobenzene, ethylene bromide, etc. The lowering of the vapor-pressure of a solvent by a dissolved substance was early investigated. Wiillner1 pointed out that the lowering of the vapor-pressure of water by dissolved substances is proportional to the amount of substance, and Raoult2 studied the influence of temperature, concentration, and nature of dissolved sub- stance, on the depression of the vapor-tension of the solvent. Raoult3 worked with a number of solvents, and found that the depression of the vapor-tension produced by one molecule of substance in one hundred molecules of solvent was the same for different solvents. Raoult also showed how the lowering of the freezing-point of a solvent by a dissolved substance, and also the lowering of its vapor- tension, may be used to calculate the molecular weight of the substance in solution. Other Lines of Work.-The earlier physical chemists were not all engaged with problems such as we have been considering. They measured the heat liberated in chem- ical reactions. They studied the behavior of substances when submitted to the action of the electric current. The velocity with which chemical reactions take place, and the conditions of equilibrium, were investigated. And the dif- 1 Pogg. Ann., 103, 529; 105, 85; no, 564. 2 Compt. rend., 103, 1125. 3 Ibid., 104, 1430; Ann. Chim. Phys. [6], 15, 375 ; Ztschr. phys. Chem., 2, 353. 32 ELECTROLYTIC DISSOCIATION ferent powers of substances to react, as depending upon their composition and constitution, were carefully deter- mined. This brief account of the nature and condition of phys- ical chemistry, before the theory of electrolytic dissociation arose, would be unsatisfactory, and, perhaps, misleading, without some statement as to the development of thermo- chemistry, electrochemistry, and chemical affinity. By knowing the condition of the several branches of physical chemistry, before the new conceptions arose, we can see the more clearly what changes have been introduced, what advances made by them. THE DEVELOPMENT OF THERMOCHEMISTRY The quantitative study of the amount of heat liberated in chemical reactions was begun very early, and has been continued from the time of Robert Boyle to the present. The problem, in one form or another, has attracted the attention of men like Davy, Lavoisier, and Laplace. In- deed, the very important discovery was made by the last two,1 that just as much heat is required to decompose a compound into its constituents as was liberated when the constituents united to form the compound. But the begin- ning of modern thermochemistry dates from the time of G. H. Hess.2 Work of Hess. - Hess discovered the principle which has come to be known as the " Constancy of the sum of the heats of reaction." If a chemical transformation takes place in one stage, a certain amount of heat is liberated, which we will call a. If the transformation takes place in 1 CEuv. de Lav., II, 287. 2 Pogg. Ann., 50, 385 (1840). THE EARLIER PHYSICAL CHEMISTRY 33 two stages, in which, respectively, h and c amounts of heat are liberated, we always have, h + c = a. This is perfectly general, regardless of the number of stages involved in the transformation. The discovery of this principle makes it possible to study, thermochemically, a great number of reactions which are comparatively complex taking place in more than one stage. In addition to this important discovery, Hess made another of very wide significance. He observed that when solutions of neutral salts are mixed, there is little or no heat liberated or absorbed. He concluded, that the heat consumed in decomposing the salts was exactly equal to that liberated in the formation of the new salts with acid and base interchanged, since it was known that under the conditions that solutions of two salts are mixed, four salts are always formed, provided all four are easily solu- ble and no precipitate is produced. This has come to be known as Hess's law of the thermoneutrality of salts. The significance of this law was not understood until it was fully explained by the theory of electrolytic disso- ciation. Favre and Silbermann. -We now come to the beautiful thermochemical investigations of Favre and Silbermann.1 They greatly improved the apparatus and method used in thermochemical measurements. The calorimeter which they devised is the same in principle as every form used since their time. They carried out elaborate thermo- chemical investigations, which were undoubtedly the most accurate up to their time. Thermochemical investigations since the time of Favre 1 Ann. Chim. Phys. [3], 34, 357; 36, 1; 37, 406. 34 ELECTROLYTIC DISSOCIATION and Silbermann have centred around two men: Berthelot in Paris, and Julius Thomsen in Copenhagen. Much work has also been done by pupils of these men, either working with them or independently. Work of Berthelot. - Berthelot1 began his very elaborate thermochemical investigations in 1865, and these have ex- tended over a long period. The results of his work are published in his well-known book, of two volumes, " Essai de Mecanique Chimique." The three principles which he developed in his work are : - First, the heat liberated in a chemical reaction depends only on the condition of the system at the beginning and at the end, and not at all on the intermediate stages. Second, the heat evolved in a chemical process is a measure of the corresponding chemical and physical work. Third, every chemical reaction tends to form those sub- stances which are formed with the greatest evolution of heat. This last principle has come to be known as the law of maximum work, but would better be known as the law of maximum heat evolution. The last of the three principles announced by Berthelot has attracted by far the most attention. As an expression of a perfectly general truth, it is, of course, not exact. There are many exceptions known to it, and some of these were recognized and pointed out by Berthelot himself. And yet, notwithstanding the exceptions, if one will care- fully read the " Essai de Mecanique Chimique," the im- pression is almost sure to be left that here is, at least, the kernel of a great truth, even if it is expressed in an imperfect and not sufficiently comprehensive manner. 1 Ann. Chim. Phys. [4], 6, 290; 28, 94. THE EARLIER PHYSICAL CHEMISTRY 35 Much of the criticism of this third principle, whether its true discoverer be Berthelot1 or Julius Thomsen,2 is evi- dently not entirely well founded, if all that Berthelot has written concerning it is taken into account. Work of Julius Thomsen. - The thermochemical work of Julius Thomsen has been collected into four volumes, and published under the title of " Thermochemische Un- tersuchungen." This, taken as a whole, undoubtedly con- tains the most elaborate and accurate thermochemical measurements which have ever been made. In order that a reaction may be studied thermochem- ically, one condition is that it should proceed rapidly to the end. Many reactions between organic compounds do not fulfil this condition. Indeed, most organic reactions are relatively slow. To study such reactions thermo- chemically, some means must be devised which would accelerate the velocity of the reaction. Berthelot3 im- proved the form of apparatus which had already been suggested for this purpose. A thick-walled, steel cylinder, lined on the inside with platinum or enamel, is used for accelerating the velocity of such reactions as organic com- bustions. The substance to be burned is placed on a suitable arrangement, and introduced into the " bomb." This is then tightly closed, and filled with oxygen under high pressure. The substance is ignited by an electric current; the combustion proceeds very rapidly, and the heat set free is measured in some convenient form of calorimeter. The use of the Berthelot bomb has greatly widened the field of thermochemical investigation. 1 Ann. Chim. Phys. [5], 4, 6; [4], 18, 103. 2 Ber. d. chem. Gesell., 6, 423. 3 Ann. China. Phys. [5], 23, 160. 36 ELECTROLYTIC DISSOCIATION Some of the most accurate thermochemical measure- ments, in which the bomb has been employed, have been made by Stohmann,1 in Leipzig (who worked for a time with Berthelot), and by his assistant, Langbein. Thermochemical Results. - A few thermochemical re- sults will suffice to bring out the kind of relations which have been discovered by such work. The heat evolved when acids and bases neutralize each other has been carefully investigated. We will give a few results for the strong acids and strong bases: - NaOH + HNO3 = 13680 cal. NaOH + HCIO3 = 13760 cal. NaOH + HBrO3 = 13780 cal. NaOH 4- HIO3 = 13810 cal. NaOH + HC1 = 13700 cal. NaOH + HBr = 13700 cal. NaOH -J- HI = 13700 cal. In the above table the base is kept constant and the acid changed; yet the heat of neutralization of equivalent quantities is nearly a constant. A few results will be cited in which a given acid is neutralized with a number of bases:- KOH 4- HC1 = 13700 cal. | Ba (OH)2 4- HC1 = 13900 cal. | Sr (OH)2 4- HC1 = 13800 cal. |Ca (OH)2 4- HC1 = 13900 cal. Here, again, the heat of neutralization is nearly a con- stant, and the same constant as in the preceding case. It can, therefore, be stated, that the heat liberated, when- 1 Journ. prakt. Chem., 33, 241; 35,40; 39,509; 40,341; 42, 367; 43, 1; 44, 336; 45. 332. THE EARLIER PHYSICAL CHEMISTRY 37 ever a strong acid is neutralized by a strong base, is a con- stant, within experimental error, independent of the nature of the acid and of the base. If either the acid or base is weak, a different heat of neutralization is found. The meaning of these facts was entirely unknown at the time of their discovery. Why should the heats of neutralization of strong acids and strong bases be a con- stant, and why should the heats of neutralization of weak acids and bases be different ? These were questions whose meaning was not even suspected before the theory of electrolytic dissociation was proposed. These facts, as we shall see, are not only explicable in terms of that theory, but are a necessary consequence of it. Indeed, the constancy of the heat of neutralization of strong acids and strong bases is a very good argument in favor of the correctness of the new theory, and this argument is even strengthened by the fact that weak acids and bases have a different heat of neutralization. Certain relations between the composition and constitu- tion of organic compounds and their heats of combustion have been worked out. Take the marsh-gas series of hydrocarbons. Substance Heat of Combustion Methane, CH4 zugoocak 58500 cal. Ethane, C2H6 370400 cal/ Si5 8800 cal. Propane, C3H8 529200 cal.f Si 58000 cal. Butane, C4HJ0 687200 cal/ S159900 cal. Pentane, C5H12 847100 cal/ 38 ELECTROLYTIC DISSOCIATION A difference of CH2 produces very nearly a constant difference in the heats of combustion of these hydrocar- bons. The constitution of these compounds seems to have no effect. The following results were obtained for the ethylene hydrocarbons: - Substance Heat of Combustion Ethylene, C2H4 333400 caK /I593°° caL Propylene, C3H6 492700 cal.f b 15 7900 cal. Isobutylene, C4H8 650600 cal/ \ 15 7000 cal. Amylene, C5H10 807600 cal; A constant difference in the heats of combustion is observed here, also, for the constant difference in compo- sition of CH2; and this is the same difference as in the case of saturated hydrocarbons. The heats of combustion of the two series are not the same, because, in addition to two hydrogen atoms more in one system than in the other, we have doubly united carbon atoms. And when- ever there is double or triple union between the carbon atoms, the heat of combustion is affected by it. The halogen substitution products of the marsh-gas hydrocarbons show, also, constant differences in the heats of formation: - Dip. Dip. CH3CI 22000 cal. CH3Br 14200 cal. 7800 cal. CH3I 2800 cal. 19200 cal. C2H5CI 29600 cal. C2H5Br 21800 cal. 7800 cal. C2H5I 9900 cal. 19700 cal. C3H7CI 36000 cal. C8H7Br 29100 cal. 6900 cal. Relations appear for the alcohols which are similar to those found for the hydrocarbons. The difference THE EARLIER PHYSICAL CHEMISTRY 39 between the heats of combustion of members of a homolo- gous series of alcohols is nearly constant, as the following results will show : - Substance Heat of Combustion Methyl alcohol, CH4O 182200 cal- ^>158300 cal. Ethyl alcohol, C2HeO 340500 cal.f • ^>158100 cal. Propyl alcohol, C3H8O 498600 cal.z The effect of constitution on heat of combustion is seen in the fact, that primary alcohols have larger heats of com- bustion than either secondary or tertiary. An interesting application of the effect of constitution on heat of com- bustion has been made by Julius Thomsen, in the case of benzene, to which reference has already been made. THE DEVELOPMENT OF ELECTROCHEMISTRY The decomposition of chemical compounds by the elec- tric current has attracted the attention of physicists and chemists ever since the discovery of the voltaic element at the close of the last century. The comparatively insig- nificant elements which were first constructed sufficed, nowever, to effect a number of decompositions, such as the electrolysis of metal salts, of water to which acid has been added, etc. But it remained for Sir Humphry Davy1 to construct the large voltaic element which effected such remarkable decompositions, and led to the discovery of the alkali metals. The current from his element was passed through the fused oxides of potassium and sodium, when small globules were seen to rise to the surface of the mol- 1 Gilb. Ann., 7, 114 (1801). 40 ELECTROLYTIC DISSOCIATION ten mass, and take fire on contact with the air. Thus were sodium and potassium first separated from their compounds. Davy's Electrochemical Theory. - The direct decomposi- tion of the oxides of the alkali metals by the electric cur- rent, also the decomposition of acidulated water, and a large number of other chemical substances, pointed to some close relation between chemical attraction and elec- trical attraction. As the net result of his very elaborate electrochemical studies, Davy was led to the electrochem- ical theory which bears his name. The atoms of sub- stances, by contact, acquire different electrical charges, and these atoms then attract one another, because they are charged, the one positive, and the other negative. These charges may be so slight, that the attraction between them will not be sufficient to cause the atoms to change their former relations, or they may be great enough to effect such a rearrangement, when a chemical compound will be formed. Chemical attraction between atoms is, then, but the electrical attraction between the opposite charges which have accumulated upon them, due to their contact with one another. Electrolysis consists in destroying the difference between the charges upon the atoms in the compound, the nega-. tively charged atom receiving positive electricity from the positive pole, to which it is attracted, and becoming neutral; the positively charged, attracted and neutralized at the negative pole. The compound would thus necessarily be broken down by electrolysis, since the force which held its constituents together no longer exists. Berzelius' Electrochemical Theory. - The theory of Ber- zelius differed fundamentally from that of Davy. Accord- THE EARLIER PHYSICAL CHEMISTRY 41 ing to Davy, an atom, as such, is electrically neutral, and becomes charged positively or negatively by contact with another atom, which takes a charge of the opposite sign. Berzelius claimed that every atom is electrically charged with both kinds of electricity. These exist upon the atom, in polar arrangement, and th^ electrical character of the atom depends upon which is present in excess. One is usually present in large excess, giving the atom a decidedly positive or negative character. One " pole " is usually much stronger than the other, so that the atom reacts as if it was "unipolar." Chemical attraction is but the electri- cal attraction of these oppositely charged atoms, and the intensity of the former is conditioned by the magnitude of the latter. A negatively charged atom is attracted to and combines with one which is charged positively. The magnitude of these opposite charges may not be the same, and the com- pound formed will itself be electrically positive or nega- tive, depending upon which charge upon the atoms is the greater. Two compounds, the one charged positively and the other negatively, may, then, in turn, combine, forming a still more complex compound. In this way Berzelius attempted to account for the more complex substances, such as the so-called double compounds. The theory, as put forward by Berzelius, did not long enjoy freedom from adverse criticism. If chemical union is produced by the electrical attraction of oppositely charged atoms, then, as soon as these atoms come together, the electrical differences would disappear, and the compound must fall apart. As soon, however, as the atoms separated, they would become oppositely charged, and again reunite. 42 ELECTROLYTIC DISSOCIATION There would thus result a continued decomposition and reunion, and a chemical compound would, at best, be in a state of unstable equilibrium. This would apply to all chemical compounds. But the theory was called upon to meet, apparently, a more serious objection. If chemical union depends only upon the attraction of the opposite electrical charges upon the atoms, then the properties of the compound formed must depend upon the nature of the charges upon the atoms in the compound. It was, however, found to be possible to substitute the three hydrogen atoms in acetic acid by three chlorine atoms, passing from CH3COOH to CC13COOH. And the remarkable fact was discovered, that the properties of trichloracetic acid were very similar to those of acetic acid itself. This, Berzelius himself could not satisfactorily reconcile with his theory. Each of the three hydrogen atoms car- ried a positive charge, while the three chlorine atoms eacn carried a negative. Yet the three hydrogen atoms, with their positive charges, could be replaced by the three chlorine atoms with their negative charges, without ma- terially changing the properties of the compound. This is cited, up to the present, as a fatal objection to the electro- chemical theory of Berzelius. The very recent work of J. J. Thomson1 has, however, thrown entirely new light on the above line of argument. Thomson has shown that the same substance may be both positively and negatively charged. Thus, hydrogen gas2 has been electrolyzed by him, with the result that positive hydrogen went to one pole and negative to the other. 1 Nature, 52, 453. 2 Ibid., 52, 451 (1895). THE EARLIER PHYSICAL CHEMISTRY 43 This was shown from the difference in the spectra of the hydrogen around the two poles. The molecule of hydro- gen is, then, very probably made up of a positive and a negative hydrogen ion. The important point in this connection, brought out by the work of Thomson, is that we must not conclude that because hydrogen is sometimes positively charged, it is always so. Thomson's own words, in connection with that portion of his paper which bears on the theory of Ber- zelius, are here given. " In many organic compounds, atoms of an electroposi- tive element hydrogen are replaced by atoms of an elec- tronegative element chlorine, without altering the type of the compound. Thus, for example, we can replace the 4 hydrogen atoms in CH4, by Cl atoms, getting, successively, the compounds CH3C1, CH2C12, CHC13, and CC14: it seemed of interest to investigate what was the nature of the charge of electricity on the chlorine atoms in these compounds. The point is of some historical interest, as the possibility of substituting an electronegative element in a compound for an electropositive one was one of the chief objections against the electrochemical theory of Berzelius. When the vapor of chloroform was placed in the tube, it was found that both the H and Cl lines were bright on the negative side of the plate, while they were absent from the positive side, and that any increase in the brightness of the H lines was accompanied by an increase in the brightness of those due to Cl. . . . The appearance of the H and Cl spectra on the same side of the plate was also observed in methylene chloride, and in ethylene chloride. Even when all the H in CH4 was replaced by Cl, as in carbon tetra- 44 ELECTROLYTIC DISSOCIATION chloride CC14, the Cl spectra still clung to the negative side of the plate." The same point was tested with SiCl4, and the Cl spectra was brightest on the negative side of the plate. " From these experiments it would appear that the Cl atoms, in the chlorine derivatives of methane, are charged with elec- tricity of the same sign as the H atoms they displace." From this, the argument against the theory of Berzelius is left without foundation, since the hydrogen atoms in acetic acid are replaced by chlorine, which has the same kind of charge. Therefore, the properties of trichloracetic acid should resemble closely those of acetic acid itself. Faraday's Law.-The next important advance in elec- trochemistry was made by Faraday, upon whose investi- gations too much stress cannot be laid. He showed the identity of electricity from different sources, whether pro- duced by friction or by chemical action; and also investi- gated the relation between the amount of a compound decomposed by the current, and the amount of current. He found that the two were proportional to one another, and then announced his law. The amount of chemical decomposition effected by the passage of the current is proportional to the amount of electricity which flows through the conductor. Faraday determined, also, the amounts of different ele- ments, which would be separated from their compounds, by passing the same current through solutions of these compounds. For example, the same current would be passed through solutions of, say, copper sulphate, zinc chloride, and silver nitrate, and the amounts of Cu, Zn, and Ag deposited determined. THE EARLIER PHYSICAL CHEMISTRY 45 The following generalization was reached by this work : - The amounts of the different elements which are sepa- rated by the same quantity of electricity bear the same relation to one another as the equivalents of these elements. The atoms of all univalent elements carry exactly the same quantity of electricity, - of bivalent elements twice as much, of trivalent three times, and so on. In a word, all atoms have either the same capacity for electricity, or a simple rational multiple of the capacity of the univalent atoms. Faraday is also the author of the system of nomencla- ture, which we use in electrochemistry up to the present. Electrolysis. - The power of the current to decompose chemical compounds had been made especially prominent by the work of Faraday. This he termed electrolysis. Some of the most interesting and important advances made in electrochemistry, at that time, were along this line; and theories were proposed to account for the facts then known, which we now recognize to contain the germ of the theory of electrolytic dissociation. If the two poles of a voltaic cell are immersed in acidulated water, hydro- gen is liberated upon the one pole, and oxygen upon the other. Between the two poles there is a layer of water particles, which apparently undergo no decomposition. The question arose, do the hydrogen and oxygen set free, come from the same or from different water particles ? It is not a simple matter to answer this question satisfac- torily, and yet it is fundamental to the solution of the question of electrolysis. 46 ELECTROLYTIC DISSOCIATION A superficial examination of what took place in electroly- sis would probably lead to the conclusion that the hydro- gen and oxygen come from different water particles. Yet it might be that the water which was decomposed was that which was exactly halfway between the poles, and that the hydrogen moved from this point in the one direc- tion, and the oxygen in the other. Humphry Davy undertook to answer this question exper- imentally. He placed the poles of a voltaic cell in sepa- rate vessels, containing acidulated water, and connected the two vessels by placing a finger of one hand in the one, and a finger of the other hand in the other, care being taken to properly insulate his body from the earth. Elec- trolysis took place, hydrogen separating at one pole of the battery, oxygen at the other. In such an arrangement, it is difficult to see how the oxygen and hydrogen set free could come from the same particle of water. It is, there- fore, very probable, that in the electrolysis of acidulated water, the hydrogen and oxygen which are liberated at the poles come from different molecules of water. Theories of Electrolysis. - The first to account at all satisfactorily for electrolysis was Grotthuss, at the early date of 1805. At the moment when the hydrogen and oxygen separate, the one becomes positive and the other negative. The positively charged hydrogen is attracted to the negative pole, and repelled from the positive pole. The negatively charged oxygen is attracted to the positive pole, and repelled from the negative. But since the at- tracting and repelling forces vary inversely as the square of the distance from the electrodes, the sum of the forces which act, respectively, upon the hydrogen and oxygen THE EARLIER PHYSICAL CHEMISTRY 47 particles, as they approach the electrodes, is constan'-. This clear and concise idea of Grotthuss is represented graphically in the accompanying figure. The atoms marked positive represent hydrogen; those marked negative, oxygen. ' Before the current is passed, each oxygen atom is combined with a definite hydrogen atom, forming water. When the current is passed, the hydrogen atom nearest the negative pole gives up its positive charge to that pole, becoming electrically neutral, and separates as hydrogen gas. The oxygen atom which Fig. i. was originally in combination with this hydrogen is now free, but it combines at once with the hydrogen of the next molecule of water. This sets another oxygen atom free, which combines with the hydrogen of the next water molecule, and so on until the positive pole is reached, when the last oxygen atom in the chain, not finding any hydrogen with which to combine, takes up a positive charge from the positive pole, becomes electrically neut-ral, and escapes as gaseous oxygen. ' The gases, which escape only at the electrodes, come 48 ELECTROLYTIC DISSOCIATION from different molecules of water, as was made probable by the experiment of Davy. The layers of molecules between the electrodes are, during the electrolysis, con- stantly interchanging their constituents. The distinctive feature of the theory of Grotthuss is, that before the current is passed, each hydrogen atom is combined fixedly with a definite oxygen atom, from which it never parts company. The current must first decom- pose the water molecules, before any electrolysis can take place. This theory accounted, satisfactorily, for all the facts which were known about electrolysis, at the time when it was proposed. Clausius' Theory of Electrolysis. - While the theory of Grotthuss accounted for all the facts which were then known, new facts were soon brought to light, which could not be reconciled with it. According to this theory, the current must first decompose the molecules before it can effect any electrolysis. If the current used is not capable of decomposing one molecule of water, it is clear that it cannot decompose more than one, and no electrolysis would result. But as the strength of the current in- creases, it must reach a point where it is capable of decomposing a molecule of water. At this point many molecules must be simultaneously decomposed, since they are all under the effect of the same force, and have almost exactly the same position to one another. If the con- ductor conducts only electrolytically, we must conclude from this theory, that as long as the driving force in the conductor is below a certain limit, no current will pass; but when it has reached this limit, a very strong current suddenly exists. THE EARLIER PHYSICAL CHEMISTRY 49 Says Clausius,1 this conclusion from the theory is in direct opposition to what are now known to be the facts. The smallest force produces a current by alternate de- composition and reunion, and the intensity of the current increases according to Ohm's law, i.e. proportional to the force. Therefore, the assumption that the part mole- cules of an electrolyte are combined rigidly to form whole molecules, and that these have a definite, regular arrange- ment, is without foundation. The assumption, then, that the natural condition of an electrolytic liquid is one of equilibrium, in which every positive part molecule is combined rigidly with a negative, was abandoned by Clausius as untenable, and his own theory proposed in its place. An electrolytic solution consists mainly of whole mole- cules of the electrolyte, but in addition there are some " part molecules," which have parted company. A posi- tive part molecule may, during the movements to which it is subjected, come into a position with respect to the negative part of another molecule, which is more favor- able for union with this than with its own negative com- panion. It would then part company with the latter, and join the former. This would have, then, a positive and a negative part molecule, each free to move about through the solution and combine with other part molecules, or break down whole molecules already existing as such in the solution. These movements and decompositions take place as irregularly as the heat movements which produce them. The two part molecules, resulting from the break- ing down of a whole molecule, may combine directly with 1 Pogg. Ann., ioi, 338 (1857). 50 ELECTROI YTIC DISSOCIATION one another, or may be prevented from doing so by the movements due to heat. The amount of such decompo- sition in a solution would depend upon the nature of the solution and upon the temperature. Allow an electric force to act upon a solution containing a mixture of whole and of part molecules. The part mole- cules will no longer move about in all directions, due to the action of heat alone, but more positive parts will move in the direction of the negative pole, and negative parts toward the positive pole, than in the other directions. This directing influence of the current will also facilitate the breaking down of the whole molecules into part molecules. This assumption of a partial breaking down of the mole- cules in an electrolytic solution, before the current is passed, accounts for the fact that a weak current will effect electrolysis -a fact which could not be brought within the range of the theory of Grotthuss. The directing influence which the current exerts would exist for a current of any strength, and would be proportional to the strength of the current. In the opinion of Clausius, the action of the current is primarily a directing one, but, at the same time, it facilitates the decomposition of the molecules into part molecules. This theory of Clausius, as will be seen later, contains the germ of the theory of electrolytic dissociation. A theory as to the condition of things in solution was proposed by Williamson1 in 1851, as the outcome of his work on the preparation of ether by the action of sulphuric acid on ethyl alcohol. The reaction which produced the ether was recognized as proceeding in two stages: - 1 Liebig's Ann., 77, 45 (1851). THE EARLIER PHYSICAL CHEMISTRY 51 /OH /OC2H5 i. soZ + hoc2h5 = soZ + h2o. \OH \ OH /OC2H5 /OH C2H5K IL SOZ + HOC2H5 = SOZ 4- >0. \ OH \0H C2H/ The first stage of the reaction consists in the replacement of a hydrogen atom in the sulphuric acid, by the ethyl group, with the elimination of a molecule of water; the second, in the replacement of the ethyl group in ethyl sul- phuric acid by the hydroxyl hydrogen of the alcohol. The reaction which takes place as represented in I is then almost exactly reversed in II, the final result being the removal of a molecule of water from two molecules of alcohol, and the formation of a molecule of ether. From this Williamson concluded, " that in an aggregate of the molecules of every compound, a constant interchange between the elements contained in them is taking place." He concluded his paper with this statement: "In recent years chemists have added to the atomic theory an uncer- tain, and, as I believe, an unsubstantiated hypothesis, that the atoms are in a condition of rest. I reject this hypothe- sis, and found my views on the broader basis, the movement of the atoms." 1 Clausius criticised the views of Williamson as being too broad. His assumption went too far beyond the facts. It was not necessary to assume that all, or even a large part, of the molecules in a solution are broken down into part 1 Liebig's Ann., 77, 48. 52 ELECTROLYTIC DISSOCIATION molecules. The assumption that a few of the molecules are thus broken down, accounted for all the facts then known. Hittorf's Work on the Migration Velocity of Ions.- The changes in concentration, which take place when solutions are electrolyzed, could be explained only by assuming that the positive and negative part molecules, or, as Faraday called them, ions, move through the solu- tion with different velocities. The measurement of these relative velocities was undertaken by Hittorf,1 and his investigation of this problem has now become a classic. He studied the effect of concentration of solution, tempera- ture, and strength of current, upon the relative velocities of ions. His work is of importance, not simply as giving us the relative velocity of ions, but as throwing light on a number of other problems. What ions are formed from the given compounds ? which constituents go to make up the cation, and which the anion ? are questions which come within the range of the work of Hittorf. Take the com- pound K2PtCl6; does the platinum form part of the ca- tion, or of the anion ? does it go to the positive or to the negative pole? Or take the compound K4Fe(CN)6; when it is electrolyzed, does the iron go with the potassium to the cathode, or with the cyanogen to the anode ? The solution of such problems is of great assistance in deter- mining the chemical constitution, especially of complex compounds. Kohlrausch's Work on the Conductivity of Solutions. - Solutions of different electrolytes show very different con- ducting power. A simple and accurate method of meas- 1 Pogg. Ann., 89, 117, 177; 98, 1; 103, 1; 106, 337, 513. THE EARLIER PHYSICAL CHEMISTRY 53 uring the conductivity of solutions has been devised by Kohlrausch.1 He has applied his method to a large num- ber of solutions of different concentrations of acids, bases, and salts; and has furnished us with the most accurate conductivity measurements which have ever been made. The results of this work will be considered in a later chapter, since their bearing upon the theory of electro- lytic dissociation is direct. Indeed, we shall learn that the conductivity of solutions of electrolytes furnishes us with one of the most rigid tests to which the theory of electrolytic dissociation can be subjected. THE DEVELOPMENT OF CHEMICAL DYNAMICS AND CHEMICAL STATICS The brief sketch which will be given here, of the de- velopment of this branch of physical chemistry, will not include the earliest suggestions to account for chemical action, since many of them are now only of historical interest. The Swedish chemist, Bergmann, attempted generalizations which were undoubtedly advances on the disconnected knowledge before his time; but it was Wenzel (1777) who first saw clearly the effect of mass on chemical action, and laid the foundation for the law of mass action, which has played such a prominent rdle since his time. He, however, gave only a qualitative expression to the law; viz., that chemical action is proportional to the concentration of the substances which are allowed to react. Berthollet developed much more fully the effect of 1 Pogg. Ann., 138, 280; 154, 1; 159, 233; Wied. Ann., 6, 1; 11, 653; 26, 161. 54 ELECTROLYTIC DISSOCIATION mass in chemical action, and showed by direct experi- ment how it comes into play. The affinities which exist between substances are not to be regarded as absolute forces, but are dependent upon the masses of the sub- stances which are present. Thus barium sulphate can be partly decomposed by boiling it with potassium hydroxide. Calcium oxalate can, similarly, be partly decomposed by the same reagent. If the potassium hydroxide is present only in small quantity, no appreciable decomposition takes place; but if the quantity is large, and is removed from time to time, new alkali being added, barium sulphate can be completely decomposed by boiling potassium hy- droxide. This was a clear demonstration of the effect of mass. Following this same idea, Berthollet pointed out the effect of the state of aggregation on chemical activity. That chemical activity should be greatest, it is necessary that all the parts should come into action. This is best effected in the liquid state of aggregation. If a solid is present, the activity is less, or if a solid is formed as the result of the reaction, its activity is far less than in the liquid condition. Similarly, if a gas is formed in the reac- tion, it quickly escapes from the field of action, and its chemical activity therefore ceases. This work of Berthollet was published in two volumes as his " Essai de Statique Chimique," but was so far in advance of its day, that it either failed to attract attention altogether, or only aroused opposition from those who did not comprehend its full significance. It was much later before any further evidence was brought forward, to show the effect of mass in chemical THE EARLIER PHYSICAL CHEMISTRY 55 activity. Heinrich Rose1 showed that the sulphides of the alkaline earths are largely decomposed when boiled with large volumes of water, liberating hydrogen sulphide, and forming the hydroxide. He also called attention2 to a process which is going on in nature. Over the surface of the earth the weak chemi- cal reagents, carbon dioxide and water, are continually decomposing some of the most stable compounds - the silicates. The geological process known as weathering is a replacement of silicates by hydroxides and carbonates, or by basic carbonates. This reaction, in which such stable compounds are broken down by such a weak acid as carbonic acid, requires, of course, a long period of time, and is the result of the mass action of a large amount of carbon dioxide, such as exists in the atmosphere, and in the soil. Such a reaction is entirely beyond the possi- bilities of the laboratory, on account of the time and mass of substance required to effect it. Rose 3 also carried out some investigations on the decom- position of insoluble salts by soluble salts. It was known, long before his time, that barium sulphate can be trans- formed into the carbonate, both by fusion with potassium carbonate, and also by boiling with an aqueous solution of potassium carbonate. Rose, however, undertook a quan- titative study of the conditions under which this transfor- mation takes place, and the amount of carbonate required to effect complete decomposition. He found that the sul- phates of strontium and calcium are more easily decom- posed by alkaline carbonates than the sulphate of barium, I Pogg. Ann., 55, 415. 2 ibid., 82, 545. 8 Ibid., 94, 481; 95, 96, 284, 426. 56 ELECTROLYTIC DISSOCIATION and concluded, correctly, that this was due to the presence of a reversible reaction between the barium carbonate and alkaline sulphate formed, resulting in the reformation of barium sulphate. The result of this work of Rose, and that of his con- temporaries, was to call attention to the role played by mass in bringing about chemical reaction. The full im- portance of the action of mass, as we shall see, was, how- ever, not recognized until somewhat later. Wilhelmy's Discovery of the Law of Reaction Velocity. - Wilhelmy1 treated cane-sugar with a number of acids, and studied the velocities with which inversion takes place. He worked with different acids, with different amounts of cane-sugar, and at different temperatures. He found that it was only the sugar which underwent change, the acid remaining unaltered. The law of mass was found to obtain; the amount of sugar transformed in a given time being proportional to the amount present at that time. Applying the principle of mass, - remembering that it is only the sugar which undergoes change, the acid being unaltered, - Wilhelmy deduced the following mathemat- ical relations, which are taken from his epoch-making paper:2 - " Let dZ be the amount of sugar inverted in unit time dT, and let us assume that this is determined by the formula:1 - -^= MZS dT • / in which M is the mean value of the infinitely small quan- tity of sugar, which is transformed in unit time, by the 1 Pogg. Ann., 8i, 413 (1850). 2 Ibid., 8i, 418. THE EARLIER PHYSICAL CHEMISTRY 57 action of the unit of acid present. (Z is the amount of the sugar, S that of the acid.) "The above equation gives, on integration: - LogZ=-J^rj7S^Z or since, as already shown, S is constant, M is also inde- pendent of Z, and at the same time of T, which should be proved later by experiment: - LogZ = - MST + C. For T - o, Z = Z^, whence: Log Z^ - log Z = MST, or Z = Z^E. Since Z^, S, and T are given, and Z is known by experi- ment, the formula can be used to determine M." This work of Wilhelmy, which must be regarded as the foundation of chemical dynamics, like most important inves- tigations, did not receive a just recognition until attention was called to it much later.1 When we consider that this was the first successful attempt to express the velocity of a chemical reaction mathematically, and that this was in 1850, we can form some conception of the rapidity of the growth of knowledge along this line. Other contributions to our knowledge of the mechanism of chemical reactions were made in the next few years. Lowenthal and Lenssen 2 showed that the amount of sugar inverted by different acids was proportional to the strength of the acids. But the next marked advance we owe to the French chemist Berthelot. 1 Ostwald, Journ. prakt. Chern., 29, 385 (1884). 2 Journ. prakt. Chem., 85, 321 (1852). 58 ELECTROLYTIC DISSOCIATION Work of Berthelot and Pean de St. Gilles. - Berthelot and Pean de St. Gilles1 made an elaborate investigation of the conditions of formation and decomposition of ethe- real salts. The reactions by which these are formed from acids and alcohols proceed slowly, and tend toward a limit, the point at which the reaction reaches a condition of equilibrium depending upon the amount of acid or alcohol present, upon the temperature, etc. On the other hand, if an ethereal salt is treated with water, a certain amount of it is decomposed, the amount depending upon the quan- tity of water used, and other conditions. A reaction of this kind is, evidently, well adapted to the study of reaction velocity, condition of equilibrium, etc. They determined the effect of temperature on the velocity of this reaction, and found that to transform 30 per cent of a given mixture of alcohol and acid, at from 6° to 90, required 95 days, while at ioo° it required less than 5 hours to effect the same transformation. Pressure was found to have no influence on reaction velocity, at least up to sixty or eighty atmospheres. Berthelot2 and St. Gilles, in the course of their study of ether formation, arrived at the following generalization : " The amount of ether formed in every moment is pro- portional to the product of the reacting substances." This was a beautiful confirmation of the action of mass. They also determined the relation between chemical composition and the amount of ether formed. A few of their results are given, using different alcohols and acids, and allowing the reaction to proceed until equilibrium was 1 Ann. Chim. Phys. [3], 65, 385; 66, 5; 68, 225 (1862-1863). 2 Ibid. [3], 68, 225. THE EARLIER PHYSICAL CHEMISTRY 59 reached, i.e. until the maximum amount of ether was formed under the conditions. This is indicated in per- centage of the theoretical amount of ether which might be formed under the conditions, if the reaction went to the end. Limit C2H6O with CH3COOH 66.9% C2H6O with CH3 • CH2 • CH2 • COOH 69.8% C2H6O with C6H5COOH 67.0% CH4O with CH3COOH 67.5% CH4O with C6H5COOH 64.5% CH4O with C2H4(COOH)2 66.1% CsH12O with CH3COOH 68.9% C5H12O with CH3 • CH, • CH2 • COOH 70.7% C5H12O with C6H3COOH 70.0% This is a remarkable result. Neither the chemical com- position of the acid, nor of the base, has any marked influence on the amount of ether formed. The effect of increasing the amount of the alcohol, with respect to the acid, was also determined. n is the number of equivalents of ethyl alcohol, to one equivalent of acetic acid. n Limit n Limit n Limit 0.2 19.3% 2. 82.8% 12.0 93.2% 0.5 42.0% 4. 88.2% 19.0 95.0% 1.0 66.5% 5.4 90.2% 50.0 100.0% i-5 77-9% These results exhibit the effect of mass in a striking manner ; all the acid being transformed into ethereal salt, when fifty equivalents of alcohol are present to one of acid. The action of mass was shown also by the work of 60 ELECTROLYTIC DISSOCIATION Deville 1 on dissociation. Many substances are partially broken down by heat into their constituents - in many cases into their elements. Thus, water-vapor at a high heat is partially decomposed into hydrogen and oxygen. The fact was established, that if either the hydrogen or oxygen resulting from the decomposition is removed, the dissocia- tion will proceed farther, and may become complete. If, on the other hand, an excess of either hydrogen or oxygen is added to the dissociating water-vapor, the amount of dissociation is decreased. Deville studied a number of cases, and concluded that this is general, that an excess of either of the products of dissociation will diminish the amount of dissociation of a vapor. An excellent ex- ample of this is furnished by phosphorus pentachloride. This compound cannot be volatilized without decomposi- tion, unless there is an excess of either chlorine or phos- phorus trichloride present. In the presence of an excess of one of these, the molecular weight of phosphorus penta- chloride, as determined, is very close to the theoretical molecular weight. This work of Deville is one of the most direct confirma- tions of the effect of mass, yet it was used by him as an argument against mass action, being a factor in chemical activity. Another example of admirable work, but erro- neous interpretation of results obtained. Guldberg and Waage's Law of Mass Action. - We have seen that the effect of mass on chemical activity was recognized as early as the time of Wenzel. A clearer expression of its action was furnished by Berthollet. Rose showed, both from nature, and by direct experiment, what 1 Compt. rend., 45, 857; 56, 195, 729; 59, 873; 60, 317. THE EARLIER PHYSICAL CHEMISTRY 61 a marked influence mass has in effecting chemical reac- tions. Berthelot and Pean de St. Gilles demonstrated the effect of mass action on the formation of ethereal salts from alcohols and acids, and thus made it probable that the effect of mass on chemical reactions is general. It was Guldberg and Waage,1 however, who gave a com- plete mathematical expression to the action of mass. If two substances react, the action is proportional to the active masses of each of them. The intensity of the reaction is, therefore, measured by the product of the active masses. The reaction is, of course, dependent also upon the nature of the substances, temperature, etc. These must be taken into account. If we represent the active masses of two substances by w and w, and the coefficient depending upon the nature of the substance, etc., by c, the force of the chemical reaction is expressed by mnc. If the reaction is reversible, i.e. if the substances formed can react and give the original substances, as e.g. in the formation of ethereal salts, then there will exist a force which tends to stop the original reaction, and to set up one in exactly the opposite sense. If we represent the active masses of the substances formed in the original reaction by m' and and the coefficient depending upon the nature of the substances by c', the magnitude of the force opposing the original reaction will be expressed by m' n'c'. When the condition of equilibrium is reached, the two forces are equal and opposite, and we have: - mnc - m1 n1 c1....... (i) 1 Etudes sur les Affinit6s Chimiques, Christiania, 1867; Journ. prakt. Chem. [2], 19, 69 (1879). Ostwald's Lehrb. d. allg. Chemie, II, 2, p. 104. 62 ELECTROLYTIC DISSOCIATION If we bring together equivalents of the four substances m, n, m', n', they will generally not be in a state of equilib- rium, but a certain amount of tn and n will pass over into m' and n', and this amount we will call x. The amounts of the four substances present will then be, m - x, n - x, in' + x, n! + x. The active masses being the amounts in a given volume v, we will have: - ni - x 11 - x in' + x n' + x V V V V where v is the entire volume of the solution. Substituting these values for m, n, m', and n' in (i), we have : - k' (in - x} (n - a ) = -(in' + x) (n' + x). tv This equation is perfectly general, applying to all values of x. If we determine x in any one case, we can calculate k' . k' - Knowing -,we can calculate the value of x for any k k amounts of the original substances brought together. In a word, we could calculate exactly how the four substances would react, whatever the quantities brought together, and how much of each would exist when equilibrium was reached. Guldberg and Waage's work also led to a more com- prehensive conception of the reversibility of many chemi- cal reactions, equilibrium being the special condition under which the reactions in the two directions were of equal velocity. The velocity of any reaction is, in reality, the difference between the velocity in one direction, and the velocity in the other. The velocity v is the amount dx transformed in unit time, v - --; but this is equal to a dT THE EARLIER PHYSICAL CHEMISTRY 63 factor 0 times the force acting in one direction, minus the force acting in the other direction. v = = 0(mnc - m1 n' If the reaction proceeds only in one direction, m'n c' be- comes equal to zero, and the equation of reaction velocity becomes: - al The above relations obtain, only when all of the sub- stances which enter into the reaction are soluble. If one or more of the substances is insoluble, the relations are much simplified. Take the reaction between potassium carbonate and barium sulphate, in which potassium sul- phate and barium carbonate are formed. Let M be the active mass of potassium carbonate. Let N be the active mass of barium sulphate. Let M' be the active mass of potassium sulphate. Let N' be the active mass of barium carbonate. Barium sulphate and barium carbonate are insoluble, and their active masses, N and N', are, therefore, con- stant. We have then : - MC- M'C or = constant. M' This is a very simple relation, and holds whenever two of the substances are insoluble. The value of the con- stants for the insoluble substances depends upon their degree of insolubility. The law of mass action has been tested in a large num- ber of directions, and by a great variety of methods. The 64 ELECTROLYTIC DISSOCIATION general result has been a thorough confirmation of the views of Guldberg and Waage. The Application of Thermodynamics to Chemical Pro- cesses.- The scope of this work will not permit of more than a brief reference to the leading investigations bearing upon this problem. Horstmann1 was the first to success- fully apply thermodynamics to chemical processes. He chose dissociation phenomena, since they are reversible processes ; and if they take place between solids and gases, obey the same laws as vaporization. If we represent by h the heat of combination, and by p the dissociation press- ure, the following relation between the two obtains : - h = Tu dT in which T is the absolute temperature, and u the volume of the vapor. Knowing either h or p, we can calculate the other. He later applied the entropy principle to conditions of equilibrium, and showed that a system will always assume that arrangement in which entropy is a maximum. The condition for equilibrium is then : - de ~dx ~ ' in which e is the entropy, and x the amount of untrans- formed substance. Willard Gibbs's2 applications of thermodynamics to con- ditions of chemical equilibrium are so comprehensive and general, that it is impossible to give any adequate concep- 1 Ber. d. chem. Gesell., 2, 137; 4, 635; Liebig's Ann., 170, 192 (1872-1873). 2 Trans. Conn. Acad., Ill, 1874-1878. Translated into German by Ostwald, Leipzig, 1892. THE EARLIER PHYSICAL CHEMISTRY 65 tion of his epoch-making work in a few paragraphs. The reader who may desire to follow out Gibbs's mathematical deductions must be referred to his original communication, or to the second part of the second volume of Ostwald's Lehrbuch, where a systematic account of his deduction is given. It should, however, be stated here, that the work of Willard Gibbs has placed the science of chemical equilib- rium on an entirely new basis, from the theoretical stand- point, and is ranked as one of the leading contributions to mathematical chemistry and physics. The work of van't Hoff1 is in part theoretical, and in part experimental. This deals largely with the velocity of reactions from both standpoints, and also investigates the influences which affect the velocity of a reaction, such as temperature, pressure, form of vessel, etc. The con- ditions of equilibrium were also investigated by van't Hoff and his pupils, and the temperatures ascertained at which a large number of transformations take place. The observations for the different kinds of equilibrium have led to the following general conclusion:2 " Every equilibrium between two different conditions of matter (systems) is, at constant volume, by a decrease in temper- ature, displaced in the sense of that system whose forma- tion liberates heat." This generalization includes all pos- sible cases of chemical as well as of physical equilibrium. This principle, termed by van't Hoff that of " movable equilibrium," is then applied to both heterogeneous and 1 Etudes de Dynamique Chimique, Amsterdam, 1884. Studien zur Chemischen Dynamik, van't Hoff and Cohen. 2 Studien zur Chemischen Dynamik (van't Hoff and Cohen), p. 223. 66 ELECTROLYTIC DISSOCIATION homogeneous equilibria. The concluding chapter of this important work by van't Hoff and Cohen is devoted to the subject of chemical affinity. The generalization reached was,1 that " the work expressed in calories, which affinity can do in a chemical transformation, at a given tempera- ture, is equal to the amount of heat which this transforma- tion produces, divided by the absolute temperature at which the transformation takes place, and multiplied by the difference between this, and the temperature at which the transformation takes place." If A is the amount of work done, q the amount of heat produced, T the temperature of the transformation, and P the absolute temperature of the transformation, we have:- which is the mathematical expression of the above gener- alization. In connection with the study of chemical equi- librium, the work of Le Chatelier2 must be mentioned. He arrived at two laws which he stated thus : Law of the opposition of action and reaction (page 210). "Every variation of a factor of equilibrium causes a transformation of the system, which tends to make the factor in question undergo a variation of sign opposite to that which we have given it." Thus, an elevation of temperature produces a reaction with absorption of heat, an increase in pressure a reaction with diminution of volume, etc. 1 Studien zur Chemischen Dynamik, p. 247. 2 Recherches Experimentales et Theoriques sur les Equilibres Chimiques. Paris, 1888. THE EARLIER PHYSICAL CHEMISTRY 67 Le Chatelier termed his second generalization the law of equivalence of systems in equilibrium, and expressed it thus : - " Two equivalent elements in a system in equilibrium, i.e. which can be substituted for one another without chang- ing the condition of equilibrium, will be equivalent in every other system where they can be substituted for one another, and further, will be mutually in equilibrium if in opposition to one another." An example cited is the equality of the vapor-tension of water and of ice at the melting-point. Methods of measuring Affinity. -The theoretical deduc- tions, especially of the last four pieces of work referred to, have been tested experimentally by a number of methods. Julius Thomsen1 determined the way in which a base is divided between two acids, by means of the amount of heat liberated. While Ostwald,2 utilizing the change in volume which occurs in chemical reactions, obtained far more satisfactory and reliable results than Thomsen. Ostwald showed that the action between acids and bases is condi- tioned by two coefficients, the one depending upon the nature of the acid, the other upon the nature of the base. The chemical affinity of an acid for a base is then expressed by the product of these two coefficients. These affinity coefficients are the numerical expressions of the strength of the acid or base, and hold, quantitatively, for all actions in which the acid or base takes part. In addition to the thermochemical method of J. Thom- sen, and the simpler and more reliable volume chemical 1 Pogg. Ann., 138, 497 (1869). 2 Journ. prakt. Chem. [2], 16, 385 (1877). 68 ELECTROLYTIC DISSOCIATION method of Ostwald, a number of other methods of measur- ing relative affinities have been devised. Ostwald1 pro- posed the velocity with which substances like zinc sulphide, or calcium oxalate, are dissolved by different acids, as a measure of the relative affinities of the acids. He2 also used the velocity, with which a reaction like the transfor- mation of acetamid into ammonium acetate takes place under the influence of acids, as a measure of the affinities of the acids. Ostwald has also studied other reactions in this same connection, such as the catalysis of methyl acetate, inversion of cane-sugar, etc., and found that the coefficients for the different acids, as determined by the different methods, agreed satisfactorily. A relation was thus discovered, which, as we will see, is of the very greatest importance, in connection with the theory of electrolytic dissociation. The affinity coefficients of acids and bases bear the same quantitative relations to one another as the conductivities of these acids and bases. The discussion of this relation belongs to a later chapter of this work, and it suffices here to merely call attention to its existence. Conclusions from the Earlier Physical Chemical Work. - From the preceding sketch of the development of the several chapters of physical chemistry, we can form a fairly clear conception of the state of physical chemistry just before the theory of electrolytic dissociation was proposed. Much work had been done on the relations between the various properties, and composition and con- stitution ; and a great number of generalizations had been reached, which, however, held only approximately. Much 1 Journ. prakt. Chem. [2], 19, 468 (1879). 2 Ibid. [2], 27, 1 (1883). THE EARLIER PHYSICAL CHEMISTRY 69 valuable experimental work had also been done on the amount of heat liberated in chemical reactions, laying stress upon the energy transformations which take place in chemical processes, and which are probably the condi- tioning causes of all chemical action. Here, also, relations were pointed out, which, however, like the above, have been shown to be only approximations. Then, the founda- tions of electrochemistry were laid, early in the century, and rapidly developed, and theories to refer chemical action to purely electrical causes were proposed. The decomposing action of the current was studied, and theo- ries advanced to explain electrolysis, which lie at the foundation of our most modern theory. The relation pointed out here by Faraday, between the amount of current and the amount of decomposition which it effects, is one of the most exact with which we have to deal. Similarly, other electrochemical relations are freer from exceptions than those which we have just considered. Some of the more important steps in the development of chemical dynamics and statics have been taken up, includ- ing, especially, the law of mass action, which underlies this entire chapter of physical chemistry. But, from what has preceded, we can see not only the state of development, but also the inherent nature of physical chemistry. What was the chief aim of the physical chemist in these earlier periods ? It was, plainly, to discover relations between apparently disconnected phenomena and disconnected facts. It attempted to con- nect, and thus systematize, the great masses of isolated facts, which were yearly being brought to light, and thus refer them, as far as possible, to common causes. 70 ELECTROLYTIC DISSOCIATION It has, however, been repeatedly shown, that these earlier relations were, in many cases, only approximations. The number of exceptions continued to increase, as more ac- curate experimental work was done, until, in some cases, the generalization almost entirely disappeared. Neverthe- less, the aim of the earlier physical chemist is the aim of the physical chemist of to-day - to discover generalizations wherever they exist. It is by this means, and this means only, that chemistry can be advanced from pure empiri- cism to the rank of an exact mathematical science. We will now follow the rise and development of the widest and most important generalization which has ever been reached by physical chemistry. CHAPTER II THE ORIGIN OF THE THEORY OF ELECTROLYTIC DISSOCIATION pfeffer's osmotic investigations Introduction. - If we would trace the origin of the theory of electrolytic dissociation, we must turn neither to chemistry nor to physics, but to the osmotic investigations of the botanist, W. Pfeffer.1 It had long been known, that when a solution of a substance is placed upon one side of a partition, through which the solvent can pass but the dissolved substance cannot, and the pure solvent placed upon the other side, the pure solvent will flow through the partition into the solution. This phenomenon is termed osmosis, and the pressure thus produced, osmotic pressure. We may demonstrate this phenomenon by filling a bladder with a solution of alcohol in water, and then immersing it in pure water. Water will flow through the bladder into the solution of alcohol, and the bladder will become distended. This is, of course, but a qualita- tive demonstration; and were we dependent upon natural membranes alone to measure osmotic pressure, it is safe to say that very little would have been accomplished. Pfeffer, however, succeeded in devising artificial mem- branes, with which he could study osmotic pressure quantitatively. 1 Osmotische Untersuchungen, Leipzig, 1877; Harper's Science Series, IV, p. 3. 71 72 ELECTROLYTIC DISSOCIATION Pfeffer's Method of measuring Osmotic Pressure. - Cer- tain precipitates have the property of allowing the solvent to pass through them, but of preventing the dissolved substance from passing. If these precipitates are de- posited at the plane of contact of two solutions, or of a solution and a solvent, they act like the animal mem- brane described above. This important fact was dis- covered by Traube, who was the first to prepare these artificial membranes, and use them to study osmotic press- ure. His method, however, was far inferior to that devised by Pfeffer. To make these membranes more resistant, Pfeffer de- termined to form them upon a support. He states that the plant cell furnished him with a model. " In these, the plasma membrane which, in its diosmotic properties, is similar to the artificially precipitated membranes, is pressed against the cell wall." Pfeffer caused the precipitate to be deposited in the walls of very fine-grained, unglazed porcelain cells. The precipitate which gave him the best results was copper ferrocyanide. A porcelain cell was filled on the inside with a solution of potassium ferrocy- anide, and immersed in a solution of copper sulphate. The two solutions penetrated the walls of the porcelain cell, and met right in the walls. Where they came in contact, there was precipitated copper ferrocyanide as a membrane, which, when the cell was broken, appeared as a fine line. The membranes deposited in this way had many of the properties desired. They were semipermeable, i.e. allowed the solvent to pass through and prevented the dissolved substance, and were sufficiently resistant to THEORY OF ELECTROLYTIC DISSOCIATION 73 withstand considerable pressure without breaking The apparatus in its complete form, as used by Pfeffer, is seen in Fig. 2. The porcelain cell, with semipermeable membrane deposited in the walls, is seen at z. This cell was about 46 mm. high, 16 mm. internal diameter, and the walls were from to 2 mm. thick. "The narrow glass tube v, called the connecting piece, was fastened into the porcelain cell with fused sealing-wax, and the closing piece t was set into the other end of this tube in the same manner. The shape and purpose of this are shown in the figure. The glass ring r was necessary only in experiments at higher tem- perature, in which the seal- ing-wax softened. The ring was then filled with pitch, which also held together firmly the pieces inserted into one another." The manometer in is attached for measuring the pressure. To give an idea of the precautions which are necessary From " The Modern Theory of Solution." Copyright, 1899, by Harper & Brothers. Fig. 2. 74 ELECTROLYTIC DISSOCIATION to prepare, successfully, such semipermeable membranes as were used by Pfeffer, a paragraph is quoted from his monograph:1 - " The porcelain cells were first completely injected with water under the air-pump, and then placed for at least some hours in a solution containing 3 per cent of copper sulphate, and the interior was also filled with this solution. The interior only of the porcelain cell was then once rinsed out quickly with water, well dried as rapidly as possible by introducing strips of filter paper, and after the outside had dried off, it was allowed to stand some time in the air until it just felt moist. Then a 3 per cent solution of potassium ferrocyanide was poured into the cell, and this immediately reintroduced into the solution of copper sulphate. " After the cell had stood undisturbed for from twenty- four to forty-eight hours, it was completely filled with the solution of potassium ferrocyanide, and closed as shown in Fig. 2. A certain excess of pressure of the contents of the cell now gradually manifested itself, since the solu- tion of potassium ferrocyanide had a greater osmotic press- ure than the solution of copper sulphate. After another twenty-four to forty-eight hours the apparatus was again opened, and generally a solution introduced which con- tained 3 per cent of potassium ferrocyanide, and i| per cent of potassium nitrate (by weight), and which showed an excess of osmotic pressure of somewhat more than three atmospheres." The osmotic pressure of solutions is measured with this apparatus as follows: The cell is completely filled 1 Harper's Science Series, IV, p. 6, THEORY OF ELECTROLYTIC DISSOCIATION 75 with the solution and then tightly closed. The solution also extends into the arm of the manometer attached to the cell. The whole apparatus is then immersed in the pure solvent, as shown in Fig. 3. The closed cell is fastened to a glass rod, and so immersed in the liquid in the bath that the entire manometer is covered. The temperature of the bath is read by thermometers. The entire apparatus is placed under a bell- jar and kept in a room at uniform tem- perature. This is necessary, since con- siderable time is required for the mer- cury to reach the highest point and remain perfectly sta- tionary. Water flows in through the semi- permeable membrane, and the pressure produced is finally read off on the ma- nometer. The water which enters the cell dilutes the solu- tion and diminishes its osmotic pressure, but the amount From " The Modern Theory of Solution." Copyright, 1899, by Harper & Brothers. Fig. 3. 76 ELECTROLYTIC DISSOCIATION of water which enters is so slight that the error from this source is not large. Some of Pfeffer's Results. - Pfeffer measured the os- motic pressure of solutions of a number of substances at different concentrations, and at different temperatures. A few of the results which he obtained are given. Osmotic Pressure for Cane-Sugar of Different Concentration Percentage Conc. by Weight Osmotic Pressure 1.0 535 mm. 2.0 1016 mm. 2-74 1518 mm. 4.0 2082 mm. 6.0 3°75 mm. Effect of Temperature on Osmotic Pressure The following results were obtained with a i per cent solution of cane-sugar : - Temperature Pressure p4-2° C. 510 mm. 132.0° C. 544 mm. ( 6.8° C- 505 mm. i3-7° c- 525 mm. I 22.0° c. 548 mm. fi5-5° C. 520 mm. 136-0° C. 567 mm. These are a very few of the results which were recorded by Pfeffer. This investigation was undertaken by Pfeffer purely from the standpoint of vegetable physiology, and with no THEORY OF ELECTROLYTIC DISSOCIATION 77 idea of throwing light on any physical-chemical problem. His work was completed and published in 1877. From the botanical standpoint it was a contribution of the very highest value. Pfeffer did not point out any bearing which his results might have on problems such as those with which we are now about to deal. Indeed, their sig- nificance was not seen until nearly ten years later, when van't Hoff showed that this work of Pfeffer marked the beginning of a new era in physical chemistry. RELATIONS BETWEEN OSMOTIC PRESSURE AND GAS PRESSURE DISCOVERED BY VAN'T HOFF Historical. - In following up the discovery of a great generalization, it is always of interest to trace the stages by which it was reached. We are very fortunate in this case, since van't Hoff himself has given us an account of the development of the ideas which led him to the discovery of the relations between osmotic pressure and gas pressure. In the winter of 1894, he was invited by the German Chemical Society to give a lecture on his physical chemical investigations. He chose for his theme, " How the Theory of Solutions Arose," and here we find a detailed statement of the steps which led to his discov- ery. This lecture is published in full in the Berichte der deutschen chemischen Gesellschaft, 27, 6 (1894). A few pages from this lecture are given, since it contains a con- cise statement of the facts which are of such unusual interest in this connection. " It was when I first began to think on chemical matters, under the guidance of Kekule and Wislicenus, that the ideas about the position of atoms in space began to germinate. 78 ELECTROLYTIC DISSOCIATION " The entire ' Arrangement of Atoms in Space ' was, in- deed, only a structure which depended upon the relation of a physical property-optical activity - to chemical constitution. " Although so young, I wished then to know, also, the relations between constitution and chemical properties. The constitution formula should, indeed, be the expression of the entire chemical behavior. "Thus arose my ' Ansichten uber die organische Chemie,' with which, indeed, you are not familiar, and which is scarcely worth knowing. It had this value, however, for me, that it pointed out, very clearly, the existence of a gap. " Let us take an example : - " It is known that oxygen in organic compounds has an accelerating action on almost all transformations. The oxidation of CH4 is more difficult than of CH3OH, etc. "To obtain relations of value in this connection, there is need of accurate knowledge of the velocity with which a reaction proceeds, and thus I began the study of the velocity of reactions, and there appeared my ' Etudes de Dynamique Chimique.' " Reaction velocity was at first the chief aim, but chemi- cal equilibrium was closely associated with it. Equilibrium resting, on the one hand, on the equality of two opposite reactions, and procuring a firm support, on the other, through its connection with thermodynamics. You see how, to obtain my object, I was ever led farther from it, which often occurs. "And I must go still farther; for the question of equilib rium borders directly on the problem of affinity, and I wa: thus concerned with the very simple affinity phenomenon THEORY OF ELECTROLYTIC DISSOCIATION 79 - at first with that which expresses itself as an attraction for water. " Mitscherlich had already raised the question, in his 'Text-book of Chemistry' (4th edition, 1844, 565), as to the magnitude of the attractive force which holds the water of crystallization in Glauber salts. He saw a means of measuring this in the diminished tension of the water of crystallization. " ' If Glauber salt is brought into the barometric vacuum at 90, the mercury falls about 2| lines (5.45 mm.), due to the liberation of water-vapor. Water itself produces, on the other hand, a fall of 4 lines (8.72 mm.). The affinity of the sodium sulphate for its water of crystallization cor- responds, therefore, to the difference, i| lines (3.27 mm.), i.e. about kg. per square inch.' " This value, ^-o of an atmosphere, appeared to me as small without precedent, for I had the impression that even the weakest chemical forces are very large, as appeared to me to follow also from Helmholtz's Faraday Lecture. Thus, the question arose, whether it is not pos- sible, in simpler cases, to measure this attraction for water in a more direct way; and for this purpose the aqueous solution is the simplest conceivable-much simpler than the compound containing water of crystallization. " Coming from the laboratory with this question vividly in mind, I met my colleague De Vries and his wife. He was just at that time carrying out osmotic investigations, and he told me about Pfeffer's determinations. "You recognize the apparatus sketched here. The so- called osmotic pressure is measured with a battery cell, whose wall is made semipermeable, i.e. permeable only 80 ELECTROLYTIC DISSOCIATION to water, but not to the dissolved substance, e.g. sugar -> by the method of Traube. This is accomplished by deposit- MITSCHERLICH PFEFFER Fig. 4. ing a membrane of copper ferrocyanide within the walls of the porcelain cell. The osmotic pressure of a one per cent solution of cane-sugar is two-thirds of an atmosphere. /'This pressure was remarkably large in comparison with that described by Mitscherlich, and yet a relation exists between the two. " Let us consider the sugar solution as placed below, on the left side, and separated by means of a semipermeable membrane from water which is on the right side below. The movement of the water is to the left, into the space containing vapor with the pressure observed by Mitscher- lich, into the water with that observed by Pfeffer. " A calculation can be based directly upon this relation. The force described by Mitscherlich is very small, because it acts on the more dilute vapor; that of Pfeffer is large, because it acts on the concentrated water. Therefore : - THEORY OF ELECTROLYTIC DISSOCIATION 81 Pfeffer : Mitscherlich = 1000 : -^-o.o8oq6-(1 H--A 760 2 ' 273 7 and thus Pfeffer's force, calculated from the decrease in tension (freezing-point): - Temperature Osmotic Pressure 0.00239 7" 6.8° O.664 0.668 15-5° O.684 0.689 22° O.721 0.704 32° O.716 0.728 36° O.746 0-737 The above proportionality is, however, not perfectly rigid. The exact formula is obtained, in case the work which the water attraction can perform is chosen as the starting-point. This is independent of whether the water is carried over as such, or as vapor; and thus we have the relation (for 18 kgs. water): - 2 Tl^ = -PV, Pi 323 in which pw and pr are, respectively, the tension of the water and of the solution, P the osmotic pressure in kgs. per qm., and V the volume of 18 kgs. of water in cbm. " This formula corresponds very accurately with Pfeffer's results, but it can be used for determining pressure only in case the tension pt is known; and thus Mitscherlich's question of water of crystallization is also solved, since it is evident that this water attraction corresponds to that of a solution of equal maximum tension. We have then the following: - 82 ELECTROLYTIC DISSOCIATION Substance Temperature Pressure Na2SO4. io H2O 9° 6oo atmos. FeSO4. 7 H2O 25° 510 atmos. FeSO4. 7 H2O 65° 245 atmos. CuSO4. 5 H2O 50° 1100 atmos. CuSO4. 3 H2O - 1730 atmos. "This means that if Na2SO4 should be prevented from taking up its water by pressure, in a suitable manner, - say in Pfeffer's apparatus, - 600 atmospheres at 90 would be necessary and sufficient. "We must now turn from Mitscherlich's question of affin- ity to dilute solutions; since where we are dealing with the union of water of crystallization, it is obvious that enor- mous concentrations obtain." We see from the above paragraphs, the exact stages by which van't Hoff arrived at the study of dilute solutions from the standpoint of osmotic pressure. From the posi- tion of atoms in space, he was led to study reaction velocity, and from this the conditions of equilibrium. But closely connected with the problem of equilibrium was that of affinity. He took up, as an example of affinity, the attrac- tion of salts for their water of crystallization, and sought to measure this more directly than had been done. This led him, through the suggestion of De Vries, directly to Pfeffer's osmotic investigations. Having dealt with con- centrated solutions, he then turned to dilute; and we shall now learn the nature of the results which he obtained, by comparing the gas pressure of gases with the osmotic pressure of dilute solutions. Boyle's Law for Dilute Solutions.-In 1887 van't Hoff published a paper in the first volume of the Zeitschrift THEORY OF ELECTROLYTIC DISSOCIATION 83 fiir physikalische Chemte, under the title, "The Role of Osmotic Pressure in the Analogy between Solutions and Gases." 1 The object of this communication, as its title im- plies, is to point out certain relations between the gas press- ure of gases and the osmotic pressure of dilute solutions. To quote from the translation in Harper's Science Series: - " The analogy between dilute solutions and gases acquires at once a more quantitative form, if we consider that in both cases the change in concentration exerts a similar influence on the pressure; and, indeed, the values in ques- tion are, in both cases, proportional to one another. " This proportionality, which, for gases, is designated as Boyle's law, can be shown for osmotic pressure, experi- mentally from data already at hand, and also theoretically." Van't Hoff then gives enough of Pfeffer's data to show experimentally, that there is proportionality between os- motic pressure and concentration. " Let us first give the results of Pfeffer's determinations of osmotic pressure (P), in solutions of sugar, at the same temperature (13.2° to 16. i°) and different concentrations (Q:- c P P C 535 mm- 535 2% 1016 mm. 5 08 2-74% 1518 mm. 554 4% 2082 mm. 521 6% 3075 mm. 5r3 p "The nearly constant value of - indicates that, in fact, a proportionality between pressure and concentration exists."2 1 Ztschr. phys. Chern., i, 481. Translated into English by H. C. Jones. Har- per's Science Series, IV, p. 13. 2 Harper's Science Series, IV, p. 16. 84 ELECTROLYTIC DISSOCIATION The work of De Vries1 is then cited, as furnishing a second line of experimental evidence, of the applicability of Boyle's law to the osmotic pressure of dilute solution. De Vries compared the osmotic pressure of solutions of sugar, potassium nitrate, and potassium sulphate, with that of the contents of a plant cell, whose protoplasmic sac contracts when the cell is introduced into a solution which has stronger attraction for water. It was found that equal changes in concentration of solutions of sugar, potassium nitrate, and potassium sulphate, exert the same influence on the osmotic pressure. The experimental evidence was thus very strongly in favor of the law of Boyle for the osmotic pressure of solutions. A theoretical demonstration of this law for solutions was also given by van't Hoff :2 - Gay Lussac's Law for Dilute Solutions. - Having found that the law of Boyle for gases applies to the osmotic pressure of solutions, one would naturally inquire whether other gas laws also apply to solutions. Thus, the attempt was made to apply to the osmotic pressure of solutions the law of Gay Lussac, which holds for the tempera- ture coefficient of gas pressure. The law was tested both experimentally and theoretically on thermodynamic grounds. For experimental demonstration, recourse was had again to the results of Pfeffer's investigations. This investiga- tor found that the osmotic pressure always increased with rise in temperature. If from one of two experiments carried out with the same solution at different tempera- 1 " Eine Methode zur Analyse der Turgorkraft,'' Pringsheim's Jahrb., 14. 2 See Harper's Science Series, IV, 17. THEORY OF ELECTROLYTIC DISSOCIATION 85 tures we calculate the result of the other, on the assump- tion of Gay Lussac's law, and compare it with the value directly obtained, we have the following relations: - i. Solution of cane-sugar.1 At 320 a pressure of 544 mm. was observed. At 14.15° the calculated pressure is 512 mm., instead of 510 as found by experiment. 2. Solution of cane-sugar. At 36° the pressure observed was 567 mm. At 15.5° the calculated pressure is 529 mm., instead of 520.5 mm. as found experimentally. 3. Solution of sodium tartrate. At 37.3° the pressure observed was 983 mm. At 13.3° the calculated pressure is 907 mm., instead of 908 found by experiment. There is evidently a close approximation, in the above results, between the observed and calculated values. The law of Gay Lussac, as applied to the osmotic press- ure of solutions, received further experimental support from the work of Bonders and Hamburger.2 They worked with animal cells (blood corpuscles) in a manner similar to De Vries. They found that solutions of potas- sium nitrate, sodium chloride, and sugar, which have the same osmotic pressure as the contents of the cells in ques- tion, at o°, and therefore the same as one another, show exactly the same relation at 340, i.e. all have the same osmotic pressure at this higher temperature. This shows that the temperature coefficient of osmotic 1 Harper's Science Series, IV, p. 19. 2 Onderzoekingen gedaan in het physiologisth, Laboratorium der Utrechtsche Hoogeschool [3], 9, 26. 86 ELECTROLYTIC DISSOCIATION pressure for solutions of these three substances is the same; and, taken with Pfeffer's results, is strong evi- dence in favor of the law of Gay Lussac as applied to solutions. Experimental Evidence in Favor of both the Laws of Boyle and Gay Lussac for Solutions. - It was observed by Soret,1 that if a homogeneous solution is placed in a tube, and the top of the tube kept warmer than the bottom, the solution will not remain homogeneous, but will become more concentrated in the colder portion. This is exactly analogous to what would occur with a gas; the colder portion would become more concentrated. The experi- ments were made by Soret in vertical tubes, the upper portions of which were warmed to a constant temperature, and the lower portions cooled to a constant temperature. It was soon found, as would be expected, that the time required to establish equilibrium was much greater for solutions than for gases. How does the " Principle of Soret " throw any light on the applicability of the laws of Boyle and Gay Lussac to solutions ? A gas will always distribute itself in a space so that the gas pressure is the same at every point in the space. If one portion of the space is colder than another, the gas pressure of any given molecule in this portion will be less than in the warmer portion; therefore, more gas particles must collect in the colder portion, to give the same pressure as in the warmer portion of the tube. Similarly, with solutions, the dissolved substance will distribute itself throughout the solvent, so that the osmotic pressure is the same at every point in the solution. If 1 Archives des Sciences Phys, et Nat. [3], 2, 48; Ann. Chim. Phys. [5], 22, 293. THEORY OF ELECTROLYTIC DISSOCIATION 87 one part of the solution is colder than another, a dissolved particle will exert less osmotic pressure where the solution is colder. It will, therefore, require more particles in the colder region, to exert a given pressure, than in the warmer region. We can calculate the change in concentration of a gas with change in temperature, from the laws of Boyle and Gay Lussac. Similarly, if the laws of Boyle and Gay Lussac apply to the osmotic pressure of solutions, we can calculate the difference in concentrations between the colder and warmer parts of a solution, for a given differ- ence in the temperature of these two regions. Then, the difference in the concentrations of the two parts can be determined experimentally, and the calculated results com- pared with the results of experiment. This has been done for solutions of copper sulphate, and the following results are given by van't Hoff : - i. Solution of copper sulphate. The part cooled to 20° contained 17.332 per cent. The concentration calculated for 8o°, is 14.3 per cent. That found experimentally was 14.03 per cent. 2. Solution of copper sulphate. The part cooled to 200 contained 29.867 per cent. 24.8 per cent was calculated for 8o°, while 23.871 per cent was found. It should be observed, that the results found by experi- ment are slightly lower than those calculated on the basis of the laws of Boyle and Gay Lussac, yet the difference is only slight. It must, however, be stated in this connection, that it has been shown that the time required to establish equilibrium in a solution is much greater than was formerly supposed, and in the earlier experiments not enough time 88 ELECTROLYTIC DISSOCIATION was allowed for the final equilibrium to be reached. Con- sequently, the difference in concentration between the colder and the warmer portions of the tube, as found by experiment, was less than the calculated, since the latter was based on perfect equilibrium having been reached. More recent experiments, in which the tubes have been allowed to stand for several months, give results which agree very closely with the calculated, and thus the " Prin- ciple of Soret " is a strong experimental support, to the applicability of the laws of Boyle and Gay Lussac to the osmotic pressure of dilute solutions. Avogadro's Law for Dilute Solutions. - It has been shown, thus far, that the osmotic pressure of solutions is proportional to the concentration, and, also, that the tem- perature coefficient of osmotic pressure is the same as that of gas pressure. In a word, gas pressure and osmotic pressure are analogous, both obeying the laws of Boyle and Gay Lussac. The more important question, however, still remains: What is the relation between the actual osmotic pressure exerted by a dissolved particle, and the gas pressure of a gaseous particle, under the same conditions of temperature and concentration ? Van't Hoff answered this question both experimentally and theoretically. He found in Pfeffer's determinations of the osmotic pressure of cane-sugar, an experimental solution of this problem. The osmotic pressure of a sugar solution of known concentration was compared with the gas pressure of hydrogen gas, containing the same number of particles in a given space. A i per cent solution of sugar was used. Hydrogen of the same concentration would con- THEORY OF ELECTROLYTIC DISSOCIATION 89 tain 3I2 x 10 grams Per litre, i.e. 0.0581 gram per litre. Since hydrogen at o° and atmospheric pressure weighs 0.08956 gram per litre, hydrogen under the above condi- tions would exert a pressure of atmosphere at o°, or 0.649 atmosphere; and at t° of 0.649(1 + 0.003671) atmosphere. Comparing this at different temperatures with Pfeffer's results, we have : - Temperature Osmotic Pressure Gas Pressure 0.649(1 -1- 0.00367 Z) 6.8 O.664 O.665 i3-7 O.691 O.681 14.2 O.671 O.682 15-5 O.684 0.686 22.0 O.721 0.701 32.0 O.716 o.725 36-0 O.746 o-735 These results suffice to bring out the relation, that the osmotic presslire of a solation of sugar at a given tem- perature is exactly equal to the gas pressure of a gas, which contains the same number of molecules in a given volume as there are sugar molecules in the same volume of the solution. This relation has been found to hold for such a large number of substances, that we are led to the all-important generalization : that the osmotic pressure of a dissolved particle is exactly equal to the gas pressure of a gaseous particle at the same temperature and concentration. The law of Avogadro, applied to gases, states that equal volumes of all gases, at the same temperature and pressure, contain the same number of ultimate particles. 90 ELECTROLYTIC DISSOCIATION The law of Avogadro, as applied to solutions, states that solutions which, at the same temperature, have the same osmotic pressure, contain in a given volume the same num- ber of dissolved particles. Van't Hoff has shown that the law of Avogadro, as applied to solutions, is confirmed also by the lowering of the vapor-tension, and of the freezing-point of the solvent, produced by the dissolved substance. He has also given a thermodynamic demonstration of the law.1 General Expression of the Laws of Boyle, Gay Lussac, and Avogadro, for Solutions and Gases. - Having shown that the three laws of gas pressure apply to the osmotic pressure of solutions, van't Hoff attempted to furnish a general expression for these three laws. "The well- known formula, which expresses for gases the two laws of Boyle and Gay Lussac : - PV=RT, is now, where the laws referred to are also applicable to liquids, valid also for solutions, if we are dealing with the osmotic pressure. This holds even with the same limita- tion, which is also to be considered with gases, that the dilution shall be sufficiently great to allow one to disre- gard the reciprocal action of, and the space taken by, the dissolved particles. " If we wish to include in the above expression also the third, the law of Avogadro, this can be done in an exceed- ingly simple manner, following the suggestion of Horst- mann,2 considering always kilogram molecules of the 1 See Harper's Science Series, IV, 22. 2 Ber. d. chem. Gesell., 14, 1243. THEORY OF ELECTROLYTIC DISSOCIATION 91 substance in question; thus, 2 k. hydrogen, 44 k. carbon dioxide, etc. Then R in the above equation has the same value for all gases, since, at the same temperature and pressure, the quantities mentioned occupy also the same volume. If this value is calculated, and the volume taken in Mr\ the pressure in K° per Mr2, and if, for example, hydrogen at o° and atmospheric pressure is chosen: - 2 273, = 845 05. The combined expression of the laws of Boyle, Gay Lussac, and Avogadro is then : - and, in this form, it refers not only to gases, but to all solu- tions, P being then always taken as osmotic pressure." 1 The conclusion from what has thus far been given of van't Hoff's paper is that the three laws of gas pressure apply directly to the osmotic pressure of solutions, and this is perfectly general for solutions such as we have been considering. But there are many exceptions, and these are of even more interest than the cases which conform to the laws of gas pressure. Exceptions to the General Applicability of the Gas Laws to Osmotic Pressure. - While the osmotic pressures of solutions of compounds like cane-sugar conform to the gas laws, the osmotic pressures of large classes of chemical substances do not conform to these laws. The excep- tions include all the acids, all the bases, and all the salts. If we will consider the number of compounds contained in 1 Harper's Science Series, IV, 24. 92 ELECTROLYTIC DISSOCIATION these three classes, it is a question whether the exceptions will not outnumber the cases which conform to rule. All of these compounds give an osmotic pressure, which is greater than would be expected from the gas laws. The expression PV=RT no longer applies to the osmotic pressure of these substances, and, therefore, a coefficient was introduced by van't Hoff; when the expres- sion became: - P V= iR T. This coefficient, which for acids, bases, and salts is always greater than unity, has come to be known as the " van't Hoff i." What was the real physical or chemical signifi- cance of these exceptions ? Why does a large class of compounds show an osmotic pressure which conforms to the gas laws, and yet a very large class give an osmotic pressure which is always too great ? Van't Hoff saw clearly the discrepancy which existed here, as will be seen from his own words: " If we are still considering ' ideal solutions,' a class of phenomena must be dealt with which, from the now clearly demonstrated analogy between solutions and gases, are to be classed with the earlier so-called deviations from Avogadro's law. As the pressure of the vapor of ammonium chloride, for example, was too great in terms of this law, so, also, in a large number of cases, the osmotic pressure is abnormally large, and in the first case, as was afterwards shown, there is a breaking down into hydrochloric acid and ammonia, so, also, with solutions, we would naturally conjecture that, in such cases, a similar decomposition had taken place. Yet it must be conceded that anomalies of this kind, existing THEORY OF ELECTROLYTIC DISSOCIATION 93 in solutions, are much more numerous, and appear with substances which it is difficult to assume break down in the usual way. Examples in aqueous solutions are most of the salts, the strong acids, and the strong bases. ... It may then have appeared daring to give Avogadro's law for solutions such a prominent place, and I should not have done so, had not Arrhenius pointed out to me, by letter, the probability that salts and analogous substances, when in solution, break down into ions." 1 The last sentence gives us the connecting link between the generalization reached by van't Hoff, and the discovery of the theory of electrolytic dissociation. The latter we owe to the Swedish physicist, Arrhenius, to whose work we will now turn. ON THE DISSOCIATION OF SUBSTANCES DISSOLVED IN WATER BY SVANTE ARRHENIUS A paper,2 under the above title, appeared in the same volume of the Zeitschrift fur physikalische CJiemie, as the paper by van't Hoff which we have just considered. Arrhenius was impressed by the generalizations reached by van't Hoff, and especially by the large number of exceptions. This will be seen best by quoting the words with which Arrhenius began his paper. " In a paper submitted to the Swedish Academy of Sciences, on the 14th of October, 1885, van't Hoff proved experimentally, as well as theoretically, the following un- usually significant generalization of Avogadro's law : - 1 Harper's Science Series, IV, 34. 2 Ztschr. phys. Chern., 1, 631 (1887). Translated into English by H. C. Jones. Harper's Science Series, IV, 47. 94 ELECTROLYTIC DISSOCIATION "The pressure which a gas exerts at a given temperature, if a definite number of molecules is contained in a definite volume, is equal to the osmotic pressure which is produced by most substances under the same conditions, if they are dissolved in any given liquid." 1 "Van't Hoff has proved this law in a manner which scarcely leaves any doubt as to its absolute correctness. But a difficulty which still remains to be overcome, is that the law in question holds only for 'most substances,' a very considerable number of the aqueous solutions investi- gated furnishing exceptions; and in the sense that they exert a much greater osmotic pressure than would be required from the law referred to." The above are the words with which Arrhenius stated the problem; we will now follow the line of thought which led him to its solution. "If a gas shows such a deviation from the law of Avo- gadro, it is explained by assuming that the gas is in a state of dissociation. The conduct of chlorine, bromine, and iodine, at higher temperatures, is a very well-known example. We regard these substances, under such con- ditions, as broken down into simple atoms. "The same expedient may, of course, be made use of to explain the exceptions to van't Hoff's law; but it has not been put forward up to the present, probably on account of the newness of the subject, the many exceptions known, and the vigorous objections which would be raised from the chemical side to such an explanation. The purpose of the following lines is to show that such an assumption, 1 Van't Hoff, Une propri6t6 generate de la matiere dilute, p. 43. Sv. Vet-ak-s Handlingar, 21, Nr. 17, 1886. THEORY OF ELECTROLYTIC DISSOCIATION 95 of the dissociation of certain substances dissolved in water, is strongly supported by the conclusions drawn from the electrical properties of the same substances, and that, also, the objections to it from the chemical side are diminished on more careful examination." 1 Arrhenius then offers his explanation of the exceptions to van't Hoff's generalization. As we shall see, he goes back to the theory put forward by Clausius to account for electrolysis, and which has already been considered, in con- nection with the development of electrochemistry (p. 48). "In order to explain the electrical phenomena, we must assume with Clausius,2 that some of the molecules of an electrolyte are dissociated into their ions, which move inde- pendent of one another. But since the ' osmotic pressure ' which a substance dissolved in a liquid exerts against the walls of the confining vessel must be regarded, in accord- ance with the modern kinetic view, as produced by the impacts of the smallest parts of this substance, as they move against the walls of the vessel, we must therefore assume, in accordance with this view, that a molecule dis- sociated in the manner given above, exercises as great a pressure against the walls of the Vessel as its ions would do in the free condition. If, then, we could calculate what fraction of the molecules of an electrolyte is dissociated into ions, we should be able to calculate the osmotic press- ure from van't Hoff's law." 3 We see from the above, that the simple qualitative sug- gestion, that some molecules are broken down into parts or 1 Harper's Science Series, IV, 48. 2 Pogg. Ann., 101, 347; Wied. Elektr., 2, 941. 3 Harper's Science Series, IV, 48. 96 ELECTROLYTIC DISSOCIATION ions, is not new with Arrhenius. This theory, as already stated, had been advanced some thirty years before by Clausius. The new feature, which was introduced by Arrhenius, was to point out a method of determining just what per cent of the molecules are broken down into ions. The merely qualitative suggestion of Clausius was thus converted into a definite theory, which could be tested experimentally. The method of calculating the amount of dissociation into ions, as worked out by Arrhenius, will now be given in his own words. "In a former communication, 'On the Electrical Con- ductivity of Electrolytes,' I have designated those mole- cules, whose ions are independent of one another in their movements, as active; the remaining molecules, whose ions are firmly combined with one another, as inactive. I have also maintained it as probable, that in extreme dilution, all the inactive molecules of an electrolyte are transformed into active.1 This assumption I will make the basis of the calculations now to be carried out. I have designated the relation between the number of active molecules, and the sum of the active and inactive molecules, as the activity coefficient.2 The activity coefficient of an electrolyte at infinite dilution is therefore taken as unity. For smaller dilution it is less than one, and from the principles estab- lished in my work already cited, it can be regarded as equal to the ratio of the actual molecular conductivity of the solution, to the maximum limiting value which the mo- lecular conductivity of the same solution approaches with 1 Bihang der Stockholmer Akademie, 8, Nr. 13 and 14, 2 Tl., pp. 5 and 13; 1 Tl., p. 6. 2 Loc. cit., 2 Tl., p. 5. THEORY OF ELECTROLYTIC DISSOCIATION 97 increasing dilution. This obtains for solutions which are not too concentrated {i.e. for solutions in which disturbing conditions, such as internal friction, etc., can be disre- garded). If this activity coefficient (a) is known, we can calculate, as follows, the values of the coefficient i, tabu- lated by van't Hoff: i is the relation between the osmotic pressure actually exerted by a substance, and the osmotic pressure which it would exert, if it consisted only of inac- tive (undissociated) molecules, i is evidently equal to the sum of the number of inactive molecules, plus the number of ions, divided by the sum of the inactive and active molecules. If, then, m represents the number of inactive, and n the number of active, molecules, and k the number of ions into which every active molecule dissociates {eg., k = 2 for KC1, i.e. K and Cl; k = 3 for BaCl2 and K2SO4, i.e. Ba, Cl, Cl, and K, K, SO4), then we have: - m+kn 1 m + n " But since the activity coefficient (a) can, evidently, be n written : - m + n i = 1 +(k - i)^."1 Arrhenius thus shows how it is possible to calculate the value of the van't Hoff coefficient i, knowing the activity coefficient («), which can be determined directly from the conductivity of the solution. He then shows how the value of i can be calculated also from the lowering of the freezing-point of water produced by the dissolved substance. 1 Harper's Science Series, IV, 48. 98 ELECTROLYTIC DISSOCIATION " On the other hand, i can be calculated as follows, from the results of Raoult's experiments on the freezing-point of solutions, making use of the principles stated by van't Hoff. The lowering (z) of the freezing-point of water (in degrees Celsius), produced by dissolving a gram-mole- cule of the given substance in one litre of water, is divided by 18.5:- . t 2 = 18.5 Arrhenius then compared the values of i, calculated from the conductivity of solution, with the values calcu- lated from the freezing-point lowerings, to see whether the two series would agree with one another. He made the comparison for a large number of bases, acids, and salts, and also for a number of organic compounds, where the value of i is unity. A few examples from each class of compounds will be given, since it is a matter of the very greatest importance to determine whether the two values of i agree. If they do, the theory just advanced is made quite probable. If they do not, it is almost a conclusive argument against the correctness of the theory. Bases Substance 18 s » = l+(A -1) a Barium hydroxide, Ba(OH)2 2.69 2.67 Strontium hydroxide, Sr(OH)2 2.61 2.72 Calcium hydroxide, Ca(OH)2 2-59 2-59 Sodium hydroxide, NaOH 1.96 1.88 Potassium hydroxide, KOH 1.91 T-93 Ammonia, nh3 1-03 1.01 Methylamine, ch3nh2 1.00 1.03 Trimethylamine, (CH3)3N 1.09 1-03 Ethylamine, C2HsNH2 1.00 1.04 Aniline, c6h5nh2 0.83 1.00 1 Harper's Science Series, IV, 49. THEORY OF ELECTROLYTIC DISSOCIATION 99 Acids Hydrochloric acid. HC1 1.98 1.90 Hydrobromic acid, HBr 2-03 i-94 Nitric acid, hno3 i-94 1.92 Chloric acid, HC1O3 1.97 1.91 Sulphuric acid, h,so4 2.06 2.19 Sulphurous acid, h2so3 1.03 1.28 Formic acid, HCOOH 1.04 1 03 Acetic acid, CHSCOOH 1-03 1.01 Tartaric acid, c4h6o6 1-05 1.11 Malic acid, C4H6O4 1.08 1.07 Lactic acid, C3H6O3 1.01 1 03 Salts Substance Potassium chloride, KC1 z=-*- 18.5 1.82 i = t + ( k - 1) a 1.86 Sodium chloride, NaCl 1.90 1.82 Ammonium chloride, NH4C1 1.88 1.84 Potassium cyanide, KCN r-74 1.88 Potassium nitrate, KNO3 1.67 1.81 Potassium acetate, CH3COOK 1.86 1.83 Silver nitrate, AgNO3 1.60 1.86 Potassium sulphate, K2SO4 2.11 2-33 Ammonium sulphate, (NH4)2SO4 2.00 2.17 Barium chloride, BaCl2 2.63 2-54 Strontium chloride, SrCl2 2.76 2.50 Calcium chloride, CaCl2 2.70 2.50 Barium nitrate, Ba(NO3)2 2.19 2.13 Strontium nitrate, Sr(NO3)2 2.23 2-23 Calcium nitrate, Ca(NO3)2 2.02 2-33 Mercuric chloride, HgCl2 1.11 1-05 Cadmium nitrate, Cd(NO3)2 2-32 2.46 100 ELECTROLYTIC DISSOCIATION Organic Compounds Methyl alcohol, CH4O 0.94 1.00 Ethyl alcohol, c2h6o 0.94 1.00 Butyl alcohol, c4h10o °-93 1.00 Mannite, c6h14o6 o-97 1.00 Invert sugar, CeH12OG 1.04 1.00 Cane-sugar, C12H22OU 1.00 1.00 Phenol, c6h6o 0.84 1.00 Acetone, c3h6o 0.92 1.00 That there is a general agreement between the two val- ues of i, in the above tables, is evident. That there are some discrepancies, is just what would be expected, from the experimental errors contained in both the freezing- point and the conductivity methods. It must be further borne in mind, that the freezing-point method was very imperfectly developed when the above determinations were made. Another cause of these discrepancies was pointed out by Arrhenius, as follows : - " There is one condition which interferes, possibly very seriously, with directly comparing the figures in the last two columns; namely, that the values really hold for differ- ent temperatures. All the figures in next to the last col- umn hold, indeed, for temperatures only a very little below o° C., since they were obtained from experiments on in- considerable lowerings of the freezing-point of water. On the other hand, the figures of the last column for acids and bases (Ostwald's experiments) hold at 250, the others at 18°. The figures of the last column for non-conductors hold, of course, also at o° C, since these substances, at this THEORY OF ELECTROLYTIC DISSOCIATION 101 temperature, do not consist, to any appreciable extent, of dissociated (active) molecules." 1 Arrhenius then refers to the general agreement between the two sets of values in the following terms : - " An especially marked parallelism appears, beyond doubt, on comparing the figures in the last two columns. This shows a posteriori, that in all probability the assump- tions on which I have based the calculation of these figures are, in the main, correct. These assumptions were : - "l. That van't Hoff's law holds not only for most, but for all, substances, even for those which have hitherto been regarded as exceptions (electrolytes in aqueous solution). "2. That every electrolyte (in aqueous solution) consists partly of active, (in chemical and electrical relation) and partly of inactive, molecules, the latter passing into active molecules on increasing the dilution, so that in infinitely dilute solutions only active molecules exist. Arrhenius then calls attention to the difference between the kind of dissociation indicated here, and that shown when a vapor- like ammonium chloride dissociates by heat. " Although the dissolved substance exercises an osmotic pressure against the wall of the vessel, just as if it were partly dissociated into its ions, yet the dissociation with which we are here dealing is not exactly the same as that which exists when, e.g., an ammonium salt is decomposed at a higher temperature. The products of dissociation in the first case (the ions) are charged with very large quan- tities of electricity, of opposite kind, whence certain condi- tions appear (the incompressibility of electricity), from which it follows that the ions cannot be separated from 1 Harper's Science Series, IV, 54. 102 ELECTROLYTIC DISSOCIATION one another to any great extent without a large expendi- ture of energy. On the contrary, in ordinary dissociation, where no such conditions exist, the products of dissociation can, in general, be separated from one another." 1 Although Arrhenius pointed out, so clearly, the charac- teristic feature of the dissociation which he believed elec- trolytes to undergo in the presence of water, namely, that the products of dissociation were charged, the one always positively, the other always negatively, yet this has often been overlooked. Summary. - In concluding this chapter, we will briefly recall the steps which led to the theory of electrolytic dis- sociation. The stages by which van't Hoff passed from the study of the position of atoms in space to Pfeffer's work on osmotic pressure have been followed in detail. Van't Hoff showed, from Pfeffer's results, and also theoreti- cally, that the laws of Boyle, Gay Lussac, and Avogadro, for gas pressure, apply to the osmotic pressure of solutions. But these apply only to solutions of non-electrolytes, i.e. substances which, when in the presence of water, do not conduct the current. All electrolytes, i.e. the acids, bases, and salts, are exceptions, showing greater osmotic pressure than would accord with the laws of gas pressure. To what was this discrepancy due ? Since osmotic pressure is proportional to the number of parts present, too great osmotic pressure means more parts present than would be expected. In order that we might have more parts present than the molecules, it is necessary that the molecules should undergo decomposition. How is it possible to think of 1 Harper's Science Series, IV, 54. THEORY OF ELECTROLYTIC DISSOCIATION 103 stable molecules, such as hydrochloric acid, potassium hydroxide, potassium chloride, suffering decomposition ? Arrhenius furnished the answer. He had resort to the old theory proposed by Clausius, to account for electrol- ysis, that in the presence of water the molecules are broken down into ions. Arrhenius pointed out two ways of calculating the amount of this dissociation, the one based on conductivity, the other on freezing-point lower- ing, and showed that the results from the two methods agreed. All of the compounds which give abnormally great osmotic pressure, and are therefore dissociated into ions, conduct the current when in solution in water, and are therefore electrolytes. This kind of dissociation has come to be known as electrolytic, and the theory advanced by Arrhenius as the Theory of Electrolytic Dissociation. It is one thing to propose a theory, and another to pro- pose a theory which is true. In the next chapter we will consider some of the lines of evidence bearing upon the theory of electrolytic dissociation. CHAPTER III EVIDENCE BEARING UPON THE THEORY OF ELECTROLYTIC DISSOCIATION THE PHYSICAL PROPERTIES OF COMPLETELY DISSOCIATED ( SOLUTIONS SHOULD BE ADDITIVE A theory in science must, first of all, be capable of experimental test. If it cannot be shown to be either true or false, it is of little value as a scientific generalization. Arrhenius pointed out in his first paper, that evidence bearing upon his theory could be obtained from a study of the physical properties of solutions, whose dissociation, in terms of the theory, was supposed to be complete. " If a salt (in aqueous solution) is completely broken down into its ions, most of the properties of this salt can, of course, be expressed as the sum of the properties of the ions; since the ions are independent of one another in most cases, and since every ion has therefore a characteristic property, independent of the nature of the opposite ion with which it occurs." He also observed that we rarely have to do with com- pletely dissociated solutions. Those of the salts, strong acids, and strong bases, are dissociated only from 80 to 90 per cent, at ordinary dilutions, and the additive nature of the properties of even such solutions would be only ap- proximate. Another class of substances, such as mercuric 104 EVIDENCE FOR THE THEORY 105 chloride, cadmium iodide, and all of the weak acids and bases, organic and inorganic, are comparatively lit- tle dissociated by water at moderate dilutions, and the physical properties of solutions of these substances are not those of the ions alone, but of both ions and molecules. The point, in a word, is this: The physical properties of completely dissociated solutions must be a function of the physical properties of the ions, as there are no mole- cules present. Since each ion has its own specific prop- erties, independent of the nature of the other ion with which it is associated, the physical properties of com- pletely dissociated solutions must be the sum of the physical properties of the ions in those solutions. If the solutions are not completely dissociated, their properties are those both of the ions and of the molecules. We must now study the physical properties of com- pletely dissociated solutions, and see what relations exist between these and the physical properties of the ions which they contain. We will take solutions of salts. Specific Gravity of Salt Solutions. - If a salt is added to water, the volume of the solution is different from that of the pure solvent, and also from the sum of the volumes of the liquid and the solid. If the resulting solution is very dilute, the salt is completely dissociated into its ions. Nernst1 has shown, from the results of J. Traube,2 that the change in volume under such conditions is an additive property of the ions. Given a solution containing a gram-molecular weight of a salt whose molecular weight is M, in m grams of water. Let the specific gravity of 1 Theoretische Chemie, p. 317. 2 ztschr. anorg. Chem., 3, 1. 106 ELECTROLYTIC DISSOCIATION the solution be 5, the specific gravity of water j. The change in volume on dissolving the salt, will be: - A _M + m _m S s The following results are given : - KCI = 26.7 KBr = 35.1 KI =45-4 NaCl = 17.7 NaBr = 26.7 Nai = 36.1 KBr - KCI = 8.4 NaBr - NaCl = 9.0 KI - KBr = 10.3 Nai - NaBr = 9.4 KI - KC1 = 18.7 Nai - NaCl = 18.4 KC1 - NaCl = 9.0 KBr - NaBr = 8.4 KI - Nai = 9.3 These results show the additive nature of the specific gravity of salt solutions. The difference between the chlorine and the bromine ions is about 8.7; between chlorine and iodine 18.5; between bromine and iodine 9.8; while between potassium and sodium it is about 9.0. The additive nature of the specific gravity of salt solu- tions had, indeed, been pointed out much earlier by Valson.1 He had shown exactly what is brought out above : Given salt solutions of comparable concentration, i.e. containing say a gram-molecule of the salt per litre, the difference between the specific gravities of solutions containing two metals combined with the same acid is constant, whatever the nature of the acid. Similarly, the difference between the specific gravities of two salts of the same acid with any metal is constant, regardless of 1 Compt. rend., 73, 441 (1874). EVIDENCE FOR THE THEORY 107 the nature of the metal. The specific gravity of a salt solution is, then, obtained by adding to a constant number two values, - the one for the acid, the other for the metal. These values Valson termed "moduli"; and he worked out their values for a large number of elements. Valson1 concluded from his work, that the molecules of salts must be completely broken down in solution. But the evidence in favor of such a view was not strong enough at that time to bring it into favor. Change of Volume in Neutralization.-The change of volume produced by neutralizing acids with bases has been extensively studied by Ostwald.2 The solutions contained a gram-equivalent of the acid or base, in a kilogram, and were, therefore, not completely disso- ciated ; so that, if the change in volume was addi- tive, it would be shown only approximately by such solutions. Ostwald3 worked with nineteen acids, including the strongest mineral acids, and some of the more strongly dissociated organic acids. He neutralized these with the three bases, potassium, sodium, and ammonium. A few of his results are given, the change in volume being ex- pressed in cubic centimetres. The differences in the hori- zontal lines are the differences between potassium, sodium, and ammonium, in combination with the same acid. The differences in the vertical columns are the differences between the different acids in combination with the same bases, obtained by subtracting the value for the acid from the value for nitric acid. 1 Compt. rend., 73, 441; 74, 103; 75, 1033. 2 Journ. prakt. Chem. [2], i3, 353. 3 Lehrb. d. allg. Chem. I, p. 788. 108 ELECTROLYTIC DISSOCIATION Potassium Hydroxide • Sodium Hydroxide Ammonium Hydroxide Nitric acid, 20.05 (0.28) (0.53) 19.77 (26.21) (°-53) - 6.44 (26.49) (O-I3) Hydrochloric acid, 19.52 (0.28) <7-69) I9-24 (25-8l) (7-6l) - 6.57 (26.09) (7-I5) Formic acid, T2.36 (0.20) (IO-53) 12.16 (25.75) (W.49) - 13-59 (25-95) (9-82) Acetic acid, 9-52 (°-24) (8-15) 9.28 (25.54) (8.29) - 16.26 (25.78) (7-91) Sulphuric acid, 11.90 (0.42) (11.82) II.48 (25.83) (11-84) - 14-35 (26.25) (11.19) Succinic acid, 8.23 (0.30) 7-93 (25-56) - 17-63 (25-86) If we take the perpendicular rows in parentheses, we find very nearly a constant difference for the strong acids and bases. Similarly, if we take the horizontal rows in paren- theses, we find very nearly a constant difference. This means that the difference of change in volume, produced by neutralizing two different bases by a given acid, is a constant, independent of the nature of the acid; and, similarly, the difference of the change in volume on neu- tralizing two different acids by a given base, is independent of the nature of the base. The change in volume, when acids and bases neutralize each other, like the specific gravity of salt solutions, is, then, an additive property, depending both upon the nature of the acid and of the base; and we could work out here, as Valson has done in the case of specific gravities, the numerical values of the constants for each constituent. Specific Refractive Power of Salt Solutions. - Gladstone calculated the refraction equivalents R, of a number of ele- ments, from the formula : - EVIDENCE FOR THE THEORY 109 R=P- 1 d in which P is the weight of the substance, n the index of refraction, and d the density. He also showed that the refraction coefficients of salts were the sum of the refrac- tion equivalents of the elements. That this is true is seen from the following table of re- sults, taken by Arrhenius1 from the Lehrbuch of Ostwald.2 Only a few examples are given here. Hydrogen Potassium Sodium Chloride, 14-44 (4-oo) 18.44 (3-3) 15.II (6.2) (6-9) (6-6) Bromide, 20.63 (4-7) 25-34 (3-6) 21.70 (3-4) (3-5) (3-o) Nitrate, i7-24 (4-6) 21.80 (3.1) 18.66 (4-o) (5-8) (5-4) Acetate, 21.20 (6.4) 27-65 (3-6) 24-05 (24-0) (30.0) (26.4) Tartrate, 45.18 (12.4) 57.60 (7.2) 5°-39 The differences, both horizontally and vertically, are as constant as could be expected, except for the two organic acids which, at the dilutions employed, are only slightly dissociated. This means that the different effect of potas- sium and hydrogen, on the refraction equivalent, is con- stant, whatever the acid with which they are combined, and the same holds for potassium and sodium. Also, that chlo- rine, bromine, etc., have a constant effect on the refractive power, whether they are combined with hydrogen, potas- sium, or sodium. In a word, the refractive power of salt 1 Ztschr. phys. Chem., i, 645. Harper's Science Series, IV, 62. 2 Lehrb. d. allg. Chem., II, p. 446. 110 ELECTROLYTIC DISSOCIATION solutions is distinctively an additive property of the con- stituents. Rotatory Power of Salt Solutions. - The power possessed by solutions of some salts to rotate the plane of polariza- tion of light, must be a property of the optically active con- stituent of the salt, or, if both constituents are optically active, it must be the sum of the activities of the two. Oudemans1 has shown that optically active bases, such as the monacid alkaloids, produce the same rotation, regard- less of the nature of the optically inactive acid with which they are combined. And optically active acids rotate the plane of polarization, independent of the nature of the inac- tive base combined with them. This is very well shown by the work of Hartmann,2 on the salts of camphoric acid. Li2 Mg (NH4)2 Ca Na2 K2 Ba 37-5 39-5 38-4 39-1 36.0 36.1 36.5 The rotatory power of salts of this acid is practically constant, independent of the nature of the base combined with it. The Color of Salt Solutions. -The absorption which light undergoes, in passing through a solution of a completely dissociated substance must, in terms of our theory, be the sum of the absorption of the cation, plus that of the anion. If one of the ions is colorless, the absorption must be entirely that of the other ion. That this is qualitatively true is a matter of common experience. We utilize the color of solutions to determine the nature of their constituents. Thus, cupric salts in di- lute aqueous solutions are blue, or bluish green, regardless 1 Beibl., g, 635. 2 Ber. d. chem. Gesell. (1888), 221. EVIDENCE FOR THE THEORY 111 of the chemical nature of the anion with which the copper is combined, provided that it is colorless. Likewise, the chromates are yellow, and the salts of nickel green. A method for determining, quantitatively, whether the absorption of light is additive, is to prepare a number of salts of an acid whose anion is colored, the cation being always colorless. Then determine whether all of the salts have the same absorption spectrum. The metallic salts of permanganic acid are particularly well adapted to this purpose, and they have been thoroughly studied by Ostwald1 in this connection. These salts show five absorption bands in the yellow and green, and four of these have been measured by Ostwald for thirteen salts of permanganic acid. The results are so striking, that they are given in the following table : - i 11 in IV Hydrogen, 2601 ± 0.5 2698 ± 0.8 2804 ±0.7 2913 ± i-7 Potassium, 2600 ± 1.3 2697 ±0.1 2803 ± 0.9 2913 ± 1.1 Sodium, 2602 ± 1.2 2698 ± 0.8 2803 ± 0.7 2913 ± 0.8 Ammonium, 2601 ± 1.3 2698 ±1.4 2802 ± O.I 2913 ± 0.1 Lithium, 2602 ± 0.2 2700 ± 0.2 2804 ± 0.8 2914 ± i-7 Barium, 2600 ± 0.9 2699 ± 0.8 2804 ± 0.6 2914 ± i-3 Magnesium, 2602 ± 0.8 2700 ± 0.6 2802 ±0.7 2912 ± 1.8 Aluminium, 2603 ± 0.4 2699 ± 0.9 2804 ± 0.9 2914 ± 0.7 Zinc, 2602 ± 0.5 2699 ± 0.7 2802 ± 1.2 2912 ± 1.1 Cobalt, 2601 ± 0.2 2698 ±0.1 2803 ± 0.9 2912 ± i-7 Nickel, 2603 ± 0.5 2700 ±0.7 2804 ±0.7 2913 ± 1.8 Cadmium, 2600 ± O.I 2700 ± 0.2 2803 ± 0.8 2913 ± 1.4 Copper, 2602 ± 1.2 2699 ± O.I 2803 ± 0.9 2913 ± 0.8 Permanganates. Absorption Bands. 1 Ztschr. phys. Chem., 9, 584. 112 ELECTROLYTIC DISSOCIATION From these results, Ostwald concluded that the absorp- tion spectra of the thirteen permanganates are just the same. A large number of other compounds were investigated,1 including ten salts of fluorescein, ten of eosin yellow, ten of eosin blue, ten of iodoeosin, ten of dinitrofluorescei'n, rosolic acid, and a number of other substances. Also a large number of cases were studied, where a colored cation was combined with a number of colorless anions. Thus, the salts of pararosaniline with twenty colorless acids, and an equal number of the salts of aniline violet, were investigated. Ostwald studied, in all, about three hundred cases, to determine whether the color of a solution with one colored ion is effected at all by the presence of the colorless ion. He concluded that salts with one and the same colored ion, in dilute solution, always show exactly the same absorp- tion spectra. The elaborate investigation just considered shows con- clusively, that the color of salt solutions is exactly the color of the colored ion, and from this it follows, that if both ions were colored, the color of the solution would be the sum of the colors of the two ions. The color of salt solutions is, therefore, an additive property. The use of indicators in quantitative analysis is based upon this fact. That a substance may be used as an indicator for acids and bases, it is necessary that one of the ions should have a different color from the molecule. Take the case of phenolphthalein. 'Its alcoholic solution is nearly colorless, and since it does not conduct the 1 Loc. cit. EVIDENCE FOR THE THEORY 113 current, it is undissociated. The molecules of phenol- phthalein are, therefore, colorless. If we add an alkali, say sodium hydroxide, to phenolphthalein, the sodium salt is formed; but this dissociates at once into the cation sodium, and the complex organic anion, which is deeply colored. The characteristic color of phenolphthalein, acting as an indicator for an alkali, is, then, always the color of the complex anion. If to the colored solution a little acid is added, the original phenolphthalein is formed, and is colorless. Take, on the other hand, the basic indicator, cyanine; the molecules of the free base are blue. It is a weak base, and, therefore, but little dissociated. Add acid; the salt is formed, which at once dissociates. The complex organic cation is colorless, and, hence, on adding acid, the color due to the molecules of the free base disappears. This is exactly the opposite of the case first considered. Finally, take methyl orange, where the molecules are red. Add a base, the salt is formed, and this breaks down at once into ions. The color of the complex organic anion is, in this case, yellow. The addition of acid, therefore, brings out the characteristic red color of this indicator. A number of other cases might be taken up, where the molecule is either colorless, or has a different color from one of its ions, but the cases considered are typical, and suffice to make the point clear. A Demonstration of the Dissociating Action of Water. - Jones and Allen1 have worked out a color demonstration of the dissociating action of water, which is based upon the principle of indicators just considered. If, to an 1 Amer. Chern. Journ., 18, 377. 114 ELECTROLYTIC DISSOCIATION alcoholic solution of phenolphthalein, a few drops of aqueous ammonia are added, there is no sign of the red color of the indicator. If water is now added to the alcoholic solution, the red color appears. When potassium or sodium hydroxide is substituted for ammonia, the red color appears at once, without the addition of water. There is, thus, a marked difference between potassium and sodium hydroxide and ammonium hydroxide. It would be difficult to interpret these facts without the aid of the theory of electrolytic dissociation. In the light of this theory they are perfectly intelligible. When a few drops of aqueous ammonia are added to several cubic centimetres of alcohol, little or no dissociation of the ammonium hydroxide is effected. The addition of water dissociates the base, the degree of dissociation de- pending upon the amount of water present with respect to + - alcohol. The presence of the ions NH4 and OH would cause the phenolphthalein to dissociate. The complex anion gives its characteristic color to the solution in which it is present. The hydrogen and hydroxyl ions would then combine and form water. It is possible that the actual course of the reaction is somewhat different from that just described. It may be that the ammonium group first combines with the phenol- phthalein in the alcoholic solution. The addition of water would then dissociate this compound, giving the colored anion referred to above. The dissociation theory furnishes this explanation. It remains to determine whether the explanation is true. If it is, then a solution, formed by adding a little aqueous ammonia to a considerable volume of alcohol, should show EVIDENCE FOR THE THEORY 115 little or no dissociation, and the amount of the dissociation should increase with the addition of water. Solutions of potassium or sodium hydroxide, in mixtures of alcohol and water, should be more dissociated than corresponding solutions of ammonium hydroxide. Indeed, a solution of sodium or potassium hydroxide, in alcohol alone, should manifest some dissociation, since, as stated above, it gives the color reaction with phenolphthalein. All of these points were tested, experimentally, by the conductivity method, with the result that the theory of electrolytic dissociation was entirely confirmed. This experiment furnishes a satisfactory lecture demon- stration of the dissociating action of water. A few drops of an alcoholic solution of phenolphthalein are placed in a glass cylinder, and diluted to, say, 50 cc. by the addition of alcohol. A few drops of an aqueous solution of ammonia are then added. A red color may appear where the aqueous ammonia first comes in contact with the alcoholic solution of phenolphthalein, but this will disappear, in- stantly, on shaking the cylinder, leaving the solution with a yellowish tint, possibly due to the formation of the ammonium salt of phenolphthalein. Water is then gradu- ally added to the cylinder, when the red color will appear, at first faint, then stronger, as the amount of water increases. When the red color has become intense, add a considerable volume of alcohol, and the entire color will disappear, leaving the solution slightly yellow again. The experiment serves, then, not only to illustrate the dissociating action of water, but the driving back of the ions into molecules by alcohol. 116 ELECTROLYTIC DISSOCIATION Conductivity is Additive. The Law of Kohlrausch. - It has been shown by Kohlrausch, that the conductivity of solutions of electrolytes is an additive property of the ions which take part in carrying the current. Indeed, the law of Kohlrausch, of the independent migration velocity of the ions, is but another expression of this fact. It is well known that the law, in the form stated by Kohlrausch, holds only for great dilutions, in which dissociation is com- plete. Ostwald1 has pointed out that the law holds for any dilution, provided that we take into account the amount of the dissociation at that dilution. This is obviously neces- sary, since it is only the dissociated molecules which take part in the conductivity. If we represent the percentage of dissociation, or the activity coefficient, by a, the law of Kohlrausch becomes: - fi = a(u +v\ 11 depending upon the cation, v upon the anion. The law in this form is applicable to all solutions of electrolytes, and illustrates, also, the additive property of conduc- tivity. A number of other properties could be adduced in evidence of the general principle, that the properties of completely dissociated solutions are additive, being the sum of the properties of the ions; but those already con- sidered are quite sufficient. The theory of electrolytic dissociation is here entirely substantiated by the facts. And these facts would be very difficult to explain without some such conception as that with which we are now dealing. 1 Lehrb. d. allg. Chem. II, p. 673. EVIDENCE FOR THE THEORY 117 PROPERTIES OF COMPLETELY DISSOCIATED, AND OF UNDIS- SOCIATED MIXTURES Mixture of Two Completely Dissociated Compounds.- The theory of electrolytic dissociation leads to some inter- esting conclusions, in the case of mixtures of completely dissociated substances, and these conclusions can be tested experimentally. Let us take the case of two salts which are completely dissociated at moderate dilutions, say, sodium chloride and potassium bromide. We would have in the solution only the ions into which these compounds had dissociated: - NaCl = Na + Cl; KBr = K + Br. We would have sodium and potassium cations, and chlorine and bromine anions. All the properties of such a mixture would be a function of the properties of these ions. Suppose we were now to prepare a mixture of potassium chloride and sodium bromide, which was completely dis- sociated. We would have in the solution: - KC1 = K + Cl; NaBr = Na + Br, potassium and sodium cations, and chlorine and bromine anions. But these are exactly the same ions which we had in our first mixture. We are led to the conclusion, that if we use gram- 118 ELECTROLYTIC DISSOCIATION molecular weights of both substances in each case, we will have exactly the same number of the same kinds of ions in the two solutions. And since the properties of a completely dissociated solution depend only upon the properties of the ions present, the properties of these two mixtures must be the same. If, then, we mix a gram- molecular weight of sodium chloride with a gram-molecu- lar weight of potassium bromide, and dilute the solution of the two until both are completely dissociated, this mix- ture must have exactly the same properties as that pre- pared by mixing a gram-molecular weight of potassium chloride with a gram-molecular weight of sodium bro- mide, and diluting the solution to the same point as the first. This is the conclusion to which we are led by our theory. What are the facts ? The facts confirm this conclusion absolutely. All of the properties of the two mixtures have been found to be exactly the same. The two solutions resemble one another as closely as the two halves of the same solution. Mixture of Two Completely Undissociated Compounds. - The conclusion to which we are led in the case of com- pletely dissociated compounds does not obtain at all for undissociated substances. Indeed, in the latter case, we are led by the theory to exactly the opposite conclusion. Take two undissociated substances - say methyl chloride and ethyl bromine - and dissolve the mixture; we will have only molecules of the two substances present. The properties of this mixture will be a function of the properties of these two kinds of molecules. Then, mix methyl bromide and ethyl chloride, we will have only these two kinds of molecules present, and EVIDENCE FOR THE THEORY 119 the properties of the mixture will be a function of the properties of the molecules which are in the mixture. But in the first mixture we have molecules of methyl chloride and ethyl bromide, in the second, of methyl bro- mide and ethyl chloride. And since we have different kinds of molecules in the two mixtures, the properties of the two must be different. If, then, we mix gram-molecular weights of methyl chloride and ethyl bromide, the mixture must have differ- ent properties from a corresponding mixture of gram- molecular weights of methyl bromide and ethyl chloride. This is the conclusion to which we are led by the theory of electrolytic dissociation, and here again the facts are in perfect accord with the theory. It has been found, experimentally, that a mixture of methyl chloride and ethyl bromide has properties quite different from a corre- sponding mixture of methyl bromide and ethyl chloride. Fact and theory thus agree, both when the constituents of the mixture are completely dissociated, and when they are not at all dissociated. HEAT OF NEUTRALIZATION IN DILUTE SOLUTIONS If the theory of electrolytic dissociation is true, a dilute aqueous solution of a strongly dissociated compound con- tains only ions, as has been stated. A solution of a base contains the hydroxyl anion, and a cation whose nature depends upon the particular base used. A solution of an acid contains the hydrogen cation and an anion whose nature depends upon the acid chosen. Similarly, a solu- tion of a salt is but a solution of anions and cations. In terms of the theory of electrolytic dissociation, the pro- 120 ELECTROLYTIC DISSOCIATION cess of neutralizing an acid by a base consists in the union of the hydroxyl anion of the base with the hydro- gen cation of the acid, forming a molecule of water. The cation of the base and the anion of the acid remain in exactly the same condition after neutralization as before. Let us take an example. A solution of hydrochloric acid is a solution of hydro- gen cations and chlorine anions: - HC1 = H + Cl. A solution of potassium hydroxide is a solution of potassium cations and hydroxyl anions: - KOH = K + OH. When the two solutions are brought together we have:- K + OH + H + Cl = K + Cl + H2O. The potassium and chlorine are in exactly the same condition after neutralization as before, i.e. both are ions; while the hydrogen and hydroxyl are united, forming a molecule of water. Neutralization of acids and bases is, then, in terms of the theory of electrolytic dissociation, nothing more than the union of the cation hydrogen and the anion hydroxyl to form a molecule of water. How can this be tested experimentally ? If neutralization consists only in the formation of a mole- cule of water, then the neutralization of any acid by any base is the same process as the neutralization of any other EVIDENCE FOR THE THEORY 121 acid by any other base. Therefore, the heat liberated by neutralizing an equivalent of any acid by an equivalent of any base must always be the same, since it is the heat of formation of the same amount of water from the ions H and OH. This can be tested directly by experiment. It is only necessary to measure the heat liberated when acids and bases are neutralized, and see whether this is the same for the different compounds. The following tables of heats of neutralization will test this point: - Strong Acids and Bases HC1 + NaOH = 13700 cal. HBr 4- NaOH = 13700 cal. HNO3 + NaOH = 13700 cal. HI + NaOH = 13800 cal. HC1 + LiOH =13700 cal. HC1 + KOH =13700 cal. HC1 + Ba(OH)2 = 13800 cal. HC1+ iCa(OH)2 = 13900 cal. Weak Acid and Strong Base CH3COOH + NaOH = 13400 cal. CHC12COOH + NaOH = 14830 cal. H3PO4 + NaOH = 14830 cal. HF + NaOH = 16270 cal. The agreement between the heats of neutralization of the strong acids with the strong bases is striking, when we consider the necessary errors involved in thermochemical measurements. The heats of neutralization of weak acids with a strong base differ very greatly from the constant obtained when both compounds are strongly dissociated. 122 ELECTROLYTIC DISSOCIATION In the application of the theory to the phenomenon of neutralization, it was assumed above, that both the acid and the base were completely dissociated. If, on the other hand, either acid or base is incompletely dissociated, then the heat set free when the two are brought together is not simply the heat liberated by the union of hydrogen and hydroxyl ions to form water, but this quantity, plus the heat of dissociation of that part of the acid or base which is undissociated. This explains the difference between the amounts of heat liberated, when both the acids and bases are strong, and when either the acid or base is weak. The theory of electrolytic dissociation is, then, strictly in accord with the facts, as far as the heat of neutralization is concerned. This applies not simply to the strong acids and bases, but to the apparently exceptional cases of the weakly dissociated compounds. It will be observed, that in the above interpretation of the process of neutralization, it is assumed that all of the hydrogen and hydroxyl ions combine to form water. It has been shown by six separate lines of work, that when- ever hydrogen and hydroxyl ions come together they combine and form water. This is the same as to say that water is undissociated. The apparent assumption is, therefore, well supported by the experimental facts. Hess's Law of the Thermoneutrality of Salt Solutions. - A dilute aqueous solution of a salt is, in terms of our theory, a solution of ions. Thus, a dilute aqueous solution of potassium chloride contains only potassium and chlorine ions. Similarly, a dilute solution of sodium chloride is but a solution of sodium and chlorine ions. When the solutions EVIDENCE FOR THE THEORY 123 of the two salts are mixed, the mixture contains only po- tassium, sodium, and chlorine ions. + - KC1 in dilute aqueous solution = K + Cl. • • - NaCl in dilute aqueous solution = Na + Cl. When the two solutions are mixed, we have : - K + Na + Cl + Cl, and there should be no thermal change produced on mix- ing such solutions. It has long been known, that if com- pletely dissociated solutions of neutral salts are mixed, there is neither evolution nor absorption of heat, provided that none of the ions unite to form molecules, or to form new complexes of ions. These facts are usually stated as Hess's law of the thermoneutrality of salt solutions, which but names them, without attempting an explanation. The theory of electrolytic dissociation not only furnishes a reason for the law of the thermoneutrality of salt solu- tions, but makes it a necessary consequence of its own validity. OSMOTIC PRESSURE LOWERING OF FREEZING-POINT RISE IN BOILING-POINT - CONDUCTIVITY It will be remembered that Arrhenius proposes the theory of electrolytic dissociation, to account for the abnor- mally large osmotic pressure shown by certain classes of substances. We may divide chemical compounds into two classes, with respect to their power to exert osmotic press- ure : First, substances like the carbohydrates, alcohols, etc., i.e. the chemically inactive organic compounds, which exert an osmotic pressure that obeys the gas laws, and 124 ELECTROLYTIC DISSOCIATION will be called normal; second, the acids, bases, and salts which exert a much greater osmotic pressure. If we determine the freezing-point lowering produced by these substances, when dissolved in water, we will find that they again divide themselves into two classes; the organic compounds giving freezing-point lowerings which we will call normal, and the acids, bases, and salts, giving a greater depression of the freezing-point. All of those compounds, and only those, which show too great osmotic pressure, give too great lowerings of the freezing-point of water. Furthermore, if we study the rise in the boiling-point of solvents produced by dissolved substances, we will find, again, that the organic compounds above referred to pro- duce a certain rise in the boiling-point, while all the acids, bases, and salts produce a greater rise in boiling-point. Substances divide themselves here, as in the last two cases, into two classes, and it is exactly the same division as shown both by osmotic pressure, and lowering of freezing- point. Finally, if we study the conductivity of solutions of chemical compounds, we will find that solutions of the neu- tral organic compounds do not conduct the current, while solutions of all acids, bases, and salts, do conduct. If we were to divide all chemical substances with respect to their power to conduct the electric current, they would again fall into two classes, and exactly the same two classes as were furnished by each of the above three properties. Substances which conduct the current are termed electro- lytes, and those which do not conduct, non-electrolytes; so that we will now refer to these two classes of chemi- EVIDENCE FOR THE THEORY 125 cal compounds as, respectively, electrolytes and non- electrolytes. We have, then, this very remarkable relation. All of those substances, and only those, which show abnormally great osmotic pressure, show abnormally great lowering of the freezing-point, rise in boiling-point, and conduct the current. These electrolytes, as we will see later, are also the most active chemically. The converse is also true, that all of those substances, and only those, which show normal osmotic pressures, show normal lowering of freezing-point, rise in boiling- point, and do not conduct the current. These non-electro- lytes, as we will also see, are the least active of chemical substances. Having found this qualitative relation, it remains to see whether it is quantitative, - whether a substance which shows too great osmotic pressure produces a lowering of freezing-point, and rise in boiling-point, which is too great, by the same amount. If the abnormally great osmotic pressure is explained by the dissociation of molecules into ions, so, also, must the abnormally great lowering of freezing-point, and rise in boiling-point, produced by electrolytes, as well as their conductivity, be due to the same cause. If the theory of electrolytic dissociation is true, there must be a quantitative relation between abnormal osmotic pressure, lowering of freezing-point, rise in boiling-point, and conductivity. If such a quantitative relation can be shown to exist, it would be a strong argument in favor of the theory we are considering. We will show that such a relation does exist. 126 ELECTROLYTIC DISSOCIATION Relation between Osmotic Pressure and Lowering of Freez- ing-point. - The relations between the four properties here considered will be pointed out, first experimentally, and then in part, theoretically. De Vries1 has measured the relative osmotic pressures of a number of solutions, using vegetable cells. Without going into the details of this method, the principle can be concisely stated. When some vegetable cells, containing colored protoplasm surrounded by a semipermeable mem- brane, are immersed in solutions which have a greater osmotic pressure than the contents of the cell, we can see the contents of the cell contracted to one side, due to the loss of water to the solution. If the solution in which the cell is immersed has the same osmotic pressure as the contents of the cell, no water will pass into or out of the cell, and it will present a normal appearance. If the solu- tion has a smaller osmotic pressure than the contents of the cell, water will pass in, and the cell will be distended. By studying the behavior of the cell in the solution, under the microscope, we can determine whether the solution has a greater, less, or the same osmotic pressure as the con- tents of the cell. By starting with a solution which has a greater osmotic pressure than the. contents of the cell, and diluting it gradually, we can determine, from the behavior of the cell, when its osmotic pressure is just equal to that of the contents of the cell. We can thus pre- pare solutions of different substances, having each the same osmotic pressure as the cell contents, and, therefore, all having the same osmotic pressure. Such solutions, which have the same osmotic pressure, were termed isos- 1 Ztschr. phys. Chem., 2, 415. EVIDENCE FOR THE THEORY 127 motic. When these concentrations were expressed in molecular quantities, their reciprocal values were termed isotonic coefficients. These show, directly, the relative osmotic pressures of solutions of equal molecular concen- tration. The coefficients for a number of compounds, as compared with the molecular lowerings of the freezing- point, are given in the following table, taken directly from the work of De Vries.1 Substance Isotonic Coefficients Molec. Low. of Freezing- MULTIPLIED BY IOO point MULTIPLIED BY IO c6h12os 181 185 C12H22Ou 188 *93 MgSO4 196 192 kno3 300 308 k2so4 391 39° NaCl 3°5 351 These are just a few of the many cases given by De Vries. But they are sufficient to show the proportionality between isotonic coefficients and molecular lowering of the freezing-point for a number of classes of substances. Relation between Osmotic Pressure and Lowering of Vapor-tension. Rise in Boiling-point.-In the same table in which the above relation is pointed out, De Vries also shows that a proportionality exists between the isotonic coefficients of a number of substances, and the molecular lowering of the vapor-tension; lowering of vapor-tension being used here, instead of rise in boiling-point, which is proportional to it. A few results taken from the table are given: - 1 Ztschr. phys. Chem., 2, 427. 128 ELECTROLYTIC DISSOCIATION Isotojtc Coefficients Lowering of Vapor-tension Substance MULTIPLIED BY IOO MULTIPLIED BY IOOO c4h6o5 198 178 c4hgo6 202 188 NaNO3 300 296 k2c2o4 393 • 372 k2so4 39i 351 CaCl2 433 5T7 k3c6h5o7 501 499 The proportionality between osmotic pressure and low- ering of vapor-tension, or rise in boiling-point, is at once apparent. Relation between Osmotic Pressure and Conductivity. - De Vries also compared the osmotic pressure of solutions and their conductivity. He calculated the sum of the molecules and ions, on the one hand from osmotic press- ure, on the other from conductivity, and then compared the two values to see how they agreed. He obtained the following results:1 - Substance From Isotonic Coefficients From Conductivity Non-conductors c3h8o3 IOO IOO C6H12O6 IO6 IOO C12H22OH IOI IOO Conductors MgSO4 125 135 kno3 176 180 KC1 l8l 187 NaCl 179 182 NH4C1 182 185 k2so4 23° 234 Sum of Molecules and Ions calculated - 1 Ztschr. phys. Chem., 3, 109; also loc. cit. EVIDENCE FOR THE THEORY 129 The agreement between osmotic pressure and lowering of freezing-point, rise in boiling-point, and conductivity, is as close as could be expected, when we consider the large experimental error involved in determining osmotic press- ure, directly, by any method, and even in determining the relative osmotic pressure of solutions by the method of De Vries. Relation between Lowering of Freezing-point and Rise in Boiling-point. - Raoult1 has shown, purely empirically, that the lowerings of the freezing-point, produced by some eighteen salts, stand in the same relation to one another as the rise in boiling-point produced by these same com- pounds. The results are not tabulated, and, therefore, will not be given here. Relation between Lowering of Freezing-point and Con- ductivity.- That a quantitative relation exists between these quantities, for any given substance, was shown by Arrhenius, when he proposed the theory of electrolytic dissociation. Some of the data which he brought forward to prove this point have already been given (p. 98). The agreement between the values of i, as calculated from freez- ing-point lowering and from conductivity, was only fairly close, because the freezing-point method at that time was in a crude state, and gave only approximate results. The freezing-point method has now been greatly im- proved,2- a number of sources of error having been elimi- nated,- until it can be used to measure the value of the coefficient of dissociation, as it is termed, with considerable 1 Compt. rend., 70, 1349 (1870). 2 Jones, Ztschr. phys. Chem., 11, no and 529; 12, 623. Loomis, Wied. Ann., 51, 500; 57, 495; 60, 523. Raoult, Ztschr. phys. Chem., 27,617. 130 ELECTROLYTIC DISSOCIATION accuracy. The values of a have been determined by Jones,1 for a large number of dilutions of different substances, using the freezing-point method. These have been com- pared with the values of « for the same dilutions of the same substances, using the conductivity method. The fol- lowing results are taken from the paper of Jones: - Compounds Concentration a FROM Conductivity a from Freezing- point Lowering NaCl 0.001 98.0 98.4 NaCl 0.01 93-5 90-5 NaCl 0.1 84.1 84.I BaCl2 0.001 93-9 94-2 BaCl2 0.005 87.9 87.6 BaCl2 0.05 75-3 77-7 HC1 0.002 100.0 98.4 HC1 0.01 98.9 95-8 HC1 0.1 93-9 88.6 H2SO4 0.003 89.8 86.0 h2so4 0.005 854 83-8 h2so4 0.05 62.3 60.7 KOH 0.002 100.0 984 KOH 0.01 99-2 93-7 KOH 0.1 92.8 83-1 K2CO3 0.003 92.0 96.6 k2co3 0.005 88.6 96.0 k2co3 0.05 71.9 77-5 The percentage of dissociation a, as measured by the freezing-point method, agrees surprisingly well with the values obtained from conductivity. The slight differences which exist are probably due to the different temperatures 1 Phil. Mag., 36, 483. EVIDENCE FOR THE THEORY 131 at which the two sets of measurements were made - con- ductivity being determined at i8°, and freezing-point lowering a little below o°. We have now demonstrated, by experiment, the quan- titative relation which exists between osmotic pressure, lowering of freezing-point, rise in boiling-point, and con- ductivity. We will now give a mathematical demonstration of one or two of these relations. Connection between Osmotic Pressure and Lowering of Freezing-point, established by Thermodynamics. - The con- nection between osmotic pressure and lowering of the freezing-point was deduced thermodynamically by van't Hoff,1 in the paper to which reference has so often been made. Van't Hoff showed that solutions in the same solvent, having the same freezing-point, are isotonic at that tem- perature. He applied this to dilute solutions, and was led to the conclusion that solutions which contain the same number of molecules in the same volume, and, therefore, from Avogadro's law, are isotonic, have also the same freezing-point. This was discovered experimentally by Raoult, and led to the expression " normal molecular lower- ing of the freezing-point." This means the lowering in degrees, produced by a gram-molecular weight of the sub- stance in 100 grams of the solvent. This normal molecular lowering of the freezing-point, which we will term the freezing-point constant for the solvent, van't Hoff then derived from the latent heat of fusion of the solvent. This deduction has been developed more fully by Ostwald,2 1 Harper's Science Series, IV, 29. Ztschr. phys. Chem. 1, 481. 2 Lehrb. allg. Chem., I, p. 759. 132 ELECTROLYTIC DISSOCIATION and it will be given here essentially as worked out by him, with some changes1 which seem to make the steps a little clearer. Let us take a solution consisting of n gram-molecules of the dissolved substance and N gram-molecules of the sol- vent. Let T be the temperature of solidification of the solvent, and A the lowering of the freezing-point. Here as much of the solvent is allowed to solidify as would serve for the solution of one gram-molecule of the sub- tance, - - molecules. n Let X be the latent heat of fusion of a gram-molecule of the solvent; the amount of heat liberated would be -X. If, n now, the ice is separated from the solution, warmed to tem- perature T, and melted, and finally allowed to mix with the solution by passing through a semipermeable membrane, it will exert an osmotic pressure /. If v is the volume of the solvent which solidified, the work = pv, the heat - X; from n which:- . A ppm _ A Tvx" T Butpv = RT, and R = 2 cal. Substituting, we have: - △ = n N X Let M be the molecular weight of the solvent, and sub- ioo stituting N = we have : - (I) IOO X 1 Jones, Phil. Mag., 36, 493. EVIDENCE FOR THE THEORY 133 K In the Raoult formula m is the molecular weight of the dissolved substance, K is the freezing-point constant, and A the specific lowering of the freezing-point. A =-, where A is the lowering of the freezing-point observed, and / the percentage concentration of the solution. Kt m = -. ■A Let n be the number of molecules of the dissolved sub- stance in ioo g. of the solvent. P n = -; m substituting, wA = Kmn; ± = Kn (2) M 2 T* From (1) and (2) K=- v 7 7 100 X, If L is the heat of fusion of 1 g. of the solvent, \ = LM. Substituting, K = . 100Z From this equation van't Hoff has calculated the value of the freezing-point constant for a number of solvents, and compared these values with those found experimentally. Solvent Constant calculated from K= - -- 100 L Constant found Experimentally Water 18.9 18.5 Acetic acid 38.8 38.6 Formic acid 28.4 27-7 Benzene 53-o 50.0 Nitrobenzene 69-5 70-7 134 ELECTROLYTIC DISSOCIATION The values of the freezing-point constant, as calculated from the van't Hoff formula, agree very satisfactorily with those found by experiment. Relation between Osmotic Pressure and Lowering of Vapor-tension (Rise in Boiling-point). Theoretical Demon- stration. - The relation between osmotic pressure and lowering of vapor-pressure has been derived in a simple manner by Arrhenius.1 The line of reasoning is as fol- lows : Given a vessel of the form shown in Fig. 5, closed at the bottom by a semiperme- able wall. Let this vessel be filled with a solution S, and dip into a vessel con- taining the pure solvent D. The whole is covered with a bell-jar, and exhausted. Equilibrium will be established when the pressure of the column of liquid, from the surface of the solvent up to h, is equal to the osmotic pressure, and the free space is saturated by the vapor D'. When equilibrium is established, the vapor-pressure of the solution at h must be just equal to the pressure of the vapor of the solvent at this point. If it were less, liquid would condense in h, if more, it would distil out of /z, and there would not be equilibrium, since liquid would flow either out or in through the mem- brane. If f is the tension of the vapor of the solution at h, f the vapor-tension of the solvent, Ji the height of the column of liquid, and d the density of the vapor in the bell-jar, we have : - f'=f-hd. Fig. 5. 1 Ztscbr, phys. Chem., 3, 115. EVIDENCE FOR THE THEORY 135 The value of h. - Let us have a very dilute solution, in which n gram-molecules of substance are contained in g grams of solvent. From van't Hoff's law of osmotic pressure we would have: - PV=RT* n, in which P is the osmotic pressure of the solution, and V its volume. Let be the specific gravity of both solution and solvent; they are practically the same for very dilute solutions. P = h x j ; J Substituting, PV= nR T = =hg; hg=nRT h = g The value of d. - Let v be the volume of a gram- molecule of the vapor of the solvent D, and f the pressure of this vapor: - fv^Rf RT v ~ ~f~' If M is the molecular weight of the solvent d=p V M RT , Mf 7=7^^ 136 ELECTROLYTIC DISSOCIATION Substituting the values, h = and d = -d- in the g equation f -f - hd, we have: - r=f_nRTm g RI f nMf> g ' f-f nM or, <-2- = , f g which is essentially Raoult's fundamental equation for the lowering of the vapor-pressure of a solvent by a dissolved substance. Raoult's equation, which has been amply veri- fied by experiment, is usually written : - f N where N is the number of gram-molecules of the solvent. It is evident that N-^ when the two equations become , M identical. Theoretical demonstrations of other relations between the four properties of solutions, which we are considering, have been furnished. Thus, Guldberg 1 has proved a direct connection between lowering of freezing-point and lower- ing of vapor-tension. Arrhenius 2 has shown how freezing- point lowering and conductivity are connected, by cal- culating the value of the coefficient i from both, and then showed, experimentally, that the two values agreed with 1 Compt. rend., 70, 1349. 2 Loc. cit. EVIDENCE FOR THE THEORY 137 one another (see p. 98). A number of other demonstra- tions of relations between these properties could be given, did space permit, but quite enough has been developed to show, both experimentally and theoretically, that they are quantitatively connected. Whatever causes electrolytes to exert a greater osmotic pressure than non-electrolytes, also causes them to produce a greater lowering of the freezing- point, rise of boiling-point, and enables them to conduct the current. Arrhenius showed that his theory explains all of the facts concerning osmotic pressure. From the above rela- tions alone it must, therefore, accord with the facts con- nected with the other three properties. We have, however, an abundance of independent evidence, were this neces- sary, that the theory of electrolytic dissociation is in per- fect harmony, not only with what is known of the osmotic pressure of dilute solutions, but with every other property possessed by them. EXPERIMENT TO SHOW THE PRESENCE OF FREE IONS If only ions conduct, then, whenever a current is passed through a solution of an electrolyte, a movement of the ions is necessarily involved. The same applies to a solution of an electrolyte charged electrostatically. If the charging body is negative, it will attract the ions which carry the positive electricity in the solution, i.e. the cations, and will repel the anions. If the solution could then be separated into two parts, the one would contain an excess of cations, and the other an excess of anions. 138 ELECTROLYTIC DISSOCIATION Illustration of a Solution charged Electrostatically. - Let two vessels, A and B, be filled with a solution of an electrolyte, say potassium chloride, and let the two be connected with a si- phon filled with the same liquid. Let a negatively charged body K be brought near to A; it will act by in- duction upon the system AHB. A will become positive and B negative. If now the siphon H is removed, and then the body K, A will remain positive and B negative. But, from the law of Faraday, electricity can move in solutions only by a movement of the ions. That A should be positive, it is necessary that it should contain an excess of the potassium ions which carry the positive charge. Similarly, B must contain an excess of chlorine ions. The number of these free ions in the solution must depend, of course, upon the intensity of the inducing action. To discharge A, introduce a platinum wire connected with the earth. The potassium ions give up their positive charge to the wire, and become atoms. These now act upon the water, forming potassium hydroxide, and hydrogen which escapes from the solution. ' This experiment was proposed by Ostwald,1 simply as an illustration. It is obvious to any one that, under condi- tions such as those described, the amount of hydrogen set free would be far too small to be seen. On account of the very great charge carried by an ion, the number of ions which would be induced from one vessel to the other, by the above arrangement, would be relatively small. Fig. 6. 1 Ztschr. phys. Chem., 2, 272. EVIDENCE FOR THE THEORY 139 The above experiment illustrates another point, as Ostwald has shown. That electrostatic charging of elec- trolytes takes place with enormous velocity, as with con- ductors of the first class. But Kohlrausch has shown that the ions move very slowly. If the above induction phenomenon takes place very rapidly in the solution, then the potassium ion, which brings the positive charge closest to K, could not have been connected with the chlorine ion, which takes the negative charge to the region most remote from K. Free ions must, therefore, be present in the solution at all times, or the electrolyte must be dissociated. Experiment of Ostwald and Nernst. - The experiment described above, while theoretically correct, must be re- garded as only an illustration. Ostwald and Nernst1 have, however, devised an experiment, which they claim demonstrates to the eye the effect described by Ostwald. To be able to see the hydrogen liberated by induction, unusual precautions must be taken, because of the very small quantity of gas which will be set free. To liberate a milligram of hydrogen would require a condenser of about one square kilometre. But one milligram of hydro- gen will fill 12 to 13 cubic centimetres, under ordinary conditions. By means of a microscope, it is possible to see a bub- ble of gas 0.01 mm. in diameter, and this amount could be liberated, using a condenser of ordinary dimensions. The gas was collected in the capillary of a Lippmann electrometer, since a small quantity could be easily recog- nized in this way. 1 Ztschr. phys. Chem., 3, 271 (1888). 140 ELECTROLYTIC DISSOCIATION The experiment of Ostwald and Nernst will now be described in detail. A glass tube 30 to 40 cm. in length, provided with a stop-cock, was drawn out at one end to a fine capillary. The diameter of the capillary was such that, when the tube was filled with mercury, it would begin to flow out of the fine point. The tube was fastened upright, and its tip allowed to dip in dilute sulphuric acid. The mercury was then drawn up into the capillary, and the acid drawn in after it. By means of the stop-cock, the surface of contact between the mercury and the acid could be kept about the middle of the capillary. A platinum wire, fused into the glass tube, connected with the mercury. A large glass flask was filled with dilute sulphuric acid. Its outer surface was covered with tinfoil, and its neck varnished with shellac. The contents of the flask were connected with the sulphuric acid into which the capillary tube dipped, by means of a moist cord. The glass flask was insulated, by placing it upon a plate of hard rubber. The outer coating on the flask was connected with the pos- itive pole of a small machine for generating electricity ; the mercury in the tube connected with the earth. When the machine was set in motion, the meniscus in the capillary rushed up with violence, and at the same time, several bubbles of gas separated, which broke the thread of mer-. cury in a number of places. This is nearly the verbatim account of what happened, as given by the experimenters themselves. They explain the facts as follows: " By charging the coating on the outside of the flask with positive electricity, the negative electricity in the interior is attracted and held, EVIDENCE FOR THE THEORY 141 while the positive is repelled. The latter passes through the thread, into the capillary electrode, and through the platinum wire in the latter to the earth. There is no closed current present; the entire movement of electricity which is produced is the result of induction." 1 As the outer coating of the flask becomes charged with positive electricity, the ions SO4, which carry the nega- tive charge, are attracted, the positive ions, hydrogen, are repelled, pass over the moist cord to the mercury, give up their charge, and appear as ordinary hydrogen gas. The objection could be raised to this experiment, that a movement of electricity takes place, electrolytically, through the glass, and that this causes the separation of the hydrogen. The authors performed a number of ex- periments to test this point, and convinced themselves that this is strictly an induction phenomenon. They worked quantitatively, as far as possible, determin- ing the amount of hydrogen which separates and the amount of the electricity induced, and found that the amount of gas liberated corresponded to that calculated from Faraday's law to within the limit of experimental error. They concluded that movement of electricity in electrolytes, corresponding to Faraday's law, can take place only with a simultaneous movement of the ions, and that in electrostatically charged electrolytes a number of ions, corresponding to the amount of electricity, are free. The question still remains, whether the ions are not set free at the moment of the electrostatic charging, so that the separation of the electricities is accompanied by a kind of electrolysis in the interior of the liquid. Ostwald and 1 Ztschr. phys. Chem., 3, 122. 142 ELECTROLYTIC DISSOCIATION Nernst point out, that Clausius1 has shown, that the movement of electricity in electrolytes obeys the weakest electromotive impulses, which would not be possible if the electricity must first perform an appreciable amount of work. They then show that such an assumption is against the laws of thermodynamics. If we consider all of the precautions which Ostwald and Nernst have taken, it seems that they have conclusively proved the point, that free ions exist in electrostatically charged electrolytes, and these are not set free at the moment of charging. THE OSTWALD DILUTION LAW Conductivity and Dilution.-It is well known, that the power of solutions of electrolytes to conduct the current increases with the dilution. If we always deal with molecular quantities, and express the conducting power of solutions in terms of molecular conductivity, we will see at a glance, that this is always larger (with a very few exceptions)2 the greater the dilution. The rate of increase with the dilution is comparatively slow for the good con- ductors, but much more rapid for the poorer conducting substances, such as the organic acids. The difference between the molecular conductivities of the good and poor conductors thus becomes less as the dilution,increases. This agrees with the view of Arrhenius, that the strength of all acids which, as we shall see later, depends only upon the number of hydrogen ions present, is the same at infi- nite dilution, since at this dilution all acids are completely dissociated. 1 Pogg. Ann., ioi, 338. 2 Kablukoff, Ztschr. pbys. Chem., 4, 429. EVIDENCE FOR THE THEORY 143 Ostwald1 found from his own work, that the molecular conductivity of all monobasic acids passes through the same series of values, and if acids A and B have the same conductivities at dilutions v and vly they will have the same conductivities at av and avx. Having found such a general relation between the con- ductivities of solutions of different substances, it remains to discover the mathematical expression connecting dilu- tion and conductivity. And since dissociation and con- ductivity are proportional, we would then have connected dilution and dissociation. Ostwald's Deduction.-Ostwald2 has pointed out, that since the laws of gas pressure apply to the osmotic press- ure of dilute solutions of non-electrolytes, if Arrhenius's theory of electrolytic dissociation to account for the excep- tions shown by electrolytes is true, we ought to be able to apply the formula for a partly dissociated gas to a partly dissociated solution.3 For the homogeneous system of one volume of a gas dissociating into two volumes of gaseous products, Ost- wald4 deduced the formula: - p q R log-rA- = A + const. A A * p, px, and /2 are the pressures of the original gas and of the decomposition products, respectively, q is the heat of decomposition, R is the gas constant, and T the abso- lute temperature. 1 Journ. prakt. Chem., 31, 433; Lehrb. allg. Chem., II, p. 653. 2 Ztschr. phys, Chem., 2, 136, 276; 3, 170. 8 See also Planck, Wied. Ann., 34, 147. 4 Ztschr. phys. Chem., 2, 36; Lehrb. allg. Chem., II, p. 723 (1st edition). ELECTROLYTIC DISSOCIATION 144 If the temperature is constant, and neither of the de- composition products is present in excess, the above expression becomes: - constant (i) P? in which p is the pressure of the original gas, and px that of the decomposition products. Turning now to solutions, we must deal with osmotic pressure instead of gas pressure. The osmotic pressure is proportional to the amount of substance present, and inversely proportional to the volume. Let u be the mass of the undecomposed electrolyte, and the mass of the decomposition products; v is the volume: - p - -, and py - -• v v Substituting these values in (i), we have: - -- - constant (2) The amount of the dissociation products is equal to the relation between the conductivity at volume v (pv), and the conductivity at infinite dilution (/x^):- P» u.= 1 A4 The amount of the undissociated substance u is the complement of u.: - Pv u - 1 ' 00 Substituting these values of u and ux in (2) we have: - u (u - . --" - v - constant .... (3) Pv EVIDENCE FOR THE THEORY 145 and this is the dilution law of Ostwald. This can, how- ever, be simplified. If we represent the activity co- efficient, or the amount of dissociation, by a: - a = -• Substituting this value in (3) and taking the reciprocal, we have: - a2 = constant (4) (1 - a) v Ostwald1 proceeded at once to test his formula by experiment. The conductivity of a number of acids at different dilutions was measured, and the values of a calculated for these dilutions. These values of a, to- gether with the volumes of the different solutions v, (volume is the number of litres which contains a gram- molecular weight of the electrolyte), were inserted in equation (4), to ascertain whether c came out a constant, over a fairly wide range of concentration. Acetic Acid V a c 8 I-I93 0.00180 i6 1.673 0.00179 32 2.38 0.00182 64 3-33 0.00179 128 4.68 0.00179 256 6.56 0.00180 512 9.14 0.00180 1024 12.66 0.00177 1 Ztschr. phys. Chem., 3, 170, 241, 369. 146 ELECTROLYTIC DISSOCIATION 0-AMIDOBENZOIC ACID v a c 64 2.03 0.00066 128 3.02 0.00074 256 4.54 0.00084 512 6.62 0.00092 1024 9.44 0.00096 The values obtained for c, for most of the acids in- vestigated, approached a constant. Ostwald studied be- tween two and three hundred organic acids, and while there are a number of cases where c did not come out very constant, yet it can be said, in general, that the law holds approximately for this class of substances. It should be said, that the organic acids are weakly dis- sociated compounds. Bredig,1 in studying the conductivity of ammonia, the amines, and other weakly dissociated bases, applied the Ostwald formula to somewhat more than thirty of these compounds. Ammonia •v c 8 0.0023 32 0.0023 64 0.0023 256 0.0024 T RIPHENYLMETH ANE v c 8 0.0069 32 0.0075 64 0.0076 256 0.0074 Piperidine V c 8 0.157 32 0.162 64 0-150 256 0.152 The values of c (for each compound) are more nearly constant in the work of Bredig on the weak bases, than in that of Ostwald on the weak acids. 1 Ztschr. phys. Chem., 13, 289. EVIDENCE FOR THE THEORY 147 While the dilution law of Ostwald holds fairly well for the weakly dissociated acids and bases, it does not apply at all satisfactorily to the strongly dissociated electrolytes - the strong acids and bases, and salts of these acids and bases. The reason for this failure on the part of Ostwald's law is yet to be discovered. Rudolphi's Dilution Law. - Rudolphi,1 from a study of the conductivity of solutions of silver nitrate of varying concentrations, discovered a new relation, which obtains for the strongly dissociated compounds. If we represent the volume by v, and the constant by c, as above, he found that when he applied the Ostwald equation to solutions of silver nitrate, he obtained the following values: - For v = 16, c = 0.26. For v = 64, c = 0.13. For v =256, c = 0.065. A glance at these figures will show that a real constant would be obtained, if the values of c were multiplied by the square root of v in each case; thus: - 0.26 x V16 = 0.13 x V64 = 0.065 V256. We must, then, substitute for v, in the Ostwald expres- sion, the square root of v, when it becomes: - a2 - -= = constant. C1 - yJv Rudolphi applied his equation to between fifty and sixty strongly dissociated compounds, and the values found for c approached a constant. While marked devia- 1 Ztschr. phys. Chem., 17, 385. 148 ELECTROLYTIC DISSOCIATION tions are not wanting, yet Rudolphi's expression applies as well to the strongly dissociated electrolytes, as that of Ostwald to those which are less strongly dissociated, as the organic acids and bases. This will be seen from the following examples: - Hydrochloric Acid v c 2 4.36 4 4-45 8 5-i3 16 5.13 Potassium Sulphite v c * O.453 8 0.454 32 0.455 128 0.544 Potassium Acetate v c 2 I.24 IOO 1.19 1,000 1.18 10,000 1.03 The Rudolphi expression is, of course, purely empirical. The physical significance of the Vt* is thus far entirely unexplained. One or two modifications 1 of the Rudolphi formula have been proposed, but these are also empirical, and cannot be regarded as essentially in advance of the original. We thus have two expressions for the relation between the dissociation of electrolytes and the dilution of the solution: That of Ostwald, which has a mathematical basis, and whose physical significance is known, apply- ing to the weakly dissociated electrolytes; and that of Rudolphi, which is purely empirical, and whose physical meaning is unknown, applying to the strongly dissociated electrolytes. The relation between gaseous and electrolytic dissociation is thus established, as far as the less strongly dissociated electrolytes are concerned; but when the dis- sociation is nearly complete at moderate dilutions, there exists a discrepancy which still remains to be explained. 1 Van't Hoff, Ztschr. phys. Chem., 18, 300; Kohlrausch, ibid., 18, 662. EVIDENCE FOR THE THEORY 149 EFFECT OF AN EXCESS OF ONE OF THE PRODUCTS OF DISSOCIATION Further Relation between Dissociation by Heat and Elec- trolytic Dissociation. - It is well known that the dissocia- tion of a vapor by heat is diminished by the presence of an excess of any of the products of dissociation. Thus, the vapor of ammonium chloride is more stable in the presence of an excess of ammonia, or of hydrochloric acid. And the vapor-density of phosphorus pentachlo- ride, which breaks down by heat into phosphorus trichlo- ride and chlorine, when determined in an atmosphere of chlorine, agrees very nearly with the theoretical density. Many such examples have been brought to light by the work of Deville and others. It would be an interesting analogy, if we could find a similar effect in the case of electrolytic dissociation. It has long been known, that when a saturated solution of sodium chloride is treated with gaseous hydrochloric acid, the gas dissolves and sodium chloride separates. A saturated solution of the salt contains sodium chloride molecules, sodium ions, and chlorine ions. When gaseous hydrochloric acid dissolves in the solution, it dissociates into hydrogen ions and chlorine ions. We have thus added one of the products of dissociation of the original compound, - chlorine ions. The dissociation of the so- dium chloride is diminished, which is shown by the fact that some of the ions combine to form molecules, and these are precipitated from the solution. The same relation is shown by Nernst1 in the case of 1 Ztschr. phys. Chem., 4, 375. 150 ELECTROLYTIC DISSOCIATION potassium chlorate. If to a saturated solution of potas- sium chlorate, either potassium or C1O3 ions are added, some of the potassium chlorate will be precipitated. Thus, if to a saturated solution of potassium chlorate, either potassium chloride or potassium hydroxide is added, there will soon result a precipitation of potassium chlorate. If, on the other hand, sodium chlorate is added to a saturated solution of potassium chlorate, some of the potassium chlorate will be precipitated. This is at least qualitatively analogous to what takes place in the dissocia- tion of a vapor by heat. It remains to study this effect quantitatively. The theory of the mutual effect of salts on each other's solubility was developed by Nernst,1 from the theory of electrolytic dissociation and the law of mass action. If the electrolyte is completely dissociated into two ions, the product of the active masses must be constant, and equal to the square of the solubility of the salt before any second compound is added. If m is the solubility of the salt after a second salt with a common ion is added, x the amount added, and the solubility of the salt alone, we have: - +x)= But since the solutions are only partly dissociated, we must take into account the amounts of dissociation. Let a0 be the dissociation of the original substance in a saturated solution, rq the dissociation of this substance in the presence of the substance added, and « the dissociation of the added substance ; the above expression then becomes : - 1 Ztschr. phys. Chem., 4, 379. EVIDENCE FOR THE THEORY 151 Ma(ma + xa^) = w02a02. The effect of one salt on the solubility of another with a common ion was tested experimentally by A. A. Noyes.1 He worked with eleven pairs of substances, determined the solubility of the one with which the solution was satu- rated, added the second, and determined the change pro- duced in the solubility. He then calculated the solubility of the first salt, after the second was added, from the formula of Nernst, and compared the solubility found with that deduced theoretically. There is a general agreement between the two sets of values, but some discrepancies appeared, which are larger than could be accounted for by experimental error. In calculating solubility from the equation of Nernst, we must know a, «b and a0, or the dissociations of all the solu- tions involved. Noyes concluded from his work that the deduction of Nernst is perfectly correct, and that the appa- rent differences are due to errors in the determination of the dissociation values. The relation between dissociation by heat and electrolytic dissociation, as effected by an excess of either of the products of dissociation, is, there- fore, established. Determination of Electrolytic Dissociation by Change in Solubility.-The slight differences between the solubilities found experimentally and calculated, led Noyes to suspect that the conductivity method of measuring dissociation was not accurate. He, therefore, reversed the above procedure, and used solubility measurements to determine dissoci- ation. Knowing the dissociation of the substance in the 1 Ztschr. phys. Chem., 6, 241. 152 ELECTROLYTIC DISSOCIATION saturated solution, and the change in the solubility of this substance produced by adding a given amount of the second substance, he could calculate the dissociation of the second substance. A condition which must be fulfilled is, that the salt with which the solution is saturated is not very soluble, since we would then be dealing with a concentrated solution, to which the laws here involved do not apply. Noyes first used thallous chloride with which to saturate his solvent, since it is not very soluble; and then added to this a number of soluble chlorides, as potassium, sodium, and ammonium, and calculated the dissociation of the latter, from the change which he found produced by them in the solubility of the thallous chloride. He1 at first obtained dissociation values for the alkaline chlorides and other compounds, which differed considerably from that calculated from conductivity. Agreement between Dissociation determined by Conduc- tivity, Freezing-point Lowering, and Solubility.-We had, then, two methods of measuring electrolytic dissociation, conductivity, and change in solubility, and the two gave values which did not agree. The question arose, which is correct, or are both methods to be discarded ? At this time H. C. Jones2 undertook, at the suggestion of Ostwald, to so improve the freezing-point method of Beckmann, that it could be applied to the measurement of electrolytic dissociation. A thermometer divided into thousandths of a degree was made, and carefully standard- ized. The apparatus to contain the liquid was enlarged 1 Ztschr. phys. Chem., 9, 603; 12, 162; 13, 412. 2 Ibid., 11, no, 529; 12, 623. EVIDENCE FOR THE THEORY 153 so as to hold a litre. The air-bath around the liquid was enlarged, and a number of precautions taken to secure more accurate determinations of the temperatures at which both solvent and solution froze. The dissociation of a number of acids, bases, and salts was worked out by this improved freezing-point method, over a considerable range of concentration. The result was, as has already been seen (p. 130), a satisfactory agreement between the dissociation calculated from freezing-point lowering and that calculated from conductivity. In calculating dissociation from solubility, Noyes had assumed that the thallous chloride was dissociated to the same extent as potassium and sodium chlorides. He afterwards found1 that this assumption was not correct. He determined the dissociation of thallous chloride, and when he introduced the correct values for this com- pound into the calculation, he found that the dissociation of the second compound, as determined by solubility, agreed very satisfactorily with the results of the other two methods. The three most general methods of measuring electro- lytic dissociation give, then, values which agree very well with one another. This fact should be carefully borne in mind, in considering the evidence bearing upon the theory of electrolytic dissociation. The Relation between the Two Kinds of Dissociation an Analogy.-The relation which has just been pointed out, between the dissociation of a vapor by heat and elec- trolytic dissociation, is only an analogy. The processes are not at all identical, as is shown by the fact that the 1 Ztschr. phys. Chem., 16, 125. 154 ELECTROLYTIC DISSOCIATION end products are very different. Take the compound ammonium chloride; it is broken down by heat into ammonia and hydrochloric acid: - NH4C1 = NH3 + HC1. Both of these are in the molecular condition, and can be isolated. When ammonium chloride is dissociated electrolytically by water, it breaks down thus: - NH4C1 = NH4 + CL The composition of the products is not only different from the first case, but both the ammonium and chlorine exist as ions, the one charged positively and the other negatively, and neither can be isolated as such. That there is some deep-seated connection between the two processes is probable. Fused salts often conduct the current just as they would do if dissolved in water. But we must leave it for the future to show the exact nature of the connection between the two kinds of dissociation. DISSOCIATION AND CHEMICAL ACTIVITY Perhaps the most interesting test of the theory of elec- trolytic dissociation yet remains. If the properties of dilute solutions of electrolytes are, in general, properties of the ions, what must be said in reference to the property of such solutions to react chemically. If there are only ions present in the solutions, it is clear that any chemical reaction which may take place is a reaction between ions only. If the solution contains molecules as well as ions, EVIDENCE FOR THE THEORY 155 the chemical reactivity may be due to the molecules, or it may be due to the ions, or it may be due to both. The problem is not only of interest from the physical chemical, but is of the very highest importance from the purely chemical, standpoint. The number of possible cases by which the relation between dissociation and chemical activity can be investi- gated is very large. We will take several acids, inorganic and organic, and a few bases which have been worked out thoroughly in this connection. The method of attack- ing the problem is comparatively simple. The dissocia- tion of substances must be determined, also their power to react chemically. Then the two must be compared. Conductivity and Reaction Velocity. - Here, again, we are indebted for our knowledge chiefly to Ostwald. In a paper on the catalysis of methyl acetate,1 he expressed the opinion that the velocity with which acids would invert cane-sugar, like other reactions of acids, depends only on their affinity. In a later paper,2 describing work along this line, this view was substantiated. It then remained to determine whether there was any relation between these two reactions produced by different acids, and the disso- ciation of the acids themselves. The following table, taken from Ostwald's Lehrbuch,3 gives a direct comparison of the conductivities of a number of acids, with their power to saponify methyl acetate, and to invert cane-sugar. Column I gives the conductivities of the acids referred to hydrochloric acid as 100; column II, the velocities with which they effect the catalysis of methyl acetate; and 1 Journ. prakt. Chem. [2], 28, 495. 2 Ibid., 29, 385. 3 Lehrb. allg. Chem., II, p. 650. 156 ELECTROLYTIC DISSOCIATION column III, the velocities with which they invert cane- suSar- 1 n nr i n in Hydrochloric acid, 100.00 100.00 100.00 Hydrobromic acid, 101.00 98.00 111.00 Nitric acid, 99.60 92.00 100.00 Sulphuric acid, 65.10 73-9° 73-20 Formic acid, 1.68 i-3i !-53 Acetic acid, 0.42 0.34 0.40 Monochloracetic acid, 4-9° 4-3° 4-84 Dichloracetic acid, 25-3O 23.00 27.10 Trichloracetic acid, 62.30 68.20 75-40 Oxalic acid, 19.70 17.60 18.60 Malonic acid, 3.10 2.87 3.08 Succinic acid, 0.58 0.50 0-55 Malic acid, i-34 1.18 1.27 Tartaric acid, 2.28 2-30 - Racemic acid, 2.63 2.30 - Ostwald adds, that when we consider that neither the temperature, nor the dilution, is the same in the three series, the agreement is satisfactory. Ostwald studied also other reactions in which acids are involved, such as the velocity with which they dissolve calcium oxalate, or the way in which they divide a base between them. He found, in all of these cases, exactly the same order of avidity as given above. A little later he carried out an investigation strictly analogous to the above, using a number of bases. The reaction studied was the velocity with which bases sapon- ify ethyl acetate. The relative reaction velocities and conductivities are given in the following table. Column I gives the reaction velocities; column II, the conductivities. EVIDENCE FOR THE THEORY 157 I n Potassium hydroxide, 161.00 161.00 Sodium hydroxide, 162.00 149.00 Lithium hydroxide, 165.00 142.00 Ammonium hydroxide, 3.00 4.08 Methylamine, 19.00 20.02 Ethylamine, 19.00 20.05 Propylamine, 18.06 18.04 Amylamine, 4.00 6.09 Dimethylamine, 22.00 23-O5 Diethylamine, 26.00 28.03 ' Trimethylamine, 7-03 9.07 Triethylamine, 22.00 20.02 Tetraethyl ammonium hydroxide, 131.00 128.00 The agreement is as satisfactory as the conditions of work would allow us to expect. Dissociation measured by Chemical Activity. - We have just seen that there is proportionality between dissociation and chemical activity, and that, therefore, the amount of dissociation may be used as a measure of the chemical activity of electrolytes. This process can, on the other hand, be reversed, and the chemical activity of substances be used as a measure of their electrolytic dissociation. The conductivity and freezing-point are the most convenient and general methods for measuring electrolytic dissociation, but there are cases to which neither of these can be applied. It is sometimes desired to know the amount of the dissociation of some acid, in the presence of other electrolytes like the salts. Since all of the electrolytes present would take part in the conductivity, and in the lowering of the freezing-point of the solvent, it would be difficult, if not impossible, to deter- 158 ELECTROLYTIC DISSOCIATION mine the amount of the dissociation of the acid by means of either of these methods. Some method must be employed which will detect one kind of ions in the presence of others. The chemical reactivity of the hydrogen ion has been made use of to solve the above problem. The rate at which cane-sugar is inverted by hydrogen ions can be determined very easily, and this reaction has been used by Trevor,1 and others, to measure the number of hydrogen ions present. Similarly, the specific chemical reactions of other ions have been used to determine the amount of these which are present, when more direct methods are not applicable. Thus, the dissociation of bases can be measured by the rate at which the hydroxyl ions saponify an ethereal salt. These examples suffice to show the proportionality between dis- sociation and chemical activity, and that either may be used as a measure of the other. Chemical Reactions usually take place between Ions. - The facts just pointed out show that chemical reactions, in which acids and bases are involved, are reactions effected by ions. The number of reactions in which ions are known to take part is very great, including by far the majority of the cases with which we have to deal. It has been supposed that gases do not conduct electricity, and are, therefore, undissociated. Reactions between gases could not be ionic, if this were true. The recent work of J. J. Thomson2 has made it very probable that gases are dissociated, to some extent, and reactions between gases may be reactions between ions only. Thom- son3 has also shown that atoms of elementary hydrogen 1 Ztschr. phys. Chem., io, 321. 2 Nature, loc. cit. 3 Ibid. EVIDENCE FOR THE THEORY 159 gas behave as if they were both positive and negative, so that it is not improbable that reactions between the parts of elementary gases are ionic, but this is far from proved. It is not safe to conclude, at present, that all chemical reactions take place between ions. There are cases known of substances which conduct very little, or do not conduct at all, and yet react chemically. We have well character- ized chemical compounds, formed by the union of two parts of the same general electrical character. Thus, phos- phorus and chlorine, sulphur and chlorine, chlorine and bromine, chlorine and iodine, iodine and bromine, combine; and we are accustomed to regard all of these ions as carrying a negative charge. But in this connection the question arises, whether anion and cation are not, after all, only relative, one ion being charged more or less positive, or negative, than another. Reactions between organic compounds, in general, take place much more slowly than between inorganic, and the former are much less dissociated. This is probably due to a slow progressive dissociation of the organic substances, as the ions already present enter into chemical combina- tion. This raises the question, whether in those reactions between apparently undissociated substances, there are not a few ions present which react, and as these take part in the reaction, more and more ions are slowly formed, which then in turn react. Whatever may be the final decision as to whether mole- cules can take part in chemical reaction, we are now justi- fied in stating, that most of the chemical reactions with which we have to do are not reactions between molecules, but between ions. 160 ELECTROLYTIC DISSOCIATION Dissociating Power of Different Solvents. - Different solvents have very different powers of breaking down electrolytes into ions. Water is the strongest dissociant known. Of the more common solvents, formic acid stands next to water in its ionizing power. Then come methyl alcohol and ethyl alcohol, respectively, then acetone, and finally the ethereal salts and hydrocarbon, which have very slight dissociating power. J. J. Thomson1 has worked out an ingenious theory, which will be considered later, connecting the dissociating power of solvents with their dielectric constants. Experi- ment has shown, that there is undoubtedly a qualitative relation between the two, but there does not seem to be a proportionality. This is shown by recent work on the dissociating power of formic acid,2 and of methyl and ethyl alcohols.3 While the dissociating powers are in general in the same order as the dielectric constants, they are not proportional to them. If water has such remarkable dissociating power, and as chemical activity is due chiefly to ions, water should play a very prominent role in bringing about chemical reaction. We will now examine a number of cases which will show whether this is true. EFFECT OF WATER ON CHEMICAL ACTIVITY Unless very special precautions are taken to exclude moisture, every chemical reaction takes place in the pres- ence of water. This is largely due to the presence of water-vapor in the air, which permeates everything with 1 Phil. Mag., 36, 320. 2 Zanninowich-Tessarin, Ztschr. phys. Chern., 19, 251. 3 Jones, Ztschr. phys. Chem. Jubelband. EVIDENCE FOR THE THEORY 161 which it comes in contact. Further, when a solvent other than water is used, water is often formed as one of the products of the many reactions. If there was a trace of water-vapor present to start the reaction, the quantity would increase rapidly as the reaction progressed. To study the effect of water on chemical activity, we must exclude all traces of moisture at the outset, and choose reactions in which no water is formed. We must see how the reaction progresses in the absence of water, then admit water, and see what difference is produced. This is the method which has been employed, and it has led to some highly interesting and surprising results. Some of these will now be taken up. Action of Dry Chlorine on Metals.-Wanklyn1 passed dry chlorine over fused metallic sodium, and found that no action resulted. The melted sodium was shaken in contact with the chlorine, so as to expose a fresh surface of the metal. Still there was no chemical action between the two. This explains the frequent failure of the lecture experiment, where sodium chloride is formed by the direct union of sodium and chlorine. If the lecturer is careful to dry the chlorine gas which is passed over the molten metal, he usually observes the sodium lying in the same condition after the experiment as before. But if moisture in any way is admitted, the reaction takes place with violence. Comper2 studied the action of dry chlorine on a number of metals. He found that metallic zinc was not acted on by the chlorine at first, but the thin zinc-foil was attacked after a time. Metallic magnesium was not acted upon at 1 Chern. News, 20, 271 (1869). 2 Journ. Chem. Soc., 43, 153 (1883). 162 ELECTROLYTIC DISSOCIATION all, and metallic silver very slowly. Bismuth was appar- ently unacted upon, but tin was rapidly attacked. Anti- mony and arsenic were rapidly acted upon, while mercury was acted upon as rapidly as by moist chlorine. In these experiments the chlorine was dried over calcium chloride for some days. This was, evidently, not sufficient to remove the last traces of moisture, so that the chlorine used by Comper was only partly freed from water-vapor. It would be of interest to repeat these experiments with perfectly dry chlorine. Comparative Inactivity of Dry Oxygen. - H. B. Baker1 carried out a number of experiments with carefully dried oxygen, which led to results of very considerable impor- tance. The gas was dried by allowing it to stand for a long time in the presence of phosphorus pentoxide. Moist carbon, in the presence of oxygen, burned with the scintillation characteristic of this reaction. A certain amount of the dried carbon was burned in dry oxygen, but much less than of the moist, and there was no scintillation in the dry oxygen. Baker concluded from a number of experiments, that pure charcoal, heated in oxygen dried over phosphorus pentoxide, does not burn with a flame; partial combustion, however, goes on, both carbon monox- ide and carbon dioxide being formed. Sulphur, boron, amorphous and ordinary phosphorus, do not burn in dry oxygen. Selenium, tellurium, arsenic, and antimony show no difference in their combustion, whether the oxygen be moist or dry. Dixon2 studied the action of dry oxygen on carbon monoxide, under the influence of the spark. He mixed 1 Phil. Trans. (1888), 571. 2 Ibid. (1884), 617. EVIDENCE FOR THE THEORY 163 three volumes of carbon monoxide and one volume of dry oxygen, and passed a spark through the mixture. There was no explosion. More oxygen was then added, and again the spark passed without explosion. A fresh charge of carbon monoxide was then prepared from oxalic acid, and an excess of dry oxygen mixed with it. The spark passed through this, also, without any explo- sion. A drop of water was then added to the mixture, the spark passed and there resulted the usual explosion. Experiments were then carried out to determine the velocity of the reaction, as affected by the amount of steam present. By the addition of steam it was found that the velocity of the reaction increased very rapidly. The con- clusions from this work were: The drier the carbon mon- oxide and the oxygen, the less the tendency to unite; a trace of aqueous vapor causes the mixture to become inflam- mable, and the velocity of the reaction increased with the amount of water present. Dry Hydrochloric Acid does not decompose Carbonates. - After Wanklyn had showed that dry chlorine would not act on fused sodium, and Baker, that dry oxygen is com- paratively inactive, it was of interest to test the chemical behavior of other substances when free from moisture. One of the most vigorous of chemical reactions is the decomposition of carbonates by strong acids. Hughes1 studied the behavior of dry hydrochloric acid toward carbonates, to see what influence moisture would have in such a reaction. Hydrochloric acid gas was dried, by passing it over sulphuric acid and then over phosphorus pentoxide. It 1 Phil. Mag., 34, 117 (1892). 164 ELECTROLYTIC DISSOCIATION was then brought in contact with carefully dried calcium carbonate. A few results will show the amount of car- bonate decomposed. In one experiment: - Amount of carbonate used 0.8705 g. Weight of carbonate after treating with dried hydrochloric acid 0.8712 g. Increase in weight 0.0007 g. Percentage increase 0.08 In a second experiment the percentage increase in weight was o. 1. The theoretical increase in weight for complete transformation is 29 per cent. Moist hydrochloric acid gas was then passed over cal- cium carbonate for the same length of time, when more than one hundred times as much carbonate was decom- posed as when dry hydrochloric acid gas was used. The experiment was then performed just as above, using witherite (BaCO3) instead of calcite. The result of one experiment is given : - Amount of witherite used 0.9976 g. Weight after treating with dried hydrochloric acid gas 0.9984 g. Increase in weight 0.0008 g. Percentage increase 0.08 The theoretical increase in weight, if all of the carbonate is transformed into chloride, is 14.7 per cent. Hughes concluded from his work, that the increase in the weight of the carbonate, after passing a stream of dry hydrochloric acid over it, was so small, that no definite proof was furnished of any action having taken place. EVIDENCE FOR THE THEORY 165 The slight variations observed may be due to experimental errors, or to the imprisonment or entanglement of the molecules of hydrochloric acid gas amongst the finely powdered particles of Iceland spar, or witherite. Dry Acids exert no Action on Litmus and do not form Salts. - Blue litmus is not changed to red in a stream of dry hydrochloric acid gas. Gore has shown that dry liquefied hydrochloric acid has no action on litmus. Marsh has proved that glacial acetic acid, which is perfectly free from moisture, has no action on litmus. Marsh1 has also shown that pure sulphuric acid, free from every trace of moisture, does not act on blue litmus, and, further, is probably incapable of forming salts. And Veley2 has proved that nitric acid, free from moisture and from nitrous acid, is probably incapable of forming salts. Dry Hydrochloric Acid does not precipitate Silver Nitrate in Ether or in Benzene. - Silver nitrate was dissolved in anhydrous ether, and in benzene. A current of dried hydrochloric acid gas was passed through these solutions for an hour. There was no precipitate formed, though the solution became slightly turbid. When the silver nitrate was dissolved in absolute alcohol, a more decided precip- itate was formed in the course of an hour, but the decom- position was far from complete. This remarkable result was also obtained by Hughes. Comparative Inactivity of Dry Hydrogen Sulphide. - Veley3 found that dry hydrogen sulphide does not act on quicklime, and this led Hughes to investigate the action of dry hydrogen sulphide upon metallic oxides. 1 Chern. News, 61, 2. 2 Phil. Trans. (1891), 279. 3 Journ. Chem. Soc. (1885), 484; Phil. Mag., 33, 471 (1892). 166 ELECTROLYTIC DISSOCIATION Magnesium oxide was used. Dry hydrogen sulphide was passed over this, and the increase in weight ascertained. One or two results will show what took place : - First Weight of magnesium oxide used 0-7597 g- Weight after passing dry hydrogen sulphide . 0.7600 g. Increase in weight 0.0003 g- Second Weight of magnesium oxide used 0.6360 g. Weight after passing dry hydrogen sulphide . 0.6368 g. Increase in weight 0.0008 g. In both cases the increase in weight is within the limit of experimental error. The change from the oxide to the sulphide, which is exothermic and would, therefore, be expected to take place, does not occur. A drop of water was then added to the magnesium oxide, and dry hydrogen sulphide passed over it as before. The white oxide quickly became greenish yellow, and the following result will show the increase in weight pro- duced. Weight of magnesium oxide and water . . . 0.7235 g. Weight after passing the hydrogen sulphide gas 0.8435 g- Gain in weight o. 1200 g. The gain in weight, which expresses the amount of oxide transformed into sulphide, is from 200 to 400 times as great as when all moisture is excluded. Similar results have been obtained with barium oxide. EVIDENCE FOR THE THEORY 167 Dry hydrogen sulphide has no action upon barium oxide, from 150 to 900. Ferric oxide showed a slight increase in weight when dry hydrogen sulphide was passed over it. But this was probably due to the incomplete drying of the oxide of iron. When dry hydrogen sulphide was passed over paper which had been moistened with lead acetate and afterwards thoroughly dried, there was no action whatever. Moist paper containing lead acetate was, of course, acted upon at once. By passing the dried gas first over dry paper, and then over moist, the difference in the action is very striking. The same experiment was performed, using antimony trichloride instead of lead acetate. The dry paper was unaltered by the dried hydrogen sulphide, while the moist paper was immediately turned yellow. The same experi- ment was performed with salts of tin, cadmium, bismuth, silver, copper, mercury, and cobalt, and exactly the same results were obtained in all cases. We may conclude, in general, that dry hydrogen sul- phide has no action on the dry soluble salts of the metals, but if moisture is present a change takes place at once. Hughes1 found that when mercuric chloride is dissolved in absolute alcohol, a current of dry hydrogen sulphide can be passed for fifteen minutes, without producing any change. Afterwards the solution became slightly turbid, then pale yellow, dark yellow, and finally greenish yellow. No further change took place when the current was passed an hour and a half. The addition of a small amount of water changed the green to a black precipitate. 1 Phil. Mag., 35, 531 (1893). 168 ELECTROLYTIC DISSOCIATION Other Reactions which do not take place without Water. - According to Baker,1 sulphur trioxide does not combine with dry lime, or dry copper oxide. Dry ammonium chloride may be sublimed from a mix- ture of this salt with dried lime, without ammonia being liberated. Dry hydrogen and chlorine may be exposed to the sunlight for two days, without anything like complete reaction taking place. Dry ammonia and hydrochloric acid can be partially separated from a mixture of these gases, when oppositely charged plates are placed in the mixture, the ammonia pass- ing to the negative plate, the hydrochloric acid to the positive. Dry Hydrochloric Acid does not act on Dry Ammonia. - The heading of this paragraph must be a surprise to any one who is familiar with the properties of these gases, and is not acquainted with the experimental work which has been done to establish this fact. Hughes2 stated, that when ammonia is dried over lime, and hydrochloric acid is dried by phosphorus pentoxide, the two would remain in the presence of one another for 24 hours, without any deposit being formed, even upon the sides of the containing tube. H. B. Baker3 published a very careful investigation of this point, in which the ammonia and hydrochloric acid gases were dried over phosphorus pentoxide, and brought together in such a manner that any change in volume could be readily observed. He concluded, that perfectly dry ammonia and perfectly dry hydrochloric acid gas are entirely without action upon one another. 1 Jouin. Chein. Soc., 65, 611. 2 Loc. cit. 8 Journ. Chem. Soc., 65, 611. EVIDENCE FOR THE THEORY 169 The conclusion of Baker was called in question by Gutmann.1 The latter claimed that ammonia and hydro- chloric acid cannot be dried over phosphorus pentoxide, since the gases are absorbed. Baker,2 in reply, shows that the phosphorus pentoxide used by Gutmann must have contained metaphosphoric acid. And, further, that Gutmann did not take sufficient care in drying the gases. The glass apparatus must be carefully heated to remove the moisture, which, as is well known, clings to it so tenaciously, and is held by it so persistently. Baker repeated his earlier experiments, working with the greatest care, and found that his original conclusion was confirmed in every respect. Dry hydro- chloric acid gas does not combine with dry ammonia gas. If this fact creates surprise, the following will be almost beyond belief. Dry Sulphuric Acid does not act on Dry Metallic Sodium. - An experiment was performed before the Chemical Society of London,3 in which a piece of metallic sodium was plunged into concentrated sulphuric acid. When the sodium, wrapped with a piece of wire which served as a handle, was immersed in the acid, there was a flash of light, showing incipient reaction; then there was perfect quiescence, the sodium remaining freely suspended in the sulphuric acid. The reaction at first was due to the presence of a few sodium ions on the surface of the metal, produced by the moisture in the air, to which it was exposed for an instant. No one should repeat this experiment, unless the greatest 1 Liebig's Ann., 299, 3. 2 Journ. Chem. Soc. (1898), 422. 3 Proceed. Chem. Soc. (1894), p. 86. 170 ELECTROLYTIC DISSOCIATION precautions are taken in drying both the sodium and the sulphuric acid. It is quite evident that ordinary methods of drying would not suffice. The facts which have been cited in this section show conclusively the necessity of the presence of water in many chemical reactions. The question still remains, why is water essential ? We believe we have the answer, in that water has a very high dissociating power, breaking down the molecules into ions, which then react. These facts are just what would be predicted, if the theory of electrolytic dissociation is true. Conclusion. - Some of the lines of evidence bearing upon the theory of electrolytic dissociation have been presented in this chapter. There are many more which might be adduced; but it seems that what has been presented suffices to show how strong the evidence is in favor of the truth of this generalization. It has already been mentioned, and stress should be laid upon it, that there are facts to which the theory, as we now conceive it, does not seem to apply. But the evidence in favor of the theory is so overwhelming, in comparison with the few apparent exceptions, that we should examine the latter very closely before concluding finally that they are real exceptions. Without for a moment ignoring the facts for which the theory does not seem to entirely account, the writer believes that the evidence in favor of a great generalization being expressed by the theory of electro- lytic dissociation is as strong as in the case of many of our so-called laws of nature. For how many of these apply under all conditions, and are entirely free from exceptions ? CHAPTER IV SOME APPLICATIONS OF THE THEORY OF ELECTROLYTIC DISSOCIATION In the last two chapters we have attempted to answer the questions, how did the theory of electrolytic dissocia- tion arise, and what are some of the reasons for believing that it is true ? There still remains the question, of what scientific use is this theory ? And this brings us to the subject of our last chapter. Few theories have ever been advanced in science which, in a dozen years, have found wider application than the theory which we are considering. It has already been applied not only to chemical problems, but also to physical, and to biological in the broadest sense. A few of these applications will now be taken up. APPLICATION OF THE THEORY OF ELECTROLYTIC DIS- SOCIATION TO CHEMICAL PROBLEMS This theory has never directly exercised any marked influence on the study of the relations between the com- position and constitution of pure substances, and their properties. This is obviously true, since pure substances are undissociated. The theory has, however, had an indirect influence in this direction. It has opened up such a number of 171 172 ELECTROLYTIC DISSOCIATION entirely new fields of research, that it has detracted from work along these lines. The number of investigations of relations, such as the above, has become less in the last few years; and although an elaborate piece of work has appeared from time to time, the physical chemist of to-day finds more promising lines of work suggested to him by the newer conceptions. Without detracting for a moment from the value of the enormous amount of labor spent in studying the properties of pure substances, yet it should be stated, that the great advances in the last few years have resulted from the study of one substance in the presence of another. THE THEORY OF ELECTROLYTIC DISSOCIATION AS APPLIED TO SOLUTIONS It will be remembered that van't Hoff showed that solutions behave, in certain respects, like gases. There is an analogy between the gas particles distributed in space and the dissolved particles distributed throughout the solvent, - space bearing a similar relation to the gas that the solvent does to the solution. It has also been shown, as stated above, that it is in solutions, chiefly, that we have molecules broken down into ions. Further, the impor- tance of a thorough study of solutions becomes at once apparent, when we consider that most chemical reactions take place in solution. This is especially true of inorganic reactions, most of them taking place in what has come to be known as the wet way. And, indeed, in organic chemistry, also, some solvent is often employed which has the property of dissociating to some extent one or more of the substances present. APPLICATIONS OF THE THEORY 173 We know matter in three states of aggregation, solid, liquid, and gas, and have, therefore, nine classes of solutions: - Gas in gas Liquid in gas Solid in gas Gas in liquid Liquid in liquid Solid in liquid Gas in solid Liquid in solid Solid in solid Examples of all of these nine classes are known. We can, however, from the standpoint of the dissociation theory, deal best with solutions in liquids as solvents, and we will, therefore, limit ourselves to solutions of this kind. Osmotic Pressure. - Since van't Hoff1 pointed out the analogy between the osmotic pressure of dissolved sub- stances and the gas pressure of gases, much work has been done on methods of measuring osmotic pressure. Osmotic pressure, as has already been shown, is a very difficult quantity to measure directly, and a number of comparative methods have been devised. These aim to measure the relative osmotic pressures exerted by different substances. If we, then, know the absolute osmotic press- ure of any one of these substances, we can calculate the absolute osmotic pressure of all the others. The rel- ative method of De Vries2 has already been considered. Those of Tammann,3 Bonders and Hamburger,4 Wladimi- roff,5 and Lob6 should be mentioned, in order that they may be examined, if desired. These methods have been applied, not only to non-electrolytes, but also to electro- 1 Loc. cit. 2 Loc. cit. 3 Wied. Ann., 34, 299. 4 Onders Physiol. Lab., Utrecht (3), 9, 26; Ztschr. phys. Chern., 6, 319. 5 Ztschr. phys. Chem., 7, 529. 6 Ibid.., 14, 424. 174 ELECTROLYTIC DISSOCIATION lytes. Since an ion exerts exactly the same osmotic pressure as a molecule, when we determine the osmotic pressure of a partly dissociated solution, we can calculate the amount to which that solution is dissociated. We know, from the study of non-electrolytes, the osmotic pressure which would be exerted if there was no dissocia- tion ; we know that if the electrolytes break down into two ions, that the solution when completely dissociated would give twice this osmotic pressure. Knowing the actual osmotic pressure exerted, we can calculate the amount of dissociation at once. Although we have more accurate methods of measuring dissociation than the above, yet this serves to confirm the results of other methods. Diffusion. - Our knowledge of the osmotic pressure of solutions has thrown light on the way in which salts diffuse in solution. It is well known that a salt always diffuses from the solution into the pure solvent, or from a more concentrated to a more dilute solution; and this continues until the whole has become homogeneous. The law of diffusion was discovered by Fick.1 "The amount of salt which diffuses through a given cross-section is propor- tional to the difference in concentrations of two cross- sections lying very close to one another." Diffusion depends, then, upon difference in concentration. The fundamental question of diffusion is, however, still unanswered. What causes it ? What is the force in operation which drives the dissolved substance from one region to another quite remote, if the solution is allowed to come in contact with the pure solvent, or if a more 1 Pogg. Ann., 94, 59 (1855). APPLICATIONS OF THE THEORY 175 concentrated is brought in contact with a more dilute solution ? We see at once a connection between the law of diffu- sion and that of osmotic pressure. Diffusion depends upon difference in concentration. Osmotic pressure de- pends also upon difference in concentration, and a quan- titative study of both the diffusion and osmotic pressure of non-electrolytes and electrolytes has shown that osmotic pressure is the cause of diffusion. Wherever there is a difference in the osmotic pressure of two solutions, diffu- sion will take place from the region of greater into that of less pressure, if the two solutions are brought in con- tact. This is analogous to the diffusion of gases, which always takes place from the region where the gas exerts a greater pressure to the one where the pressure is smaller. But there exists a marked difference between the two kinds of diffusion. With gases this takes place very rapidly, and equilibrium is usually established in a short time. But diffusion in solution proceeds very slowly, and it may require weeks and months for a condition of equi- librium to be reached, if the column of liquid has any considerable length. Nernst1 has worked out a theory of diffusion based upon osmotic pressure, first for non-electrolytes, which are simpler because there is no dissociation, and then for elec- trolytes, taking into account their dissociation. This leads to the conclusion, that the forces required to drive dis- solved particles through the solvent at any appreciable velocity are enormous. Ostwald2 has calculated that the force required to drive 60 grams of urea through water, 1 Ztschr. phys. Chem., 2, 613. 2 Lehrb. allg. Chem., I, p. 697. 176 ELECTROLYTIC DISSOCIATION with the velocity of i cm. per second, has the value of 2500 million kilograms. He suggests that the cause of this is the very fine state of division of the dissolved sub- stance. The force required to throw a small stone with a considerable velocity is not great. But powder the stone very finely, and an enormous force would be required to project the particles of dust with the same velocity. Now let this process of division be continued until the mole- cules were reached, and forces of the above order of magnitude would be required. The principle of Soret,1 which has already been con- sidered, as furnishing evidence for the applicability of the law of Gay Lussac to the osmotic pressure of solutions, should be referred to again in this connection. The change in the concentration of a homogeneous solution, produced by keeping the different parts at different tem- peratures, has been shown to agree with that calculated from the above law. This principle applies as well to solutions which are dissociated as to those which are not, since an ion exerts the same osmotic pressure as a mole- cule, and is, therefore, subject to the same law of diffusion. Lowering of Freezing-point.-The theory of electro- lytic dissociation has been applied to the lowering of the freezing-point of the solvent produced by the dissolved substance. Reference has already been made to this fact, in connection with the evidence bearing upon the theory. It was there shown that Arrhenius proved that the values of the coefficient " z," calculated from freez- ing-point lowering, agreed with those calculated from conductivity. 1 Loc. cit., see p. 86. APPLICATIONS OF THE THEORY 177 The freezing-point method was used for a long time, chiefly to determine the molecular weights of substances in solvents which do not dissociate them. The applicabil- ity of the freezing-point method to the problem of molec- ular weights was pointed out by Raoult,1 several years before the theory of electrolytic dissociation was proposed. By working with solvents other than water, such as formic and acetic acids, benzene, and nitrobenzene, he was able to discover certain general laws of the freezing-point low- ering of solvents. When water was used as a solvent, so-called abnormal values were obtained. The freezing- point lowerings were usually much greater than would be expected from what was found in other solvents. The experimental method used at first by Raoult was necessarily crude, as it had just been devised by him. This has since been very greatly improved by Beckmann.2 And the method of Beckmann has been enlarged and improved by Jones,3 Loomis,4 Lewis,5 Ponsot,6 and others. The most refined of all is probably the method described very recently by Raoult,7 in which he has utilized the best points in all of the above-described methods. However this may be, the freezing-point method has now been developed to a fair degree of perfection. The direct object in improving the freezing-point method was not the determination of molecular weights, - the method of Beckmann would suffice for this purpose,-but to measure the electrolytic dissociation of acids, bases, and 1 Ann. Chim. Phys. [6], 2, 66; Harper's Science Series, IV, 71. 2 Ztschr. phys. Chem., 2, 638, 715; 7, 323. 5 Ztschr. phys. Chern., 15, 365. 8 Ibid., 11, no, 529; 12, 623; 18, 283. 6 Ann. Chim. Phys. [7], 10, 79. 4 Wied. Ann., 51, 500; 57, 495; 60, 523. 7 Ztschr. phys. Chem., 27, 617. 178 ELECTROLYTIC DISSOCIATION salts in water. There were also certain theoretical questions involved, in connection with the freezing-point constant. The freezing-point method has already been applied extensively to the measurement of electrolytic dissocia- tion, and is now to be regarded as one of the most gen- eral methods for this purpose. The results obtained by Jones, compared with those of Kohlrausch from conduc- tivity, have already been given. Ions lower the freezing-point of a solvent exactly the same amount as molecules, so that with a partly disso- ciated electrolyte we have the sum of the lowering of the molecules plus that of the ions. We know, however, from non-electrolytes, how much lowering the molecules alone would produce, and we can calculate from the lowering found, what percentage of the molecules is broken down into ions. The application of the freezing-point method to the prob- lem of molecular weights in solution has helped to solve a large number of questions, especially in organic chem- istry. But from a physical chemical point of view, the newer application of the freezing-point method to the de- termination of electrolytic dissociation is by far the more important. Lowering of Vapor-tension, Rise in Boiling-point. - What has been said in reference to the lowering of the freezing-point of solvents, can be applied directly to the lowering of their vapor-tension by substances dissolved in them. Here, again, Raoult1 did much of the pioneer work. The laws of the lowering of vapor-tension, or rise in boiling- 1 Ann. China. Phys. [6] ,15, 375; Compt. rend., 104, 1430; Harper's Science Series, IV, 97, 125. APPLICATIONS OF THE THEORY 179 point, had not been discovered, mainly because dissociat- ing solvents had been used. Raoult worked with solutions in ether, and discovered the general law of the lowering of vapor-tension : One molecule of any undissociated sub- stance, dissolved in one hundred molecules of any volatile liquid, lowers the vapor-pressure of this liquid by a nearly constant fraction of its value. He showed how the lowering of vapor-tension, like the lowering of the freezing-point, can be used to determine the molecular weight of the dissolved substance. Beckmann1 improved this method of Raoult, as he had improved the freezing-point method. Instead of measur- ing the depression of the vapor-tension, he determined the rise in boiling-point, - a quantity which could be much more easily and accurately ascertained. The Beckmann method of determining molecular weights has been modified by a number of investigators. The more important of these improvements are those introduced by Hite,2 Jones,3 and Landsberger.4 The boiling-point method, like the freezing-point, has been applied also to the measurement of the dissociation of electrolytes. The freezing-point method can be used in this connection, with only a few solvents, since many of the solvents with high dissociating power freeze at a tempera- ture which is too low to deal with successfully in this con- nection. Indeed, the freezing-point method, as a measure of dissociation, has been applied mainly to aqueous solu- tions. The boiling-point method for measuring electrolytic 1 Ztschr. phys. Chem., 4, 532; 6, 437; 8, 223; 15, 656; 17, 107; 18, 473; 21, 239. 2 Amer. Chem. Journ., 17, 507. 3 Results will appear in Ztschr. phys. Chem. Jubelband. 4 Ber. d. chem. Gesell., 31, 458. 180 ELECTROLYTIC DISSOCIATION dissociation admits of much wider application. It can be employed with formic acid, methyl alcohol, ethyl alcohol, acetone, etc., solvents which have a fairly great dissociating power. This application of the boiling-point method is of very considerable importance, since it is the only method avail- able for measuring accurately the dissociation of electro- lytes in these solvents. The conductivity method cannot give very close results, because of the difficulty of deter- mining the value of the molecular conductivity (/zoo) at complete dissociation. These solvents all dissociate so much less than water, that, with the exception of formic acid, the dilution at which the dissociation is complete is so great that the conductivity method does not give accu- rate results. The impurities in the solvents, at these very high dilutions, also render the results imperfect. The importance of measuring dissociation in solvents other than water will be evident, when we consider that this is the first step toward a physical chemistry in other than aqueous solutions. And, in addition, there is in- volved a theoretical question of interest and importance. J. J. Thomson 1 has shown, as already mentioned, that if the molecules are held together by the attraction of oppo- sitely charged parts, and if the molecules are broken down into these parts by solvents, the dissociating power of sol- vents should stand in the same relation as their dielectric constants. Jones2 has measured the dissociation of a number of salts in methyl and ethyl alcohol, using his modification 1 Phil. Mag., 36, 320. 2 Results will be published in Ztschr. phys. Chem. Jubelband. APPLICATIONS OF THE THEORY 181 of the Beckmann boiling-point apparatus. While he found a qualitative relation between the dielectric constants of these solvents and their dissociating power, compared with water, a proportionality between dielectric constants and dissociating power does not exist, as has already been stated. The application of the boiling-point method to the prob- lem of electrolytic dissociation has been made only in the last year or two, and much of value will undoubtedly result from further work with this method. It would, doubtless, have been applied much earlier, but for the experimental difficulties involved. The method at first was, of course, imperfect, containing a large number of errors, and, further, the boiling-point constants of solvents are small, and therefore the quantity to be measured was always small. A number of sources of error have now been removed from the boiling-point method, and when all the details are carefully observed, and the entire work carried out with the greatest care and precaution, results can be obtained for the electrolytic dissociation in the alcohols, which should be accurate to within about I per cent. The rise in the boiling-point, like the lowering of the freezing-point, is that produced by both molecules and ions, - an ion lowering the boiling-point to the same extent as a molecule. But in partly dissociated solutions we know, from a study of non-electrolytes, the rise produced by the molecules. We know, further, that if the mole- cules of the electrolyte were completely broken down into two ions each, the rise in the boiling-point would be twice as great as if there was no dissociation. From the rise 182 ELECTROLYTIC DISSOCIATION actually found, we can calculate, at once, the percentage of dissociation of the solution in question. The theory of electrolytic dissociation has been applied to solutions, in a much wider sense than would be inferred from the foregoing. The additive nature of the properties of completely dissociated solutions has already been dis- cussed. It is not necessary to deal, moreover, with solutions of only one electrolyte in a solvent. Two or more electro- lytes can be brought simultaneously into the solvent, and the resulting solution studied. The effect of one dis- sociated substance on another with a common ion has already been indicated. Some interesting properties of solutions, which, when mixed, do not reciprocally affect each other's properties, have been worked out by Arrhe- nius1 and others. Arrhenius2 worked with solutions of acids, and termed those which fulfil this condition, "iso- hydric." The study of such solutions from the standpoint of his theory, brought out much of interest. Then, again, we are not limited to one or more electro- lytes in one solvent. We can have one or several electro- lytes, in one or more solvents; and such cases have been studied. The electrolytes may, or may not, have a common ion, or the solvents may, or may not, be mixable with each other. The number of possibilities is very great, and some have already been studied. But the scope of this work will not allow further detail. The Theory of Electrolytic Dissociation as applied to Electrochemistry. - New light has been thrown upon this entire field, by the theory of electrolytic dissociation. Many facts which were discovered before the theory was 1 Wied. Ann., 30, 51. 2 Ztschr. phys. Chem., 2, 284. APPLICATIONS OF THE THEORY 183 proposed, have now, by means of it, been correlated, and rationally explained. Electrolysis. -We can now interpret much more clearly the phenomenon of electrolysis. A dilute solution of an electrolyte is completely dissociated; there are no mole- cules present, all of them having been broken down into ions. When the current is passed through such a solu- tion, it directs the ions, the one to the cathode, the other to the anode, where they give up their charges and sepa- rate in the atomic or molecular condition. There appears to be a marked difference between the way in which metallic conductors carry the current, and the manner in which it passes through a solution of an electrolyte. A metal wire carrying a current apparently undergoes no change except in temperature, while a solution con- ducts only by undergoing simultaneous decomposition, - the positively charged parts moving in one direction, the negatively charged in the other. Although there is appar- ently such a marked difference in the way in which the two classes of conductors carry the current, a closer study of the two processes brings out relations between them which do not appear on the surface. Indeed, the work of J. J. Thomson has made it probable that there is a close relation between metallic and electrolytic conduction. The view seems to be gaining ground that conduction in metals is also ionic, the ions here being, of course, very much more restricted in their movements. The ions into which electrolytes dissociate all carry the same amount of electricity, or a simple rational multiple of this unit quantity. This was discovered early in the cen- tury by Faraday, and is now the well-known Faraday's 184 ELECTROLYTIC DISSOCIATION law. All univalent ions carry the same amount of electric- ity. This we will call the unit. All bivalent ions carry twice, all trivalent ions three times this amount, and so on. This was proved by the fact, that when a current is passed through solutions of metallic salts containing uni- valent, bivalent, trivalent, etc., metallic ions, the quantities of the metals which separate stand in the same relations as their chemical equivalents. Univalent metals separate in the ratios of their atomic weights, bivalent in the ratios of one-half their atomic weights, trivalent metals in the ratios of one-third of their atomic weights, and so on. This connects, directly, the charges carried by the ions with their valence. The combining power of ions is condi- tioned by the amount of electricity which they carry. If they carry one unit of electricity, they have the smallest valence or combining power. If two units, they have twice the combining power; if three units, three times the power to combine, and so on. This is exactly what would be expected, if the power to enter into chemical combination was the attraction between oppositely charged parts. The larger the charge carried by the ion, the greater its combining power. We may now say that chemical valence is conditioned by the amount of electricity carried by the ion, and we thus give a more definite and precise meaning to a term which has hitherto been characterized chiefly by vagueness and obscurity. The law of Faraday, which applies to the amount of electrical energy carried by the ions, has its analogue in APPLICATIONS OF THE THEORY 185 the law of Dulong and Petit, which says, that the capacity for heat energy is the same for all atoms. After the law of Faraday had been shown to be a true expression of the amount of electricity carried by ions, it became a matter of importance to determine the amount of electricity carried by some unit quantity of ions. The most convenient quantity to use was the atomic weight of the element in grams. The problem, then, was to deter- mine the amount of electricity which would electrolyze a gram-atomic weight of a univalent metal, or half a gram-atomic weight of a bivalent metal. This quantity, termed the " electrochemical equivalent," has been worked out with great care, and with the following result: To separate a gram-atomic weight of a univalent element like silver, requires, in round numbers, 96,540 coulombs of electricity - more accurately 96,537 coulombs. This value is given to show the enormous charges carried by the ions, and also for future reference. The large amount of electrical energy carried by the ions explains the great difference between the properties of atoms or molecules, and ions. Potassium, sodium, and such substances, when present in the metallic or molecular con- dition, act upon water with great vigor, while potassium and sodium ions are perfectly inactive toward water. The same distinction applies to a large number of other substances. The failure to recognize the distinction between atoms or molecules, and ions, that the one is charged and the other not, led to confusion in the early days of the theory of electrolytic dissociation. This distinction, however, has so often been insisted upon, that it is now pretty generally understood. 186 ELECTROLYTIC DISSOCIATION When electrolytes are decomposed by the current, the ions may give up their charges and separate on the elec- trodes as metallic ions do, yielding the free metal. Or the ion may be of such a nature that when it loses its charge, and passes over into the atom, or group of atoms, this may act chemically upon the water present, and decom- pose it. Thus, when a sodium salt is electrolyzed, the sodium ion gives up its charge to the cathode and becomes an atom. But, of course, free sodium cannot exist as such in the presence of water. It decomposes water, forming sodium hydroxide, and hydrogen gas separates from the cathode : - Na + HOH = NaOH + H. This is true of a large number of ions. When they lose their charge, they act upon the water present. When an acid is electrolyzed the hydrogen ion passes to the cathode, gives up its positive charge to this, and escapes as hydro- gen gas. The anion, whose nature depends upon the acid used, passes to the anode, and gives up its negative charge (in reality takes up a positive charge). The anion, after it becomes electrically neutral, decomposes the water pres- ent. If the acid is hydrochloric, the free chlorine around the anode decomposes water, forming hydrochloric acid, and sets oxygen free: - 2 Cl + H2O = 2 HC1 + O. When an acid is electrolyzed, we thus have hydrogen set free at one pole and oxygen at the other. It may be said, in general, that anions, after they have lost their charge, are incapable of existing in the presence APPLICATIONS OF THE THEORY 187 of water, but decompose it chemically, setting oxygen free. A current can, then, be passed through a solu- tion of an electrolyte in only one way. The ions must carry the electricity, and must separate at the electrodes after losing their charge. The cation may separate directly, as the metals do, or it may act upon water, liberating hydrogen. The anion, after losing its charge, usually decomposes water, liberating oxygen at the anode. The decomposing action of the current has often been used to determine what part of a compound forms the cation, and what part the anion. The principle is simple. The electrolyte is dissolved in water, and the current passed. The cation moves to the cathode, the anion to the anode. After electrolysis, determine what constituents have collected around the two electrodes; that around the cathode is the cation, that around the anode is the anion. In all acids hydrogen is the cation, and the remainder of the molecule, whatever its nature, forms the anion. In the case of some of the organic acids the anion is very complex. The metal in salts forms the cation, the remainder the anion. Bases dissociate into a hydroxyl anion, and the remainder forms the cation. The characteristic ion of acids is hydrogen, of bases is hydroxyl. This same method of determining how a molecule will dissociate has been applied also to very complex cases. How will compounds like K4Fe(CN)6, K2PtCl6, KMnO4, dissociate; what will be the cation, and what the anion ? This has been determined by electrolyzing solutions of these salts. We would expect that all of the metals would go to the cathode, and the 188 ELECTROLYTIC DISSOCIATION remainder of the compounds to the anode. These com- pounds, however, dissociate as follows: - "F+H-F - - - - K4Fe(CN)6 = K4 + Fe(CN)6. K2Pt(Cl)6=K2+PtCl6. KMnO4 = K + MnO4. These examples serve to show the relative nature of cation and anion. What is a cation under one condition, may be a part of an anion under other conditions. Take the above cases, iron in iron salts is always the cation, and this applies, also, to platinum and manganese. But in these complex salts, where there is a more positive ion present, such as potassium, these three metals become, respectively, a part of the anion. A number of other cases, similar to these, have been worked out, and many interesting results have been found. A fact of unusual interest in connection with the charge which ions may carry has been pointed out by Ostwald.1 An ion having exactly the same chemical com- position may carry different charges under different con- ditions. The ion (FeCN6) may carry four charges, as it does if it comes from the compound K4Fe(CN)6, or it may have only three charges, if it is a product of the dissociation of K3Fe(CN)6. Similarly, the ion MnO4 is univalent, if it comes from the compound KMnO4, and bivalent if from K2MnO4. As Ostwald points out, these are especially interesting cases of isomerism, since it cannot be referred to a different "position of the atoms." The only differ- 1 Lehrb. allg/Chem., II, p. 588. APPLICATIONS OF THE THEORY 189 ence here is in the charges which the ions carry. The properties of MnO4 are very different from MnO4. Trivalent iron, manganese, cobalt, etc., have very different properties from bivalent, and there is no more reason to expect them to have the same properties, than to expect that red phosphorus would have the same properties as yellow. In both cases there is a different amount of energy present. This is proved by electrolysis for iron, manganese, etc., compounds. Only two-thirds as much ferric iron will separate for a given current as ferrous, and the same applies to the other compounds. That there are different amounts of energy in the two modifications of phosphorus, is shown by their heats of combustion, which are very different. The ions with the larger charge usually tend to lose some of it, and pass over into the condition where they carry less electricity. Many of the phenomena which we describe as oxidation and reduction are due only to the in- crease and decrease, respectively, of the electrical charges upon the ions, - a ferrous ion passes over into a ferric by taking up one positive charge; a cupric ion becomes a cuprous ion by losing one positive charge. Modes of Ion Formation.-We have spoken of molecules dissociating directly into two, three, and more ions, and have, perhaps, left the impression that electrolytic dissocia- tion can take place in only one way. There are, however, a number of ways in which molecules can break down into ions. The following have been pointed out by Ost- wald :1 - (i) A molecule may break down directly into an equiva- 1 Lehrb. allg. Chem., II, p. 786. 190 ELECTROLYTIC DISSOCIATION lent number of positive and negative ions. This is the case when acids, bases, and salts are dissolved in water. The amount of dissociation depends upon the dilution. Strong acids, strong bases, and salts are completely dis- sociated in about one one-thousandth normal solutions; while weak acids and bases are completely dissociated only at much greater dilutions. (2) An electrically neutral substance may take the charge from an ion and become itself an ion, while the original ion, having lost its charge, becomes electrically neutral. The example given by Ostwald is that of one metal displacing another from its salts. When a bar of zinc is immersed in a solution of copper sulphate, the zinc takes the positive charge from the copper, becoming zinc ions, while the copper ions, having lost their charge, separate as metallic copper. (3) One neutral substance may pass over into positive ions, while another neutral substance may pass over into an equivalent of negative ions. Metallic gold is electri- cally neutral. Chlorine, when dissolved in water, does not pass over into the ionic condition. But when metallic gold is brought into the presence of chlorine water, the gold passes over into cations, and the chlorine into an equivalent of anions. It should have been stated earlier, that when gold dis- solves in chlorine water auric chloride is formed, and, indeed, this compound is obtained if the solution is evaporated. If the solution is dilute, we have only gold ions and chlorine ions present, and no molecules what- ever of gold chloride. Neither the gold nor the chlorine can pass into ions APPLICATIONS OF THE THEORY 191 when alone, but in the presence of each other they both become ions. (4) An ion may take up a larger charge than it already carries, converting a neutral substance into an ion with the opposite charge. Thus, a ferrous ion in the presence of chlorine becomes a ferric ion, the chlorine passing from the molecular into the ionic condition. This is an example of a large number of reactions, which are usually termed processes of oxidation. But, on the other hand, an ion may lose a part of the charge which it already carries, converting a neutral sub- stance into an ion of the same electrical character. Thus, when a solution of potassium manganate is treated with chlorine, the MnO4 ions, carrying two charges, pass over into the MnO4 ions carrying one charge, the negative charge which it has lost going to the chlorine, converting this into an ion. The processes where ions lose part of the charge which they already carry are processes of reduction. These methods of ion formation have all been described by Ostwald,1 as already stated, and the above examples are those which he has chosen to illustrate the several processes. Velocity of Ions.-Whenever a current is passed through a solution of an electrolyte, there is a mechanical movement of the ions toward the electrodes. To under- stand the electrochemical behavior of ions, we must study the velocities with which they move through solutions. If we pass a current through a solution of copper sulphate, using copper electrodes, copper will be deposited 1 Loc. cit. 192 ELECTROLYTIC DISSOCIATION on the cathode, and exactly an equal amount will pass into solution from the anode. The total amount of copper in solution will thus remain constant, but the color of the solution in the neighborhood of the anode will become deeper, while in the neighborhood of the cathode it gradu- ally becomes less intense. The solution becomes more concentrated in copper around the anode, and less concen- trated around the cathode. If platinum electrodes were used in this experiment, copper would separate at the cathode, and since there is no metallic copper present to pass into solution, the amount in solution would become constantly less. In this case the color would disappear more rapidly around the cathode. Relative Velocity of Ions. - Hittorf1 was the first to cor- rectly explain this phenomenon. He suggested that it was due to the different velocities with which the anions and cations move. How this explanation can account for the facts, we can see from the following diagram, which we owe in principle to Ostwald.2 In the following figure, I represents the condition in the solution of the electrolyte before the current has been passed through it. The black circles represent the anions, and the white circles the cations. For each anion present in the solution there is a corresponding cation, and neither anions nor cations have separated at the electrodes. Let us take a case where the velocity of the anion dif- fers greatly from that of the cation, and for simplicity, let us say that the velocity of the anion is twice as great as 1 Pogg. Ann., 89, 177; 98, 1; 103, 1; 106, 337, 513. Ueber die Wanderungen der lonen, Ostwald Klassiker, 21 and 22. 2 Lehrb. allg. Chem., II, p. 595. Fig. 7. 194 ELECTROLYTIC DISSOCIATION that of the cation. Pass a current through the solution until three molecules have been decomposed, and the con- dition represented in II will exist. Three anions will have separated at the anode, and three cations at the cathode. But the solution will have become, relatively, more con- centrated on the anode side of the middle layer marked m. Of the three molecules which have separated from the solution, two have come from the cathode (C) side of the middle layer in, and one from the anode side (A). If we divide the loss around the cathode by the total number of molecules electrolyzed, we will obtain the value f. If, on the other hand, we divide the loss around the anode by the total number of molecules electrolyzed, the result is |. But these two values stand to one another in exactly the same relation as the relative velocities of our anion and cation. From this we can make two general statements. First, to find the relative velocity of the cation, divide the loss around the anode by the total amount of electrolyte decomposed. Second, to find the relative velocity of the anion, divide the loss around the cathode by the total amount of electrolyte decomposed. There are thus three quantities which can be deter- mined experimentally: the change in concentration around the cathode, the change in concentration around the anode, and the total amount of the electrolyte decomposed. It is necessary to determine only two of these, the third being obtained by difference. The total amount decomposed is, from Faraday's law, proportional to the amount of current passed through the solution; and this is ascertained by measuring the latter by means of a voltameter. APPLICATIONS OF THE THEORY 195 A number of methods, based upon the above principles, have been devised for measuring the relative velocity of ions. The solution must be electrolyzed in part, and the apparatus so constructed that the change in concentration can be measured. To accomplish this, the parts of the solution around the two electrodes must not be allowed to mix after the current is passed, or even while the cur- rent is passing. A number of forms of apparatus were devised, and used, by Hittorf, in which a membrane was interposed to pre- vent the parts of the solution from mixing again, but it has been found that the membrane affects the results obtained. Kistiakowsky1 has devised and used a form of apparatus without any membrane, and thus removed this source of error. Loeb and Nernst2 have used a form of apparatus which is essentially a Gay Lussac burette. The electrode around which the solution becomes more concentrated is placed below, and the electrolysis is interrupted while there is still an unaltered layer of solution between the two electrodes. This method is not capable of any very high degree of accuracy, since there is no means by which the solutions of different concentrations can be completely separated from one another, removed, and analyzed. The method of blowing out the solution around the anode, together with enough of the unaltered middle layer to wash out the heavier solution, is not in keeping with the nost refined work. From work on this problem, which has been carried out in this University, it seems to be far better to measure the amount of current directly, by means 1 Ztschr. phys. Chem., 6, 97. 2 Ibid., 2, 952. 196 ELECTROLYTIC DISSOCIATION of a voltameter, than by an indirect method, such as that used by Loeb and Nernst. The work of Bein,1 on the relative velocity of ions, has extended over a number of years, and very recently an elaborate investigation2 has been published by him on this problem. The forms of apparatus used by him are modifications of burettes, some of them very elaborate and complex. The work of Bein, taken as a whole, is probably the best which has ever been done on the relative velocity of ions. The objection, how- ever, to the apparatus of Loeb and Nernst, seems to apply here with some force. There does not seem to be any means of completely separating the solutions, after the electrolysis is brought to an end. At the suggestion of the writer, W. T. Mather,3 working in this University, undertook to devise a form of apparatus for determining the relative velocity of ions which would be free from the above-mentioned objection. The form of apparatus which he constructed, and ap- plied successfully in a few cases, consists, essentially, of two upright tubes connected by a U tube, which joins the upright tubes near the top. In the centre of the U tube a stop-cock of large bore is introduced. When the electrol- ysis has proceeded as far as desired, the stop-cock is closed, and then the solutions in the two arms removed and analyzed. The two parts of the solution are thus completely separated, which is not possible in any form hitherto described. The methods just described have to do only with the 1 Wied. Ann., 46, 38. 2 Ztschr. phys. Chem., 27, 32; 28, 439. 3 Dissertation, Johns Hopkins University. APPLICATIONS OF THE THEORY 197 relative velocities with which the ions move, and con- siderable stress has been laid upon this point, because of a generalization which has been reached in connection with these velocities. Kohlrausch's Law of the Independent Migration Velocity of Ions. - F. Kohlrausch 1 carried out a beautiful investi- gation on the power of solutions of electrolytes to conduct the current, which will be referred to again. The con- ductivity of a solution, referred to molecular quantities, he termed its " molecular conductivity." He studied the con- ductivity of solutions at different dilutions, and found that the molecular conductivity increased with the dilution, up to a certain point, and then remained constant, no matter how far the dilution was carried beyond this point. This maximum constant value of the molecular conductivity we will call Kohlrausch observed that the difference between the values of for two electrolytes with a common anion and different cations (say, KC1 and NaCl), is the same as the difference when there is another common anion and the same cations as before, thus, KNO3 and NaNO3. This will be seen from the following examples: - Difference KC1 = 140^ >20 NaCl p<K = 120' KNO3 i35-7\ >22 NaNO3 113.7' 1 Wied. Ann., 26, 160. 198 ELECTROLYTIC DISSOCIATION Kohlrausch concluded, from a large number of such facts, that the value of for any electrolyte is the sum of two constants, the one depending upon the anion, the other upon the cation. And these constants are the same for any given ion, regardless of the nature of the other ion which is present in the solution. These constants are, moreover, the velocities of the anions and cations respectively, and thus Kohlrausch was led to his law of the independent migration velocities of ions. If we represent the velocity of the cation by c, and of the anion by a : - = c + a. From the method of determining the relative velocities, c just discussed, we determine the value of -. Knowing c + a and -, we can calculate, at once, the values of c a and a. The absolute velocity of ions can be calculated from the law of Kohlrausch, for a definite fall in potential. The absolute velocity of at least one ion can be determined directly by experiment; and should the calculated value agree with the value found, it would argue very strongly in favor of the law with which we are dealing. According to Kohlrausch, the absolute velocities of cation and anion (c and a respectively) are obtained from the relative velocities {c and a), by multiplying by a factor. For a fall in potential of one volt per centimetre along the tube, or a potential gradient of one volt per centimetre, the value of the factor is iio.io-7. The absolute velocity of hydrogen, as calculated by Kohlrausch for the above potential gradient, is 0.0032 cm. per second. APPLICATIONS OF THE THEORY 199 The absolute velocity of the hydrogen ion has been measured directly by the beautiful experiment of Lodge.1 A glass tube 8 cm. wide and 40 cm. long was carefully graduated. The ends were bent down at right angles. The tube, placed horizontally, was filled with gelatine in which sodium chloride was dissolved. This material was colored red by a little phenolphthalein, to which just enough sodium hydroxide had been added to bring out the color. The ends of the glass tube were dipped into vessels filled with dilute sulphuric acid. The apparatus was then allowed to stand, and the rate ascertained at which the acid diffused into the jelly. The current was then passed from one vessel containing the acid, through the horizontal tube, to the other vessel. The hydrogen ions of the sul- phuric acid move with the current, displace the sodium ions from the salt, and form hydrochloric acid. This decolorizes the phenolphthalein in the jelly, and the move- ment of the hydrogen ions can thus be traced. When the proper correction is introduced for diffusion, we have at once the velocity of the hydrogen ion for the potential gradient used. Lodge found, in three experiments, that under a fall of potential of one volt per centimetre, the hydrogen ion has a velocity of 0.0029, 0.0026, and 0.0024 cm. per second. This value agrees very closely with that calculated by Kohlrausch, from his law of the independent migration velocity of ions. Whetham 2 has measured the absolute velocity of a few ions, using a somewhat different method, which is, how- ever, the same in principle as that of Lodge. The ve- 1 B. A. Report (1886), 393. 2 Phil. Trans. (1893), A. p. 337. 200 ELECTROLYTIC DISSOCIATION locities of the copper ion, and the Cr2O7 ion, found by Whetham, agree closely with those calculated from the law of Kohlrausch. It would be difficult to interpret the law of Kohlrausch, if molecules existed as such in very dilute solutions. The law is, however, not only explained by the theory of elec- trolytic dissociation, but is a necessary consequence of it. In dilute solutions, the molecules are completely broken down into ions, and each of these moves through the solution with a velocity which is definite for a given fall in potential. The law of Kohlrausch applies to very dilute solutions of strongly dissociated compounds. It holds, at medium dilution, for comparatively few substances, and does not hold at all for the weak acids and bases. How are these facts to be explained ? The theory of electrolytic dissociation furnishes not only an explanation of the law, but an equally satisfactory explanation of the exceptions. Those solutions to which the law applies are completely dissociated. All of the molecules are completely broken down into ions, and all of the ions take part in conducting the current. The conductivity is, then, a maximum, and gives the true value of iia. In those cases, however, where the law of Kohlrausch does not apply, the solutions are not completely dissociated. Some of the molecules are not broken down into ions, and these, therefore, take no part in conducting the current. The molecular conductivity of such solutions is not the maximum conductivity - is not the true value of but is always less. This applies to the fairly concentrated solutions of the most strongly dis- APPLICATIONS OF THE THEORY 201 sociated electrolytes, and even to the very dilute solutions of the weakly dissociated electrolytes, such as the organic acids and bases. In all such cases, where the solutions are not com- pletely dissociated, we must take into account the amount of the dissociation. When this is done, the law of Kohlrausch becomes much more general, and can be applied, as Ostwald1 has shown, to partially dissociated solutions. If we represent the degree of dissociation by a, the law becomes: - = a(c + a), which holds for completely dissociated solutions, where a= i, and also for solutions in which the dissociation is not complete. The relation between the migration velocity of the ions and conductivity is thus completely accounted for by our theory. The Conductivity of Solutions. - The conducting power of a solution is evidently closely connected with its dis- sociation, since only ions carry the current. We can then obtain new light on the dissociation of solutions by study- ing their conductivity. The conductivity of any conductor of electricity is the reciprocal of the resistance of that conductor. The resist- ance r, from Ohm's law, is expressed thus: - 7F r = -, c 1 Lehrb. allg. Chern., II, p. 673. 202 ELECTROLYTIC DISSOCIATION in which it is the difference in potential at the two ends of the conductor, and c is the strength of current. The con- ductivity C is therefore : - c=-- 7T The unit of resistance most generally used is that of a column of pure mercury 106 cm. in length and i sq. mm. in section, at o° C. Specific Conductivity. - The resistance of conductors depends upon their form as well as upon their chemical nature. In order, therefore, that the resistances of different substances may be measured so as to be com- parable, it is necessary that the conductors should have the same or comparable forms. The dimensions usually chosen are a cylinder I m. in length and i sq. mm. in sec- tion. The resistance offered by substances of these dimensions is known as their specific resistance. The term "specific resistance" is, sometimes, applied also to the resistance offered by a cube whose edge is i cm. in length. This is y of the former. The term "specific resistance," or its reciprocal, "spe- cific conductivity," can be applied to conductors of the second as well as to those of the first class. In this case, the specific conductivity would be the conductivity of a cylinder of the liquid I m. in length and I sq. mm. in cross-section. Conductors of the second class are, however, generally solutions of some electrolyte in some solvent, and their con- ductivity is conditioned by the presence of the electrolyte. That the resistances of such solutions should be com- parable, it is clear that we must deal with comparable APPLICATIONS OF THE THEORY 203 quantities of the dissolved substances. The most con- venient quantities are gram-molecular weights of the different substances. Given a normal solution, which contains a gram-molecu- lar weight of the electrolyte in a litre. Let us place the litre of solution between two electrodes which are I cm. apart. The cross-section of this solution would be 1000 sq. cm. If we represent by v the number of cubic centimetres of any solution which contains a gram-molecular weight of the dissolved substance, and by 5 the specific conductivity of a cube of the solution whose edge is i cm. in length, the molecular conductivity, /y is the product of these two : - /x - vs. But if we represent by j the specific conductivity of a prism of the solution, i m. in length and I sq. mm. in cross- section, the molecular conductivity is expressed thus: - /x = i oooo vs. A general expression for the molecular conductivity, where gram-molecular weights are contained in a litre of the solution, is : - 5 x io 3 j x io 7 /x = or ^x = » g depending upon our definition of specific resistance, whether it is referred to a cube of the solution whose edge is i cm. long, or to a cylinder of it I m. long and i sq. mm. in cross-section. Method of Measuring the Conductivity of Solutions. - If a continuous current is passed through an aqueous solution of an electrolyte from, say, platinum electrodes, 204 ELECTROLYTIC DISSOCIATION the electrodes will become covered with gas. The resist- ance of the solution cannot then be measured as such, since this polarization of the electrodes will introduce a new source of resistance into the circuit. The effect of polarization must be overcome by some means. Kohl- rausch has accomplished this by using an alternating current. His method consists in passing an alternating current from a very small induction coil between platinum Fig. 8. plates immersed in the solution. The resistance of the solution is balanced against a rheostat, using a Wheatstone bridge and telephone. A dynamometer may be used instead of the telephone, for determining the reading on the bridge. A galvanometer cannot, of course, be used with an alternating current. The Kohlrausch apparatus is sketched diagrammatically in Fig. 8. J is a small induction coil, tuned to a very high pitch, and should be placed at some distance from the APPLICATIONS OF THE THEORY 205 bridge, or enclosed in a box lined with cotton, to deaden the sound. It is driven by a storage cell. AB is a metre stick divided accurately into millimetres. Over this is stretched a wire of platinum, or, better, of manganine (an alloy containing manganese) or nickelic, which have a very small temperature coefficient of resistance. W is a rheostat. R is the vessel containing the solution and elec- trodes. The electrodes are cut from thick sheet platinum, and into each plate a piece of stout platinum wire, about an inch in length, is welded. The wire is sealed into a glass tube which is filled with mercury, and electrical connection thus established between the plate and the copper wire which is immersed in the mercury. One arm of the tele- phone T is thrown into the circuit between the rheostat and the resistance vessel, and the other arm is connected with the bridge wire by means of a slider. This is moved along the wire until that point is found at which the hum of the induction coil ceases to be audible in the telephone. If this is some point C, and we represent A C by a, BC by b, the resistance in W by w, and the resistance of the solu- tion in the vessel by r, then from the principle of the bridge we have : - ra = wb r = -. a But the conductivity of a solution c is the reciprocal of the resistance r\ therefore: - c _ a wb The conductivities of solutions determined from this expression would , not be comparable with one another, 206 ELECTROLYTIC DISSOCIATION since there is nothing in this expression which takes into account the concentration of the solution. It is most con- venient to refer all concentrations to molecular normal, which contains a gram-molecular weight of the electro- lyte in a litre. If we represent by v the number of litres of the solution which contains a gram-molecular weight of the electrolyte, the above expression becomes: - va c = -?• wb Instead of c, we now write for the molecular conduc- tivity the letter /x. And to indicate the concentration at which the is determined, we write ^v. va wb Even this expression does not take into account the dimensions of the cell used. A cell constant k must be introduced and determined for each cell, before it can be employed for conductivity measurements. The complete expression for calculating the molecular conductivity is then: - , va ^ = k - wb Carrying out a Conductivity Measurement.-To carry out a conductivity measurement, the constant k for the cell must first be determined. For this purpose a solution must be used whose value of is known. The value of for a one-fiftieth normal solution of potassium chloride at 250 is 129.7. The platinum plates are covered with platinum black, by electrolyzing, in the cell, a dilute solution of platinic APPLICATIONS OF THE THEORY 207 chloride. The solution of potassium chloride is placed in the cell, the latter introduced into a thermostat which is exactly at 250, and the values of a, b, and w ascertained; v and are known, and k can be calculated at once. Having determined the cell constant, the measurement of the conductivity of a solution is comparatively simple. The solution of known concentration is placed in the cell, warmed accurately to the temperature desired, and then the values of a, b, and w ascertained; k and v being known, is calculated at once. Conductivity of Water. -The conductivity of the water used is very important. When we determine the conduc- tivity of an aqueous solution, what we actually measure is the sum of the conductivities of the electrolyte and of the water used in preparing the solution. For this reason very pure water must be used in such work, and a number of methods for purifying water for conductivity measure- ments have been devised. It is quite certain that perfectly pure water has never been prepared. The purest has undoubtedly been obtained by Kohlrausch and Heydweiller.1 They distilled in a vacuum the purest water obtainable by other methods, and determined its conductivity without allowing it to come in contact with the air. A millimetre of this water, at zero degrees, has a resistance equal to that of a copper wire 1 mm. in diameter, extending one thousand times around the earth. It is, of course, not practicable to prepare water of this degree of purity for ordinary conductivity measurements. 1 Ztschr. phys. Chem., 14, 317. 208 ELECTROLYTIC DISSOCIATION A number of methods are, however, available for purifying water sufficiently for such measurements. Nernst1 suggests fractional crystallization. Hulett2 dis- tilled water first from potassium bichromate and sulphuric acid, and then redistilled it from a solution of barium hydroxide. Jones and Mackay3 distilled ordinary distilled water from potassium bichromate and sulphuric acid, and then passed the vapor directly into a boiling alkaline solution of potassium permanganate. Two distillations were thus effected at once. Any of the above methods will yield water of sufficient purity for ordinary conductivity work. The fact that pure water does not conduct the current, means that it is practically undissociated. This same fact has been shown by a number of independent investiga- tions, in which widely different methods have been used. Space will not permit of a discussion of these exceedingly interesting pieces of work. Reference only can be made to that of Wijs,4 Arrhenius,5 Ostwald,6 Bredig,7 Nernst,8 and Kohlrausch.9 The reader is urgently advised to care- fully examine these investigations, which all agree in showing that water is very slightly dissociated. The fact that water is undissociated is of great im- portance. It means that hydrogen and hydroxyl ions cannot remain in the presence of each other uncombined. This has already been referred to (p. 122), in connection 1 Ztschr. phys. Chem., 8, 120. 2 Ibid., 21, 297. 3 Ibid., 22, 237; Amer. Chem. Journ., 19, 91. 4 Ibid., 11,492. 5 Ibid., 5, 16. 6 Ibid., ii, 521. 7 Ibid., 11, 829. 8 Ibid., 14, 155. 9 Ibid., 14, 317. APPLICATIONS OF THE THEORY 209 with the explanation of the phenomenon of neutralization of acids and bases. The great tendency of hydrogen and hydroxyl ions to unite is, undoubtedly, the conditioning cause of a large number of chemical reactions. This will become apparent, when we recall how many chemical reac- tions there are in which a molecule of water is formed. Calculation of Dissociation.-The calculation of disso- ciation from conductivity is comparatively simple. The molecular conductivity of strong acids and bases and salts increases from any moderate dilution up to a dilution of about 1000 litres, where it becomes constant. This maxi- mum constant value of the molecular conductivity means complete dissociation. If the solution is not dissociated at all, the conductivity, and, consequently, the molecular con- ductivity, is zero. To calculate the dissociation of any partially dissociated solution, it is only necessary to deter- mine the ratio between the molecular conductivity of the solution in question and the molecular conductivity of the substance when completely dissociated. Representing the molecular conductivity of the solution of volume v by and the molecular conductivity when the substance is completely dissociated by the per- centage of dissociation a is calculated thus: - Pv a = -• The value of for any dilution of any substance can be ascertained at once by means of the conductivity method. The value of ^=0 for the strongly dissociated electrolytes can alsu be determined directly by the con- ductivity method. It is only necessary to increase the 210 ELECTROLYTIC DISSOCIATION dilution of the solution until the molecular conductivity attains a constant maximum value. This is usually reached at about 1000 litres. If the electrolyte is not strongly dissociated, as in the case of the organic acids and bases, resort must be had to an indirect method of determining the value of This, again, can only be referred to,1 since space will not allow it to be more fully discussed. It will be seen at once from Kohlrausch's law, that the conductivity method can also be used to determine the velocity of ions. In terms of this law the value of /zM, for any compound, is the sum of two constants, the one depending upon the anion, and the other upon the cation. These constants represent, further, the relative velocities of the two ions. Given a compound like hydrochloric acid ; we determine the value of for the compound, by the conductivity method. This is the sum of the velocities of the hydrogen and chlorine ions. We know the velocity of the hydro- gen ion. If we subtract this from the value of /z^ for hydrochloric acid, we obtain the velocity of the chlorine ion. This principle has been used extensively, especially by Ostwald2 and Bredig,3 for determining the relative velocity of ions. The work of Ostwald is typical. He wished to determine the relative velocities of the anions of a number of organic acids. He prepared the sodium salts of each of these acids, and determined the value of ^□0 for these sodium salts, by the conductivity method. The value of /zx for the sodium salts is, from Kohlrausch's 1 Ostwald, Lehrb. d. allg. Chem., II, p. 692. 2 Ztschr. phys. Chem., 2, 840. 3 Ibid. APPLICATIONS OF THE THEORY 211 law, the sum of the velocities of the sodium cation and of the organic anion of the acid. Knowing the velocity of sodium to be 44.5 in terms of the units used, he had but to subtract this number from the for the acid, to obtain the velocity of the anion of the acid. Bredig1 worked on a very large number of organic bases. Here, it was necessary to prepare a salt of the base which would be strongly dissociated, and would give the value of at moderate dilutions. If the hydro- chloric acid salt was used, the velocity of chlorine must be subtracted from the found, and the difference would be the velocity of the organic cation. It is thus a very simple matter to determine the relative velocities of cations and anions, since Kohlrausch discovered the law to which these conform. A number of stoichiometric relations between the com- position and constitution of ions, and their velocities, have been pointed out by Ostwald and Bredig. In general, the more complex the ion the slower it moves. Isomeric anions have very nearly the same velocity, while con- stitution has a marked influence on the velocity of cations. The effect of certain atoms, and also of the symmetry of the molecule, have been worked out by Bredig.2 For details in this connection, his original communication must be consulted. The conductivity of solutions in the different solvents varies very greatly. Solutions in water were thought to have the greatest conductivity, until it was recently shown that solutions in liquid ammonia conduct better than in water. This fact has been confirmed by Goodwin 1 Loc. cit. 2 Loc. cit. 212 ELECTROLYTIC DISSOCIATION and Thompson, in their work on the dielectric constant of liquid ammonia. Next to these solvents, in dissociat- ing power, come formic acid, methyl alcohol, ethyl alcohol, acetone, and finally the oils, hydrocarbons, and ethereal salts. When substances which conduct well in water are dissolved in the last-named solvents, the solutions, as has already been mentioned, show very little conductivity, and are, therefore, very slightly dissociated. The dissociation in solvents whose solutions conduct but little cannot be measured accurately by the con- ductivity method, on account of the difficulty of deter- mining the value of The most strongly dissociated electrolytes are not completely dissociated by these sol- vents, at dilutions which come within the range of the conductivity method. Thus, it is impossible to determine the value of for any substance in ethyl alcohol, by the conductivity method. The values of for any dilution, can be determined in these solvents as well as in water. Some assumption, however, must be made in calculating the value of p^, which may introduce considerable error. The freezing-point method can be used with only a few solvents, because most substances freeze at temperatures which are too far removed from the ordinary to secure accurate measurements. The boiling-point method is, at least theoretically, the freest from objections in such cases, and could be used to measure dissociation, if the experimental difficulties could be overcome. This has been accomplished, in part, by H. C. Jones.1 He has devised a boiling-point apparatus which diminishes 1 Amer. Chern. Journ., 19, 581. APPLICATIONS OF THE THEORY 213 some of the sources of error inherent in other forms, and he has applied this to the measurement of electrolytic dissociation in methyl and ethyl alcohols.1 The results obtained are fairly satisfactory. A comparison of the dis- sociation of a few salts, by water, methyl alcohol, and ethyl alcohol, taken from the paper of Jones, is given in the following table: - Substance Dilution Normal Dissociation in Water Dissociation in Methyl Alcohol Dissociation in Ethyl Alcohol KI, O.I 88% 52% 25% Nai, O.I 84% 60% 33% NHJ, O.I 5°% KBr, O.I 86% 5°% NaBr, O.I 86% 60% 24% NH4Br, 0.2 49% 21% CH3COOK, O.I 83% 36% 16% CH3COONa, O.I 38% M% The dissociation in methyl alcohol is more than half of that in water. The dissociation in ethyl alcohol is less than one-third of that in water. This method can also be applied to the investigation of solutions in other solvents. Thomson's Theory. - Reference has already been made to a theory proposed by J. J. Thomson,2 which connects the dissociating power of solvents with their dielectric con- stants. This theory will now be given, in Thomson's own words. " If we take the view that the forces which hold the atoms in the molecules together are electrical in their origin, it is evident that these forces will be very much diminished when the molecule is close to the surface of, or 1 Ztschr. phys. Chem., Jubelband, van't Hoff. 2 Phil. Mag., 36, 320. 214 ELECTROLYTIC DISSOCIATION surrounded by, a conductor, or a substance like water, pos- sessing a very large specific inductive capacity (dielectric constant). "Thus, let A, B represent two atoms in a molecule, placed near a conducting sphere, then the effect of the electricity induced on the sphere by A will be repre- sented by an oppo- site charge placed at A', the image of A in the sphere. If A is very near the surface of the sphere, then the negative charge at A' will be very nearly equal to that at A. Thus, the effect of the sphere will be practically to neutralize the electric effects of A ; as one of these effects is to hold the atom B in combination, the affinity between the atoms A and B will be almost annulled by the presence of the sphere. Molecules condensed on the surface of the sphere will thus be practically dissociated. " The same effect would be produced, if the molecules were surrounded by a substance possessing a very large specific inductive capacity. Since water is such a sub- stance, it follows, if we accept the view that the forces between the atoms are electrical in their origin, that when the molecules of a substance are in aqueous solution, the forces between them are very much less than they are when the molecule is free, and in a gaseous state." Fig. 9. APPLICATIONS OF THE THEORY 215 The above results show that the solvent with the higher dielectric constant has the higher dissociating power, but that the two are not proportional is seen by comparing the above values for dissociation, with the dielectric constants of these three solvents. Dielectrc Constant Water, 76 to 78 Methyl alcohol, 32.5 to 34 Ethyl alcohol, 25.7 to 26 We have not yet sufficient data to fairly test the value of Thomson's theory. It is so beautiful and simple, and is such a welcome application of the theory of electrolytic dissociation, that we are inclined to hope that it may be of wide-reaching significance. Conductivity at Elevated Temperatures. - We have, thus far, dealt with the conductivity of solutions - of one substance in the presence of another. The question still remains: Do any substances conduct by undergoing de- composition when alone ? Pure substances conduct with- out undergoing decomposition, such as the metals, carbon, etc., which belong to conductors of the first class. But substances which undergo decomposition when they con- duct are called conductors of the second class. Do any pure homogeneous substances belong to the second class ? At elevated temperatures, a number of pure substances are known to conduct like conductors of the second class, or electrolytes. Substances which are liquid at ordinary temperatures do not conduct, and are, therefore, non- electrolytes. It thus seems that heat acts, to a certain extent, like 216 ELECTROLYTIC DISSOCIATION a solvent, converting a substance which does not conduct into one which has the power to carry the current- Electromotive Force. - The theory of electrolytic dis- sociation has also been applied, with beautiful results, to the problem of the source of the electromotive force in primary cells. This could properly be dealt with under the head of electrochemistry, but is so distinctly physical in its nature, that it will be taken up as an example of the application of this theory to physical problems. Strength of Acids and Bases. - The applications of the theory of electrolytic dissociation, described in this sec- tion, we owe almost entirely to Ostwald. Reference has already been made to his extensive investigations of the conducting power of electrolytes, and especially of the organic acids. His law connecting dissociation with dilu- tion has already been deduced. It will be remembered that, if we represent the percentage of dissociation by a, and the dilution of the solution, or number of litres which contains a gram-molecular weight of the electrolyte, by v, the Ostwald dilution law is : a2 = constant, (i - a)v It has already been pointed out, that this law does not hold for the strongly dissociated electrolytes, the strong acids and bases, and the salts; but does apply to the more weakly dissociated compounds, such as the organic acids and bases. Ostwald has shown that the value of the constant for a substance is a characteristic of that substance, and an expression of its chemical activity. APPLICATIONS OF THE THEORY 217 The constant for any substance is determined by meas- uring the conductivity of the substance at several dilutions, calculating the dissociation from these measurements, by means of the formula a = -, already considered ; and knowing a and v, the constant c is calculated from the Ostwald dilution law, just given. An example, taken from the work of Ostwald,1 will make this clear. Formic Acid (HCOOH). ^ = 376 V Mv a cX IOO 8 15.22 4-05 O.O214 i6 21.19 6.63 0.0210 32 29.31 7-79 0.0206 64 40.50 10.78 O.O2O3 128 55-54 14.76 0.0200 256 75-66 20.12 O.OI98 512 102.1 27.10 O.OI97 1024 134-7 35-^o O.OI95 The constants of other acids and bases were deter- mined in exactly the same manner. In this investigation, Ostwald studied between two and three hundred organic acids, and brought out some interesting and important facts in connection with the strength of these acids, and pointed out certain relations between the strength of the acids and their composition and constitution. In the preceding chapter, it was shown that the strength of acids thus determined by conductivity, agreed with that found by other methods, such as the velocity with which they inverted cane-sugar, saponified methyl acetate, 1 Ztschr. phys. Chem., 3, 170, 241, 369. 218 ELECTROLYTIC DISSOCIATION etc. We can, then, regard conductivity as the true meas- ure of the strength of acids. But conductivity is proportional to dissociation, since only ions conduct the current. Therefore, the strength of an acid is conditioned by the amount to which it is dissociated. All acids dissociate into a hydrogen cation, and into the remainder of the molecule which forms the anion. The anion may be simple, consisting of the halogen alone, as with the halogen acids, or it may be very complex, as with the higher members of the homologous series of organic acids. The anion differs in its nature with every acid. The cation of all acids, however, is hydrogen, and, there- fore, the acidity of these compounds is due to this common constituent into which all acids dissociate. The strength of acids, then, resolves itself into the num- ber of hydrogen ions present in their solutions. When we say an acid is strong, we mean that it is largely dis- sociated in solution, or that its solution contains a large number of hydrogen ions. And this leads us to an inter- esting conclusion pointed out by Ostwald. All acids are completely dissociated at infinite dilution; therefore, at infinite dilution all acids have the same strength. Exactly the same remarks apply to bases. Bases dissociate into a hydroxyl anion, and the remainder of the compound forms the cation. The latter may be simple, as with the alkalies, or may be very complex, as in the organic bases. The common constituent of bases is, then, the hydroxyl anion, and basicity is due to the presence of this ion. A strong base means one which is largely dissociated, or in whose solution there is a large number of hydroxyl ions. But all bases, like all acids, are completely disso- APPLICATIONS OF THE THEORY 219 ciated at infinite dilution. Therefore, all bases have the same strength at infinite dilution. These generalizations for acids and bases are of very- wide significance, and greatly simplify and correlate phe- nomena, which have been hitherto regarded as more or less disconnected. Relations between Acidity and Composition and Constitu- tion. - Some of the relations between acidity and com- position and constitution will be considered. Hydrochloric, hydrobromic, and hydriodic acids are to be ranked among the strongest acids. They have very nearly the same strength, as is shown by the fact that they conduct to just about the same extent. Hydrofluoric acid is much weaker, as is shown by its comparatively small conductivity. These facts are established by the following results: - s: - HCl HBr HI HF V Mv 2 331 341 341 - 4 343 354 353 27.8 8 355 361 360 33-6 32 369 373 372 55-8 4096 376 372 373 - Hydrocyanic acid conducts but little better than pure water, and is, therefore, one of the weakest acids. When sulphur is introduced into this acid, we have, in sulpho- cyanic, one of the strongest acids. HCN HCNS V 2 - 326 4 o-33 337 8 0.38 - 32 0.46 358 220 ELECTROLYTIC DISSOCIATION Hydrocyanic acid, judged by its conductivity, can, there fore, scarcely be regarded as an acid, while sulphocyanic acid is nearly as strong as hydrochloric acid. The introduction of oxygen usually increases the acidity, that is to say, forms a compound which is more dissociated by the solvent. This is by no means general. Take the acids of phosphorus; the more oxygen there is present the weaker the acid, as is seen in the following results : - h3po2 h2po3 h3po< & Mr Mr Mr 2 131 121 60 8 194 J75 90 64 293 274 183 256 330 316 262 1024 344 336 320 The order of strength of some of the more common mineral acids is as follows, expressed in terms of hydro- chloric acid = 100 : - HC1 100 HBr ioi HNO3 99.6 HI 92 H2SO4 65.1 h3po4 17 Turning to the organic acids, we find a number of rela- tions established. The introduction of chlorine into the fatty acids increases the acidity. Take the chlorine sub- stitution products of acetic acid : - CH3C00H CH2C1COOH CHC12COOH CC13COOH V IM; IM; IM; 2 - 21.2 109 245 32 8.65 73-4 256 327 128 16.99 126.0 308 336 1024 46.OO 236.0 342 339 APPLICATIONS OF THE THEORY 221 The introduction of oxygen into an acid, forming the hydroxyl group, increases the acidity. This is seen from the following example : - Succinic Acid Malic Acid Tartaric Acid C2H4(COOH)2 C2H3(OH)(COOH)2 C2H2(OH)2(COOH)2 V Pv 1^ 2 3-73 8-45 - 32 15-7 26.6 58.1 64 22.1 50.8 79-4 512 58.6 126.0 183.0 4096 142.0 255-° 34I-O The effect of introducing one and two hydroxyl groups is shown in these examples. In the aromatic series we have to take into account not simply the nature of the group, but the position which it takes, whether ortho, meta, or para. The introduction of oxygen into benzoic acid, forming a hydroxy acid, has a very different influence on the acidity, depending upon the position occupied by the oxygen. Benzoic Acid Salicylic Acid Af-OxYBENZOIC T'-Oxybenzoic (0) Acid Acid C6H5COOH C6H4(OH)COOH C6H4(OH)COOH C6H4(OH)COOH V Me 64 22.1 8l.2 25-5 i4-3 256 42.3 I37-O 47-7 28.3 2048 IO4.O 255-° 114.0 73-o Hydroxyl in the ortho position increases the acidity very markedly. In the meta position it has but a slight effect, while in the para position it actually lessens the acidity. The introduction of the nitro group has a very different influence, depending upon its position. 222 ELECTROLYTIC DISSOCIATION Benzoic Acid O-Nitrobenzoic M-Nitrobenzo ic P-Nitrobenzoic Acid Acid Acid V IM) IM> IM) IM> 64 22.1 *59 47-5 - Si2 57-9 263 11 7.0 123 2048 104.0 301 19O.O T95 The nitro group in the ortho position has the greatest acidifying power, while in the para position it has some- what greater power than in the meta. The introduction of more and more nitro groups, in general, increases the acidity. Thus, take phenol, which is a very weak acid. Introduce one nitro group, we have its acidity increased. Introduce a second nitro group, and its acidity is still further increased. Introduce the third nitro group, and we have picric acid, which is nearly as strong as the mineral acids. As the unsaturated acids contain less and less hydro- gen, the affinity increases. Thus, acrylic acid, C3H4O2, is stronger than propionic, C3H6O2. The effect of constitu- tion can be seen by studying the acidity of maleic and fumaric acids, which have the same composition. Maleic Acid Fumaric Acid V 32 166 58.8 512 305 179.O 2048 338 275.O 8192 339 337-o Maleic is much stronger for the greater concentrations, but never has a molecular conductivity greater than a monobasic acid. Fumaric, at high dilution, has a greater conductivity than a monobasic acid. The second hydro- APPLICATIONS OF THE THEORY 223 gen takes part in the conductivity, before the first has reached a maximum. Take citraconic acid and two of its isomeres: - Citraconic Itaconic Mesaconic V P-v 8 56-4 II.7 25-5 5'2 250.0 84.7 162.0 4096 322.0 186.O 291.0 From its conductivity, citraconic acts like a monobasic acid. In itaconic one carboxyl is weaker than the other, while mesaconic conducts itself like a dibasic acid, whose hydrogen atoms are nearly or quite equivalent. By a careful study of the conductivity of acids, as Ostwald has shown, some light can be thrown on their constitution. The introduction of the amido group weakens the acid properties, as would be expected from the basic nature of this group. Bases. - Some work has been done on strength of bases by Ostwald,1 Bredig,2 and others. But these have not been worked up as thoroughly as the organic acids. The conductivities of the strong bases, like those of the strong acids, reach a maximum at a dilution of about one thousand litres. The value of for the bases is less than for the acids, since the velocity of the hydroxyl ion is only about I/O, while the velocity of the hydrogen ion is about 325 at 25°C. The strong bases include the hydroxides of the alkalies and alkaline earths. Ammonia is sometimes regarded as a strong base, but it is not. 1 Journ. prakt. Chem. (2). 33, 352. 2 Ztchr. phys. Chern., 13, 289. 224 ELECTROLYTIC DISSOCIATION It was found that the conductivity of ammonia is slight, compared with that of, say, potassium hydroxide. Other reactions with ammonia were also studied, such as the velocity with which it would effect reactions, and these results confirmed those from conductivity. Ammonia is, then, a comparatively weak base. We will now compare the strength of ammonia with that of the substituted ammonias: - nh3 nh2ch3 nh2c,h5 nh2c3h7 nh2c4h9 V Mt; Mv Mt; Mr Mv 2 I.46 6.41 6.06 - - 32 6-13 26.4 26.8 23-7 i9-5 256 17.8 64.8 66.9 59-2 49-2 1024 37-o 108.0 11 2.0 97-7 82.3 Thus, all monamines are stronger than ammonia. We will examine some of the di- and triamines. NH(CH3)2 NH(C2H5)2 N(CH3)3 N(C2H6)3 V 2 6.88 - 2.63 4.76 128 55-9 65.8 23-7 49-7 1024 120.7 130-3 56.8 11.6 Dimethylamine is only a little stronger than methyl amine, and, similarly, diethylamine is but little stronger than ethylamine. The triamines are not as strong as the diamines. The results for one of the tetramines are given: - (C2Hb)4NOH •v i6 176.2 128 186.4 1024 182.6 APPLICATIONS OF THE THEORY 225 and these show that the compound is a fairly strong base; indeed, much stronger than either of the other amines. The effect of introducing two amido groups into a compound can be seen from ethylene diamine. C2H4(NH2), V Mu 32 8.90 256 23.16 1024 4O.91 It is surprising that the ethylene diamine is much weaker than the ethylamine, since two amido groups should increase the basic property. This suggests the acids of phosphorus, where the weaker acid is the one containing the greater number of oxygen atoms. A large number of relations between composition and constitution and chemical activity have been worked out, but those already given suffice to show the nature of the relations which have been discovered. No generalization of very wide significance has been reached, and exceptions are usually present to any general statement which may be made. This work resembles, in many respects, the earlier physical chemical investigations, which had to do with problems of this same general type. Although many exceptions appear in work of this kind, nevertheless, its value is great, since it is only step by step that we arrive at the truth, and a great many steps are required to arrive at truth in its broader relations. We will leave here the chemical side of modern physical chemistry, and turn to the application of the theory of electrolytic dissociation to a physical problem. 226 ELECTROLYTIC DISSOCIATION APPLICATION OF THE THEORY OF ELECTROLYTIC DISSOCIA- TION TO A PHYSICAL PROBLEM The theory of electrolytic dissociation has not been applied as widely to physics as it has been to chemistry. This, from the nature of the case, was to be expected. Ions are the main, if not the sole factors in chemical activity; while molecules are generally the units with which' the physicist has to deal. That chapter of physics, which is most concerned with ions, is the one which has to do with electrical phenomena, and, especially, with electricity as generated in primary cells. Here, one of the essential agents is a solution of some electrolyte, or solutions of more than one electrolyte, and these solutions are always more or less dissociated. The ions are, thus, essential to the action of such cells, and here our theory bears directly upon a problem which is, indeed, a physical one. THE SEAT OF THE ELECTROMOTIVE FORCE IN PRIMARY CELLS The question as to the origin of the electromotive force in primary cells is as old as the cell itself. Volta con- cluded that the main source of the electromotive force was at the point of contact of the two metals. Others have supposed that the contact of the two solutions was the chief source of the electromotive force. Others, again, sought for the electromotive force of such elements, at the points of contact of the electrodes with the electrolytes. The question was unsettled when the theory of electro- lytic dissociation was proposed. We shall see that this APPLICATIONS OF THE THEORY 227 theory has furnished us with a solution to this problem, and we now have a pretty clear conception of what takes place in the primary cell. The application of the van't Hoff laws of osmotic press- ure, and the Arrhenius theory of electrolytic dissociation, to explain the action of the cell, we owe to Nernst,1 who did this epoch-making work while in the laboratory of Ostwald in Leipzig. It will be assumed that the reader is familiar with the method of measuring the electromotive force of elements. The method, in general, is to balance the cell in ques- tion against one of standard electromotive force, such as the Clarke element, by means of a convenient resistance box, and using the Lippmann electrometer to determine the point of equilibrium. We will not spend more time upon this experimental side of the problem, but proceed at once to the calculation of the electromotive force of elements. Calculation of Electromotive Force from Osmotic Press- ure. - The method of calculating electromotive force from osmotic pressure is given essentially as deduced by Ostwald2 from the work of Nernst. If we allow a substance to pass, isothermally, from one condition to another, the maximum amount of ex- ternal work is always the same, regardless of how this takes place, whether osmotically, or electrically, or in any other way. If we know the maximum external work which is obtainable from a process, we know the amount of electrical energy; and, as we shall see, the electro- motive force is calculated directly from the* electrical 1 Ztschr. phys. Chem., 4, 129. 2 Lehr. d. allg. Chem., II, p. 825. 228 ELECTROLYTIC DISSOCIATION energy. The first step is, then, to determine the maximum external work which is obtainable in a given process. This can be done by allowing the substance to pass, at constant temperature, in a reversible manner, from one condition over to the other. • Given a gas under a pressure px, and volume v, and allow it to expand isothermally to a pressure /2. When a gas expands isothermally it takes up heat, and gives it up as volume energy. The energy set free under these con- ditions is: - Pi - §vdp. Pi But pv = RT, where R is the gas constant and T the absolute temperature, whence the above expression be- comes for gram-molecular weights: - Pi - RT J P Pi which expresses the volume energy obtained under the condition. This becomes on integration: - A'7'ln*-' Pi This amount of energy, which is converted into work by an ideal gas in passing from pressure px to pressure p^ is exactly equal to the work obtained from an ideal solution * In is natural logarithm. APPLICATIONS OF THE THEORY 229 under the same conditions. That is, a solution of volume v passing, isothermally, from an osmotic pressure /j to an osmotic pressure /2. But with the movements of the ions, we have the move- ments of the electrical charges which they carry. And, from what has been said, the amounts of work correspond- ing to the movements of the ions can be transformed into electrical energy. We have, then, shown, thus far, how to calculate the maximum external work obtainable, when a solution of osmotic pressure passes isothermally and reversibly over to osmotic pressure /2, and the relation between this work and the electrical energy obtainable. But knowing the electrical energy, how can we deter- mine the electromotive force ? Electrical energy, like every other manifestation of energy, can be factored into an intensity and a capacity factor. The intensity factor of electrical energy is the electromotive force, or potential, and the capacity factor the amount of electricity. If we call the former tf, and the latter ^0, we have the energy electric ee = ire^. If we know ee, we can calculate 7r at once, since is known from Faraday's law. Knowing the quantity of ions which pass from one osmotic pressure over to the other, we know the amount of electricity ; knowing we calculate tt. Let us deal with a gram-molecular weight of univalent ions. These will carry 96,540 coulombs of electricity, and this quantity we will now designate by r0. If the ions are bivalent they will carry twice as much; if trivalent three times, and so on. Let us represent the valence of the ions by v; then a gram-molecular weight will carry veQ 230 ELECTROLYTIC DISSOCIATION amount of electricity. Suppose a gram-molecular weight of these ions is charged tf potential. The amount of electrical energy required to effect this charge is: - ttw0. But this electrical energy is equal to the osmotic, calcu- lated above, where a gram-molecular weight was taken into account. We have: - 7FW0 = R T In or . 0 A ^rin^l A 7T - LA. This is the fundamental equation for calculating the electromotive force of elements, from the osmotic pressures of the electrolytes around the electrodes. This equation has been very much simplified by Ostwald,1 by introducing numerical values wherever it is possible. R = 2 calories, and i calorie = 4.18 x io7 ergs. T, the absolute temperature, can be taken as 29O°C. for the aver- 7? jT age conditions. The constant = 0.0251 volt, since _ ^0 volt x coul = 10' ergs. The above equation then becomes: - " A or in case the ions are univalent: - 1 A 7r = 0.0251 In - • A 1 Lehrb. d. allg. Chem., II, p. 827. APPLICATIONS OF THE THEORY 231 Thus far we have been using the natural logarithm obtained in the process of integration, which we have writ- ten In. It is far more convenient in practice to use the Briggsian. To pass from the former to the latter we must divide the above constant by 0.4343, when we obtain 0.058. The final expression of the general formula for calcu- lating the electromotive force of an element, from the osmotic pressure of the electrolytes around the electrodes, is then : - 7T = O.O58 10g where log is the Briggsian logarithm. If the valence of the ion is greater than one, this must be divided by the valence. Before attempting to apply this expression to any concrete cases, we must examine another conception introduced by Nernst. Electrolytic Solution-tension.-We are perfectly famil- iar with the fact that when a solid or liquid is evaporated, the molecules pass into the space above the liquid; and equilibrium is established, for a given temperature, when the vapor exerts a certain definite pressure. This press- ure is designated as the vapor-tension, or vapor-pressure, of the substance in question. Says Nernst:1 "If, in accordance with van't Hoff's theory, we assume that the molecules of a substance in solution exist also under a definite pressure, we must ascribe to a dissolving substance in contact with a solvent, simi- larly, a power of expansion, for here, also, the molecules are driven into a space, in which they exist under a certain 1 Ztschr, phys. Chem., 4, 150. 232 ELECTROLYTIC DISSOCIATION pressure. It is evident that every substance will pass into solution until the osmotic partial pressure of the molecules in the solution is equal to the ' solution-tension ' of the substance." Nernst thus introduced the conception of solution-ten- sion ; and, at the same time, called attention to the close analogy between evaporation and solution, which can be seen only through a knowledge of the osmotic pressure of solutions. The metals, like many other substances, have the possibility of passing into solution as ions. Every metal, in water, has, then, a certain solution-tension pecul- iar to itself, and we will designate this by P. If we dip a metal into pure water, let us see what will take place. In consequence of the solution-tension of the metal, some ions will pass into solution. When metallic atoms pass over into ions, they must secure positive electric- ity from something. They take it from the metal itself, which thus becomes negative. The solution becomes positive, because of the positive ions which it has received. At the plane of contact of the metal and solution, there is formed the so-called electrical double layer, whose exist- ence was much earlier recognized by Helmholtz.1 The positively charged ions in the solution and the negatively charged metal attract one another, and a difference in potential arises. The solution-tension of the metal tends to force more ions into solution, while the electrostatic attraction of the double layer is in opposition to this. Equilibrium is established when these two forces are equal. Since the ions carry such enormous charges, the number which will pass into solution before equilibrium is 1 Wied. Ann., 7, 337 (1879). APPLICATIONS OF THE THEORY 233 established is so small that they cannot be detected by any ordinary method. When we are dealing with a metal immersed in pure water, it is evident that the difference in potential which obtains in the double layer is conditioned only by the magnitude of the solution-tension of the metal in question. If we dip a metal of solution-tension P, into a solution of one of its salts, the case is not quite as simple. Let the osmotic pressure of the metallic ions in the solution of the salt be /, then either of three conditions may exist. The solution-tension may be greater than the osmotic pressure, less than the osmotic pressure, or just equal to it. We may have : - P>p- (i) P<P- (2) P=P- (3) Let us first take case No. I, where a metal of solution- tension P is immersed in a solution of one of its salts, in which the osmotic pressure p of the metallic ions is less than its own solution-tension. At the moment the metal touches the solution, a number of metallic ions, which always carry a positive charge, will pass into solution. These ions have carried positive elec- tricity from the metal into the solution, and the metal has thus become negative, the solution positive. At the places where the metal and solution come in contact, the double layer is formed, due to the attraction of the opposite charges. "This double layer has a component of force, which acts at right angles to the plane of contact of the metal 234 ELECTROLYTIC DISSOCIATION and solution, and tends to drive back the metallic ions from the electrolytes to the metal. It acts in direct opposition to the electrolytic solution-tension." 1 The condition of equilibrium is reached when these two opposing forces just equalize one another; and the final result is the existence of an electromotive force between the metal and the solution, the metal being negative, the solution positive. It is clear that a metal cannot throw as many ions into a solution of its salt, as into pure water, because the osmotic pressure of the metallic ions already in the solu- tion acts against the solution-tension of the metal. Let us now take the second case; where the solution- tension of the metal is less than the osmotic pressure of the metallic ions in the solution. Metallic ions will separate from the solution upon the metal. When a metallic ion passes over into an atom it gives up its positive charge, and in this case it gives it up to the metal, which becomes positive. The solution, having lost some of its positively charged ions, becomes negative. At the points of contact of solution and metal, we have again the electrical double layer, but this time the metal is positive and the solution negative, which is exactly the reverse of the case first con- sidered. Metal ions will separate from the solution until the electrostatic component of force of the double layer, at right angles to the plane of contact of metal and solution, is just equal to the excess of the osmotic pressure over the solution-tension. Equilibrium is established when the sum of the solution-tension of the metal and this component of force is just equal to the osmotic pressure of the metallic 1 Ztschr. phys. Chem., 4, 151, APPLICATIONS OF THE THEORY 235 ions in the solution. An electromotive force exists here, also, between the metal and the solution, but in the reverse direction from the case first considered. The third case is where the solution-tension of the metal is just equal to the osmotic pressure of the metallic ions in the solution. Just as soon as the metal touches the solution, equilibrium is established. Ions neither dis- solve from the metal, nor separate from the solution. There is no double electrical layer formed, and there is no difference in potential between the metal and the solution. If now we inquire which metals have high, and which low solution-tensions, we will find that magnesium, zinc, aluminium, cadmium, iron, cobalt, nickel, and the like, are always negative when immersed in solutions of their own salts. This means that the solution-tension of the metal is always greater than the osmotic pressure of the metal ion, in any solution of their salts which can be prepared. If, on the other hand, we take gold, silver, mercury, copper, etc., we usually find the metal positive when immersed in a solution of its salt. This means that the solution-tension of the metal is so small, that it is less than the osmotic pressure of the metallic ion in the solu- tion. When a very dilute solution of salts of these metals is prepared, the osmotic pressure of the metallic ion may become less than the very slight solution-tension of these metals ; and then the metal would be negative with respect to its solution. We have, thus far, spoken chiefly of the solution-tension of metals, which tends to drive the metal over into cations. Substances which can pass over into anions have also a 236 ELECTROLYTIC DISSOCIATION solution-tension, as is pointed out by Le Blanc.1 If the chlorine ions in a solution had an osmotic pressure which was greater than the solution-tension of chlorine, the chlo- rine ions would pass over into ordinary chlorine. But Le Blanc adds, that, as far as we know, all substances which can yield negative ions have a high solution-tension. Constancy of Solution-tension. - It was supposed for a time, that the solution-tension of a metal is a characteristic constant for the substance. This view was held by Ostwald and developed in his Lehrbuch. On page 852 it is stated that "the value P, of the electrolytic solution-pressure, is a constant peculiar to the metal, which depends upon the temperature only, and generally increases with increasing temperature." So far as we know, this holds for a given solvent, but does not apply to different solvents.2 Jones has found that the solution-tension of metallic silver, when immersed in an alcoholic solution of silver nitrate, is only about one- twentieth of that in an aqueous solution. We can, there- fore, regard solution-tension as a constant only for any given solvent in which the salts of the metal are dissolved. Indeed, this is what we would expect, when we consider that nearly every substance dissolves differently in, or has a specific solution-tension towards, every solvent. If the substances which dissolve readily in solvents, vary so greatly from solvent to solvent, as we know they do, why should not substances which are only slightly soluble, such as the metals, show this same difference ? Calculation of the Difference in Potential between Metal 1 Lehrb. der Elektrochemie, p. 121. 2 Ztschr. phys. Chem., 14, 346; Phys. Rev., 2, 81. APPLICATIONS OF THE THEORY 237 and Solution. - The difference in potential between a metal of solution-tension P, and a solution of one of its salts in which the metal ion has an osmotic pressure /, can be calculated as follows. When a substance of solution-tension P is converted into ions of osmotic pressure P, no work is done. There- fore, to convert a substance of solution-tension P into ions of osmotic pressure /, the maximum work to be obtained is the same as that obtained by transferring the ions from osmotic pressure P to osmotic pressure /. Now we have seen that the gas laws apply to the osmotic pressure of solutions, and the amount of work can be calculated from a gas in passing from gas pressure P to gas pressure /. If we deal with a gram-molecular weight, we have seen (p. 228) this to be: - 7? Tin -• We have seen that this osmotic work is equal to the electrical work for an isothermal transformation. The electrical work is the potential times the amount of elec- tricity. If we are dealing with gram-molecular quantities, it is 7FW0. Equating these two values, we have : - irve^ = RT In -> p or, if the ions are univalent, v = 1, when we have: - RT. P nr = In - ^0 / 238 ELECTROLYTIC DISSOCIATION J? T Now we know, from page 230, that =0.0251 volt. ^0 Passing from natural to Briggsian logarithms, this becomes 0.058 volt. The potential between metal and solution is, then, when T= 2900:- 7T = O.O58 We have learned, thus far, how to calculate the electro- motive force of elements from the osmotic pressures of the solutions around the electrodes; and also how to cal- culate the potential between a metal and the solution of one of its salts in which the metal is immersed. With these two conceptions in mind, we will now study a few elements to see how these principles are applied. Types of Cells. - If the chemical process in the cell remains the same during the time it is closed, the cell is constant. If the chemical process changes, it is inconstant. Constant elements differ among themselves. Through some of these we can send a current in the opposite direc- tion without changing their electromotive force. This class of constant elements is termed reversible. This applies to elements in which the electrodes are immersed in solutions of their salts. Take as an example the Daniell element. This consists of a bar of zinc immersed in a solution of zinc sulphate, and a bar of copper in a solution of copper sulphate. When the current is passed in the opposite direction through this cell, its nature is not changed. The normal action is that the zinc dissolves and copper separates. When a current is passed in the opposite APPLICATIONS OF THE THEORY 239 direction, copper dissolves and zinc separates. But neither process changes the nature of the cell. Concentration Elements of the First Type. - We will first consider a very simple type of a reversible element, the two electrodes being of the same metal, and are immersed in solutions of the same salt of that metal, the solutions having different concentrations. To take a con- crete example : Two bars of metallic zinc are immersed in solutions of zinc chloride, the one bar in a tenth-normal solution of the salt, the other in a hundredth-normal solu- tion. The two solutions are connected by a tube filled with either solution. When the two zinc bars, which are the electrodes, are connected externally, the current flows, and we have an element. Ostwald defines a cell or element as any device in which chemical energy is converted into electrical. The only difference between the two sides of this element is in the concentration of the electrolytic solutions. The element is, therefore, termed a " concentration element." Further, since the salt of the metal is soluble, this is termed a " concentration element of the first class," to distinguish it from other concentration elements which will be taken up later. Take the example given above, of two bars of zinc in two solutions of zinc chloride of different concentrations. The action of the cell is such as to make the two solutions become more and more nearly of the same concentration. The more dilute solution becomes more concentrated, and the more concentrated more dilute, until when the two become equal the element ceases to act. Zinc then passes into solution in the more dilute solution, and zinc ions 240 ELECTROLYTIC DISSOCIATION separate as metal on the bar from the more concentrated solution. The electrode in the more concentrated solution is always positive, since metallic ions are giving up their positive charges to it, and separating as metal upon it. The electrode in the more dilute solution is negative, because ions are passing from it into the solution, and carrying with them positive charges, which come from the electrode. In an element of this kind, the current always flows on the outside, from the electrode which is immersed in the more concentrated solution. The action of this cell is just what we would expect. The solution-tension of the zinc is the same on both sides of the cell. The osmotic pressure of the zinc ions is, of course, greater in the more concentrated solution. The osmotic pressure, which works directly against the solu- tion-tension, will cause the ions to separate from the solution in which this pressure is the greater. The electromotive force of such an element would be the difference in the potential upon the two sides of the cell. RT , P RT , P RT , ir = -- In In - = In - • Pl P\ veo Pl Here v is the valence of the cation, and /2 the osmotic pressures of the zinc ions in the two solutions. This, however, does not take into account the changes in the concentrations of the solutions, which are taking place while the current is passing. If eQ electricity passes from the electrode into the electrolyte, a gram-molecular weight of univalent cations separates from the electrode, dissolves, and increases by unity the concentration around this electrode. But, at APPLICATIONS OF THE THEORY 241 the same time, cations are moving from this electrode, with the current, over towards the other electrode. The amount depends upon the relative velocities of anion and cation. If we represent the relative velocity of cation by c, and of anion by a, the number of the cations which will £ move over with the current is The increase in the c + a- concentration, due to a gram-molecular weight of cations passing into solution, is then : - c a i c T ci c 4- ci This factor is to be multiplied into the former equation to obtain the osmotic work, which can then be equated to its equal, the electrical energy. Let represent the number of ions in the electrolyte. Taking into account both sides of the cell, we have : - 2 a UiR T , 7T = In -; c + a /2 2 a nt , A or, 7T = - 0.0002 7^ log - • c + a v ° p^ According to this formula, the only variables are px and p^ the osmotic pressures of the cation in the two solutions around the electrodes. The electromotive force of such elements should depend only upon the relative osmotic pressures of the solutions, and not upon the absolute osmotic pressures. This has been found to be true. The electromotive force should also be independent of the kind of zinc salt used, provided the salt is soluble, and yields the same number of zinc ions in each solu- tion as the salt in question. Thus the chloride could be replaced by the bromide, iodide, nitrate, etc., of such 242 ELECTROLYTIC DISSOCIATION concentration that the osmotic pressure of the zinc ions remained the same, and the electromotive force of the element should remain unchanged, and such again is the fact. The reason for this will be seen at once by examin- ing the last equation; since it is only the osmotic pressure of the cations which comes into play - the anion having nothing whatever to do with the electromotive force of the element. The electromotive force of a number of elements of the type we are considering has been measured, and to within the limits which could reasonably be expected has been found to agree with that calculated from the above equation. To calculate the electromotive force, a number of quantities must be measured, c and a, the relative velocities of cation and anion, must be determined ; simi- larly, px and the osmotic pressures of the cations in the solutions, must be ascertained by indirect methods, which involve the measurement of the dissociation of these solutions. Since each of these processes introduces an error of greater or less magnitude, we could not expect a very close agreement between the electromotive force as measured and as calculated. When we take all of these facts into account the agreement is often surprisingly close. The following results, obtained by Moser, for solutions of copper sulphate, with copper electrodes, are cited by Ostwald.1 The concentrations of solutions, I and II, are the number of parts of water to one part of copper sulphate. tf is the electromotive force expressed in thousandths of a Daniell cell. The unit is o.ooi i volt. i Lehrb. d. allg. Chem., II, p. 833. APPLICATIONS OF THE THEORY 243 I II it Observed 7T Calculated 128.5 4.208 27 27-4 6-352 25 23.8 8.496 21 21.4 17.07 16 15-8 34-22 10 io-3 The concentration of one solution was maintained con- stant throughout, and that of the other varied at will. The agreement in these cases is very satisfactory. Concentration Elements of the Second Type. - The char- acteristic of the element which we have just been consid- ering is that the metal is surrounded by one of its soluble salts. We may also have concentration elements in which the metal is surrounded by one of its insoluble salts; thus, silver surrounded by silver chloride. In the latter case we must have present, in addition, a soluble chloride; and the soluble chloride must be of different concentra- tions on the two sides of the cell. The element would consist then of a bar of silver, surrounded by solid silver chloride, and over this a solution of some chloride, say potassium chloride; and on the other side, a bar of silver surrounded by solid silver chloride, and over this a solu- tion of potassium chloride, of different concentration from that used on the side first described. This element is termed a concentration element *of the second class. The action of this cell will be such as to dilute the more concentrated solution of potassium chloride, and to concentrate the more dilute solution. Silver dissolves from the electrode surrounded by the more concentrated potassium chloride, and the ions of silver unite with the 244 ELECTROLYTIC DISSOCIATION chlorine ions, and solid silver chloride is formed. The potassium ions move with the current over to the other side of the element, and form potassium chloride with some of the chlorine which was there in combination with silver as silver chloride. This silver then separates as metal upon the electrode. In this way the more concentrated potassium chloride becomes more dilute, and the more dilute becomes more concentrated. The electrode immersed in the more concentrated po- tassium chloride is the one from which silver ions separate; therefore, this is the negative pole. The pole in the more dilute solution of potassium chloride, receiving silver ions, is positive. The current then flows upon the outside, from the pole in the more dilute potassium chloride, to the pole in the more concentrated. This is exactly the reverse of what takes place in a concentration element of the first type. There, as we have seen, the current flows on the outside, from the pole surrounded by the more concentrated electrolyte. The electromotive force of a concentration element of the second type is calculated in a manner perfectly analogous to that employed with concentration elements of the first type. The electromotive force it is equal to the dif- ference in the potential at the two poles : - RT P RT ; P RT . 7t - In m - = In - • A A Pi As in the case of the concentration element of the first class, this does not take into account the changes in the concentrations of the electrolytes which are taking place. At the anode the metallic silver is passing into solution, APPLICATIONS OF THE THEORY 245 and when electricity is allowed to flow, a gram- molecular weight of the silver will pass over into ions - will dissolve. This will change the concentration of the potassium chloride around this pole by - I. But at the same time potassium is moving with the current, and chlorine in the opposite direction, and this further changes the concentration. If we represent the relative migration + - • velocities of K and Cl, respectively, by c and a, the total change in concentration around the anode will be: - a c - 1 _| .- - - c + a c + a The change in concentration around the cathode would be, of course : - c + --- c + a This factor: - --> c + a must be multiplied into the above expression for electro- motive force; when taking into account both sides of the cell, we have: - 2 c v jR T , p. tv = In c + a ve^ pi 2 c nl -7-1/1 % = 0.0002 T log-; c + a v 'pi where is, as before, the number of ions yielded by the electrolyte, and v the valence of the cation. The electromotive force of a number of such elements has been measured by Nernst.1 . Mercury was used as the metal, since it could easily be obtained in pure condition. 1 Ztschr. phys. Chem., 4, 159. 246 ELECTROLYTIC DISSOCIATION It was covered with an insoluble salt of mercury, and the soluble electrolyte then added. The chloride, bromide, acetate, and hydroxide of mercury were used, and the soluble electrolyte on both sides of the cell must con- tain the same anion as the salt of mercury which was employed. If the chloride was used, the soluble elec- trolyte must be a chloride. If the hydroxide of mercury was employed, a soluble hydroxide must be used, and so on. Some of the combinations which were made and meas- ured by Nernst are given in the following table. The first column contains the soluble electrolyte which was em- ployed. Columns II and III give the concentrations of the solutions of this electrolyte on the two sides of the cell. " 7r calculated " is the electromotive force calculated from the preceding formula, and " tt found " is the electromotive force of the combination, as measured by Nernst. I Soluble Electrolyte II Concentration i III Concentration 2 7T Calculated IT Found HC1 O.IO5 O.Ol8 0.071 7 O.O71O HC1 O.I 0.01 O.O939 O.O926 HBr 0.126 0.0132 O.O917 O.O932 KC1 0.125 0.0125 O.O542 O.O532 NaCl 0.125 0.0125 0.0408 0.0402 LiC) O.I 0.01 O.O336 O.O354 NH4C1 O.I 0.01 O.O531 0.0546 NaBr 0.125 0.0125 0.0404 O.O417 CH3COONa 0.125 0.0125 0.0604 0.0660 NaOH 0.235 0.030 O.O183 0.0178 KOH O.I 0.01 0.0298 O.O348 nh4oh 0.305 0.032 O.O188 O.O24 APPLICATIONS OF THE THEORY 247 Liquid Elements. - It has long been known that there may be differences in potential at the contact of two solu- tions of electrolytes. This can be shown by constructing an element in which the two electrodes are of the same metal, and immersed in the same solution of the same electrolyte. There can, therefore, be no difference in po- tential between the two metals, nor- between the metals and electrolytes, for the tensions between the metals and electrolytes are the same on the two sides, and act in direct opposition to one another. If two solutions of electrolytes of different concentrations are introduced into the circuit between the solutions in which the electrodes are im- mersed, we will have an element with a certain definite electromotive force. A typical liquid element would be the following: - Mercury-mercurous chloride. - potassium chloride, io -^-potassium chloride. IOO hydrochloric acid. IOO - hydrochloric acid. - potassium chloride, io Mercurous chloride-mercury. Theory of the Liquid Element. - The first satisfactory theory of the liquid element we owe to Nernst.1 What is the 1 Ztschr. phys. Chem., 4, 140. 248 ELECTROLYTIC DISSOCIATION source of the differences in potential in liquid elements ? That differences in potential should exist in electrolytes there must be a lack of uniform distribution of ions. The region which is positive must contain an excess of cations, and that which is negative, an excess of anions. The cause of this lack of uniform distribution of ions is to be found in the different 'velocities with which the different ions diffuse. Take the case of a solution of hydrochloric acid in con- tact with pure water. The hydrogen and chlorine ions in the solution of the acid are present in the same number. They are, therefore, under the same osmotic pressure, and are driven with the same force into the water. But they move with very different velocities, from regions of higher to those of lower osmotic pressure. Hydrogen is, as we have seen, the swiftest of all ions, and moves very much .faster than chlorine. It will thus diffuse into the water .more rapidly than chlorine, and will tend to separate from ithe chlorine. But the positive ions cannot separate from the negative ions, without producing a separation of the two kinds of electricity. There will result, therefore, elec- trostatic attractions between the layers, which will retard the hydrogen ions and accelerate the chlorine ions, until the two have the same velocity. Differences in potential will result; and always in the sense, that the water or the more dilute solution will have the sign of the swifter ion. Hydrogen being the swiftest of all ions, water, or the more dilute solution of acid, is always positive with respect to the more concentrated. Next to hydrogen, in order of velocity, comes hydroxyl. Water, or the more dilute solution of a base, must, there- APPLICATIONS OF THE THEORY 249 fore, always be negative with respect to the more con- centrated. Nernst has shown not only how it is possible to account, qualitatively, for the differences in potential between elec- trolytes, but has furnished us also with a method of calcu- lating these differences quantitatively. Given two solutions of different concentrations of an electrolyte like hydrochloric acid, which is composed of a univalent cation and a univalent anion. Let the velocity of the cation be c, and that of the anion a. Let px be the osmotic pressure of both ions in the more concentrated solution, and /2 the osmotic pressure in the more dilute. If electricity is passed from the more concentrated to the more dilute solution, of a gram-equivalent of c ci cations will move with the current, and of a gram- c 4- a equivalent of anions will move against the current. c • of cations have moved from a region of greater to c + a one of less osmotic pressure. The work is: - --/?rin c + a But -O- of anions have moved from a region of lower C 4" Cl into one of higher osmotic pressure. The work done upon them is: - c + a p^ The total gain is the difference between these two: - -?RT In C 4- a p2 250 ELECTROLYTIC DISSOCIATION Equating this against the electrical energy 7r^0, we have:- c - a RT /. tt = - In --; c + a €q /2 c - a ~. p, or, 7r = -- 0.0002 T log c + a /2 If c is greater than a, the more.dilute solution is positive, as already stated, and the current flows on the outside, from the more dilute solution to the more concentrated. If a is greater than c, the more dilute solution is negative, and the current flows in the opposite direction. If the velocities of the two ions are equal (c = a), the right member of the above equation becomes zero, and there is no electromotive force. It is, therefore, impossible to construct a liquid element from solutions of an electrolyte whose cation and anion have the same velocities. If the valence of either ion is greater than unity, this must be taken into account. If we represent the valence of the cation by v, and that of the anion by the above ex- pression becomes: - c a V V, '7-1/1 7F = 10.0002 T log - • c + a Pl Nernst prepared liquid elements and determined their electromotive force. He then calculated the electromotive force from the above equation, and compared the values found experimentally with those from calculation. The following element already referred to was con- structed : - j 2 34 Hg - HgCl- KC1- KC1 - HC1- HC1- KC1- HgCl- Hg. n n n n n 10 100 100 10 10 APPLICATIONS OF THE THEORY 251 The potential differences at the ends are equal and opposite, and therefore equalize one another. The four differences in potential which must be taken into account are indicated above. But the potential differences are dependent upon the relative not upon the absolute osmotic pressures. The potentials at 2 and 4 are, therefore, equal and opposite, and can also be left out of account. This leaves the potentials at 1 and 3, and these can be calcu- lated by the method already given. Let cx and ax be the relative velocities of potassium and chlorine ions, and and a2 the relative velocities of hydrogen and chlorine ions; the electromotive force of this element would be calculated as follows, from the equation just deduced. The electromotive force would be the difference between these two potentials: - c,-a} RT . p c^ - a^RT p' ir _ 1 in z 4 In ^-7. ^1 + ax px r2 + a2 px p and px are the osmotic pressures of the potassium and chlorine ions in the more concentrated and more dilute solutions, respectively; p' and p^ the osmotic pressures of the hydrogen and chlorine ions in the solutions of hydro chloric acid. £ = / A A' Introducing this into the last equation, we have : -• (cA - aA c.-a^RT. p ir = 1 - -~ - ) In - ; ^2 + ^2/ A Cl, Cn Cl o\ ~ . P or, 7F = - i -- - ) 0.0002 T log - ■ Vi + ^2 + <?2/ A 252 ELECTROLYTIC DISSOCIATION This is the expression for calculating the electromotive force in liquid elements, like the above, where the valence of the cation is the same as that of the anion. If they are different, we will represent the valence of the cations by w and v', and that of the anions by zq and the equa- tion for the electromotive force would then become : - £1 £2 ^2 V V. v' vJ / 7F = 1 - O.OOO2 T log- • q + «x J A The electromotive force of the liquid elements which have been studied, as calculated from the above equation, agrees with that measured, to within the limits of experi- mental error. It should be observed, that the expression deduced above holds only for the potential at the contact of solu- tions of the same electrolyte, the solutions being of dif- ferent concentrations. If different electrolytes are used, we have no general means of calculating the potential at their surface of contact. It should be stated before leaving the subject of liquid elements, that the potential at the contact of two solutions is usually not great, and that the electromotive force of liquid elements is in general not large. Sources of Potential in a Concentration Element. - We may now analyze, more closely, the electromotive force in a concentration element, in the light of what we have learned about the liquid element. Thus far, we have dealt with the concentration element as if the only sources of the potential were at the points of contact of the electrodes and the solutions. And indeed this is practically true in APPLICATIONS OF THE THEORY 253 the cases of the concentration element which we have studied. We have learned from the study of the liquid ele- ment, that the plane of contact of two solutions of an electrolyte is also a seat of potential. In the concentra- tion element there is always such a contact between two solutions of the electrolyte, and this must be a source of potential. In the concentration element which we have studied, this potential is so small that it can practically be neglected. While the potential between solutions is usually small, it may, however, easily assume proportions which must be taken into account. We must now see how it is possible to calculate the potential at the contact of the two solutions in the concentration element. We can then analyze the electromotive force of a concentration element into its three constituents, and calculate the magnitude of the potential at each electrode, and also at the surface of contact of the electrolytes. Let the potential at one electrode be tt', at the other electrode tt", and at the contact of the two electrolytes 7r'". The values of these potentials are calculated by means of the following formulas: - p tt' = 0.0002 T log -; A p tt" = - 0.0002 T log -; A 7T1" = 0.0002 TC--- log -• c + a These equations obtain for univalent ions. If the valence of the ion is greater than one, this must be taken 254 ELECTROLYTIC DISSOCIATION into account in the way already described. The sum of the three potentials must then be the potential of the con- centration element. 7r' + tf" = - 0.0002 Tlog ; (nr' + 7r") + 7r'" = 0.0002 T 2 a log - c + a This must be the same as the equation already deduced (p. 241) for the concentration element. It will be seen to be the case, if we consider that = 2, and v for univalent ions equals 1. We can thus calculate the magnitude of the three sources of potential in a concentration element of the first class. An element of this class has been chosen, since the relations are somewhat simpler. The main sources of potential are at the contact of electrode and electrolyte, while a very small potential exists at the contact of the two electrolytes. In elements of this kind, it is perfectly clear that there is no potential where the two electrodes come in contact, because these are of the same metal. The Electromotive Force of the Daniell Element. - The elements which we have considered thus far have both electrodes of the same metal. The solution-tension of the metal was, therefore, the same upon both sides of the cell, and being of equal value and opposite sign, it disappeared from the equation for the electromotive force of the element. In most of our common elements, however, two metals are used as electrodes, or a metal and carbon. It is evi- dent that in these cases the solution-tension of the electrode APPLICATIONS OF THE THEORY 255 must be taken into account, since it is different for different metals. The Daniell element is taken as a type of the two metal elements with which we are so familiar. The application of our fundamental equation to this element will serve as an example of the way in which it may be applied to other well-known elements. The Daniell element consists of zinc in zinc sulphate, and copper in copper sulphate. Zinc dissolves and copper separates from the solution. The zinc electrode is there- fore negative, and the copper positive, the current passing on the outside from the copper to the zinc. The electro- motive force is equal to the difference in potential at the two electrodes, since the potential at the contact of the zinc sulphate and copper sulphate is so slight that we can practically disregard it. Representing the potential at the two electrodes by 7r1 and 7f2, we have: - RT , P tt. = In -; 2^0 / RT. ?1. ?r9 = In -- , 2 in which P and Px are the solution-tensions of the two metals. RT , P RT . P. 7T, - 7T9 = 7T = In In 12 2^/2^./! In the light of this example, the application of the con- ceptions here developed, to other special cases, should be a simple matter. 256 ELECTROLYTIC DISSOCIATION The Gas-battery. - The typical gas-battery consists of an electrolyte, two gases which can act chemically upon one another, and two platinum electrodes which are partly surrounded by the electrolyte, and partly by the gases. Take as a simple example, hydrogen over one electrode and chlorine over the other, the electrolyte hydrochloric acid, and the electrodes platinum. Hydrogen and chlorine will pass into solution at the two poles until there is an equilibrium between the force driving these substances into solution (solution-tension), and the osmotic pressure of the hydrochloric acid solution, which acts against the above-named force. The hydrogen pole is negative, since the solution-tension of the hydrogen is greater than the osmotic pressure of the solution; the hydrogen atoms becoming ions by taking positive electricity from the platinum electrode, which thus becomes negative. Exactly the opposite result is obtained at the other electrode, chlorine atoms becoming ions by taking negative electric- ity from the electrode, which therefore becomes positive. Ostwald 1 has shown that the theory of Nernst can be applied also to the electromotive force of the gas-battery. He has worked out even a simpler case than the one given above. We will take up first the simplest possible case, where we have the same gas, say hydrogen, over both electrodes, the hydrogen upon the two sides being at different pressures. The action of such an arrangement would be, as Ost- wald shows, to equalize the pressure of the gas upon the two sides of the cell. Hydrogen must pass into solution as ions upon the side where it is under the greater 1 Lehrb. d. allg. Chem., II, p. 895. APPLICATIONS OF THE THEORY 257 pressure, and ions of hydrogen must separate as gas upon the other side of the cell. Upon the side where hydrogen atoms are becoming ions, they take positive electricity from the electrode, which becomes negative, and the other electrode positive, because positive hydrogen ions are giving their charges up to it. We have here an analogue of the concentration element, and the electromotive force can be calculated in a similar manner. The electromotive force of this element also is the difference in the potential upon the two sides: - RT , P RT, P 7T = In In - ; A A where P is the solution-tension of hydrogen, and px and p^ the pressures of the hydrogen gas upon the two sides. The solution-tension, being the same upon both sides of the cell, disappears, as in the concentration element, and then we have : - 0.0002 T. IT = 10g - • A Since for hydrogen, v-2, we have: - 7F = 0.0290 log - Pv Ostwald 1 has also calculated the electromotive force for a gas-battery consisting of two gases. But as this has been worked out much more fully by Smale,2 we will turn to his work. Take the case of oxygen at one pole and hydrogen at the other. 1 Loc. cit. 2 Ztschr. phys. Chem., 14, 577, and 16, 562. 258 ELECTROLYTIC DISSOCIATION Let Px be the solution-tension of hydrogen. Let P2 be the solution-tension of oxygen. Let T be the absolute temperature. The potential at the hydrogen pole is: - p TTj = O.OOO2 T l°g~' Since the solution-tension of oxygen is negative: - 7t2 = 0.0002 T log^-; "*2 ■Wi - = 'r = o-ooo2 P log - - 0.0002 T log ~; A ^2 p p TT = 0.0002 T log ™ + 0.0002 T log • The theoretical consequences of this equation are very interesting. Px and P2, the solution-tensions of the gases, are independent of the nature and concentration of the electrolyte used on the two sides of the element; and /q and /2 are practically constant for solutions of nearly the same dissociation. Smale1 has tested this point, using seven acids, three bases, and seven salts. The concentrations for the same electrolyte vary in most cases from o. i to o.ooi normal. He found that the electromotive force of the hydrogen- oxygen battery was practically constant, independent of both the nature and concentration of the electrolytes used beneath the gases. A few results taken from the work of Smale will bring out this fact. 1 Loc. cit. APPLICATIONS OF THE THEORY 259 Electrolyte Used Concentration Normal E.M.F. HC1 O.I O.998 HC1 0.01 I.O36 HC1 0.001 !-O55 KOH O.I 1.098 KOH 0.01 1.095 KOH 0.001 1.093 K,SOt O.I 1-074 K2SO4 0.01 1.069 k2so4 0.001 1.069 The results thus agree satisfactorily with the deduction from theory. If, instead of oxygen, other gases, as chlorine, are used, the electromotive force depends upon the concentration of the electrolyte, which also agrees with theory, as is shown by Smale. But the theory admits of still further experimental test. If the electrodes are of two different metals, say plati- num and palladium, and are surrounded by the same gas which does not attack them, and are immersed in the same electrolytes, the electromotive force at each electrode is in terms of the theory formulated thus: - p = 0.0002 T log ; p = 0.0002 T log- Pi Px and P^ are the solution-tensions of the gas in plati- num and palladium, respectively; px and /2 the osmotic pressures at the electrodes; which are equal in this case, 260 ELECTROLYTIC DISSOCIATION since the same electrolyte is used on both sides. There- fore, we have:- p = tt = °-oo°2 T log -1 volts. The metal electrodes then play only this role, they offer a large surface to the gas, which facilitates its solution in them. The electromotive force of such an element should, therefore, be independent of the nature of the electrode used, since solution-tension is a constant for any given metal, according to the theory. It should, further, be inde- pendent of the size of the electrode. Both of these points were tested experimentally by Smale. The nature of the electrode, whether platinum, palladium, or gold, had no influence on the electromotive force. The size of the electrode, beyond a certain point, had no influence. A certain amount of surface is, how- ever, necessary in order that the electrode should reach its full tension. This work of Smale furnishes then another beautiful experimental confirmation of the consequences of that theory, which has enabled us to calculate the electromotive force of concentration elements, liquid elements, etc. A number of other types of elements might be taken up, and their electromotive force calculated from the method of Nernst, which, as we have already seen, is based upon van't Hoff's laws of osmotic pressure, and Arrhenius's theory of electrolytic dissociation. This is, however, not necessary, since the application to special cases is simple, if the fundamental principles are once grasped. APPLICATIONS OF THE THEORY 261 Chemical Action at a Distance. - Before concluding this section, we will describe a phenomenon of unusual inter- est. On account of its close relation to solution-tension, it should appear in this connection. In 1891, a paper was published by Ostwald,1 under the surprising title " Chemische Fernewirkung." It was sur- prising, because chemical action, as ordinarily understood, takes place only between substances which are close to one another. Ostwald begins his paper by calling attention to the fact that amalgamated zinc is not dissolved by dilute acids, but if the zinc is surrounded by a platinum wire, it is dissolved by the acid. It is not even necessary for the platinum wire to surround the zinc, for if the wire touches the zinc at any one point, solution will take place. Ostwald suggests that the zinc and platinum wire be joined at one place, and then the free ends of both im- mersed in a vessel containing, say, potassium sulphate. Let a screen of some porous material be placed between these free ends of the platinum and zinc, so that the salt solution around the one is separated from that around the other. He then asks the question: To which metal must sulphuric acid be added, in order that the zinc may be dissolved by the acid ? " The question seems at first sight to be absurd; since, in order that the zinc should dissolve, it appears to be self- evident that the acid should be added to the zinc. If we carry out the experiment we find exactly the reverse to be true. The zinc does not dissolve rapidly, if acid is added to the solution of potassium sulphate around the zinc. If, on the contrary, the acid is added to the solution around 1 Ztschr. phys. Chem., p, 540. 262 ELECTROLYTIC DISSOCIATION the platinum, the zinc dissolves with a copious evolution of hydrogen gas. The hydrogen appears on the platinum, as is always the case when zinc is in combination with plati- num. To dissolve the zinc under the conditions described, the solvents must not be allowed to act on the metal to be dissolved, but on the platinum which is in contact with the zinc." A number of other cases are cited. Zinc in sodium chloride behaves in the same manner, when hydrochloric acid is added to the platinum. Cad- mium also behaves like zinc. Tin, surrounded by sodium chloride, dissolves when hydrochloric acid is added to the platinum. Aluminium behaves like tin. Silver con- nected with platinum dissolves in sulphuric acid when a few drops of chromic acid are added to the platinum. Gold dissolves in sodium chloride, if chlorine is brought in contact with the platinum. Experiment to demonstrate Chemical Action at a Distance. Fill a beaker with a solution of potassium sulphate. Take a piece of glass tubing about io cm. long and 2 cm. wide, and close the lower end with vegetable parchment. Fit a bar of pure zinc, about 10 cm. long, tightly into a cork which just closes the top of this glass tube. Fill the glass tube with some of the same solution of potassium sulphate, and insert the bar of zinc - the cork closing the top of the glass tube. Around the top of the zinc bar above the cork wrap a piece of platinum wire of sufficient length to reach nearly to the bottom of the beaker, when the glass tube is introduced into the beaker in the manner to be hereafter described. The free end of the platinum wire should be coiled upon itself a num- APPLICATIONS OF THE THEORY 263 ber of times, or it is better if it is connected with a piece of platinum foil a few centimetres square, so as to expose a larger surface. The glass tube is now immersed in the beaker until the surface of the solution in the tube is only a centimetre or two above the surface of the solution in the beaker, the free end of the platinum wire, or the platinum foil, being allowed to rest on the bottom of the beaker. If a few drops of sulphuric acid are introduced into the potassium sulphate just around the bar of zinc, the zinc will be very slightly affected. But if a few drops of sul- phuric acid are poured upon the coiled end of the platinum wire, or upon the platinum foil, the zinc will dissolve rapidly in the neutral potassium sulphate which surrounds it, and a copious evolution of hydrogen will take place from the platinum, where it is in contact with the sulphuric acid. After a few moments the presence of zinc can be demonstrated in the inner tube, by any of the well-known reactions for zinc. As Ostwald states, similar phenomena have long been known. Nearly forty years ago Thomsen 1 described a galvanic element, which consists of copper in dilute sul- phuric acid, and carbon in a chromate mixture. When the carbon and copper were connected, the metal dissolved as the sulphate, in sulphuric acid, in which copper alone is not soluble. While similar facts were known, there was no rational explanation offered to account for them, until Arrhenius proposed the Theory of Free Ions. It is almost self-evident that the phenomenon is closely connected with electrical changes. Ostwald demonstrated 1 Pogg. Ann., in, 192 (i860). 264 ELECTROLYTIC DISSOCIATION this, by introducing between the metal and the platinum a fairly sensitive galvanoscope. When the acid was added to the platinum, the presence of a current was shown by the throw of the instrument. The explanation of this phenomenon is perfectly simple, now that we have the theory of electrolytic dissociation, and are familiar with its application to the primary cell. When metallic zinc is immersed in a solution of a neutral salt, like potassium sulphate, it sends, in consequence of its own solution-tension, a certain number of zinc ions into the solution. The zinc is thus made negative, and the solution, which has received the positive ions, positive. This continues until a definite difference in potential be- tween metal and solution is established. The amount of metal required to effect this condition is, as we have seen, so small that it cannot be detected by any chemical means. The zinc cannot dissolve further, because of the excess of positive ions in the solution. In order that more zinc may pass into solution, some of these positive ions must be removed. If the zinc is in combination with another metal, such as platinum, the latter takes the same nega- tive charge as the zinc. When the platinum is immersed in the solution, it attracts the excess of positive ions in the solution, and these collect upon the platinum. We would expect the excess of positive ions in the solution to give up their charge to the negative platinum, and separate from the solution, or, in case of potassium, decompose the water which is present. This depends both upon the nature of the ion and of the electrode. If the positive ion is the potassium of potassium sulphate, the difference in potential produced by introducing the APPLICATIONS OF THE THEORY 265 zinc is not sufficient to cause this ion to lose its charge to the platinum. If sulphuric acid is added to the platinum, the difference in potential, produced by intro- ducing the bar of zinc, is sufficient to compel the hydrogen to give up its positive charge to the platinum, and separate as ordinary hydrogen. The platinum, having received positive electricity from the hydrogen ions, con- ducts this over to the zinc. The zinc becomes less nega- tive than before the hydrogen separated at the platinum, and the difference in potential between the zinc and the surrounding solution is less than before. More zinc dissolves or passes over into ions, more hydrogen ions give up their charge to the platinum and separate as gas; and this continues until all of the zinc has dissolved, or all of the hydrogen ions have separated as gas. As Ostwald observes, this explanation shows not only why the acid must be added to the platinum and not to the zinc, but throws light also on the problem of the solution of metals in general. A word or two on this subject. It has long been known that pure zinc does not dissolve in acids, while impure zinc readily dissolves. It is quite evident that the zinc in the two cases has the same tendency to dissolve. Pure zinc dissolves readily when in contact with a metal, such as platinum, which has a small solution-tension. As we have seen from the fore- going explanation, the difference is not in the solution of the zinc, but in the ease with which the hydrogen can escape from the solution. The presence of a metal with small solution-tension allows this to take place more readily, and this is the reason that impure zinc dissolves in acids. 266 ELECTROLYTIC DISSOCIATION The reason why pure zinc does not dissolve in acids is because this metal has a strong positive solution-tension; it sends positively charged ions into solution under a high solution-tension, and, therefore, opposes the separa- tion of any other positive ion, like hydrogen, upon it. Pure zinc, therefore, does not dissolve in acids, because the hydrogen ions cannot give up their positive charges and escape. When a metal like platinum, which has a small solution- tension, is present, the hydrogen can easily give up its charge to this metal and escape as gas. The zinc, because of its high solution-tension, and because the hydrogen cations can so easily escape, then dissolves. To repeat the essential steps in the explanation of the experiment described above: Pure zinc immersed in po- tassium (or any soluble) sulphate, to which sulphuric acid is added, or in a solution of pure sulphuric acid itself, does not dissolve, because the zinc has such a high solution-tension that the hydrogen ions cannot give up their charge to it and escape. The zinc, however, throws a few ions into solution, and becomes negatively charged. If now the zinc is connected with platinum, which has a small solution-tension, and the acid added to the plati- num, the hydrogen ions can easily give up their charge to the platinum and escape as gas. The platinum, which was at the potential of the zinc with which it is in com- bination, now becomes positive with respect to the zinc, and a positive charge, therefore, flows from the platinum to the zinc. The zinc, having received positive electricity, can begin dissolving anew, and continue to pass into solution as long as it receives positive electricity from APPLICATIONS OF THE THEORY 267 the platinum - as long, therefore, as there are any hydro- gen ions in the -solution to furnish positive electricity to the platinum. Or, as we are accustomed to express it, as long as there is any acid in contact with the platinum. This subject will be concluded with a paragraph from this fascinating paper by Ostwald: " We see that the usual explanation, that solution takes place because of galvanic currents between the zinc and the other metals, is not in strict accord with the facts. The galvanic currents are inseparably connected with the process of solution, but they are not the primary causes of the solution. They are set up, rather, by the process of solu- tion, which they must necessarily accompany, since solu- tion is a question of ion formation and disappearance. If it is possible for the positive ions present to separate in any way from the solvent, solution takes place." Ostwald then goes on to show that it is not necessary for the ion to separate from the solution. The positive ion may be destroyed in the solution, or a negative ion pro- duced ; and in' either case the metal will dissolve. But for these and similar facts the original paper must be consulted. Conclusion. - In concluding this chapter on the calcula- tion of the electromotive force of elements, attention should again be called to the fact, that the method worked out by Nernst was based directly upon van't Hoff's laws of osmotic pressure, and the theory of electrolytic dissocia- tion. Without either of these conceptions the work of Nernst would have been absolutely impossible. With them, he has thrown entirely new light on the whole ques- 268 ELECTROLYTIC DISSOCIATION tion of the electromotive force of elements, and has fur- nished us, for the first time, with a satisfactory theory of the action of the primary cell. APPLICATION OF THE THEORY OF ELECTROLYTIC DISSOCIA- TION TO BIOLOGICAL PROBLEMS The application of a theory of solution to biological problems is not so evident as to chemical, where solutions are always involved. Solutions are, however, very fre- quently used by the physiologist, and any theory of solution must, therefore, bear upon many physiological problems. It is only in the last few years that the theory of electro- lytic dissociation has found its way into physiology, and work along this line may be said to have just been begun. A few examples of the application of the theory in this direction will be given. Toxic Action and Electrolytic Dissociation. - Kahlenberg and True1 published a paper in 1896 on "The Toxic Action of Dissolved Salts and their Electrolytic Dissocia- tion," which was the pioneer work along this line. It had been thought that the physiological action of any substance was due to its chemical nature. In the case of a solution, all of the chemical and physical properties are a function of the properties of the ions, plus those of the undissociated molecules which it contains. It would, there- fore, seem probable, that the physiological action of such solutions was due to the same cause. Many investigations on the physiological action of aqueous solutions oh bacteria and higher forms of plant life, as well as on animals, have 1 Botan. Gazette, 22, 81. APPLICATIONS OF THE THEORY 269 been made. In work of this kind, percentage concentra- tion has been dealt with, and this obscures any general relations which might exist. If a dilute solution of sodium chloride differs from a dilute solution of hydrochloric acid, in that the former contains sodium ions and the latter hydrogen ions, then the poisonous character of the latter must be due to the hydrogen ions. Since a very dilute solution is completely dissociated, the poisonous properties of such a solution must be due to one or both of the ions which it contains, since there are no molecules present. If the toxic action of acids on plants is due only to the hydrogen ion, then solutions of different acids containing the same number of hydrogen ions should be equally poisonous. Solutions of hydro- chloric acid, nitric acid, and sulphuric acid are completely dissociated at a volume of about one thousand litres; hence, solutions of these acids which are of this strength, or more dilute, should have the same toxic action; since the ions Cl, NO3, SO4, have none. This has been tested, experimentally, for the higher plants, by finding the strength of the solution of the acid in which the root of the plant will just live. Seedlings of Lupinus albus L. were employed. They have a straight, clean radicle, and are well adapted to this work. The root was suspended in the acid solution, and its condition determined by the rate of growth. It was a simple matter to determine when the root was dead, since it lost its satiny lustre and acquired a dead-white color. Its appearance may be described as coagulated. The root was immersed in the solution for fifteen to twenty-four hours, which was 270 ELECTROLYTIC DISSOCIATION the time chosen for an experiment. The root of the plant was first placed in a more concentrated solution of the acid. If this was found to kill it, another root was placed in a more dilute solution, and so on, until a dilution was reached in which the root just lived. In the case of strong acids, the root would just live in a solution which contained a gram-molecular weight of the acid in 6400 litres of solu- tion ; expressed in ordinary terms, the solution had a volume of 6400 litres. This expresses the toxic action of the hydrogen ion, and it is the same for all strong acids. The hydroxyl ion was studied, and found to be far less poisonous than the hydrogen ion. The root would just live when the solution contained a gram-molecular weight of the base in 400 litres of solution. The effect of the ions of certain salts was also studied. The copper ion was especially toxic. The roots would just survive in a solution which contained a gram-molecular weight of copper ions in 51,200 litres of solution. Whenever copper forms part of an ion, and is not the whole ion, the result is very different. Thus, in Fehling's solution copper forms part of the ion, it being in com- bination with an organic complex. We would expect it, therefore, to have a different action, under these condi- tions, than when alone. This was tested by experiment. In preparing the Fehling's solution, cane-sugar was used instead of Rochelle salt, in order to avoid the excess of other ions in the solution. An excess of caustic alkali was avoided, in order to keep out hydroxyl ions, which are known to be poisonous. The roots would grow in a solution of this salt, which contained a gram-atomic weight of copper in 400 litres. Copper, when alone as an ion, is, APPLICATIONS OF THE THEORY 271 thus, far more poisonous than when in combination with this complex. Iron in its ionic state has very different toxic action than when the iron atom is combined with other things to form an ion. Thus the iron in a ferric salt has very different effect from the iron in potassium ferrocyanide. It would be indeed surprising if this were not true, since iron in a ferric salt forms a cation, while iron in potassium ferrocyanide is combined with the 6 CN groups, forming a part of the complex anion. Cobalt and nickel have the same toxic action as iron. The question is raised, whether there is any connection between this action and the fact that the three elements have very nearly the same atomic weights. The experi- mental data are yet far too meagre to answer this ques- tion. Cadmium and silver also are found to be very poisonous. The Cu ion is about as toxic as the hydrogen ion. Hydrocyanic acid is almost completely undissociated, yet it is very poisonous. The plant will stand only of a gram-molecule'per litre. This is an excellent example of how molecules as well as ions may be poisonous. The investigation was extended to the organic acids, and these, with some exceptions, fell in line with the above relations. This investigation has shown that the toxic action of solutions of electrolytes, which are completely dissociated, is due to the ions present. When the electrolyte is only partly dissociated, the undissociated portion may exert a toxic action. We have here a recognition of the theory of electrolytic dissociation in the organic world. The paper 272 ELECTROLYTIC DISSOCIATION of Kahlenberg and True contains the following significant passage: - " It will be seen that a wide field for research along physiological lines opens up, by applying to the field of biology the dissociation theory which has proved so fertile in chemistry and physics. Further work in this direction, using the latest and best that the new physical chemistry has to offer, it is to be hoped, will place our knowledge of the physiological action of solutions of electrolytes on a better basis than the purely empirical one on which it has thus far rested. It does not seem too much to expect that the effect of such study will soon be felt in agriculture and therapeutics, while bacteriological study, pursued from the standpoint of the new theory, will yield important additions to our knowledge of antiseptics." Another investigation in the same field has been carried out by F. D. Heald.1 He studied the toxic action of acids and salts upon different plants. He used the three plants: - Ptsum sativum, Zea Mais, Cucurbita Pepo. The conclusions of Kahlenberg were all confirmed by this work, in which more than one plant was used. Says the author, " The theory of electrolytic dissociation has thus thrown light upon the physiological action of different substances, and the theory has, itself, been strengthened by these experiments upon living things." Toxic Action of the Phenols and their Dissociation. - The work begun by Kahlenberg and True has since been 1 Botan. Gazette, 22, 125. APPLICATIONS OF THE THEORY 273 extended by True and Hunkle1 to the phenols. They investigated a number of phenols, using different con- centrations, and determined the greatest concentration in which the roots of Lupinus albus would just live and grow. The conductivity of the solutions of the different phenols was also measured. They conclude that, except in isolated instances, the electrolytic dissociation plays but a subordinate role in determining the toxic properties of phenylic compounds. Picric and salicylic acids are strongly dissociated, and are very poisonous because of the large number of hydrogen ions in their solutions. Electrolytic dissociation exerts a pronounced influence in the cresols and mononitrophenols. Dissociation and Disinfecting Action. - In 1896 a paper appeared by Paul and Kronig,2 describing the action of a large number of reagents on bacteria. The work was done chiefly with the bacillus anthracis, and the staphylococcris pyogenes aureus. As will be seen, the problem is one of disinfection, the toxic action of the various substances being investigated. The bacteria were distributed over the surfaces of carefully washed and completely disin- fected garnets of equal size. That approximately the same number of bacteria should be used in each experi- ment, the same number of garnets was employed, and the mean of six results was taken. The garnets were placed in vessels made of platinum gauze, and introduced into the solution, which was kept at a constant tempera- ture. After the action had taken place as long as desired, it was instantly brought to an end by adding some sub- 1 Botan. Centralb., 76, 289, 321, 361, 391 (1898). 2 Ztschr. phys. Chem., 21, 414. 274 ELECTROLYTIC DISSOCIATION stance which destroyed the disinfecting property of the solution. The spores were then washed from the garnets by shaking in water, and agar-agar jelly added to the water containing the spores. This mixture was poured into convenient dishes, and kept at a constant temperature. The bacteria, which were still alive, began to form dis- tinctly visible colonies in twenty-four hours, and could easily be counted. The number of colonies was found to depend upon the time during which the toxic reagent acted, and upon the concentration of the solution. In general, the more dilute the solution the less the dis- infecting action. The' nature of the solvent was found to effect the relative toxic action of compounds. Some of the more important results obtained by Paul and Krbnig are : - The disinfecting action of metallic salts depends, not only on the concentration of the metal in the solution, but also on the specific properties of the salt and the solvent. The action of a salt of a metal depends not only on the specific action of the metallic ion, but also on that of the anion, and of the undissociated part of the salt. Solutions of metallic salts, in which the metal forms part of a complex ion, are only weakly disinfecting. The strong acids are toxic, not only in proportion to the concentration of the hydrogen ions, but the specific prop- erties of the anions come into play. The bases which are equally dissociated, such as potassium, sodium, and lithium hydroxides, have the same disinfecting action. The weakly dissociated base, ammonium hydroxide, disinfects much less. The disinfecting action of the halogens, Cl, Br, I, like APPLICATIONS OF THE THEORY 275 their chemical action, decreases with increasing atomic weight. Solutions of substances in absolute alcohol and ether are almost without action on bacillus anthracis. The disinfecting action of mercuric chloride and silver nitrate in alcohol is increased by the addition of more and more water. These results are very interesting, as being an applica- tion of the theory of electrolytic dissociation in an entirely new direction. We have here a clear recognition of dis- sociation in the field of bacteriology. Toxic Action of Substances on Certain Fungi.-We have seen the relation between the dissociation of solutions and their toxic action on certain phanerogams, as brought out by the work of Kahlenberg, True, and Heald; also the same relation when lower forms of life, the bacteria, were used. We must refer, in this connection, to the very recent investigation of Clark, in which the toxic action of sub- stances on certain fungi was studied, and this action com- pared with the dissociation of the substance. Five fungi were used, and all were found to be much more resistant to injurious agents than the higher plants. The spores of moulds require, to inhibit germination, from two to four hundred times the strength of acid which is fatal to the higher plants. The hydroxyl ion was found to be more toxic to moulds than the hydrogen ion. The toxic value of the ions, Cl, Br, I, increases with increasing atomic weight. It was found that in the case of several acids dissociation lessens their activity, the molecule being more active than the ions. Of the eight acids investigated, six were more active in the molecular than in the ionic form. The toxic 276 ELECTROLYTIC DISSOCIATION action of the molecule, in the case of hydrocyanic acid, was as much as 76.6 times that of the hydrogen ion. The anions of hydrochloric, nitric, and sulphuric acids are only slightly toxic to fungi. These results, like those previously described, show that both molecules and ions may be poisonous to certain forms of life, just as both molecules and ions may be colored. The poisonous nature of the molecule or ion depends greatly upon the nature of the plant on which it acts. Application of the Dissociation Theory to Animal Phys- iology.- The theory of electrolytic dissociation has been applied not only to vegetable, but has already found its way into animal physiology. The work of Loeb1 was the first of importance in this field. He studied the action of certain electrolytes on the muscle of a frog. When the muscle from the leg of a frog is placed in a 0.7 per cent solution of sodium chloride, and a small amount of acid or base added to the solution, the muscle, by taking up water, undergoes an appreciable increase in weight. Loeb determined the increase in the weight of the muscle, produced by hydrochloric acid, nitric acid, and sulphuric acid, of known concentrations, and was led to this interesting conclusion. Solutions of these three acids, which contain the same number of hydrogen atoms in equal volumes, produce the same in- crease in the weight of the muscle. He showed that it is only the hydrogen cation which is active, the anion having little or no effect; and that when the same number of hydrogen ions is contained in equal volumes of their solu- tions, all of these acids produce exactly the same effect. 1 Pfliiger's Archiv f. Physiologic, 69,1. APPLICATIONS OF THE THEORY 277 This does not hold for the weakly dissociated organic acids, since, in these cases, the anions as well as the mole- cules exert an influence. Loeb then studied the action of the following bases: lithium hydroxide, sodium hy- droxide, potassium hydroxide, strontium hydroxide, and barium hydroxide, and found that they all had the same influence in causing the muscle to take up water, when they are used at such concentrations that an equal number of hydroxyl groups is contained in equal volumes of each of the solutions. The action of all these alkalies was found to depend entirely upon the anion of the base, i.e. hydroxyl; just as the action of the strong mineral acids depended entirely upon the cation hydrogen. The hy- droxyl ions have, however, a stronger influence than an equal number of hydrogen ions. Solutions of potassium and sodium carbonate also cause the muscle to take up water. This is due to the hydroxyl ions in their solutions, formed by the hydrolysis of the salt and the subsequent dissociation of the base. That the theory of osmotic pressure, deduced by van't Hoff, applies to this phenomenon, is shown by the fact that solutions of lithium, potassium, rhubidium, caesium, magnesium, calcium, barium, and strontium chlorides, produce the same change in the weight of the muscle as a solution of sodium chloride of equal osmotic pressure. Loeb also studied the toxic action of a number of ions on muscle, and found that for any given group, as Li, Na, + 4-4" K, Rb, Cs, the relative toxic action is proportional to the migration velocity of these ions, and not to their atomic 278 ELECTROLYTIC DISSOCIATION + + 4- + weights. The same relation obtains for the ions, Be, Mg, Ca, Ba, Sr, but does not extend from one natural group of the elements to another. A second investigation was carried out by Loeb,1 which is an extension of the one just considered. While the physiological action of the inorganic acids is conditioned by the number of hydrogen ions present, there is an apparent exception presented by the organic acids. The physiological activity of the fatty acids is not proportional to their dissociation. Thus, lactic acid, which, at the dilu- tion employed is only eleven per cent dissociated, causes the muscle to take up as much water as trichloracetic acid and oxalic acid, in which nearly all of the molecules are dissociated. Similarly, mandelic acid causes the muscle to take up as much water as the more strongly dissociated organic acids, although, at the dilution used, it is only nine- teen per cent dissociated. Loeb does not offer any final explanation of this phenomenon, but suggests that since the difference in the action of the different acids is so much less than the difference in their dissociation, it seems probable that those acids which are very slightly dissociated are transformed in the muscle into products with stronger dissociation. The author offers this as a possible explanation, and promises further investigation, especially with the aromatic acids. Physical Chemical Methods applied to Animal Physi- ology. - Physical chemical methods have been applied by Bugarszky and Tangl2 to a very different physiological problem. They have been employed to determine the con- 1 Pfluger's Archiv f. Physiologic, 71, 457. Ibid., 72, 531. APPLICATIONS OF THE THEORY 279 centration of the dissolved substances in the blood serum, and also the relation between the electrolytes and non- electrolytes contained in it. The freezing-point method was used to determine the molecular concentration of the dissolved substances. The freezing-point of the serum was first determined, then the freezing-point of pure water. Since blood serum is practically water containing electrolytes and non-electro- lytes, the difference between the two freezing-points is the lowering of the freezing-point of water produced by the substances present in the blood serum. A gram-molecular solution of a non-electrolyte freezes 1.870 lower than pure water. To determine, therefore, the number of gram- molecular concentrations to which the substances in blood serum are equivalent, the difference between the freezing- point of water and of blood serum must be divided by 1.87. In this calculation the ions which result from the dissociation of any electrolytes present are treated as if they were molecules, since an ion produces the same low- ering of the freezing-point as a molecule. The above method shows the total concentration of elec- trolytes and non-electrolytes present in blood serum, but does not enable us to determine the amount of each. To accomplish this, some method must be employed which will enable us to discriminate between undissociated molecules and ions. Molecules in solution do not conduct the elec- tric current; only ions conduct. We can, therefore, use the conductivity method to determine the amount of electro- lytes present in the serum. This was done by Bugarszky and Tangl. The electrolytes present in blood serum are, almost all, salts. The alkaline reaction of the blood comes 280 ELECTROLYTIC DISSOCIATION from a few hydroxyl ions, which result from the hydro- lysis of carbonates in the blood. Further, the salts in the blood are nearly all inorganic; organic salts being present only in very small quantity. The conductivity method is used as an approximate measure of the inorganic salts present, and is regarded as more accurate than the method of determining the amount of ash obtained from 4- 4- the serum. While the serum contains the cations, Na, K, Ca, Mg, and the anions Cl, CO3, HCO3, HPO4, SO4, OH ; 4- - = the main ions are Na, Cl, and some CO3. The determination of the concentration of the electrolytes in the blood serum, by the conductivity method, is some- what complicated by the presence of the non-electrolytes in the serum, as the authors point out. The conductivity of an electrolyte is diminished by the presence of a non- electrolyte, and the magnitude of the effect depends both upon the nature of the electrolyte and the non-electrolyte. The non-electrolytes in the blood serum consist chiefly of albumens, with traces of a number of other substances. The albumens were isolated, and their effect on the con- ductivity determined. One gram of albumen in 100 cubic centimetres of blood serum, diminished the conductivity 2.5 per cent. By applying this correction to the observed conductivity of the serum, we obtain its true conductivity. The corrected conductivity can be used for calculating the concentration of the electrolytes dissolved in the serum. Knowing the amount of the electrolytes in the serum, it is a very simple matter to determine the amount of the non-electrolytes. The freezing-point method gives the sum of the two, as already stated. By subtracting from the APPLICATIONS OF THE THEORY 281 sum the amount of the electrolytes, we have at once the quantity of the non-electrolytes. A number of conclusions of interest and importance were reached through this work, but since these lie almost wholly in the field of physiology, they do not come within the scope of this book. The authors point out that these same methods can, and should be applied to other liquids in the animal body. Application of Osmotic Pressure and Dissociation to the Mechanics of Secretion.-The work of Dreser1 illustrates the application of van't Hoff's laws of osmotic pressure and the theory of electrolytic dissociation, to the mechanics of secretion. The problem is to calculate the work done by the kidneys in secreting urine. This is accomplished by determining the osmotic pressure of the blood serum, and also that of the urine. There is no direct method of measuring osmotic pressure, which is of general applica- bility, so that an indirect method must be employed. The well-known freezing-point method was used, and from the difference in the freezing-point of the serum and of the urine, the difference in their osmotic pressures was cal- culated. If the volume secreted by the kidneys is taken into account, the osmotic work done by the kidneys is ascertained. And if we note the time during which the secretion takes place, the osmotic work done by the kidneys can be expressed in C.G.S. units. A number of other investigations have already been carried out, in which the theory of electrolytic dissociation and the van't Hoff laws of osmotic pressure have been applied to biological problems.2 We should mention es- 1 Archiv f. experimentelle Pathologic, 29, 301. 2 For a fuller discussion of this question see the admirable book by Hamburger, Osmotischer Druck und lonenlehre (1902). 282 ELECTROLYTIC DISSOCIATION pecially the work of Dreser,1 Hamburger,2 Hedin,3 Heiden- hain,4 van Karanyi,5 and van Limbeck.6 But the investi- gations already referred to, suffice to show the nature of the biological questions upon which modern physical chemistry is throwing light. It would seem that the theory of electrolytic dissocia- tion must find wide application in pharmacology. If chemical action is due mainly to ions, it is very probable that the pharmacological action of many chemical sub- stances is largely ionic. This probability is increased, when we consider how many electrolytes are used in medicine, and that they are either taken in solution, or pass into solution in the fluids of the body. It is quite safe to predict, that many interesting and important results await the investigation of the relation between the dis- sociation of drugs, and their action upon the human body. CONCLUSION By following a few of the many applications of the theory of electrolytic dissociation to problems in chemistry, physics, and biology, we can form some conception of its wide-reaching significance. The examples which have been taken up and studied are, in each case, a few chosen from the many. And if so much has been done in the short time which has elapsed since the theory was pro- 1 Ztschr. phys. Chem., 21, 108. 2 Du Bois' Archiv, 1886, 476; Virchow's Archiv, 140, 539; Centralb. f. Physi- ologic, 1893-94, 24. 8 Skandinav. Archiv f. Physiologic, 5, 238, 385; Pfliiger's Archiv f. Physiologic, 63, 248. 4 Pfliiger's Archiv, 56, 600. 6 Centralb. f. Physiologic, 1893, Heft 3; Ungar. Archiv f, Med., 1895. 6 Archiv f. exper. Pathologic, 25, 64. APPLICATIONS OF THE THEORY 283 posed, what may we not reasonably expect from the future ? Since so many, substances are broken down into ions, by water and similar solvents, it is almost certain that our theory will find application wherever aqueous solutions of electrolytes are employed. A moment's reflection will show that comparatively few branches of natural science lie wholly without its scope. A careful study of the applications of the theory, which have already been made, will bring out a fact of pro- found significance. The theory coordinates and corre- lates heterogeneous masses of facts, which apparently bore little or no relation to one another, and refers them to a common cause. As an illustration, take the neutrali- zation of acids and bases, or the strength of acids and bases in general. But this is just what the physical chemistry of to-day has done, and is doing for several branches of science, and especially for the science of chem- istry. Physical chemistry is furnishing us, largely with the aid of the theory of electrolytic dissociation, with rational explanations of chemical processes whose mean- ing was entirely concealed, and is rapidly placing chem- istry upon that exact mathematical basis which physics has so long enjoyed. INDEX Acids and bases, strength of, 216. Acids, dry, do not act on litmus, 165. Acidity, relations between, and composi- tion and constitution, 219. Additive nature of conductivity. Law of Kohlrausch, 116. Additive property of salt solutions, 104. Affinity, methods of measuring, 67. Ammonia, dry, no action, on dry hydro- chloric acid, 168. Animal physiology, application of physi- cal chemical methods to, 278. Animal physiology, application of the dis- sociation theory to, 276. Arrhenius, dissociation of substances in water, 93. Arrhenius explains exceptions to gas laws, 94. Asymmetric carbon atom, 25. Atomic and molecular volumes, n. Avogadro's law for dilute solutions, 87. Baeyer describes an exception to van't Hoff's hypothesis, 24. Bases and acids, strength of, 216. Bases, strength of, and composition, and constitution, 223. Benzene, constitution determined by a thermal method, 21. Benzene, constitution determined by re- fractivity, 20. Bergmann, work of, 53. Berthelot and Pean de St. Gilles, work of, 58. Berthelot, thermochemical work of, 34. Berthollet, work of, 54. Berzelius, electrochemical theory of, 40. Biological problems, application of the theory of electrolytic dissociation to, 268. Blagden, on freezing-point lowering, 30. Boiling-points and composition, 5. Boiling-points and constitution, 5. Boiling-points of liquids, 4. Boiling-point rise, 178. Boyle and Gay Lussac's laws applied to solutions. Experimental evidence for, 85- Boyle's Law confirmed by Pfeffer's re- sults, 83. Boyle's Law confirmed by results of De Vries, 83. Boyle's Law for dilute solutions, 82. Bruhl, on refractive power of liquids, 19. Calculation of dissociation from conduc- tivity, 209. Cell for measuring osmotic pressure, 74. Cells, types of, 238. Chatelier, Le, chemical equilibrium, 66. Chemical action at a distance, 261. Chemical action at a distance, demon- strated by experiment, 262. Chemical activity as a measure of disso- ciation, 157. Chemical dynamics and statics, develop- ment of, 53. Chemical problems, electrolytic dissocia- tion applied to, 171. Chemical reactions between ions, 158. Chlorine, dry, action on metals, 161. Clausius, theory of electrolysis, 48. Cohen and van't Hoff, 66. Color of salt solutions, no. Composition and acidity, 219. Composition and boiling-points, 5. Composition and heat of combustion, 37. Composition and magnetic rotation, 28. Composition and molecular heats, 8. Composition and refractivity, 18. Composition and strength of bases, 223. Concentration and osmotic pressure, 75. Concentration element of the first type, 239- 285 286 INDEX Concentration element of the second type, 243. Concentration element, sources of poten- tial, 252. Conductivity and dilution, 142. Conductivity and lowering of freezing- point, 129. Conductivity and osmotic pressure, 128. Conductivity and reaction velocity, 155. Conductivity at high temperatures, 215. Conductivity in different solvents, 211. Conductivity, molecular, 203. Conductivity of solutions, 201. Conductivity of solutions, Kohlrausch, 52. Conductivity of solutions, method of measuring, 203. Conductivity of water, 207. Conductivity, specific, 202. Constancy of solution-tension, 236. Constitution and acidity, 219. Constitution and boiling-points, 5, 7. Constitution and heat of combustion, 37. Constitution and molecular heats, 9. Constitution and molecular volume, 12. Constitution and refractivity, 18. Dale and Gladstone, refraction formula, 17- Daniell elements, electromotive force of, 254- Davy, electrochemical theory of, 40. Deville, on dissociation, 60. Diffusion, 174. Dilution Law of Ostwald, 143. Dilution Law of Rudolphi, 147. Disinfection and dissociation, 273. Dissociating action of water, demonstra- tion of, 113. Dissociating power of different solvents, 160. Dissociation and chemical activity, 154. Dissociation by heat and electrolytic dis- sociation, 149. Dissociation calculated from conduc- tivity, 209. Dissociation measured by boiling-point method, 213. Dissociation measured by different methods, 152. Dissociation of substances in water, 93. Distance, chemical action at a, 261. Distance, chemical action at a, demon strated by experiment, 262. Dittmar, on boiling-points of metameric compounds, 6. Earlier physical chemistry, 1. Earlier physical chemical work, conclu- sions from, 69. Edwards, refraction formula, 17. Electrochemical Theories of Davy and Berzelius, 40. Electrochemistry and electrolytic disso- ciation, 182. Electrochemistry, the development of, 39. Electrolysis, 45, 183. Electrolysis, theories of, 46. Electrolytic dissociation and dissociation by heat, 149. Electrolytic dissociation and toxic action, 268. Electrolytic dissociation, origin of the theory, 71. Electrolytic dissociation, theory of, 94. Electrolytic solution-tension, 231. Electromotive force, 216. Electromotive force, calculated from osmotic pressure, 227. Electromotive force, seat of in primary cells, 226. Electrostatically charging a solution, 138. Elements, concentration, first type, 239. Elements, concentration, second type, 243- Elements, liquid, 247. Evidence for the theory of electrolytic dissociation, 104. Exceptions to laws of gas pressure being applicable to osmotic pressure, 91. Excess of one of the products of disso- ciation, effect of, 149. Faraday's Law, 44. Favre and Silbermann, thermochemical investigations, 33. Fick's Law of diffusion, 30. Freezing-point, lowering of, 176. Fungi, toxic action of substances on, 275. Gas-battery, 256. Gas pressure and osmotic pressure, rela- tions, 76. INDEX 287 Gay Lussac's Law and Boyle's Law, ex- perimental evidence for, 85. Gay Lussac's Law and Pfeffer's results, 84. Gay Lussac's Law for dilute solutions, 84. Gibbs, application of thermodynamics to chemical equilibrium, 64. Gladstone and Dale, refraction formula, 17- Goodwin and Thompson, the dielectric constant of liquid ammonia, 211. Graham, work on diffusion, 30. Grotthuss, theory of electrolysis, 46. Guldberg and Waage, law of mass action, 60. Guye, hypothesis of, 26. Hantzsch and Werner, stereochemistry of nitrogen, 27. Heat of combustion, and composition and constitution, 37. Heat of neutralization in dilute solutions, 119. Heat of neutralization of acids and bases, a constant, 36. Hess, G. H., work of, 32. Hess's law of thermoneutrality of salts, 33. Hess's law of thermoneutrality of salt so- lutions, 122. History of van't Hoff's laws, 76. Hittorf, work on migration velocity of ions, 52. Horstmann, application of thermody- namics to chemistry, 64. Hydrochloric acid, dry, does not decom- pose carbonates, 163. Hydrochloric acid, dry, does not precipi- tate silver nitrate in ether or benzene, 165. Hydrochloric acid, dry, no action on dry ammonia, 168. Hydrogen sulphide, dry, inactivity of, 165. Indicators, theory of, 112. Ion formation, modes of, 189. Ions, experiment to demonstrate the presence of, 137. Ions the cause of chemical reaction, 158. Ions, velocity of, 191. Jones and Allen, experiment to demon- strate the dissociating action of water, "3- Jones' measurement of dissociation by freezing-point lowering, compared wita dissociation from conductivity, 130. Jones, measurement of dissociation by the boiling-point method, 213. Kohlrausch's Law of independent migra- tion velocity of ions, 197. Kohlrausch, on conductivity of solutions, 52. Kopp's work on atomic volumes, 12. Kopp's work on boiling-points ol liquids. 4* Law of Avogadro, for dilute solutions, 87. Law of Faraday, 44. Law of Hess, 122. Law of Kohlrausch, 116. Law of mass action, Guldberg and Waage, 60. Law of reaction velocity, discovery of, 56, Laws of Boyle and Gay Lussac, applied to solutions, 82. Laws of Boyle, Gay Lussac, and Avo- gadro for solutions and gases, general , expression of, 89. Laws of gas pressure not always applica- ble to osmotic pressure, 91. Le Bel's hypothesis, 23. Liquid elements, 247; theory of, 247. Lodge, experiment on absolute velocity of ions, 199. Lorenz-Lorentz, refraction formula, 17. Lossen, on molecular volume, 13. Lowering of freezing-point and conduc- tivity, relation between, 129. Lowering of freezing-point, and osmotic pressure, relation between, 126, 131. Lowering of freezing-point and rise in boiling-point, 129. Lowering of vapor-tension and osmotic pressure, relation between, 127. Magnetic rotation and composition and constitution, 28. Magnetic rotation of plane of polariza- tion, 27. Marignac, specific heat of aqueous solu- tions, 11. Measurement of conductivity, 206. 288 INDEX Metamerism and properties, 2. Mixtures of completely dissociated com- pounds, 117. Mixtures of completely undissociated compounds, 118. Molecular conductivity, 203. Molecular heats and composition, 8. Molecular heats and constitution, 9. Molecular rotatory power, 22. Molecular volume and composition, n. Molecular volumes, 11. Molecular volumes and constitution, 12. Nernst and Ostwald, experiment to de- monstrate free ions, 139. Nernst, calculation of electromotive force, from osmotic pressure, 227. Nernst, effect of an access of one of the ions on dissociation, 149. Neutralization, change of volume in, 107. Neutralization, heat of, in dilute solu- tions, 119. Neutralization of acids and bases, con- stant heat of, 36. Noyes, dissociation measured by change in solubility, 151. Optical activity and composition and constitution, 23. Optically inactive and optically active substances, 22. Origin of the theory of electrolytic dis- sociation, 71. Osmotic investigations of Pfeffer, 71. Osmotic pressure and conductivity, re- lations between, 128. Osmotic pressure and gas pressure, re- lations between, 76. Osmotic pressure and lowering of freez- ing-point, relations between, 126, 131. Osmotic pressure and lowering of vapor- tension, relations between, 127, 134. Osmotic pressure, electromotive force calculated from, 227. Osmotic pressure, results of Pfeffer, 75. Ostwald and Nernst, experiment to de- monstrate the presence of free ions, 139- Ostwald, change in volume in neutral- ization, 107. Ostwald, dilution law, 143. Ostwald, method of measuring affinity, 67. Oxygen, inactivity of dry, 162. Pean de St. Gilles, work of, 58. Perkin, W. H., work on magnetic rota- tion, 28. Pfeffer's apparatus for measuring osmotic pressure, 73. Pfeffer's method of measuring osmotic pressure, 72. Pfeffer's osmotic pressure results, 75. Phenols, toxic action of, and their dis- sociation, 272. Physical problem, electrolytic dissocia- tion applied to, 226. Physiology, animal, application of physi- cal chemical methods to, 278. Physiology, animal, application of the dissociation theory to, 276. Polarized light, rotation of plane of, 21. Potential difference between metal and solution, 236. Potential, sources of, in concentration element, 252. Raoult, on freezing-point lowering and lowering of vapor-tension, 30. Refraction of light, 16. Refraction values of the elements, 20. Refractive power of salt solutions, specific, 108. Rise in boiling-point, and osmotic press- ure, relation between, 127. Rodger and Thorpe, on viscosity, 14. Rose, work of, 55. Rotation of plane of polarized light, 21. Rotatory power of salt solutions, no. Rudolphi's dilution law, 147. Salt solutions, properties are additive, 105. Schiff, specific heat and composition, 10. Schorlemmer, boiling-point results, 6. Secretion, application of osmotic press- ure and dissociation to, 281. Semipermeable membranes, 72. Silbermann and Favre, thermochemical work, 33. INDEX 289 Solubility, change in, as a measure of dissociation, 151. Solutions and electrolytic dissociation, 172. Solutions, the study of, 30. Solution-tension, constancy of, 236. Solution-tension, electrolytic 231. Solvents, different dissociating power of, 160. Soret, principle of, 86. Specific conductivity, 202. Specific gravity of salt solutions, 105. Specific heats of liquids, 8. Specific refractive power of salt solutions, 108. Stereochemistry of carbon, 23. Stereochemistry of nitrogen, 27. Stohmann, thermochemical work of, 36. Strength of acids and bases, 216, Sulphuric acid, dry, no action on dry metallic sodium, 169. Temperature and osmotic pressure, 76. Temperatures, conductivity at high, 215. Theories of electrolysis, Grotthuss, Clau- sius, and Williamson, 46. Thermochemical results, 36. Thermochemistry, the development of, 32. Thermodynamics applied to chemistry, 64. Thomsen, J., method of measuring affin- ity. 67. Thomsen, J., thermochemical work of, 35. Thomson, J. J., overthrows argument against the Berzelius chemical theory, 42. Thomson's, J. J., theory, 213. Thorpe and Rodger on viscosity, 14. Thorpe's work on molecular volumes, 13. Toxic action and electrolytic dissocia- tion, 268. Toxic action of phenols and their disso- ciation, 272. Toxic action of substances on fungi, 275. Valson's " moduli," 107. Van't Hoff's coefficient "i" calculation of, 96. Van't Hoff's coefficient " i" from freez- ing-point lowering and conductivitv, 98. Van't Hoff's Laws, history of, 76. Van't Hoff's Lecture, 77. Van't Hoff, the asymmetric carbon atom, 23- Van't Hoff, velocity of reactions, 65. Vapor-tension, lowering of, 178. Vapor-tension, lowering of, and osmotic pressure, relation between, 134. Velocity, absolute, of ions, 198. Velocity of ions, Hittorf, 52. Velocity of ions, 191. Velocity, relative, of ions, 192. Viscosity, 14. Water, conductivity of, 207. Water, rdle of, in chemical activity, 160. Wenzel, work of, 53. Whetham, experiment on absolute veloc- ity of ions, 199. Williamson, theory of solution, 50. Wislicenus, application and extension of van't Hoff's hypothesis of the asym- metric carbon atom, 25. Wiillner, lowering of vapor-pressure, 31. THE STORAGE BATTERY BY AUGUSTUS TREADWELL, Jr. E. E., Associate Member A. I. E. E. X PRACTICAL TREATISE ON THE CONSTRUCTION, THEORY, AND USE OF SECONDARY BATTERIES 257 PP« Fully Illustrated. i2mo. $1.75, net. "A welcome, serviceable, and up-to-date work on storage batteries; in fact the only published collection of practical data on the general construction, installation, and operation of the larger type of cells now so generally utilized in central station lighting, power, and railway plants, both as equalizers and reser- voirs, as well as in isolated lighting plants, and in telegraph and telephone plants. . . . The work concludes with practical in- structions and suggestions on the care and charging of accumu- lators, etc." - Electrical Engineering, Chicago. The book is not a dry, theoretical treatise, but of practical value not only to the professional electrician who wishes to keep abreast of modern invention in his own line, but to all who have anything to do with the installation of plants for giving motive power, light, etc., on whatever scale. THE MACMILLAN COMPANY 66 FIFTH AVENUE, NEW YORK THE PRINCIPLES OF THE TRANSFORMER. By FREDERICK BEDELL, Ph D., Assistant Professor of'Physics in Cornell University. 8vo. Cloth. 250 Illustrations. Price $3.25 net. This work constitutes a systematic treatise on the Alternating Current Transformer, and a logical exposition of the principles involved, of the most modern methods of transformer design, construction, and testing, and of trans- former systems of distribution. Portions of the book were originally prepared with the collaboration of Dr. A. 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