ENGINEERING BIBRAR* THE PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS Including' Electrolytes and Metals BY CHARLES A. KRAUS PROFESSOR OF CHEMISTRY IN CLARK UNIVERSITY WITH 70 FIGURES IN THE TEXT American Chemical Society Monograph Series BOOK DEPARTMENT The CHEMICAL CATALOG COMPANY, Inc. ONE MADISON AVENUE, NEW YORK, U. S. A. 1922 ENGINEERING LIBRAHY COPYRIGHT, 1922, BY The CHEMICAL CATALOG COMPANY, Inc. All Rights Reserved Press of J. J. Little & Ives Company New York, U. S. A. GENERAL INTRODUCTION American Chemical Society Series /(of Scientific and Technologic Monographs By arrangement with the Interallied Conference of Pure and Applied Chemistry, which met in London and Brussels in July, 1919, the Ameri- can Chemical Society was to undertake the production and publication of Scientific and Technologic Monographs on chemical subjects. At the same time it was agreed that the National Research Council, in coopera- tion with the American Chemical Society and the American Physical Society, should undertake the production and publication of Critical Tables of Chemical and Physical Constants. The American Chemical Society and the National Research Council mutually agreed to care for these two fields of chemical development. The American Chemical Society named as Trustees, to make the necessary arrangements for the publication of the monographs, Charles L. Parsons, Secretary of the American Chemical Society, Washington, D. C.; John E. Teeple, Treas- urer of the American Chemical Society, New York City; and Professor Gellert Alleman of Swarthmore College. The Trustees have arranged for the publication of the American Chemical Society series of (a) Scientific and (b) Technologic Monographs by the Chemical Catalog Company of New York City. The Council, acting through the Committee on National Policy of the American Chemical Society, appointed the editors, named at the close of this introduction, to have charge of securing authors, and of consider- ing critically the manuscripts prepared. The editors of each series will endeavor to select topics which are of current interest and authors who are recognized as authorities in their respective fields. The list of mono- graphs thus far secured appears in the publisher's own announcement elsewhere in this volume. The development of knowledge in all branches of science, and espe- cially in chemistry, has been so rapid during the last fifty years and the fields covered by this development have been so varied that it is difficult for any individual to keep in touch with the progress in branches of science outside his own specialty. In spite of the facilities for the 3 M542792 4 GENERAL INTRODUCTION examination of the literature given by Chemical Abstracts and such compendia as Beilstein's Handbuch der Organischen Chemie, Richter's Lexikon, Ostwald's Lehrbuch der Allgemeinen Chemie, Abegg's and Gmelin-Kraut's Handbuch der Anorganischen Chemie and the English and French Dictionaries of Chemistry, it often takes a great deal of time to coordinate the knowledge available upon a single topic. Con- sequently when men who have spent years in the study of important subjects are willing to coordinate their knowledge and present it in con- cise, readable form, they perform a service of the highest value to their fellow chemists. It was with a clear recognition of the usefulness of reviews of this character that a Committee of the American Chemical Society recom- mended the publication of the two series of monographs under the aus- pices of the Society. Two rather distinct purposes are to be served by these monographs. The first purpose, whose fulfilment will probably render to chemists in general the most important service, is to present the knowledge available upon the chosen topic in a readable form, intelligible to those whose activities may be along a wholly different line. Many chemists fail to realize how closely their investigations may be connected with other work which on the surface appears far afield from their own. These mono- graphs will enable such men to form closer contact with the work of chemists in other lines of research. The second purpose is to promote research in the branch of science covered by the monograph, by furnish- ing a well digested survey of the progress already made in that field and by pointing out directions in which investigation needs to be extended. To facilitate the attainment of this purpose, it is intended to include extended references to the literature, which will enable anyone interested to follow up the subject in more detail. If the literature is so voluminous that a complete bibliography is impracticable, a critical selection will be made of those papers which are most important. The publication of these books marks a distinct departure in the policy of the American Chemical Society inasmuch as it is a serious attempt to found an American chemical literature without primary regard to commercial considerations. The success of the venture will depend in large part upon the measure of cooperation which can be secured in the preparation of books dealing adequately with topics of general interest; it is earnestly hoped, therefore, that every member of the various organizations in the chemical and allied industries will recog- nize the importance of the enterprise and take sufficient interest to justify it. GENERAL INTRODUCTION AMERICAN CHEMICAL SOCIETY BOARD OF EDITORS Scientific Series: — Technologic Series: — WILLIAM A. NOYES, Editor, JOHN JOHNSTON, Editor, GILBERT N. LEWIS, C. G. DERICK, LAFAYETTE B. MENDEL, WILLIAM HOSKINS, ARTHUR A. NOYES, F. A. LIDBURY, JULIUS STIEGLITZ. ARTHUR D. LITTLE, C. L. REESE, C. P. TOWNSEND. American Chemical Society MONOGRAPH SERIES Other monographs in the series, of which this book is a part, now ready or in process of being printed or written: Organic Compounds of Mercury. By Frank C. Whitmore. 397 pages. Price $4.50. Industrial Hydrogen. By Hugh S. Taylor. 210 pages. Price $3.50. The Chemistry of Enzyme Actions. By K. George Falk. 140 pages. Price $2.50. The Vitamines. By N. C. Sherman and S. L. Smith. 273 pages. Price $4.00. The Chemical Effects of Alpha Particles and Electrons. By Samuel C, Lind. 180 pages. Price $3.00. Zirconium and Its Compounds. By F. P. Venable. Price $2.50. Carotinoids and Related Pigments: The Chromolipins. By Leroy S. Palmer. About 200 pages, illustrated. Thyroxin. By E. C. Kendall. The Properties of Silica and the Silicates. By Robert S. Sosman. About 500 pages, illustrated. Coal Carbonization. By Horace C. Porter. The Corrosion of Alloys. By C. G. Fink. Piezo-Chemistry. By L. H. Adams. About 350 pages. Cyanamide. By Joseph M. Braham. Ammonia Compounds. By E. C. Franklin. Wood Distillation. By L. F. Hawley. Solubility. By Joel H. Hildebrand. Glue and Gelatin. By Jerome Alexander. The Origin of Spectra. By Paul D. Foote and F. L. Mohler. Organic Arsenical Compounds. By George W, Raiziss and Joseph L. Gavron. Valence, and the Structure of Atoms and Molecules. By Gilbert N. Lewis. Shale OH. By Ralph H. McKee. Aluminothermic Reduction of Metals. By B. D. Saklatwalla. The Analysis of Rubber. By John B. Tuttle. The Chemistry of Leather Manufacture. By John A. Wilson. About 400 to 500 pages. Absorptive Carbon. By N. K. Chaney. The Chemistry of Cellulose. By Harold Hibbert. The CHEMICAL CATALOG COMPANY, Inc. ONE MADISON AVENUE, NEW YORK, U. S. A. PREFACE The history of the development of chemistry and molecular physics during the past few decades is largely an account of the growth of our conceptions of matter in the ionic condition. Whatever the shortcomings of the older ionic theory may have been, it has proved itself a powerful tool for the purpose of disclosing the structure of material substances. The intimate relation existing between matter and electricity, first in- ferred by Helmholtz as a consequence of Faraday's laws, has been estab- lished as securely as the atomic theory itself. Present day conceptions as to the nature of matter are, in a large measure, the outgrowth of fundamental conceptions underlying the ionic theory. It is true that certain branches of molecular physics, to the development of which the ionic theory has contributed, have outstripped this theory in the impor- tance of the results obtained. Nevertheless, the further advance of chemistry is largely dependent upon the further development of our con- ceptions of matter in the ionic condition. A vast amount of experimental material relating to this subject has accumulated during the past thirty years. It is found scattered through the volumes of many journals and the transactions of scientific societies. Unfortunately, this material has nowhere been collected in a form ren- dering it available to those who are not primarily interested in this field. The purpose of the present volume is to present the more important of this material in a comprehensive and systematic manner, thus enabling the reader to gain a knowledge of the contemporary state of this subject without an undue expenditure of time and effort. It is hoped, too, that this volume will prove useful to those investigators in allied sciences, who find it difficult to ascertain the precise limitations underlying methods and ideas which they often find it necessary to apply in their own subjects. The systems treated are those in which ionic phenomena are most clearly in evidence. Metallic systems are included, for, although the nature of the metals is but little understood, the existence of a relation between the phenomena in metallic and electrolytic systems is unmis- takable. The treatment of metals is necessarily brief, since our knowl- edge of them is still very uncertain. The chemical aspects of metallic systems are, so far as possible, kept in the foreground. A more detailed 7 8 PREFACE treatment of the experimental material relating to metals is unnecessary, since much of this has already been collected in various handbooks. Naturally, the major portion of this volume is devoted to a con- sideration of the properties of electrolytic solutions. The attempt has been made to present the subject broadly in order to bring out those elements of the phenomena which are common to solutions in all solvents. Solutions in non-aqueous solvents are treated somewhat more extensively than aqueous solutions, sinc'e the data relating to these solutions have not been collected heretofore. The subject is presented from an empirical standpoint, since an ade- quate theory of electrolytic solutions does not exist. Such theories as have been advanced in recent years give evidence of having been adapted to fit particular cases. In the end, the theory of electrolytic solutions will probably be a composite of various theories which now appear more or less applicable. Such a theory will doubtless embody some of the more fundamental elements of the older ionic theory. A complete bibliography has not been attempted. References given as footnotes will serve as a key to the literature. In conclusion, I wish to express my indebtedness to my colleague, Professor B. S. Merigold, for reading the manuscript and to Mr. Gordon W. Browne for his assistance in preparing the figures. C. A. K. Clark University, January 5, 1922. CONTENTS CHAPTER PAGE I. INTRODUCTION 13 1. Classification of Conductors. 2. Gases. 3. Metallic Conductors. 4. Electrolytic Conductors; a. Electrolytes Which Conduct in the Pure State; b. Electrolytic Solutions. 5. Electricity and Matter. 6. The Ionic Theory. II. ELEMENTARY THEORY OF THE CONDUCTION PROCESS IN ELEC- TROLYTES 19 1. Material Effects Accompanying the Conduction Process. 2. Concentration Changes Accompanying the Current: Hittorfs Numbers. 3. The Conductance of Electrolytic Solutions. 4. lonization of Electrolytes. 5. Molecular Weight of Electrolytes in Solution. 6. Applicability of the Law of Mass Action to Electrolytic Solutions. III. THE CONDUCTANCE OF ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 46 1. Characteristic Forms of the Conductance-Concentration Curve. 2. Applicability of the Mass-Action Law to Non- Aqueous Solutions. 3. Comparison of the Ion Conductances in Different Solvents. IV. FORM OF THE CONDUCTANCE FUNCTION 67 1. The Functional Relation between Conductance and Concentration. 2. Geometrical Interpretation of the Con- ductance Function. 3. Relation between the Properties of Solvents and Their Ionizing Power. 4. The Form of the Conductance Curve in Dilute Aqueous Solutions. 5. Solu- tions of Formates in Formic Acid. 6. The Behavior of Salts of Higher Type. V. THE CONDUCTANCE OF SOLUTIONS AS A FUNCTION OF THEIR VISCOSITIES . . , .-.'.."; 109 1. Relation between the Limiting Conductance A0 and the Viscosity of the Solvent. 2. Change of Conductance as Result of Viscosity Change due to the Electrolyte Itself. 3. 9 10 CONTENTS CHAPTER PAGE Relation between Viscosity and Conductance on the Addition of Non-Electrolytes. 4. The Influence of Temperature on the Conductance of the Ions. 5. The Influence of Pressure on the Conductance of Electrolytic Solutions. VI. THE CONDUCTANCE OF ELECTROLYTIC SOLUTIONS AS A FUNC- TION OF TEMPERATURE 144 1. Form of the Conductance-Temperature Curve. 2. Conductance of Aqueous Solutions at Higher Temperatures. 3. The Conductance of Solutions in Non-Aqueous Solvents as a Function of the Temperature. 4. The Conductance of Solutions in the Neighborhood of the Critical Point. VII. THE CONDUCTANCE OF ELECTROLYTES IN MIXED SOLVENTS . 176 1. Factors Governing the Conductance of Electrolytes in Mixed Solvents. 2. Conductance of Salt Solutions on the Addition of Small Amounts of Water. 3. The Conductance of the Acids in Mixtures of the Alcohols and Water. 4. Con- ductance in Mixed Solvents over Large Concentration Ranges. VIII. NATURE OF THE CARRIERS IN ELECTROLYTIC SOLUTIONS . . 198 1. Interaction between the Ions and Polar Molecules. 2. Hydration of the Ions in Aqueous Solution. 3. Calculation of Ion Dimensions from Conductance Data. 4. The Hydro- gen and Hydroxyl Ions. 5. Ions of Abnormally High Con- ductance. 6. The Complex • Metal- Ammonia Salts. 7. Positive Ions of Organic Bases. 8. Complex Anions. 9. Other Complex Ions. IX. HOMOGENEOUS IONIC EQUILIBRIA 218 1. Equilibria in Mixtures of Electrolytes. 2. Hydro- lytic Equilibria. X. HETEROGENEOUS EQUILIBRIA IN WHICH ELECTROLYTES ARE INVOLVED 232 1. The Apparent Molecular Weight of Electrolytes in Aqueous Solution. 2. The Molecular Weight of Electrolytes in Non- Aqueous Solutions. 3. Solubility of Non-Electro- lytes in the Presence of Electrolytes. 4. Solubility of Salts in the Presence of Non-Electrolytes. 5. Solubility of Elec- trolytes in the Presence of Other Electrolytes ; a. Solubility of Weak Electrolytes in the Presence of Strong Electrolytes with an Ion in Common; b. The Solubility of Strong Binary Elec- CONTENTS 11 CHAPTER *AGB trolytes in the Presence of Other Strong Electrolytes; c. The Solubility of Salts of Higher Type in the Presence of Other Electrolytes. XI. OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS .... 280 1. The Diffusion of Electrolytes. 2. Density of Electro- lytic Solutions. 3. Velocity of Reactions as Affected by the Presence of Ions. 4. Optical Properties of Electrolytic Solu- tions. 5. The Electromotive Force of Concentration Cells. 6. Thermal Properties of Electrolytic Solutions. 7. Change of the Transference Numbers at Low Concentrations. 8. Reactions in Electrolytic Solutions. 9. Factors Influencing lonization; a. The Ionizing Power of Solvents in Relation to Their Constitution; b. The Relation between the lonization Process and the Constitution of the Electrolyte. XII. THEORIES RELATING TO ELECTROLYTIC SOLUTIONS . . . 323 1. Outline of the Problem Presented by Solutions of Elec- trolytes. 2. Electrolytic Solutions from the Thermodynamic Point of View; a. Scope of the Thermodynamic Method; b. Jahn's Theory of Electrolytic Solutions; c. Comparison of the Thermodynamic Properties of Electrolytes; Inconsistencies in the Older Ionic Theory; The Thermodynamic Method; Numerical Values ; Solubility Relations According to Bronsted. 3. Theories Taking into Account the Interionic Forces; a. Theory of Malmstrom and Kjellin; b. Theory of Ghosh; c. Milner's Theory; d. Hertz's Theory of Electrolytic Conduc- tion. 4. Miscellaneous Theories. 5. Recapitulation. XIII. PURE SUBSTANCES, FUSED SALTS, AND SOLID ELECTROLYTES 351 1. Substances Having a Low Conducting Power. 2. Fused Salts. 3. Conductance of Glasses. 4. Solid Elec- trolytes. 5. Lithium Hydride. XIV. SYSTEMS INTERMEDIATE BETWEEN METALLIC AND ELECTRO- LYTIC CONDUCTORS 366 1. Distinctive Properties of Metallic and Electrolytic Con- ductors. 2. Nature of the Solutions of the Metals in Am- monia. 3. Material Effects Accompanying the Current. 4. The Relative Speed of the Carriers in Metal Solutions. 5. Conductance of Metal Solutions. XV. THE PROPERTIES OF METALLIC SUBSTANCES . . . . . 384 1. The Metallic State. 2. The Conduction Process in Metals. 3. The Conductance of Elementary Metallic Sub- 12 CONTENTS stances. 4. The Conductance of Elementary Metals as a Function of Temperature. 5. The Conductance of Metallic Alloys; a. Heterogeneous Alloys; b. Homogeneous Alloys; c. Solid Metallic Compounds; d. Liquid Alloys. 6. Variable Conductors. 7. The Conductance of Metals as Affected by Other Factors; a. Anisotropic Metallic Conductors; b. Influ- ence of Mechanical and Thermal Treatment; c. The Influence of Pressure on Conductance; d. Photo-Electric Properties. 8. Relation between Thermal and Electrical Conductance in Metals. 9. Thermoelectric Phenomena in Metals. 10. Galvanomagnetic and Thermomagnetic Properties. 11. Op- tical Properties of Metals. 12. Theories Relating to Metallic Conduction. INDICES 409 THE PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS Chapter I. Introduction. 1. Classification of Conductors. The property of electrical con- ductance appears to be one common to all forms of matter. The value of the conductance of different forms of matter, however, varies within very wide limits. Thus, the specific conductance of silver has a value of 6.0 X 105, while that of paraffin is 3.5 X 10~19. The specific con- ductance of gases under ordinary conditions is scarcely measurable. Nat- urally, the conductance of any given system depends upon its state; and, in general, any change in the condition of the system will materially affect the value of its conductance. Conductors may be conveniently grouped into a number of classes, the members of which possess many properties in common. 2. Gases. Under ordinary conditions the conducting power of gases is of a very low order, and such conductance as they possess is not an intrinsic property of the gases themselves, but is due, rather, to the in- fluence of external agencies. Thus, under the action of various radia- tions, gases are ionized and when in this condition conduct the current. This power of conduction, however, is lost when the external source of excitation is cut off. Whether or not the gases themselves may possess in some slight degree the power of conducting the current is uncertain, since the conducting power of gases which have been entirely freed from disturbing effects is of such a low order that the usual methods of meas- urements fail. The conductance of a gas is a function of its density. It is probable that at high densities gases will exhibit properties com- parable with those of many liquids. In the case of hexane it has been shown that the residual conductance on purification is for the most part due to the action of external radiations, which indicates that the con- ductance, which many liquid substances of low conducting power possess, is not a property of the pure substances themselves. In gases, as well as in insulating liquids, under the action of external 13 14 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS radiations, we have systems which are not in a state of equilibrium. These systems will not be further considered here, since they have been treated extensively in treatises dealing with the conduction of gaseous systems. In what follows we shall treat only such systems as are nor- mally in a conducting state. These may be divided into two classes; namely, metallic and electrolytic conductors. 3. Metallic Conductors. Metallic conductors are characterized by the absence of material effects when a current passes through a system comprising one or more conductors of this class alone. In this respect metallic conductors are for the most part sharply differentiated from electrolytic conductors, in which concentration changes or other material effects accompany the passage of the current through any surface of discontinuity. It does not follow, however, that metallic and electro- lytic conduction are entirely unrelated and that the two processes of conduction may not take place more or less simultaneously. Certain substances apparently conduct electrolytically when in one condition and metallically when in another. In other cases, a portion of the current appears to be carried by a process similar to that in the metals and another portion by a process similar to that in electrolytes. Metallic conductors are also characterized by the relatively high value of their conducting power. While a few metals exhibit a value of the conductance comparable with that of electrolytes, the conductance of most metals is many times greater than that of electrolytes. If this is true at ordinary temperatures, it is even more true at lower tempera- tures where the resistance may ultimately fall off to practically zero. The problem of metallic conduction is one possessing great interest and one whose solution cannot but prove to be of great importance in the development of chemistry and molecular physics. At the present time, however, its solution appears far from complete. While metallic con- ductors come within the scope of the present monograph, it is not in- tended to treat this subject exhaustively. 4. Electrolytic Conductors. Electrolytic conductors are character- ized, in the first place, by the fact that the passage of the current through them is accompanied by a transfer of matter. In a homogeneous elec- trolytic conductor this transfer of matter within the body of the con- ductor does not become apparent, but at any point of discontinuity material effects make their appearance. The material effects accom- panying the current are subject to certain definite laws commonly known as Faraday's Laws. Conductors for which Faraday's Laws hold true within the limits of the experimental error are termed electrolytic con- ductors. We have here to consider two classes of electrolytic conductors: INTRODUCTION 15 First, those which conduct the current when in a pure state and, second, those which conduct the current as a result of the presence of other sub- stances. This latter class of conductors is embraced within the term electrolytic solutions. a. Electrolytes Which Conduct in the Pure State. Within this class is included, in the first place, the fused salts. With a few exceptions, the fused salts are excellent conductors of the electric current. Their specific conductance near the melting point being of the order of 1.0, their conductance, therefore, is about 1 X 10"5 that of silver. The salts are compounds between a strongly electronegative and a strongly electro- positive constituent, and it is seldom that such substances do not possess the power of conducting the current in a marked degree. As the electro- positive or electronegative nature of one or the other of the constituents becomes less pronounced, however, the conductance of the resulting compound is diminished. This is the case, for example, with mercuric chloride. When hydrogen is combined with a strongly electronegative element or group of elements, the resulting compound, as a rule, exhibits electro- lytic properties. This, for example, is the case with water, which has been shown to conduct the current slightly when in a pure state. At 18° its specific conductance has a value of 0.042 X 10~6. Other com- pounds of hydrogen exhibit similar properties. When hydrogen is combined with elements which are less strongly electronegative, the resulting compounds exhibit a lower conducting power. In the case of the hydrocarbons the conductance reaches ex- tremely low values and it is possible that these substances in the pure state do not possess the power of conducting the current. While substances in the fused state are, as a rule, better conductors than in the solid state, electrolytic conductors are not restricted to the fused state, since certain substances in the solid state have been found to conduct the current quite as readily as the fused salts. b. Electrolytic Solutions. The most common electrical conductors are those in which the conductance is due to a mixture of two or more substances. As a rule, one of these, the solvent, is present in consider- able excess and may itself be only a very poor conductor. In this case, the conductance is said to be due to the addition of the second compo- nent, termed the electrolyte. To this class belong all the ordinary solu- tions of salts in water. In some cases an electrolytic solution results when a substance, which itself in the pure state is a poor conductor, is added to a second substance which likewise is a poor conductor in the pure state. As an example, we may cite solutions of the acids in water. 16 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS Hydrochloric acid, for example, in the pure state has a conductance even lower than that of water. When dissolved in water, however, the con- ductance of hydrochloric acid is much greater than that of ordinary salts dissolved in the same solvent. This class also includes solutions of various organic oxygen and nitrogen compounds in the liquid halogen acids. This behavior, moreover, is not restricted to acids, since solu- tions of many bases, such as ammonia, result from a mixture of two components neither of which possesses considerable conductance in the pure state. Where an electrolytic solution results from a mixture of two components which are themselves non-conductors, it is probable that reaction takes place when the two components are brought together, as a result of which an electrolyte is formed. Apparently, electrolytic solutions result in all cases when typical salts are dissolved in liquids up to sufficiently high concentrations. The property of forming electrolytic solutions with dissolved salts is thus not peculiar to water or solvents of the water type, but is a property common to all fluid media. It is true that the phenomena are materially altered as the nature of the solvent medium changes, but otherwise, if the solutions are sufficiently concentrated, the order of the conductance values will not differ greatly in different solvents. Among the various properties of the solvent medium which appear to have a marked influence upon the properties of the resulting electro- lytic solution, the dielectric constant stands out as the most important factor. As the dielectric constant of the solvent medium decreases, the conductance of the resulting solutions is altered, but the power to con- duct the current is never lost, no matter how low the dielectric constant of the solvent medium may be. Thus, solutions of salts of organic bases in chloroform conduct fairly well. From the standpoint of the development of chemistry, solutions of electrolytes are of first-rate importance. Electrolytic solutions exhibit a variety of phenomena and admit of a variety of reactions which are not to be found in the case of any other system of substances. A great variety of reactions take place at the electrodes when solutions of elec- trolytes are electrolyzed, and, when solutions of electrolytes are mixed, reactions take place between the constituent electrolytes. Reactions be- tween electrolytes are characterized by the extreme facility with which they occur. It is only in exceptional cases that the rate of such reac- tions is sufficiently low to admit of measurement. In solutions of elec- trolytes, therefore, we are dealing essentially with systems in equilibrium. This is of importance in their theoretical treatment, since thermodynamic principles may be readily applied to systems in equilibrium. INTRODUCTION 17 5. Electricity and Matter. While electrolytic solutions are thus of great importance from a practical point of view, they have played no less important a role in the development of our conceptions of the nature of matter and the nature of chemical reactions. That electricity and matter are intimately related was long since pointed out by Helmholtz as a consequence of Faraday's Law. Since in electrolytes electricity and matter are associated in definite and fixed proportions, and since matter appears to be discrete in its structure, it follows that electricity also must be discrete in its fundamental structure. Corresponding to the atoms, the smallest subdivisions of elementary substances, we have the funda- mental charge of electricity, the charge associated with a single univa- lent ion, which represents the smallest known subdivision of the electric charge. The development of the mechanics of the atoms in the last two decades has greatly enlarged our knowledge of the fundamental relation between electricity and matter. The fundamental charge of electricity, the charge associated with the negative electron, is objectively as real as the atoms and the molecules themselves. The intimate relation of the fundamental charge with the atoms or groups of atoms, which play so important a part in many chemical reactions, makes it appear probable that in chemical reactions the negative electron is primarily concerned. The horizon of chemistry is rapidly broadening in this direction, and a study of electrolytic systems will unquestionably play a great part in the ultimate elucidation of the mechanics of chemical reactions. 6. The Ionic Theory. To account for the various phenomena which have been observed in electrolytic solutions, the ionic theory has been introduced. While ordinarily the ionic theory is supposed to include fundamentally those concepts first introduced by Arrhenius, this theory is, in fact, a composite theory in which many molecular mechanical hypotheses are combined. It is to Arrhenius that is due the credit of first having developed a theory of electrolytes, quantitative in its nature, the correctness of which it was possible to determine by exact quantita- tive methods. While the gaps left in the theory of electrolytic solutions by the work of Arrhenius may not be overlooked, it should not be for- gotten that up to the present time no other theory has been proposed which is equally well able to account for so many and for so large a variety of facts. The introduction of the theory of Arrhenius has, from the start, met with the most determined opposition on the part of many chemists. It is interesting, now, to note that in recent years the basis of the objections to the theory of Arrhenius has greatly shifted and many of the originally proposed objections have since been found to be without foundation. 18 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS Nevertheless, the opposition to the theory of Arrhenius has continued to find supporters even up to the present time. In part, at least, this oppo- sition has been due to a realization on the part of chemists of the limi- tations of the theory of which its author has himself been aware. One of the fundamental truths which the theory of Arrhenius has brought to the attention of chemists is the existence of equilibria in electrolytic systems; and, however the details of his theory may subsequently be modified, it would appear that this most fundamental element of his theory must always be retained. Chapter II. Elementary Theory of the Conduction Process in Electrolytes. 1. Material Effects Accompanying the Conduction Process. That material effects accompany the passage of the current through a non- metallic medium was known at an early date. Thus Nicholson and Carlisle * observed the decomposition of water, and Sir Humphrey Davy 2 isolated the element potassium by electrolysis of the hydroxide. While it was thus recognized that chemical action is intimately associated with the passage of the current through an electrolyte, the quantitative rela- tionships were not studied until Faraday carried out his classical re- searches. It is unnecessary to give here in detail the results of Faraday's investigations. It will be sufficient to state the laws which now bear his name; namely, that chemical action accompanying the passage of the current is proportional to the quantity of electricity passing, and that, for a given quantity of electricity, the chemical effects in the case of different reactions are equivalent. These laws have since been verified by a multitude of observations on the action of the current passing through electrolytes. The most exact measurements have been made on the deposition of silver and on the liberation of iodine.3 In all cases, Faraday's Law has been found to hold within the limits of experimental error. It has been found to hold in the case of fused salts at higher tem- peratures,4 as well as in that of certain solid electrolytes.5 There are cases, indeed, where apparent exceptions to Faraday's Law appear. For example, when a current is passed through a solution con- taining a compound of sodium and lead in equilibrium with metallic lead, there are deposited on the anode 2.25 equivalents of lead per equiva- lent of electricity.6 Similar results have been obtained in the case of solutions of certain other metallic complexes in liquid ammonia.7 These cases, however, do not constitute an exception to Faraday's Law, since there are present in these solutions, presumably, a series of complexes 1 Nicholson and Carlisle, Nicholson's Jour. 4, 179 (1800) ; Gilbert's Ann. 6 340 (1800) 'Phil. Trans. 100, 1 (1808). 1 Bates and Vinal, J. Am. Chem. Soc. 36, 936 (1914). * Richards and Stull, Proc. Am. Acad. S8, 409 (1902). "Tubandt and Lorenz, Ztschr. f. phys. Chem. 87, 513 (1914). •Smyth, J. Am. Chem. Soc. 39, 1299 (1917). 7 Peck, J. Am. Chem. Soc. 1,0, 335 (1918). 19 20 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS whose average composition corresponds to the reaction which occurs at the electrode on electrolysis of these solutions. The precipitation at the anode in these solutions corresponds to the average composition of the complex. The solutions of the alkali metals and the metals of the alkaline earths in liquid ammonia constitute another apparent exception to Fara- day's Law, and in order to reconcile the results obtained in the case of these solutions with Faraday's Law it is necessary to extend it.8 When, for example, a current is passed through a solution of sodium in liquid ammonia, only a fraction of the current appears to be accompanied by an observable material process. These solutions, therefore, behave as though the current were in part carried by an electrolytic and in part by a metallic process. In order to reconcile these results with Faraday's Law, it is necessary to assume that the process of metallic conduction is likewise an ionic one, the current in this case being carried by the nega- tive electrons. If this hypothesis is made, then Faraday's Laws hold in these cases also. Faraday's Laws lead to important conclusions, not only with regard to the mechanism of the conduction process in electrolytes, but also with regard to the relation between electricity and matter. Interpreted from a molecular kinetic point of view, Faraday's Laws state that definite fixed quantities of electricity are associated with definite amounts of matter. As Helmholtz 9 pointed out, if matter consists of discrete particles, then electricity likewise is discrete in character. Corresponding to the atom, the smallest subdivision of matter, we have a fundamental electric charge, namely, the charge on a univalent ion. The charge, therefore, on any given particle of matter, whether it be of molecular or atomic dimensions or whether it be of larger dimensions as, for example, a drop of oil, may not be varied continuously but only in multiples of the unit charge. The discontinuous nature of the electric charge is one of the fundamental facts underlying electrochemical phenomena and must be taken into account in the interpretation of these phenomena. The reactions accompanying the passage of the current through an electrode surface indicate clearly that an intimate relation exists between chemical and electrical phenomena. Berzelius 10 attempted to account for the structure of chemical compounds by means of an electrical hypothesis. In this, however, he was unsuccessful, largely because he assumed a false mechanism as representing the association between electricity and matter. Instead of associating the charge with the atoms •Kraus, J. Am. Chem. Soc. 30, 1323 (1908) ; 36, 864 (1914). •Helmholtz, J. Chem. Soc. 39, 277 (1881) ; Wiss. Abh. 3, p. 52. 10 Berzelius, Lehrbuch, Ed. 3, Vol. 5 (1835) ; Ostwald, Electrochemie, p. 335. CONDUCTION PROCESS IN ELECTROLYTES 21 themselves, in his theory, he associated the charge with certain atomic complexes, which complexes in fact do not exist. Present day concep- tions regarding the constitution of chemical compounds do not differ in many respects from those of Berzelius save that it is assumed that the charge is associated with the atoms. In recent years, as a result of ex- perimental methods which have enabled us to gain an insight into the structure even of the atoms themselves, it is becoming more and more apparent that, in their compounds, the elements exist not in an atomic, but in an ionic, that is, in a charged, state. Under ordinary conditions this state of the elements in a compound is not clearly evidenced, except in the case of such compounds as are electrolytes when dissolved in suitable solvents or when in a fused state. From the standpoint of chem- istry, the study of the properties of electrolytes is therefore not so much an end as a means. In other words, the study of the properties of electrolytes constitutes a convenient method of acquiring knowledge regarding the constitution of various chemical compounds. Faraday was not content to merely state the results of his observa- tions and to combine these observations in the form of general laws. He attempted to gain an insight into the mechanism of the processes involved. It is often assumed that the ionic theory dates from the time when Arrhenius co-ordinated the work of earlier investigators and suggested a means for determining the relative amount of carriers present in an electrolytic solution under given conditions. The ionic theory, however, is much older than this. Its foundation was laid by Faraday,11 who recognized that in an electrolyte the current is carried by positive and negative electrical charges associated with definite material com- plexes moving in opposite directions through the solution. The terms which we now employ to describe the phenomena observed in the pas- sage of the current through an electrolyte are due to Faraday, and in themselves contain the concept of motion. The chief contribution of the later ionic theory consisted in devising methods which made it possible to determine the number of carriers present in an electrolytic solution. Whether or not these methods, in fact, give us a true measure of the number of ions present under various conditions in no wise affects the correctness of the more general conceptions upon which the ionic theory is based. 2. Concentration Changes Accompanying the Current: Hittorf's Numbers. The concentration changes in the neighborhood of the elec- trodes were first investigated by Hittorf.12 The fundamental conception "Faraday, "Experimental Researches," Vol. 1. "Hittorf, Pogg. Ann. 89, 177 (1853). 22 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS underlying these concentration changes is that, within the solution, the electric current is carried by positive and negative carriers which move with velocities proportional to the potential gradient existing in the solution. Within the body of the electrolyte itself, Ohm's law is obeyed. The observed concentration change at an electrode is thus the resultant of two effects; namely, loss or gain due to the reaction at the electrode and loss or gain due to the motion of the positively and negatively charged carriers. The simplest case is that in which precipitation of the ions takes place at the electrodes. Let us assume that the charge u is transported through the solution by the cation and the charge v by the anion. Then — — — will be the fraction of the charge carried by the positive ion and — -p— the fraction of the charge carried by the negative ion. If one equivalent of material is precipitated at the cathode, then u and v will represent the number of equivalents of matter carried up to the electrodes as cation and anion respectively. The concentration change in the neighborhood of the cathode will correspond to a loss of one equivalent of the electrolyte due to precipitation at the electrode and to a gain of — -:-— equivalents carried up to the electrode by the cations. The total observed concentration change, therefore, will be equal to the difference of these two or to a loss of — -r— - equivalents. Similarly, at the anode, the change will correspond to equivalents. It is evident that, if the concentration change due to the passage of a given charge is known and if the nature of the electrode reactions is known, ? J ?/ then the ratios — — — and — — — may be determined. These ratios, which Hittorf termed the "transference numbers" of the cation and anion, respectively, we shall denote by the symbols n and 1 — n. In determining the transference numbers of an electrolyte by the method of Hittorf, the concentration changes are measured with respect to water. In other words, the determination of these numbers is based upon the assumption that water itself remains at rest, and is in no wise concerned in the process of the transfer of electricity through the solution. We now know that this condition is not strictly fulfilled and that water plays a part in the conduction process. When a current of electricity passes through an aqueous solution, the solvent itself is transferred to some extent along with the ions. Obviously, this will affect the concen- CONDUCTION PROCESS IN ELECTROLYTES 23 tration changes observed at the electrodes. In order to determine the relative amounts of solvent transferred by the two ions, it is necessary that there should be present in the solution some reference substance which remains at rest when the current passes through the solution. The concentration changes may then be referred to this reference substance and the true transference numbers of the electrolyte determined, together with the relative amounts of water associated with the transfer of the charge through the solution. Since the results of such measurements will be discussed in detail in another chapter, it will be unnecessary to proceed further with their discussion here. They have been alluded to at this point merely for the purpose of calling attention to the fundamental assumption underlying the Hittorf method of determining transference numbers. That the passage of the current through an electrolyte is accompa- nied by a transfer of matter may also be shown by other means, as, for example, by introducing a surface of discontinuity 13 in the path of a conducting electrolyte. Such surfaces of discontinuity may be observed visually and thus yield a very direct method for demonstrating the trans- fer of matter by means of the current within the body of the electrolyte. If, for example, a solution containing hydrochloric acid is superimposed on a solution containing potassium chloride and a current is passed through the boundary of these solutions in such direction that the more rapidly moving ion, namely, in this case, the hydrogen ion, precedes the more slowly moving ion, the potassium ion, then the boundary be- tween the two solutions will advance in the direction of the positive current. The rate of motion of the boundary under a given potential gradient will depend upon the speed of the carriers. If a solution of an electrolyte is placed between solutions of two other electrolytes, each of which has one ion in common with the first, then, under the action of a potential, the two boundaries will move in opposite directions, the boun- dary between the cations moving toward the cathode and that Between the anions toward the anode. It is of course necessary that the condi- tions for stability of the boundaries should be fulfilled. This requires that at each boundary the more rapidly moving ion shall move in ad- vance of the more slowly moving ion. Allowing for certain corrections which must be made, the ratio of the speeds of the two boundaries is proportional to the current carrying capacities of the two ions.14 While the method of moving boundaries may thus be employed for measuring the transference numbers of electrolytes, its chief value, per- u Lodge, Brit. Ass. Reports, p. 389 (1886). "Lewis, J. Am. Chem. Soc. 32, 863 (1910). 24 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS haps, lies in that it enables us to observe the motion of the electrolyte within the solution visually. The results of transference measurements cannot be interpreted with- out a knowledge of the nature of the ions within the solution. The transference numbers are calculated from the observed concentration changes on an assumption as to the nature of the ions themselves. For example, in determining the transference numbers of potassium chloride by the Hittorf method, it is assumed that only potassium is transferred to the cathode and chlorine to the anode. If, however, ions different from those assumed exist in the solution, these will take part in the transfer of electricity and will have an influence upon the observed concentration changes at the electrodes. The question as to whether or not the ions have the simple structure commonly assumed is one which ultimately must be answered on the basis of considerations derived from other prop- erties of these solutions. That complex ions are formed in the case of certain solutions was conclusively shown by Hittorf.15 He found that in solutions of cadmium iodide the transference number of the cation, as measured, is greater than unity. Since this ion cannot transport more current than the total passing through the solution, it is obvious, as Hittorf pointed out, that the result may be accounted for by assuming that complex cations are formed by means of which iodine is transferred from the anode to the cathode. The effect of this is to lessen the con- centration increase of iodine in the neighborhood of the anode due to the transfer of the iodide ion. If either positive or negative ions of more than one kind occur in solution, an equilibrium must exist among them by virtue of which the relative concentration of these ions will be a function of the total con- centration of the salt. In general, with decrease in concentration, the more complex ions break up into simpler ones. It follows, therefore, that if complex ions exist in solution, the transference numbers should vary as a function of the concentration. We may now examine the numerical values of the transference num- bers which have been determined for various electrolytes and which are given in Table I.16 At a concentration of 5 millimols per liter, the cation transference number for sodium chloride, for example, is 0.396. Corre- spondingly, the anion transference number is 0.604. This means that in a sodium chloride solution of this concentration the fraction 0.396 of the current is carried by positively charged carriers, and the remainder by negatively charged carriers. It will be observed that, in general, the "Hittorf, loc. cit. "Noyes and Falk, J. Am. Chem. Soc. S3, 1436 (1911). CONDUCTION PROCESS IN ELECTROLYTES TABLE I. 25 CATION TRANSFERENCE NUMBERS (X 103) OF VARIOUS ELECTROLYTES IN WATER AT OR NEAR 18°. Electrolyte Temp. Concentration 0.0050.01 0.02 0.05 0.1 0.2 0.3 0.5 1.0 NaCl ... 18° 396 396 396 395 393 390 388 382 369 Kri 18 496 496 496 496 495 494 LiCl ...18 332 328 320 313 304 299 NH Cl 18 492 492 492 NaBr 18 395 395 395 KBr 18 495 495 A (/NO 18 471 471 471 471 HC1 ...18 832 833 833 834 835 837 838 840 844 HNO 20 839 840 841 844 BaCl 16 420 408 401 391 CaCl .. 20 440 432 424 413 404 395 389 SrCl 20 441 435 427 CdCl 18 430 430 430 430 430 CdBr, ...18 430 430 430 430 429 410 389 350 222 OdL ...18 445 444 44?, 396 296 127 46 3 Na SO 18 392 390 383 K SO 18 494 492 490 Tl SO 25 478 476 H2S04 ...20 822 822 822 820 818 816 812 Ba(N(X), .. . 25 456 456 456 Pb(NO ) 25 487 487 MeSO. ...18 388 385 381 373 CdS04 ...18 389 384 374 364 350 340 323 294 CuSO, , 18 375 375 373 361 348 327 transference numbers are functions of the concentration. This concen- tration effect is much more pronounced in concentrated than in dilute solutions, where these numbers appear to approach limiting values. If the underlying assumptions are correct and if complex ions are not present in solutions of these electrolytes, then the change in the trans- ference numbers at higher concentrations indicates a change in the rela- tive speed of these ions. In general, at higher concentrations the trans- ference number of the more slowly moving ion decreases. A portion of the effect at higher concentrations may be due to a transfer of water with the ions. But this is not sufficient to account for the entire change in the transference numbers. In most cases, the change in the transfer- ence numbers does not become pronounced until concentrations are reached where the viscosity of the solution is materially affected by the electrolyte. Since the motion of a particle through a viscous medium 26 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS is a function of its viscosity, it may be inferred that in part, at least, the variation in the transference numbers at the higher concentrations is due to the change of the viscosity of the solution. It will be observed that the transference numbers for potassium chloride are very nearly 0.5. In other words, in the case of this salt, each ion carries very nearly one half of the current. If the frictional resistance, which an ion meets in its motion through the medium, is inde- pendent of the sign of its charge, then this indicates that the two ions have approximately the same dimensions. This is borne out by the measurements of Washburn 16tt who showed that these ions are hydrated to approximately the same extent. The transference numbers of electrolytes are functions of the tem- perature. In Table II 17 are given the transference numbers of a number TABLE II. CATION TRANSFERENCE NUMBERS (X 10:l) OF VARIOUS ELECTROLYTES AS FUNCTIONS OF THE TEMPERATURE. Temp. NaCl KC1 HC1 BaCl2 0° 387 493 845 437 10 ... 495 841 441 18 397 496 833 30 404 498 823 444 50 ... ... 801 475 96 ... ... 748 of electrolytes at temperatures from 0° to 96° at concentrations in the neighborhood of 0.015 N. In the case of potassium chloride, the trans- ference number varies only very little with the temperature, whereas in that of sodium chloride the transference number of the cation increases, and in that of hydrochloric acid it decreases. As we shall see later, it is a general rule that with increase of temperature the transference numbers of all electrolytes approach the value 0.5. The transference numbers of ions having values greater than 0.5, therefore, decrease with increasing temperature; and those having smaller values increase under the same conditions. 3. The Conductance of Electrolytic Solutions. The conductance of an electrolytic solution is a function of the various factors which deter- mine its condition, such as concentration, temperature, etc. The quan- tity actually measured is the specific conductance of the solution. This is defined as the conductance in reciprocal ohms of a column of electro- "* Washburn, J. Am. Chem. 800. 31, 322 (1909). 17 Noyes and Falk, loc. cit. CONDUCTION PROCESS IN ELECTROLYTES 27 lyte having a cross-section of 1 sq. cm. and a length of 1 cm. The spe- cific conductance is a function of concentration, increasing, in general, with increasing concentration. However, in the case of certain electro- lytes at very high concentrations, the specific conductance passes through a maximum. This is the case, for example, with sulphuric and hydro- chloric acids dissolved in water, as well as with certain other electro- lytic solutions. The specific conductance, however, is a quantity which is not well adapted to the purpose of comparing the conductance of different electro- lytes. In the case of this property, as in that of many others, it is ad- vantageous to refer the numerical values to equivalent amounts of the dissolved electrolyte. If, therefore, the conductance of a given electro- lyte at two given concentrations is to be compared, the specific con- ductance is divided by the equivalent concentration. This quantity is called the equivalent conductance. As stated above, the specific con- ductance is referred to a unit cube of the electrolyte; that is, to a cube having a length of 1 cm. and a cross-section of 1 sq. cm. In order to avoid unnecessary factors in the expression for the equivalent con- ductance, it is desirable to express the concentration of the electrolyte in equivalents per cubic centimeter, rather than in equivalents per liter.18 In what follows we shall employ the Greek letter j\ to express the con- centration in equivalents per c.c., while the letter C will be employed to express the concentration in equivalents per liter. We have therefore lOOOi] = C. If we represent the equivalent conductance by the Greek letter A, and the specific conductance by the Greek letter \L, then we obviously have: »> : *-$ The value of the equivalent conductance A measures, in fact, the conducting power of the electrolyte in a solution of a given concentra- tion. Suppose, for example, that one equivalent of electrolyte were con- tained between two electrodes 1 cm. wide, separated by 1 cm., and of indefinite extent vertically. If the entire electrolyte were contained in 1 cu. cm. of liquid, then the equivalent conductance would obviously be equal to the specific conductance at this concentration, which is unity. If, now, more solvent were added to this solution, the amount of solute remaining constant, the concentration of the solution would be decreased. At the same time there would be an increase in the electrode area, but the total amount of conducting material between the electrodes and the » Kohlrausch and Holborn, "Leitvermogen der Elektrolyte," 1898, p. 84. 28 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS THC^^ O»O»« -^rHrHOS . . rH . . •**« T* 1O . . *>. CO co oj o* OJ * . . . cp *o Oi O5 *n oo -^ cp . cp . . . . c* . . TH *o ^. . -^j O5 TH . p oq t>. O5 CO O • • • • O O3 1> »O !>• CO 00 CO -CO • • • -CO • -t>-COCO « C- . . . rH ^. X O5 rH OO • • • T-J 00 ^ —- »- — o " OQ 00 O rH'C^rH'lOtO~O- O5 CO CO CO O O O5 O O0t>. CD O I - ^ rH I X § K ^ «o 2 S s" ^H S X rHrH- rHrHrHrHrHrHrH— rHrHrH -'rHrHrHrH^ COCO rHrHr-l ^.j H d 5 „ ^3 cqco co"^ p o cp i>- co o o OO4O5COeOC^ '(SlC^lrHCSQnrHOr^aidrH^^CSI^CScO^- 3 , w § x ^_.^ ^^^ 03 ^O ^ r™' |>» 00 t^» • ^H ^5 • C5 ^^ Oi C^ CO "^ ^^ H v O CS O> -COCO • CO C^l rH i-H OO rH O Ci O O> ^^ _ y XN rH rH r-^ r-H rn rH rH rH rH rH rH rH rH rH CO \ ? 1° d § | ^Kxt.-irtJr^r-.h^K^k^tk^K^t^riH^-kvl ^rl^jK^k^lhykvl ^^T^H^*5^r^"S^r'^r•^r^>v•^.,JS^^ CONDUCTION PROCESS IN ELECTROLYTES c* . .1-1 . .co .--4 1 »o O CO,CO.eo| t^pOSGQ ife 4 *° Q3 O .g x t?®QO=JSffi -oo oop *S 6 X- .QO • ' • • — • I »o rH » ^ : :§ X* ' i— i ,-H (M ^ i I : I £ 29 30 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS average distance which the conducting particles would have to travel between these electrodes would remain fixed. If the cell were filled to a height of I centimeters and if the conductance of the solution between the pair of electrodes were A, then, since the electrode area is equal to the reciprocal of the concentration, i.e., to I/ 1, it follows that the specific conductance of this solution would be: Therefore, in order to compare the conducting power of a solution of a given electrolyte at different concentrations, we divide the specific con- ductance of the solution by the concentration and compare the values of this ratio, namely the values of A. Similarly, in comparing the con- ducting power of solutions of different electrolytes in the same or different solvents at the same concentration, the values of the equivalent con- ductance of the electrolytes at that concentration are obviously to be compared. The equivalent conductance is a measure of the conducting of an equivalent amount of material. In comparing the conducting power of solutions, therefore, we require the values of the equivalent conductance A for these solutions. Values of the equivalent conductance of typical electrolytes in water at 18° are given in Table III.19 The concentrations in this case are ex- pressed in equivalents per liter. It will be observed that as the concen- tration of an electrolyte in water decreases, its equivalent conductance increases. For a decrease in the concentration in the ratio of one to two between normal and half normal, the equivalent conductance of a binary electrolyte increases approximately 30%. For a corresponding decrease in concentration between 1 and 0.5 milli-equivalent per liter, the equiva- lent conductance increases less than 1%. It is apparent, therefore, that as the concentration decreases, the equivalent conductance approaches a limiting value. The relation between the equivalent conductance and the concentra- tion is shown graphically in Figure 1, where values of the equivalent conductance of aqueous solutions of KC1, NaCl and LiI03 are plotted as ordinates and the logarithms of the concentrations as abscissas. The curves for different electrolytes are evidently similar in form. As the concentration decreases, the equivalent conductance apparently ap- proaches a definite value as a limit. A curve of this type, however, does not lend itself to a determination of the limiting value which the con- ductance approaches as the concentration 'decreases indefinitely. For 19Noyes and Falk, J. Am. Client. Soc. 3^, 454 (1912). CONDUCTION PROCESS IN ELECTROLYTES 31 the purposes of graphical extrapolation it is preferable to employ some function of the concentration which brings the point of zero concentra- tion, to which the extrapolation must be carried, to one of the axes on the plot. A convenient function which yields a simple type of curve is the cube root of the concentration. Such plots for potassium chloride and sodium chloride are shown in Figure 2. If the curves for potassium chloride and sodium chloride are extrapolated, they yield for the limit- ing value of the equivalent conductance values in the neighborhood of 130.0 and 108.9 respectively. The value obtained for A0 will, of course, depend upon the extrapolation function employed. In another chapter I 140 \zo 100 60 40 20 £S 4.0 4S AO 3* ?.0 ZJS T.O f.5 0.0 Log C. FIG. 1. Showing A as a Function of Log C for Aqueous Solutions at 18°. various functions proposed for this purpose will be discussed more in detail. For the present it will be sufficient to employ approximate values for the purpose of comparing the behavior of different electrolytes. The equivalent conductance of hydrochloric acid is much greater than that of the salts. The conductance curve, however, is similar in form to that of the salts. That is, with decreasing concentration, the equiva- lent conductance approaches a limiting value. In the case of hydro- chloric acid this value is in the neighborhood of 380 at 18°. We may now ask the question: To what are the differences in the values of the equivalent conductance of the different electrolytes due? Why, for ex- ample, is the equivalent conductance of hydrochloric acid greater than that of potassium chloride? Or, in other words, to what is the greater 32 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS conductance of hydrochloric acid due? It will be recalled that at a temperature of 18° and a concentration of 0.01 normal, for example, the value of the transference numbers of the positive ions in sodium chlo- ride, potassium chloride and hydrochloric acid are 0.396, 0.496 and 0.833 respectively. In the case of these electrolytes the negative carrier Equivalent Conductance A. * 8 g 5 | g X x \. X \ x \«, \ 70 x o.o as 0.4 o.e o.& 1. Cube Root of Concentration, C%. FIG. 2. Showing A as a Function of C^. is presumably the same, namely, the chloride ion, and it is only the posi- tive carriers which differ in these electrolytes. If, then, the negative carriers are the same in solutions of these electrolytes, it may be assumed that the current carried by these carriers in these solutions under the same conditions of temperature and concentration will be approximately the same, and consequently the difference in the conducting power of these electrolytes is due to the difference in the conducting power of their positive carriers. The carrying capacities of the spdium, potassium CONDUCTION PROCESS IN ELECTROLYTES 33 and the hydrogen ions are, therefore, 0.656, 0.984 and 1.972 times that of the chloride ion respectively. In other words, the carrying capacity of the hydrogen ion is 3 times that of the sodium ion and 2 times that of the potassium ion. If the tables of the conductance and of the trans- ference numbers are compared, it will be seen that in the more dilute solutions it is generally true that, for salts having an ion in common, those salts whose ions have greater transference numbers likewise have greater conducting power. We now come to an important generalization due to Kohlrausch,20 namely: In a solution of a single electrolyte, the two ions move inde- pendently of each other. Therefore, we may determine the fraction of the current carried by each ion, or, in other words, the conductance of each ion in a given solution, by multiplying the equivalent conductance of the solution by the transference number of the electrolyte in this solu- tion. If this is true, then, in a solution of sodium chloride having a concentration of 0.01 normal at 18°, the conductance due to the sodium ion is 101.88 X 0.396 =rANa= 40.34. Similarly, the conductance of the potassium and hydrogen ions under the same conditions is: AK = 122.37 X 0.496 = 60.69 and AH = 369.3 X 0.833 = 307.63 In these solutions the conductance of the chloride ion is 61.54, 61.68 and 61.67 for NaCl, KC1 and HC1 respectively. The conductance of the chloride ion is thus very nearly the same in equivalent solutions of these electrolytes. It is, however, by no means certain that the conductance of a given ion will in all cases be the same in solutions of different salts. If the transference numbers of an electrolyte are known at a given con- centration, then the conductance of its ions may be calculated. 4. lonization of Electrolytes. As we have seen, the equivalent con- ductance of a solution, which measures, so to speak, the conducting power of the dissolved electrolyte under given conditions, increases with decreasing concentration and appears to approach a limiting value. The current passing through an electrolyte under given conditions is carried, in the case of the simpler types of salts, by two charged constituents, namely the positive and the negative carriers, which, according to Fara- day, are termed the cation and the anion respectively. The relative amounts of the current carried by the positive and negative ions may be determined by means of transference experiments, which depend ulti- mately upon the concentration changes produced by the motion of the "Gottinger, "Nachrichten," 1876, p. 213. 34 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS carriers. If the current in a solution of an electrolyte is effected through the motion of charged carriers within the electrolyte, then we may in- quire: What fraction of the electrolyte present in the solution is con- cerned in the process of conduction; that is, what fraction of the electro- lyte exists in an ionic condition? Clausius 21 suggested that electrolytes are ionized, but he failed to draw any definite conclusion as to the extent of this ionization. In his time, the notion that a stable compound, such as potassium chloride, could be dissociated and moreover dissociated into oppositely charged constituents was contrary to accepted theories. Clausius was therefore content to merely throw out the suggestion that electrolytes are to some extent dissociated. The conclusion that an electrolyte is dissociated follows almost neces- sarily from the work of Kohlrausch and Hittorf, although neither of these investigators actually drew this conclusion. It was Arrhenius22 who proposed the fundamental hypothesis that an electrolyte in solution is dissociated and that the degree of its dissociation may be determined by means of the conductance of its solutions. Moreover, he showed that the dissociation as measured in this way is in agreement with many other well-known properties of these solutions. We have seen that, as the concentration of a solution decreases, its equivalent conductance increases and approaches a limiting value. We have also seen that the positive and negative ions within the electrolyte appear to move at definite rates under fixed conditions, provided the con- centration of the solution is not too great, and that the motion of the ions under these conditions takes place independently for each ion. If these conclusions are correct, then it appears that a logical explanation of the facts would be that, in the more concentrated solutions, a portion of the electrolyte has been removed from a condition in which it is able to take part in the conduction process, while the fraction of the sub- stance which remains in a conducting condition is measured by the ratio of the conductance at a given concentration to the conductance at very low concentrations, where apparently all the electrolyte takes part in the conduction process. Let y represent the fraction of the salt present in a conducting state; then the relative amount of the salt present in this state at any con- centration will be given by the ratio: "Clausius, Pogg. Ann. 101, 338 (1857). » Arrhenius, Bijlumj till K. Svenska, Vet. Akad. Handl. No. 13, 1884; Sixth Circular of the British Association Committee for Electrolysis, May, 1887 ; Zfschr. f. nhys. Cfiem.. 1, 631 (J887), CONDUCTION PROCESS IN ELECTROLYTES 35 where A is the equivalent conductance of the solution at the concentra- tion C, and A0 is the limiting value which the conductance approaches as the concentration decreases without limit. According to this theory, we may calculate the fraction of electrolyte in an ionized condition, if we know the equivalent conductance and the limiting value which the equivalent conductance approaches at zero concentration. In Table III were given values of the equivalent conductance of a number of electro- lytes at a series of concentrations. The approximate limiting values A0, which the equivalent conductance approaches at low concentrations, appear in the second column of that table. From these values we may calculate the degree of ionization of the electrolytes at any concentration falling within the intervals given. In the case of potassium chloride, for example, A0 = 130.0, approximately, and the equivalent conductance at normal concentration is 98.22. Therefore, the ionization of potassium chloride at this concentration is approximately 75% ; that is, of the total potassium chloride present in solution at this concentration, 75% is con- cerned in the actual process of conduction and 25% takes no part in this process. The ionization values of various electrolytes in water at 18° are given in Table IV.23 It will be observed that the ionization of salts of the TABLE IV. IONIZATION VALUES OF ELECTROLYTES IN WATER AT 18°. Concentra- tion, C. 10-8 2 x 10-3 5 x 10-3 10-z 2 X 10-2 5 X 10-* 10'1 2 X 10-1 5 X- 10-1 1.0 NaCl 977 .969 .953 .936 .916 .882 .852 .818 .773 .741 KC1 979 .971 .956 .941 .922 .889 .860 .827 .779 .742 Lid 975 .966 .949 .932 .911 .878 .846 .812 .766 .737 RbCl 980 942 855 748 CsCl 978 .969 .954 .937 847 T1C1 976 .965 .942 .915 KBr 978 .970 .955 .940 .921 .888 .859 .825 .766 .... KI 978 .970 .956 .941 .922 .890 .869 773 .727 KSCN 978 .970 .955 .940 .920 .888 .860 KF 978 .970 .954 .937 .915 .878 NaF 974 .964 .945 .925 .899 .854 T1F 961 .936 .908 .865 NaK03 977 .968 .950 .932 .910 .871 .832 .788 .719 .660 » Noyes and Falk, J. Am. Chem. Soc. 34, 454 (1912). In calculating the ionization at the higher concentrations Noyes and Falk have cor- rected for the viscosity change of the solution due to the added electrolyte. While there is every reason for believing that the change in the viscosity of the solution entails a change in the speed of the carriers, in general, the change in speed is probably not directly proportional to the change in the fluidity of the medium. All ionization values at higher concentrations, therefore, are more or less in doubt. As a rule the viscosity effects are small at concentrations below 10'2 N. In comparing the ionization of various electrolytes, therefore, it is best to choose concentrations at which the viscosity effect may be neglected. 36 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS TABLE IV.— Continued Concentra- tion, C. 10-82 X 10-« 5 X 10-' 10-2 2 X 10-2 5 X 10-2 10 J 2 X 10-1 5 X 10-' 1.0 KN03 978 .970 .953 .935 .911 .867 .824 .772 .688 .613 LiN03 975 .965 .950 .932 .911 .874 .840 .803 .750 .703 T1N03 977 .967 .948 .926 843 .788 AgN03 977 .968 .950 .931 .908 .859 .814 683 .617 KBr03 980 .970 .954 .934 .910 .868 .830 KC103 978 .969 .952 .933 .910 .866 .827 .780 .703 .... NaI03 971 .960 .939 .917 .890 .842 .801 .752 KI03 975 .965 .946 .928 .903 .860 .819 .775 LiIO3 970 .958 .936 .912 .883 .834 .789 .740 .682 .643 HC1 990 .988 .981 .972 .962 .944 .925 HN03 992 .987 970 940 .921 BaCl2 956 883 .850 .798 .759 .720 .672 .642 CaCl2 954 .938 .910 .882 .849 .802 .764 .727 .686 .662 MgCl2 955 .939 .910 .883 .851 .803 .765 .728 .687 .669 PbCl2 943 .917 .865 .808 .738 .627 CdCl2 931 .891 .803 .735 .664 .559 .453 .375 .289 .217 CdBr2 .897 .858 .749 .661 .573 CdI2 870 .809 .675 .573 .469 Ba(N03)2 . .953 .934 .898 .861 .818 .744 .679 .609 .504 .... Sr(N03)2 .. .953 .935 .904 .871 .833 .770 .719 .661 .579 .511 Ca(NO,)2 . .954 .937 .907 .876 .838 .781 .731 .679 .609 .549 Mg(N03)2. .953 .936 .907 .880 .847 .799 .760 .721 Pb(N03)2 . .947 .926 .886 .845 .793 .708 .635 .559 .454 .377 Cd(N03)2 . .996 .974 .917 .871 .848 .792 .731 .684 .628 .577 Ba(Br03)2.. .947 .927 .892 .856 .812 K2S04 954 .937 .905 .872 .832 .771 .722 .673 .618 .592 Na2S04 939 .925 .893 .857 756 .704 .652 LiS04 946 854 .811 .744 .688 .633 .567 .528 T12S04 948 .924 .882 .837 .780 .694 .625 .561 Ag2S04 949 .927 .885 .840 .784 K2C204 ... -960 .945 .916 .886 .849 .795 .753 .711 643 MgS04 873 .823 .740 .669 .596 .506 .449 .403 349 ZnS04 854 .799 .710 .633 .556 .464 .405 .360 309 CdS04 850 .791 .694 .614 .534 .437 .377 .332 .290 .277 CuS04 862 .804 .709 .629 .550 .455 .396 .351 309 MgC204 . . . .582 .472 .350 K4Fe(CN)6 859 .... .712 591 .538 .498 La(N03)3 902 802 701 K3C6H60T 926 .882 .817 705 La2(S04)3 464 289 198 Ca2Fe(CN)6 514 339 .... .262 same type is approximately the same at the same concentration. This is particularly true at the lower concentrations where the divergence in many cases is scarcely greater than the experimental error. The strong CONDUCTION PROCESS IN ELECTROLYTES 37 acids and bases, however, have a markedly higher ionization than the salts. Salts of higher type exhibit a lower degree of ionization than simpler salts. But here, again, salts of the same type have approxi- mately the same ionization at corresponding concentrations. If electrolytes approach complete ionization at low concentrations and if the ions in these solutions move independently of one another, then, if the transference numbers of the electrolytes are known, the value of the equivalent conductance of the individual ions may be calculated. If the conductances of a sufficient number of pairs of electrolytes have been determined, it is only necessary to know the transference number of a single electrolyte. In general, the values of the ionic conductances are based upon the transference number of potassium chloride. The values of the equivalent conductances of various ions in water at 18° are given in Table V.24 TABLE V. EQUIVALENT CONDUCTANCES OF THE INDIVIDUAL IONS AT 18°. Cs 68.0 Ba 55.4 Cl 65.5 Rb 67.5 Ca 51.9 N03 61.8 Tl 65.9 Sr 51.9 SON 56.7 NH4 64.7 Zn 47.0 C103 55.1 K 64.5 Cd 46.4 Br03 47.6 Ag 54.0 Mg 45.9 F 46.7 Na 43.4 Cu 45.9 I03 34.0 Li 33.3 La 61.0 S04 68.5 H 314.5 Br 67.7 C204 63.0 Pb 60.8 I 66.6 Fe(CN)6 95.0 The equivalent conductance values of the different ions are of the same order of magnitude, although the values for the hydrogen and hydroxyl ions are markedly greater than for the other ions. This is in agreement with the greater values of the conductance of solutions of the strong acids and bases. The conductance values of the different ions appear to bear no simple relation to their constitution. So, for ex- ample, lithium, which is lighter and has a smaller atomic volume than the remaining alkali metals, has the lowest conductance of any of the ions whose conductance values are tabulated. On the other hand, the nitrate and the chloride ions have markedly higher values than the fluoride ion. 5. Molecular Weight of Electrolytes in Solution. The hypothesis of Arrhenius, that the ionization of an electrolyte may be measured by the "Noyes and Falk, loc. cit. 38 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS ratio of the equivalent conductance at any concentration to the limiting value of the equivalent conductance at low concentrations, is supported by other important properties of these solutions. Raoult 25 had observed that the freezing point depression produced by electrolytes in water is greater than that of other substances at equivalent concentrations, van't Hoff,26 finally, supplied the theoretical foundation which made it pos- sible to calculate from the measurements of Raoult the molecular weight of substances in solution. Since in the case of aqueous salt solutions the depression was found to be abnormal, van't Hoff introduced an arbitrary factor i, which he apparently assumed to be a constant independent of concentration. Arrhenius at once recognized the significance of van't Hoff's factor and pointed out the relation between this factor and the coefficients derived from conductance measurements. According to Arrhenius, if electrolytes are dissociated, the freezing point depression of their solutions as measured should be greater than that calculated ac- cording to the method of van't Hoff, the molecular weight being assumed equal to the formula weight of the dissolved substance. If we let M where M is the formula weight and MQ the molecular weight calculated from freezing point measurements, then, obviously, there exists between i and y> the relation: (4) t=l+(n— lh, where n is the number of ions resulting from the dissociation of a single molecule. The values of y as calculated from freezing point or other similar determinations should thus agree with the values of y as calcu- lated from conductance measurements. In Table VI 27 are given the TABLE VI. COMPARISON OF IONIZATION VALUES DERIVED FROM CONDUCTANCE AND FROM FREEZING POINT MEASUREMENTS. Electrolyte Method 5 X 10a 10-2 2 X 10-2 5 X 10-2 10-1 2 X 10-1 5 X 10-1 KC1 ........ ... F .963 .943 .918 .885 .861 .833 .800 C .956 .941 .922 .889 .860 .827 .779 NH4C1 ......... F .947 .928 .907 .878 .856 .832 .... C .941 .921 " C. R. 94, 1517; 95, 188 and 1030 (1882). »« van't Hoff, 8v. Vet.-Akad. Handlingar 91, No. 17 (1886), p. "Noyes and Falk, J. Am. Chem. 8oc. 3J,, 485 (1912). Th< 148. e concentrated solutions have been corrected for the viscosity effects. (See footnote above, p. 35.) CONDUCTION PROCESS IN ELECTROLYTES 39 TABLE VI.— Continued Electrolyte Method 5 X 10-' 10 J 2 X 10-2 5 X 10-' 10-1 2 X 10-1 5 X 10-1 NaCl .. F .953 .938 .922 .892 .875 .850 .824 CsCl C .. F .953 .936 .916 .930 .882 .892 .852 .863 .818 .829 .773 .778 Lid C .. F .954 .944 .937 .937 ^928 .912 .847 .901 KBr C .. F .949 .932 .890 .929 .878 .889 .846 .863 .812 .839 .766 .813 NaN03 C .. F .955 .940 .903 .921 .885 .888 .855 .859 .830 .825 .798 .766 KNOg C ... F .950 .932 .901 .910 .880 .871 .836 .832 .781 .788 .711 .719 KC10 C .. F .953 .935 914 .911 891 .867 849 .824 798 .772 .688 KBrO C . F .952 .933 923 .910 896 .866 854 .827 805 .780 .703 C .954 .934 .910 .868 KI03 ... F .941 .913 .882 .828 .765 NaIOs C ... F .946 .939 .928 .916 .903 .890 .860 .842 .819 .773 .775 .... KMn04 , C ... F .939 .938 .917 .921 .890 .913 .842 .801 .752 • ... C .968 .951 .930 HC1 ... F .991 .975 .957 .933 .917 HN03 C ... F .981 .974 .972 .960 .962 .942 .944 .912 !900 879 •• • • C .970 .940 BaCl2 ... F .899 .878 .855 .819 788 758 CaCl2 C ... F .883 .850 .876 .798 .837 .759 815 .720 804 .672 MgCL C ... F .910 .882 .849 .885 .802 .854 .764 .839 .727 .833 .688 CdCl2 C ... F .910 .883 .791 .851 .768 .803 .690 .765 .605 .728 539 .687 CdBr2 C ... F .803 .735 .780 .664 .704 .559 .589 .453 .482 .375 367 .289 C .749 .661 .573 CdL ... F .593 .540 .400 225 100 C .675 .573 .469 Cd(NO«)2 ... F .948 .921 .901 887 884 • Ba(N03)2 ... C ... F .917 .917 .871 .888 .848 .855 .792 .731 .684 .628 PbCNCU, C ... F .898 .890 .861 .850 .818 .804 .744 724 .679 649 .609 568 .504 497 K2S04 C ... F .886 .929 .845 899 .793 857 .708 785 .635 730 .559 667 .454 ^fi« C .905 .872 .832 .771 .722 .673 .618 40 'PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS TABLE VI.— Continued Electrolyte Method 5X10-3 10 J 2X10-2 5X10-2 10-1 2X10-1 5X10-1 Na S04 . . . .. F .867 .795 .736 .672 .567 MgSCX, C .. F .893 .694 .857 .618 .756 .420 .704 .324 .652 .223 OuSO C F .740 616 .669 545 .596 455 .506 .318 .449 .403 .... ZnSO C F .709 665 .629 582 .550 489 .455 .396 .351 .... CdS04 C .. F .710 .658 .633 .569 .556 .477 .464 .343 .405 .360 .... "K" TJWP.'Nn C F .694 894 .614 868 .534 778 .437 .377 .332 .290 G 869 827 K4Fe(CN)e ... .. F .634 .581 .520 .425 C .. .... • • • • .591 .538 .498 values of y as determined from freezing point (F) and from conductivity (C) measurements. It will be observed that in the case of certain electrolytes the values of y derived by the two methods correspond very closely. This is par- ticularly true of potassium chloride where the two values correspond practically within the limit of experimental error up to concentrations as high as 0.1 normal. In the case of other salts, the divergence at higher concentrations is considerably greater. In general, however, the two values approach each other the more nearly, the lower the concentration of the solution. The correspondence between the two values is closest in the case of the binary salts. The more complex a salt, the greater is, as a rule, the divergence between the two values and the lower the con- centration at which a given divergence appears. The cause of the divergence of the ionization values as determined by the two methods is as yet uncertain. It is possible that the ionization is not correctly measured by the conductance ratio. At higher concen- trations, at any rate, it is to be expected that various influences will make themselves felt, such as the effect of viscosity, as a result of which the conductance as measured will not yield a true measure of the ionization. On the other hand, the molecular weight, as determined by osmotic methods, may be expected to be in error, since the laws of dilute solu- tions are assumed in calculating these values. The only assurance we have that the laws of dilute solutions are applicable under given condi- tions is that the results obtained are in agreement with other facts re- lating to these solutions. When a disagreement occurs, therefore, it is CONDUCTION PROCESS IN ELECTROLYTES 41 not known whether the laws of dilute solutions are inapplicable or whether some other discrepancy has arisen. In the case of salts of higher type, and even in that of the simpler types of salts, there is always a possibility that the ionization process as assumed in calculating the ionization from conductance measurements does not correspond to the true reaction. For example, in calculating the ionization of barium chloride, it is assumed that the reaction takes place according to the equation: BaCl2 = Ba" + 2CK It is possible, however, that ionization may take place in several stages, an intermediate reaction of the type: BaCl2 = BaCl+ + Cl- intervening. If an intermediate reaction of this type takes place, then it is obviously impossible to calculate the degree of ionization from con- ductance measurements. So far, it has proved difficult to establish the existence of intermediate ions. In general, it is to be expected that if intermediate ions exist, the transference numbers will vary markedly with the concentration. It should be noticed in this connection that those electrolytes, which exhibit the greatest divergence between the ionization values as calculated from conductance and from freezing point data, also exhibit a marked change in their transference numbers with change of concentration. In the case of sulphuric acid 28 the existence of an intermediate ion has been definitely established; and various consid- erations, based upon the solubility of salts in the presence of other salts, lend support to the view that intermediate ions exist in solutions of many salts of higher type.29 In any case, it is important to note that the values of i as deter- mined from freezing point and from conductivity determinations appar- ently approach the same limit at low concentrations, and, moreover, the limits approached are in agreement with the constitution of the salts in question. So, for example, in the case of the binary electrolytes, the limit approached is 2, in that of ternary electrolytes 3, in that of quater- nary salts 4, etc. No case has been observed in which the limit ap- proached is greater than that corresponding to the constitution of the salt. 6. Applicability of the Law of Mass Action to Electrolytic Solutions. On their surface, the results of conductance and of freezing point meas- urements appear to be in substantial agreement with the fundamental M Noyes and Eastman, Carnegie Report No. 19, p. 241. »Harkins, J. Am. Chem. Soc. 5Sf 1808 (1911). 42 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS hypothesis of Arrhenius; namely, that an electrolyte in solution is ion- ized, and its ionization is a function of the concentration, decreasing with increasing concentration. There exists, therefore, in solutions of electro- lytes an equilibrium between the ions and the un-ionized molecules, and this equilibrium must be subject to the usual laws governing equilibria. It is obvious that, according to the law of mass action, the ionization should increase with decreasing concentrations, since there is an increase in the number of molecular species as a result of the reaction. If we assume a simple system, as for example a binary salt MX which forms the ions M+ and X~, according to the equation: MX = M+ + X-, then, according to the law of mass action, we should have a relation: (5) , CMX where C^ represents the concentration of the molecular species X. If the solution is sufficiently dilute, so that the laws of dilute solutions may be applied, then K will be a function of the temperature only. On the other hand, it is obvious that a concentration must ultimately be reached where the laws of dilute solutions fail, in which case K becomes a func- tion of the concentration as well as of the temperature.30 If y is the degree of ionization of the salt and if C is its total concen- tration, then the concentrations of the two ions will be equal to Cy and the concentration of the un-ionized fraction will be equal to C(l — y). If these values are substituted in Equation (5), they lead to the equation: (6) The value of y mav be calculated either from conductance or from osmotic measurements. If the values of y according to the two methods agree, then obviously the two methods must lead to identical results, so far as the mass-action law is concerned. Since the degree of ionization is given by Equation 2, we may substitute this value of y in Equation 6 which yields the equation: m CA2 _ A0(A0_A)-X- This equation, involving the two constants K and A0, therefore expresses the relation between the concentration and the conductance of a solution 80 Van der Waals-Kohnstamm, "Lehrbuch der Thermodynamik," part 2, pp. 604, et seq. CONDUCTION PROCESS IN ELECTROLYTES 43 of a binary electrolyte. In general, to test the applicability of this equation, the value of A0 must first be determined by some method of extrapolation, after which the constancy of the function K may be determined by substituting in the above equation. In Table VII 31 are TABLE VII. VALUES OF K FOR ACETIC Aero IN WATER AT 25°. V A K X 100 0.989 1.443 0.001405 1.977 2.211 0.001652 3.954 3.221 0.001759 7.908 4.618 0.001814 15.816 6.561 0.001841 31.63 9.260 0.001846 63.26 13.03 0.001846 126.52 ' 18.30 0.001847 253.04 25.60 0.001843 506.1 35.67 0.001841 1012.2 49.50 0.001844 2024.4 68.22 0.001853 oo 387.9 — given values for the conductance of acetic acid in water at 25° at a series of concentrations. In this table, V denotes the dilution in liters per equivalent, A the equivalent conductance and K the ionization con- stant, calculated according to Equation 7. It will be seen that at higher concentrations, down to about 0.1 nor- mal, there is a marked change in the value of the function K, but at concentrations below 0.1 normal the function K remains constant, prac- tically within the limits of experimental error.31* At the highest dilution in the table the function K shows a slight increase, which is probably due to a discrepancy between the experimental values and the assumed value of A0. In general, the weaker the acid, the greater the range of concentration over which the function K remains constant. In other words, the concentration, at which the function K varies measurably from constancy, increases as the strength of the acid increases. In Table VIII 32 are given values of the equivalent conductance and the ionization constant of trichlorobutyric acid at a series of concentrations. It will be 11 Kendall, Med. Veten. Aka4. Nobelinstitut 2, No. 38, p. 1 (1913). »ia The decrease in the value of K at higher concentrations is in part, if not largely, due to the increasing viscosity of the solution. Compare Washburn, "Principles of Physi- cal Chemistry," 2nd Ed., p. 340. «a Kendall, loc. cit. 44 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS TABLE VIII. VALUES OF K FOR TRICHLOROBUTYRIC ACID IN WATER AT 25°. V A K X 100 5.90 237.3 18.3 11.80 276.8 17.4 23.59 308.5 15.9 38.63 326.4 14.8 47.18 331.8 14.0 53.98 336.0 13.9 77.26 343.9 12.7 107.96 350.4 11.8 154.5 357.0 11.5 215.9 361.2 10.9 309.0 365.1 10.5 431.8 368.2 10.7 618.0 370.9 (11.6) oo 376.0* — observed that the function K decreases throughout as the concentration decreases, but that the decrease is more marked at higher concentrations and that, apparently, at lower concentrations a limiting value is ap- proached. The slight variation in the value of K at the lowest con- centrations may be due either to experimental errors or to a discrepancy in the value of A0. In general, we may say that electrolytes, such as acetic acid, fulfill the condition that in the more dilute solutions the function K remains substantially constant. The same holds true in the case of the weak bases. Obviously, these results afford strong confirmative evidence of the correctness of the fundamental assumption that these electrolytes are ionized in solution according to a reaction equation of the following type: CH3COOH = CH3COO- + H+. On the other hand, when we proceed to a consideration of typical salts, or what are commonly known as strong electrolytes, we find that K ap- pears throughout to be a function of the concentration, its value decreas- ing as the concentration decreases. Below are given the values of the function K at a series of concen- trations for solutions of potassium chloride in water at 18°: 33 " The manner in which K varies with the concentration at very low concentrations is uncertain, since small errors in the extrapolated value of A0 cause a large variation in the resulting value of the function K. The values here given are based on the va A0 derived by the author. J. Am. Chem. Soc. W,\ (1920). Compare, also, Weiland, CONDUCTION PROCESS IN ELECTROLYTES 45 TABLE IX. VALUES OF K FOR KC1 IN WATER AT 18°. c= io-5 io-4 io-3 io-2 lo-1 i.o K=. 00518 .0147 .0474 .1542 .5052 2.14 It will be observed that in this case the function K decreases enormously with decreasing concentration. Whether the function approaches a finite limit, or whether it approaches a limit zero at low concentrations, cannot be determined with certainty. In general, the stronger the electrolyte, the more does the function K vary with the concentration and the greater is its value at a given concentration. In the case of hydrochloric acid the values of .K at a number of concentrations are as follows: TABLE X. VALUES OF K FOR HC1 IN WATER AT 18°. c= io-3 io-2 io-1 K = 0.189 0.366 1.11 If these values are compared with those for potassium chloride, it will be seen that the value of K is considerably greater for hydrochloric acid than it is for potassium chloride. At 0.1 normal the value of K for hydrochloric acid is approximately twice that for potassium chloride. In the more dilute solutions, however, this ratio appears to increase, since in a 0.001 normal solution the value for hydrochloric acid is approxi- mately four times that of potassium chloride. In view of the fact that electrolytes of a given type appear to be ionized to practically the same extent in water, it follows that the dis- crepancies found for different electrolytes of the same type will be of the same order of magnitude. Chapter III. The Conductance of Electrolytic Solutions in Various Solvents. 1. Characteristic Forms of the Conductance-Concentration Curve. The property of forming solutions which possess the power of con- ducting the current is one not restricted to water. Nor, indeed, are electrolytes in non-aqueous solvents restricted entirely to those sub- stances which are electrolytes in aqueous solution. As the field of non- aqueous solutions has been extended in recent years, it has become more and more apparent that the property of forming solutions which conduct the current is one which is common to a great many substances. Indeed, it seems not improbable that all liquid non-metallic media yield elec- trolytic solutions when suitable substances are dissolved in them. In attempting to account for the properties of electrolytic solutions in water, it is difficult to distinguish between those properties which are characteristic of electrolytic solutions in general and those which are characteristic of aqueous 'solutions alone. Such a knowledge can be obtained only from a study of the properties of electrolytic solutions in a large variety of solvents, and it appears unlikely that the properties of electrolytic solutions may be successfully accounted for until we possess reliable data as to the properties of non-aqueous solutions. While this field has been greatly extended during the past two decades, it is only in the case of a few solvents that we possess a sufficient mass of facts to enable us to treat the subject with a measurable degree of completeness. From a constitutional point of view, the alcohols are more nearly related to water than are any other solvents, since they may be looked upon as water in which one of the hydrogen atoms has been substituted by a hydrocarbon group. We should expect the properties of these solvents to diverge progressively from those of water as the size and complexity of the hydrocarbon group increases, and such has indeed been found to be the case. In general, the ionizing power of the alcohols diminishes as the complexity of the carbon group increases. Accord- ingly, methyl alcohol stands much nearer to water than do any of the other representatives of this class of solvents. For the purposes of illustration we may consider the conductance of 46 ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 47 sodium iodide in ethyl alcohol, the values of which are given in Table XI:1 TABLE XI. CONDUCTANCE OF SODIUM IODIDE IN ETHYL ALCOHOL AT 18°. V 125 250 500 1000 2000 4000 8000 oo A 28.6 31.3 33.5 35.2 36.5 37.6 38.3 39.4 Y 0.726 0.794 0.850 0.894 0.926 0.954 0.972 1.0 It will be observed that the conductance of solutions in ethyl alcohol increases with decreasing concentration in a manner similar to that of solutions in water. The limiting value of the equivalent conductance, that is the value of A0, for a solution of sodium iodide in ethyl alcohol is in the neighborhood of 39.4. It follows, therefore, that the ionization values of solutions in ethyl alcohol are considerably smaller than those of solutions in water. In Figure 3, the ionization of sodium iodide in ethyl alcohol is shown as a function of concentration. In the same figure, the ionization of sodium chloride in water is likewise shown. Acetone is another solvent whose solutions resemble those in water in many respects. The conductance of sodium iodide in acetone at 18° at a series of concentrations is given in Table XII: 2 TABLE XII. CONDUCTANCE OF SODIUM IODIDE IN ACETONE AT 18°. V .... 292.6 1030 4083 8874 18660 39700 64827 oo A .... 112.8 131.1 147.7 151.0 154.8 155.2 156.0? 156.0 Y 0.723 0.841 0.947 0.968 0.992 0.995 Here, again, it will be observed that the equivalent conductance rises throughout with decreasing concentration. While the conductance values of acetone solutions are greater than those of solutions in ethyl alcohol, the degree of ionization is very nearly the same in the two solvents. In both ethyl alcohol and acetone the ionization is much lower than it is in water. Another typical solvent is found in liquid sulphur dioxide. The con- ductance values of solutions of potassium iodide in sulphur dioxide at — 33° and at — 10° are given in Table XIII: 3 1Dutoit and Rappeport, Jour. d. Chim.-Phys. 6, 545 (1908). 1 Dutoit and Levrier, Jour. d. Chim.-Phys. 3. 43 (1905), •Franklin, J. Pliys. Chem. 15, 675 (1911), 48 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 1.00 •90 .80 I I I! .70 .60 .50 o.o 3.0 4.0 l.O 2.O Log V. FIG. 3. lonization of Binary Electrolytes in Different Solvents. TABLE XIII. CONDUCTANCE OF KI IN SO, AT — 33° AND — 10°. — 33C — 10C 0.50 27.5 39.7 1.00 37.7 46.9 2.0 40.1 46.8 4.0 40.5 44.8 8.0 41.0 42.5 16.0 42.7 43.5 32.0 64.0 47.2 55.1 47.8 55.7 V 128.0 256.0 512.0 1000.0 2000.0 4000.0 8000.0 cx> — 33C — 10C 65.9 66.5 78.8 81.7 93.4 99.2 108.6 118.8 124.2 140.5 139.0 162.5 153.0 167.5 181.8 199.0 Again, we find that as the concentration decreases the equivalent con- ductance increases and approaches a limiting value in the neighborhood of 167.5 at — 33°. The ionization of the solutions of potassium iodide in sulphur dioxide is, however, markedly lower than that of correspond- ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 49 ing solutions in acetone and alcohol. At higher concentrations the solu- tions of potassium iodide exhibit a marked divergence from the aqueous type. While it is true that at —33° the conductance falls throughout as the concentration increases, it will be observed that in the concentra- tion interval between V = 2 and V = 16 the conductance undergoes only an inappreciable increase, whereas at both higher and lower concentra- tions the conductance change is quite marked. This behavior of the more concentrated solutions in sulphur dioxide indicates the appearance of a new type of curve. At a slightly higher temperature this irregu- larity at the higher concentration becomes more pronounced and a maxi- mum and a minimum occurs in the curve, as may be seen from the values given for the conductance of these solutions at —10°. The curve at — 10° is a typical example which is met with in the case of a large number of solvents. Before discussing this case in detail, however, let us examine a type of solution the conductance curve of which has a form radically different from that of aqueous solutions. In Table XIV 4 are given values of the conductance of methyl alcohol in liquid hydrogen bromide at —90°. TABLE XIV. CONDUCTANCE OF CH3OH IN LIQUID HBr AT — 90°. V 0.1250 0.2500 0.500 0.769 1.00 2.00 7.69 A 0.600 0.631 0.211 0.0378 0.00925 0.001660 0.000615 It will be observed that in the more dilute solutions the conductance diminishes continuously as the concentration decreases. There is no in- dication that, at lower concentrations, the conductance approaches a limiting value other than zero. In the more concentrated solutions the conductance increases greatly as the concentration increases, until a maximum is reached, after which the conductance falls off sharply. It is interesting to note also that, in this solvent, methyl alcohol functions as an electrolyte, although in most solvents methyl alcohol exhibits no electrolytic properties. Actually, however, the solutions of methyl alcohol in hydrogen chloride do not differ materially in properties from solutions of typical salts, such as the substituted ammonium salts in this solvent, although the value of the equivalent conductance is larger for typical salts. Another example of this type of conductance curve is that of solu- tions of trimethylammonium chloride in liquid bromine. The values of the conductance at 25° are given in Table XV: 5 'Archibald, J. Am. Chem. Soc. 29, 665 (1907). "Darby, J. Am. Chem. Soc. 40, 347 (1918). 50 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS TABLE XV. CONDUCTANCE OF TRIMETHYLAMMONIUM CHLORIDE IN BROMINE AT 25°. C . . 0.029 0.0595 0.2093 0.3427 0.5334 0.9323 1.236 1.314 A 0.0253 0.1038 2.063 5.259 6.469 9.865 11.49 11.00 This case is, if anything, even more extreme than that of methyl alcohol in hydrogen bromide. The increase in the conductance with increasing concentration is extremely marked. At a concentration of 0.029 mols per liter, the equivalent conductance is only 0.0253, whereas at a concen- tration of 1.236 mols per liter the equivalent conductance is 11.49. It is to be noted that in the neighborhood of normal the equivalent conduct- ance of these solutions in bromine is comparable with that of solutions in ordinary solvents. At slightly lower concentrations, however, this is no longer the case. For a concentration change in the ratio of 43 to 1, the conductance increases in the ratio of approximately 450 to 1. It is apparent that the relation between the conductance and the concentration, as we observe it in aqueous solutions, is not a property characteristic of electrolytic solutions in general. It represents one ex- treme of two types of solutions, the other of which is exemplified in solutions in hydrogen bromide and in bromine. Between these two ex- treme types we have an intermediate type which appears to combine the characteristics of these extreme types. A typical example is fur- nished by solutions of potassium iodide in methylamine at — 33°, values of which are given in Table XVI: 6 TABLE XVI. CONDUCTANCE OF KI IN CH3NH2 AT — 33°. V .... 0.6094 1.190 2.320 8.833 33.62 107.4 408.9 1557 5927 A .... 31.12 32.97 28.49 17.40 14.64 17.72 27.79 45.86 74.53 The conductance curve in this case is intermediate in type between that of solutions in water and in bromine. In the more dilute solutions, be- ginning at a dilution of approximately 33 liters, the conductance increases continuously with decreasing concentration and apparently approaches a limiting value. At a dilution of 33.62 liters, the conductance has a minimum value. At higher concentrations it increases markedly, reach- ing a maximum in the neighborhood of 1.19 liters, after which it again decreases. In the more concentrated solutions, therefore, the curve re- sembles that of solutions in bromine. •Fitzgerald, J. Phya. Chem. 16, 621 (1912). ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 51 These intermediate curves apparently form a continuous series be- tween the two extreme types and, by suitably changing the condition of the solutions, a continuous shift takes place in the curve from one ex- treme toward the other. For example, as the temperature of a solution is increased, there is a shift from the aqueous type toward the type exemplified by the solutions in hydrogen bromide. This is clearly the case with solutions in sulphur dioxide. As we have already seen, at —33° the conductance of solutions in sulphur dioxide increases continu- ously with decreasing concentration, although there is a certain concen- tration interval over which the conductance change is extremely small. At a temperature of — 10° this curve exhibits a maximum and a mini- mum, similar to that just described in the case of solutions in methyl- amine. At still higher temperatures, the maximum and minimum be- come more pronounced. Methylamine may be looked upon as a derivative of ammonia and the relation between methylamine and ammonia solutions may be ex- pected to be similar to that between the alcohols and water. As we shall see presently, ammonia solutions, for the most part, belong to the aqueous type; that is, the conductance increases throughout with de- creasing concentration. In the case of methylamine solutions, as we have seen, the curve exhibits a pronounced maximum and minimum. Solutions in ethylamine are still further removed toward the bromine type, as is apparent from the values given for the conductance of silver nitrate in ethylamine in Table XVII: T TABLE XVII. CONDUCTANCE OF AgN03 IN C2H5NH2 AT — 33°. V 0.9928 1.981 3.953 15.73 62.65 125.0 A 5.67 5.820 4.320 1.677 1.038 1.041 In this case the conductance decreases with decreasing concentration, but it is evident that at the lower concentrations the conductance does not approach the value zero as a limit. In fact, it is apparent that, at dilu- tions slightly greater than 125 liters per mol, the conductance curve will again rise. Indeed, solutions of certain other salts in ethylamine exhibit a distinct minimum in the neighborhood of 0.01 normal. The conductance curve of solutions in amylamine resembles that of solutions in bromine very closely, the conductance decreasing throughout with decreasing con- centration and apparently approaching a value of zero so far as has been observed. T Fitzgerald, Joe. ctt. 52 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS It is evident that, in order to account for the phenomena of electro- lytic solutions, it is necessary to take into consideration the fact that the form of the conductance curve as observed in water is not a general type, but is only one extreme of several types. Any comprehensive theory of electrolytic solutions must obviously account for both types. The only non-aqueous solvent with regard to whose solutions we have anything like complete information at the present time is liquid ammonia. This solvent yields electrolytic solutions with an extremely large variety of substances and we shall have frequent occasion to refer to these solutions below. At this point it will be sufficient to give an example of the conductance curve for a typical salt dissolved in liquid ammonia. In Table XVIII 8 are given values of the conductance of solutions of potassium nitrate in liquid ammonia at its boiling point, approximately —33°, at a series of dilutions. It is evident that these solutions belong to the aqueous type, the conductance increasing throughout with decreas- ing concentration and approaching a limiting value at very low concen- trations. The limiting value for potassium nitrate is 339.9 TABLE XVIII. CONDUCTANCE OF KN03 IN NH3 AT — 33°. V 324 1001 2514 6162 23060 69820 oo A 192.7 245.0 282.7 309.9 330.1 338.6 339. Y 0.567 0.720 0.831 0.912 0.972 0.995 Solutions of typical salts in liquid ammonia exhibit a somewhat higher conductance than do the corresponding salts in water, but it is evident that the ionization of these salts in liquid ammonia solutions is consid- erably lower than in water, as may be seen from Figure 3. Ammonia apparently approaches ordinary alcohol and acetone in its ionizing power. In the case of certain solutions in liquid ammonia, an intermediate type of conductance curve is found. This is the case, for example, with potas- sium amide whose curve exhibits a minimum.10 A similar, but in some respects a slightly different, case is found in certain of the cyanides, of which mercuric cyanide and silver cyanide may serve as examples. The conductance values for solutions of mer- curic cyanide in ammonia are given in Table XIX.11 •Franklin and Kraus, Am. Chem. J. 23, 277 (1900). 9 Kraus and Bray, J. Am. Chem. Soc. 35, 1037 (1913). 10 Franklin, Ztachr. f. phj/s. Chem. 69, 290 (1909). "Franklin and Kraus, loc. cit. ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 53 TABLE XIX. CONDUCTANCE OF Hg(CN)2 IN NH3 AT —33°. V 1.16 3.37 5.71 21.8 33.0 55.6 A 2.48 1.86 1.79 1.63 1.64 1.75 The solutions of this salt exhibit a conductance curve with a very flat minimum, the curve thus being similar to that of potassium iodide in methylamine. Silver cyanide likewise exhibits a curve with a minimum. The values are given in Table XX.12 TABLE XX. CONDUCTANCE OF AgCN IN NH3 AT — 33°. V 4.48 9.02 17.85 35.25 69.69 137.7 272.8 538.0 1063.0 A .... 15.58 15.39 14.28 13.45 12.83 12.41 12.12 12.00 12.00 It is evident from these values that the conductance curve for silver cyanide has a very flat minimum in the neighborhood of 10~3 normal. What is more striking, however, is the fact that the conductance changes so little with the concentration. The entire change between 10~3 normal and 0.5 normal is only from 12.00 to 15.5 or about 30 per cent. We see that solutions in non-aqueous solvents exhibit a great variety of properties many of which diverge largely from those of aqueous solu- tions. A great variety of liquids are capable of forming electrolytic solu- tions with various substances and many substances which do not form electrolytic solutions when dissolved in water form such solutions in other solvents. 2. Applicability of the Mass-Action Law to Non-Aqueous Solutions. From a study of aqueous solutions of electrolytes, the conclusion was reached that the conductance is due to the motion of charged carriers through these solutions and that these charged carriers are in equilibrium with the neutral molecules of the electrolyte. In other words, the elec- trolyte is dissociated, or ionized, to use the accepted term for this process, and the degree of ionization may be measured by means of the ratio of the equivalent conductance of the solution to the limiting value which the equivalent conductance approaches as the concentration diminishes in- definitely. If this hypothesis is correct, then, as we have seen, the mass- action law should apply, and, if the laws of dilute solutions may be assumed to hold, Equation 7 expresses the relation between the con- ductance and the concentration of an electrolytic solution. It was found u Franklin and Kraus, loc. cit. 54 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS that this relation is fulfilled in the case of aqueous solutions of weak acids and bases, but is not fulfilled in the case of solutions of electrolytes which are more largely ionized. It is at once apparent that non-aqueous solutions furnish exceptions to the simple mass-action law, since we have here cases in which the conductance increases with increasing concentration, which result is not in accord with Equation 7. To solve the problem resulting from this discrepancy, three methods of attack at once present themselves. In the first place, the ionization may not be correctly measured by the ratio A/A0. Then, again, we may assume that the reaction equation on which the calculations are based is not correct. Finally, we may assume that the equilibrium is of the type as assumed, but the conditions assumed in deriving the mass- action law are not fulfilled in the solutions in ques- tion; in other words, the solutions may not be considered as dilute. It is of course impossible to state on a priori grounds the concentration at which the deviations from the laws of dilute solutions will become appre- ciable. The only method that we have of attacking this problem at present is to carry out measurements at different concentrations and examine the change in the mass-action function as the concentration de- creases. If the fundamental assumption underlying the hypothesis of Arrhenius is correct, then the mass-action function should approach a definite limiting value as the concentration decreases. Let us examine, therefore, the conductance curves of the more dilute non-aqueous solutions in order to determine whether the mass-action function approaches a definite limiting value. It is obvious that, in order to calculate the degree of ionization, the value of A0 must be known and this value can be obtained only by extrapolation. If the mass-action equation in its simple form actually holds, then it is possible to determine the value of A0 by a very simple graphical extrapolation. Equation 7 may be written in the form: (8) It is obvious that, if this equation holds, the reciprocal of the equivalent conductance, A, is a linear function of CA, which is equal to the specific conductance multiplied by 103. In other words, if the mass-action law is obeyed, the reciprocal of the equivalent conductance and the specific conductance are connected by means of a linear equation. If, therefore, the experimental values of CA and of I/A are plotted in a system of rec- tangular co-ordinates, the points will lie on a straight line if the mass- action law holds. This straight line extrapolated to the axis of I/A ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 55 yields the value of A0 while, obviously, the value of K results from the slope of the curve. Leaving aside for the moment the exact values of A0, we may roughly compare the variation of the function K for solutions in different solvents. In Table XXI13 are given the values of this function for potassium nitrate dissolved in ammonia and in water at corresponding degrees of ionization. TABLE XXI. VALUES OF K FOR SOLUTIONS OF KN03 IN NH3 AND H2O. . 57.00 0.2277 1.279 70.00 0.197 0.9528 85.59 0.167 0.3389 91.66 0.1635 0.2332 94.30 0.1699 0.1710 It is at once apparent that the variation of the function K in dilute am- monia solutions is much less than it is in aqueous solutions. Indeed, between the ionization values of 70% and 94% the value of the con- ductance function for potassium nitrate in ammonia changes only by a few per cent, whereas, in aqueous solutions, this function increases ap- proximately five times. Apparently, therefore, dilute solutions in am- monia approach the mass-action law much more nearly than do solutions of the same substances in water. A circumstance which greatly facilitates the study of the applicability of the mass-action law to dilute solutions in non-aqueous solvents is the relatively low ionization of the solutions in these solvents. In the case of the strong electrolytes in water, a comparison of the experimental re- sults with the mass-action law is rendered difficult by the high ionization of these salts. Since the expression 1 — y, the value of the un-ionized fraction, appears in the denominator of the mass-action expression, and since y is very nearly unity, it follows that the equivalent conductance must be determined with a high degree of precision in order to determine the applicability of the mass-action function. It is only in the case of potassium chloride that sufficiently precise data are at hand to make a study of this kind possible in aqueous solutions, and even in this case the results of such a comparison remain uncertain. Only a small portion of the data relating to the conductance of non- aqueous solutions has sufficient precision to make a comparison with the consequences of the mass-action law possible. It is only in the case of u Franklin and Kraus, Am. Chem. J. £3f 299 (1900). 56 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS solutions in liquid ammonia that we have such data relating to a large number of electrolytes. Kraus and Bray 14 have examined the conduct- ance of ammonia solutions from this point of view. In Figures 4 and 5 are plotted values of the reciprocal of the equivalent conductance as /V3K) /V330 JL&, 2.5 3.0 7.5 10.0 tooo(cA) 12.5 15.0 17.5 FIG. 4. Showing Approach of Dilute Solutions in Liquid NH3 to the Mass-Action Law. ordinates against values of the specific conductance as abscissas. In Figure 4 the symbol of the electrolyte is shown in the figure, while in Figure 5 the curves in order from 1 to 7 are for: 1, thiobenzamide ; 2, orthomethoxybenzenesulphonamide; 3, paramethoxybenzenesulphona- "Kraus and Bray, J. Am. Chem. Soc. 35, 1315 (1913). ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 57 mide; 4, metamethoxybenzenesulphonamide; 5, nitromethane; 6, sodium- nitromethane; and 7, orthonitrophenol. Examining the figure for the typical salts, it will be observed that in the case of silver iodide, am- monium chloride, potassium nitrate, and ammonium nitrate the curves -Afi- A.-JA4 ff 0.76X10*, KO 90X10* 2.5 5-0 2-5 12.5 150 175 20.O IO.O ioo(cA) FIG. 5. Showing Approach of Dilute Solutions of Organic Electrolytes in NHs to the Mass-Action Law. in dilute solution approach a straight line. In the case of ammonium bromide and potassium iodide the number of points is not sufficient to actually determine the form of the curve in dilute solutions. In the case of other salts, the figures of which are not shown here, similar results were obtained; that is, in those cases where sufficient data are available at low concentrations, the points approximate a straight line and this 58 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS is the more true the more consistent the data are among themselves. In the case of the seven electrolytes in Figure 5, the correspondence with the mass-action law is much more certain. One reason for the better agreement in the case of these electrolytes is their lower ionization, as a result of which errors in the value of the equivalent conductance pro- duce a smaller variation in the mass-action constant. Moreover, in these cases the mass-action law appears to apply to greater total salt concen- trations. In view of the fact that the original experimental results are independent of any considerations as to the applicability of the mass- action law, the conclusion appears justified that in the case of solutions in liquid ammonia the mass-action function approaches a limiting value at low concentrations. The total salt concentration at which the deviations from the simple mass-action law become appreciable is the lower, the greater the ioniza- tion of the electrolyte. In this respect solutions in ammonia resemble solutions of the acids and bases in water. The lower the ionization of an acid or a base in water, the higher the concentration up to which the mass-action law appears to hold. From an examination of their results, Kraus and Bray drew the conclusion, however, that the deviations from the mass-action law become appreciable for different electrolytes in ammonia solution at about the same ion concentration. They found that the mass-action function for a number of electrolytes was increased over the limiting value by 5% at ion concentrations lying in the neigh- borhood of 1 X 10"4 N. It is, however, apparent that in certain cases the ion concentration is considerably greater and in other cases considerably lower than this value. So, for example, in the case of potassium amide this concentration is 2.76 X 10~*, while in that of trinitraniline it is 0.22 X 10-4. We may now consider the values of the mass-action constant for different electrolytes in ammonia solution. The values for the inorganic electrolytes are given in Table XXII 15 (see opposite page) . It is apparent, in the first place, that the values of the mass-action con- stant for the different inorganic electrolytes differ considerably. The ex- treme values lie between 0.056 X 10~4 for sodium amide and 42 X 10'4 for potassium iodide. The greater number of the salts, however, have ionization constants lying between 21 X 10~4 and 28 X 10~4. This varia- tion of the ionization constants for different inorganic electrolytes in am- monia is in striking contrast with the nearly identical ionization of the same electrolytes in water. It should be borne in mind, however, that in aqueous solution the degree of ionization is so high, in any case, that dif- 18 Kraus and Bray, loc. cit. ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 59 TABLE XXII. VALUES OF K AND A0 FOR DIFFERENT ELECTROLYTES IN NH3 AT — 33°. Salt WK A0 NaNH2 0.056 263 KNH2 1.20 301 Agl 2.90 287 NH4C1 12.0 310 NaCl 14.5 309 KN03 15.5 339 KBr 21.0 340 T1N03 21.0 323 NaBr03 23.0 378 NaN03 23.0 301 NH4Br 23.0 303 LiN03 26.0 283 NaBr 27.0 302 Nal 28.0 301 AgN03 28.0 287 NH4N03 28.0 302 KI 42.0 339 ferences in the ionization values of the different electrolytes are neces- sarily very small. Nevertheless, we must conclude that the ionization values of typical salts in water are much more nearly the^same in that solvent than they are in ammonia or in any other solvent for which reliable data are available. The order of the ionization constants does not appear to bear any relation to the constitution of the electrolytes. So ammonium chloride has an ionization constant of 12 X 10"* and am- monium nitrate of 28 X 10~4, while silver iodide has an ionization con- stant of 2.9 X 10"* and silver nitrate 28 X 10"*. Sodium nitrate has a greater ionization constant than potassium nitrate, while sodium iodide has a smaller ionization constant than potassium iodide. The constants for sodium and potassium amides are of interest owing to the fact that these substances are bases in liquid ammonia solution. Apparently these substances are relatively weak bases when compared with the typical salts in ammonia or when compared with corresponding bases in water. Indeed, it is apparent that all electrolytes in ammonia solution have comparatively small ionization constants. For example, the ionization constant of acetic acid in water is 0.182 X 10"*. The ionization constant of this acid, therefore, is approximately three times that of sodium amide and 1/7 that of potassium amide. The ionization constants for a number of organic electrolytes in liquid 60 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS ammonia are given in Table XXIII.16 Here, again, we find a large varia- tion in the value of the ionization constant for different electrolytes. TABLE XXIII. VALUES OF K AND OF A0 FOR ORGANIC ELECTROLYTES IN NH3 AT — 33°. Salt 104# A0 Cyanacetamide 0.045 260 Thiobenzamide 0.40 204 Orthomethoxybenzenesulphonamide 0.40 208 Paramethoxybenzenesulphonamide 0.50 208 Nitromethane 0.53 278 Sodiumnitromethane 0.78 278 Benzenesulphonamide 1.39 208 Metamethoxybenzenesulphonamide 1.81 208 Orthonitrophenol 3.90 246 Methylnitramine 8.4 256 Phthalimide 8.7 248 Benzoicsulphinide 12.0 206 Metanitrobenzenesulphonamide 12.5 231 Potassiummetanitrobenzenesulphonate 15.0 275 Nitrourethaneammonium 21.6 262 Trinitrobenzene 30.0 234 Trinitraniline 30.0 234 The strongest "of these, trinitraniline and trinitrobenzene, have ionization constants as great, or greater, than those of typical salts in ammonia. On the other hand, cyanacetamide has an ionization constant of only 0.045 X 10~4. Cyanacetamide, therefore, is a weaker acid in ammonia solution than acetic acid is in water, and of course a much weaker acid than cyanacetic acid in water. In other respects, as regards the relation of the ionization constants of these electrolytes to their constitution, we find relations similar to those in aqueous solutions. The introduction of strongly electronegative groups into the negative constituent increases the value of the ionization constant. It will be observed that many of the organic substances which act as electrolytes in ammonia solution are not electrolytes in water. This is true of nearly all the acid amides and of such compounds as trinitrobenzene. The positive ion, in the case of the acid amides, as indeed in the case of all the acids in ammonia solu- tion, is presumably the ammonium ion.17 Having seen that the mass-action law applies to dilute solutions of practically all electrolytes in ammonia, we may inquire whether the same " Kraus and Bray, loc. cit. » Ibid., loc. cit., p. 1357. ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 61 is true of solutions in other non-aqueous solvents. In Table XXIV18 are given values of the mass-action constants for sodium iodide in a num- ber of different solvents. In Figure 6 are plotted values of the reciprocal conductance against those of the specific conductance for these solutions. A.-M A,-** 130 .0* goo 3 4 5 6 7 S ioo(cA) [for Isoamylalcohol iooo(cA)J FIG. 6. Showing how Solutions of Binary Electrolytes in Different Solvents Approach the Mass-Action Relation at Low Concentrations. An examination of the figure shows that in all cases the conductance curves approach a linear relation in the more dilute solutions. We may conclude, therefore, that in the case of non-aqueous solvents, in general, the mass-action law is approached as a limiting form at low concentra- tions. "Kraus and Bray, loc. cit. 62 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS TABLE XXIV. VALUES OF K AND OF A0 FOR ELECTROLYTES IN DIFFERENT SOLVENTS. Solvent Solute Temp. °C. K X 10* A0 Benzonitrile Nal 25° 55.0 49.0 Epichlorhydrin (C2H5)4NI 25° 48.5 62.1 Propylalcohol Nal 18° 45.0 20.6 Acetone Nal 18° 30.0 167.0 Acetophenone Nal 25° 34.0 35.6 Methylethylketone Nal 25° 23.0 139.0 Pyridine Nal 18° 13.0 61.0 Isobutylalcohol Nal 25° 12.0 13.7 Acetoaceticester NaSCN 18° 9.5 32.1 Isoamylalcohol Nal 25° 3.9 9.2 Ethylenechloride (C3H7)4NI 25° 1.45 66.7 The mass-action constant varies with the nature of the solvent. The greatest value is that for benzonitrile, which is 55 X 10~4, and the smallest that for ethylenechloride, which is 1.45 X 10'4. The change in the value of the ionization constant among the alcohols is of particular interest in view of their relation to water. The constant for solutions in propyl alcohol is 45 X 10~4, in isobutylalcohol 12 X 10~4, and in isoamylalcohol 3.9 X 10~4. It is evident that, as the substituting hydrocarbon group becomes more complex, the ionization constant decreases. These results also have a bearing on the probable behavior of aqueous solutions. The properties of solutions in the lower alcohols differ only inconsiderably from those of aqueous solutions. It seems probable, therefore, that in going from water through the lower alcohols to the higher alcohols the change in the phenomenon underlying the ionization process undergoes an alteration in degree rather than in kind. It might be concluded, therefore, that in aqueous solutions, also, the mass-action law is ap- proached as a limiting form. This question, however, will be discussed at somewhat greater length in a succeeding chapter. A considerable number of data are available on the conductance of dilute solutions in acetone. In the following table are given values of the mass-action constant and the limiting values of the equivalent con- ductance for a series of electrolytes in this solvent. TABLE XXV. VALUES OF K AND OF A0 FOR DIFFERENT ELECTROLYTES IN ACETONE AT 18°. Solute 104 K A0 KI 51.0 156 Nal 39.0 156 Lil 31.0 154 ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 63 TABLE XXV.— Continued. Solute 104K A0 NH4I 15.0 159 KSCN 31.0 169 LiSCN 18.0 167 NH4SCN 8.3 172 KBr 16.0 156 NaBr 13.0 156 LiBr 5.7 154 NH4Br 2.3 159 LiN03 2.6 125 AgN03 0.28 100 LiCl 0.94 154 From an examination of this table it is obvious that the ionization con- stants of typical salts in acetone vary within very wide limits. So, the ionization constant for silver nitrate is 0.28 X 10'*, whereas that for potassium iodide is 51.0 X 10"*. More remarkable still is the regularity in the variation of the constants as a function of the constitution of the electrolyte. The ionization constants of the iodides diminish in the order potassium, sodium, lithium, ammonium. The same order holds in the case of all other salts, namely the sulfocyanates, bromides, and nitrates. On the other hand, the ionization constants of salts with a common posi- tive ion vary in the order: iodides, sulfocyanates, bromides, nitrates, chlorides. This order holds true in every case. It appears, therefore, that the ionization constant K is an additive function of the constituent ions of the electrolytes. This is the only solvent for which such a rela- tion appears to hold true. What the significance of this may be is at present uncertain. It is important, however, to observe that the ioniza- tion of different typical salts in acetone varies within extremely wide limits. The similarity in the behavior of strong electrolytes in aqueous solutions, as regards their ionization, is therefore not to be considered as a property which may be ascribed primarily to the electrolytes them- selves, but rather one in which the solvent itself appears as the chief factor. 3. Comparison of the Ion Conductances in Different Solvents. If the values of A0 are known and if the transference numbers of the electrolytes are known, then the values of the ion conductances may be determined. However, before proceeding to a comparison of the values of the ion conductances in different solvents, it will be well to point out that the value of A0 is dependent upon the form of the extrapolation function which must be assumed. Only in the case of solutions which 64 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS approach the mass-action law as a limiting form may we be reasonably certain that the extrapolated value of A0 is correct. In other cases, therefore, the limiting conductance values are more or less arbitrary. In a subsequent chapter this question will be discussed somewhat more at length. For the present we shall assume that the A0 values obtained by the ordinary methods of extrapolation are approximately correct. The values of the equivalent conductances of the different electrolytes in ammonia and water have been given in Tables III, XXII and XXIII. In comparing the conductances in the two solvents, however, it is pre- ferable to compare the conductance of the individual ions, rather than that of the sum of the ions of any given electrolyte. Before proceeding further, therefore, we shall resolve these values of the conductance for the various electrolytes into two parts, namely the conductance of the positive and of the negative ion respectively. In order that this may be done, it is necessary that the transference number of at least one elec- trolyte shall be known. In the case of ammonia solutions the transfer- ence numbers of a considerable number of electrolytes have been deter- mined by Franklin and Cady.19 With the aid of their data, the follow- ing values of the equivalent conductance of the typical inorganic ions have been calculated.20 For the sake of comparison, the ion conduct- ances of the same ions in water at 18° are given as well as the ratio of the ion conductances in ammonia and in water. TABLE XXVI. ION CONDUCTANCES IN AMMONIA AND IN WATER. Ion In NH3 In H20 ANH /AR Q Positive Li+ 112 33.3 3.36 Ag+ 116 54.0 2.15 Na+ 130 43.4 3.00 NH4+ 131 64.7 2.03 T1+ 152 65.9 2.31 K+ 168 64.5 2.61 Negative Br03- 148 47.6 3.11 N03- 171 61.8 2.77 I- 171 66.6 2.57 Br- 172 67.7 2.54 Cl- 179 65.5 2.73 NH2- 133 "Franklin and Cady, J. Am. Chem. Soc. 26, 499 (1904). 10 Kraus and Bray, loc. cit. ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 65 It will be observed that the ion conductances in ammonia and in water do not stand in a fixed ratio. For example, for the silver ion, the ion conductance in ammonia is 2.15 times that in water, whereas for the lithium ion the conductance in ammonia is 3.36 times that in water. Similarly, the conductance of the bromide ion in ammonia is 2.54 times that itf water, while the conductance of the bromate ion is 3.11 times that in water. We may naturally inquire as to what are the factors upon which depends the conductance of different ions in different solvents. If the current is carried through a solution by the translation of charged particles of molecular dimensions, then we should expect the speed of these particles to be a function of the viscosity of the medium through which they move. It might be assumed, for example, that the conductance is proportional to the reciprocal of the viscosity, or to the fluidity of the solvent. The viscosity of water at 18° is 10.63 X 10"3 and that of ammonia is 2.558 X 10'3 at its boiling point. Consequently the fluidity of ammonia is 4.15 times as great as that of water. If the con- ductance of the ions were directly proportional to the fluidity of the solvent, then the conductance of all ions in ammonia should be 4.15 times as great as that of the same ions in water. We see, however, that while the conductance of the various ions in ammonia is markedly greater than that in water, nevertheless the ratio of the ion conductances in the two solvents is in all cases smaller than this value. Furthermore, the effect is one specific with respect to the individual ions. For example, for the sodium ion, the value is 3.0, while for the lithium ion it is 3.36. It is noticeable that the ratio for the ions increases in the order: am- monium, potassium, sodium, lithium. In other words, in ammonia the lithium ion possesses a relatively much higher conductance with respect to water than does the ammonium ion. The same general relations hold in the case of the negative ions. The conductance of the bromate ion in ammonia is 3.11 times that in water, whereas that of the bromide ion is only 2.54 times that in water. On the whole, the ion conductances in ammonia vary less than they do in water. The extreme variation in the case of ammonia solutions is from 112, for the lithium ion, to 168, for the potassium ion, or a ratio of 1.5, whereas in the case of aqueous solutions the extreme variation is from 33.3, for the lithium ion, to 65.9, for the thallous ion, or a ratio of 1.98. For the negative ions in ammonia solution the extreme ratio is 1.21, whereas for aqueous solutions it is 1.37. In general, however, the order of ionic conductances in the two solvents is the same. With a few ex- ceptions, ions which move very slowly in water also move very slowly in ammonia. 66 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS It is evident that the conductance of an ion is a function of the con- stitution of the solvent as well as of that of the ion itself. In this con- nection it should be observed that a given electrolyte dissolved in two different solvents does not necessarily yield the same ions. In other words, complexes may be formed between the ions and the solvent proper- ties of which will depend upon the nature of the solvent. It -is well known that certain ions tend to form complexes with certain solvents. For example, the silver ion forms a complex with ammonia even in aqueous solutions. It may be assumed, therefore, that the silver ion has a great tendency to form complexes with ammonia. The cause for the relatively low value of the conductance of the silver ion in ammonia may be ascribed to the formation of a relatively large complex silver-ammonia ion in ammonia solution. Similarly, those ions whose salts show a marked tendency to form complexes with water, which, for example, give stable crystalline hydrates, show a relatively higher speed in am- monia than in water. Thus, the speed of the lithium ion in ammonia is relatively much greater with respect to its speed in water than is that of the potassium ion. We may therefore conclude that the lithium ion is relatively less complex in ammonia than it is in water. Chapter IV. Form of the Conductance Function. 1. The Functional Relation between Conductance and Concentra- tion. If an equilibrium exists between the ions and the un-ionized mole- cules in a solution, then the relation between the conductance and the concentration is expressed by Equation 7, which follows from the mass- action law. We have seen that this equation is fulfilled in solutions of weak electrolytes in water and that it is approached as a limiting form in solutions of strong electrolytes in non-aqueous solvents. This equa- tion is the only one so far suggested to account for the relation between the conductance and the concentration which has a substantial theoretical foundation for its support. At higher concentrations, in the case of the stronger electrolytes, both in water and in non-aqueous solvents, the simple form of the mass-action law no longer holds. Except at very high concentrations, where viscosity effects become pronounced, the con- ductance in all cases varies in such a way that the value of the mass- action function increases with increasing concentration. If the reciprocal of the equivalent conductance is plotted against the specific conductance, then, in the case of strong electrolytes, it is found that the experimental curve is concave toward the axis of specific conductances. We have seen that in different solvents the conductance curve, as a function of the concentration, varies greatly in form, and the conclusion might be drawn that the process involved in these solutions is entirely different in character. Since the form of the conductance function in the case of the concentrated solutions is thus far not determinable from theoretical considerations, various attempts have been made to deter- mine empirical functions which should express the conductance in terms of the concentration. In the case of aqueous solutions the equation of Storch a appears to apply over a considerable concentration range. This equation may be written in the form: where D and m are constants. This equation applies remarkably well in the case of aqueous solutions, even up to high concentrations. It will 'Storcb, Ztschr. /. pJiyg. Chem. 19, 13 (1896). 67 68 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS be observed that in this equation the mass-action function K' is expressed as a function of the ion concentration raised to the ra'th power. The equation may be tested very simply by graphical methods. It may be written in the form: (10) (2 — m) log (CY) — log [C (1 — Y) ] = log D. If, therefore, we plot the logarithms of (7(1— y) against the logarithms of the ion concentrations Cy or the specific conductances, the experi- mental points should lie on a straight line, provided the equation holds. This method of treatment was first proposed by Bancroft2 and has proved extremely useful in determining the behavior of very concen- trated solutions. In Figure 7 are shown the curves for potassium chloride and potassium nitrate in water at 18°. It will be observed that the points lie very nearly on a straight line. 0.0 5.0 2.0 0.0 3.0 LogC (1 — Y). FIG. 7. Plot of Storch Equation for Aqueous Solutions of Binary Electrolytes. It is evident, however, that an equation of this type cannot apply generally, since it does not approach the mass-action expression as a limiting form. As we have seen, dilute solutions in non-aqueous solvents approach the mass-action function at low concentrations. It has there- fore been proposed 3 to express the relation between the conductance and the concentration by means of the equation: (ii) K'= 0(1 — 2 Bancroft, Ztschr. f. phys. Chem. SI, 188 (1899). •Kraus, Proc. Am. Chem. Soc. 1909, p. 15; Bray, Science 35, 433 (1912) ; Trans. Am. Electro-Ch. Soc. 21, 143 (1912) ; MacDougall, J. Am. Chem. Soc. 34, 855 (1912) ; Kraus and Bray, J. Am. Ohem. Soc. 35, 1315 (1913). Somewhat similar four-constant equations FORM OF THE CONDUCTANCE FUNCTION 69 In this equation y is written for the ratio -r- for the sake of brevity. An A0 inspection of this equation shows that at low concentrations the first term of the right-hand member, involving the ion concentration Cy, will diminish as the concentration decreases, and will ultimately become neg- ligible in comparison with the constant K. On the other hand, at higher concentrations, the constant K will become negligible in comparison with the term involving the ion concentration. In other words, at high con- centrations this equation approaches the Storch Equation 9 as a limiting •form. Obviously, this equation involves the four constants A0, K, D and ra. These constants may in most cases be determined readily by graphical means. If conductance data are available at very low concentrations, the second term of the right-hand member may be neglected, in which case the reciprocal of the equivalent conductance becomes a linear func- tion of the ion concentration; that is, the equation degenerates into the form of Equation 7. The value of A0 and of K may therefore be de- termined with a considerable degree of precision from this plot. Hav- ing determined these two constants, the values of m and D may be de- termined from data at higher concentrations. At very high concentra- tions K may be neglected and from a plot of Equation 10, which is linear if the equation holds, the values of ra and D may be determined. In case the constant K is not negligible at higher concentrations, it is necessary to take this into account. This may be done by means of a second approximation. It is seen from Equation 11 that the mass-action Cv* function K' = _ is a linear function of the ion concentration raised to the ra'th power. If the value of ra in the more concentrated solutions, as determined by the first approximation, is correct, then the values of K and D may be corrected by means of a plot of K' against (Cy)m. The value of K is then determined by extrapolating to the concentration zero and the value of D is determined from the slope of the line. The values of the constants having been determined, it is possible to calcu- late the conductance of a given electrolyte at any desired concentration and to compare the calculated with the experimental values. In Figure 8 is shown a plot of the reciprocal of the equivalent con- ductance against the specific conductance or ion concentration for solu- tions of potassium amide in liquid ammonia.4 This plot yields for A0 have been proposed by Bates (J. Am. Chem. Soc. 37. 1431 (1915)) and bv de (Medd. K. Vet. Akad's Nobelinstitut, Vol. 3, Nos. 2 and 11 (1914)) While equations represent the course of the conductance curve fairly well in the case of aaueoua solutions, they are not generally applicable to non-aqueous solutions « Franklin, Ztschr. f. phys. Chem. 69, 290 70 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS the value 301 and for K the value 1.26 X 10'4.5 That is, the straight line drawn corresponding to this slope passes through the points in the more dilute solutions. o 0.0 2.5 5.0 7.5 10 12.5 15 100 (CA). FIG. 8. A0 — K Plot for KNH2 in NH3. 17-5 Having determined the preliminary values of K and of A0, we may plot the values of the logarithm of K'— K against the logarithm of Cy. The plot for this function is shown in Figure 9, where it will be observed 2.0 5-0 3* £| |g / D-0093 |g ^ P o 3'5 2.0 2.5 T.o 1.5 o. Log tar) FIG. 9. M — D Plot lor KNH2 in NH3. that the points lie upon a straight line well within the limits of experi- mental error. This plot yields a value of D = 0.095 and ra = 1.18. Finally, in order to obtain a more precise value of K, values of K.' are •Kraus and Bray, loc. cit. FORM OF THE CONDUCTANCE FUNCTION 71 plotted against the values of the ion concentration to the power 1.18. This plot is shown in Figure 10. The value for D in this case is not altered from that originally determined, but the value of K is altered from 1.26 to 1.20. It will be observed that, throughout, the points lie upon a straight line within the limits of experimental error. The equation connecting K-UOXMT* •0.0 2.5 5.0 7-5 12.5 15 17.5 20.0 FIG. 10. K— D Plot for KNH, in NH,. the equivalent conductance with the concentration for solutions of potas- sium amide in liquid ammonia is, therefore: K' = n yl* — Y/ = 0.095 (Cy)118 + 1.20 X 10"4 where y=_. The calculated values are compared with the experimental values in Figure 11, where the equivalent conductances are plotted as ordinates against the logarithms of the concentrations as abscissas. It will be ob- served that the calculated curve corresponds with the experimental curve up to a concentration of approximately 2 normal. Beyond this concen- tration the experimental curve departs rapidly from the calculated curve. As we shall see presently, at higher concentrations, the viscosity of the solutions increases very largely and it is therefore not possible to test the applicability of the equation at these concentrations. It becomes a matter of interest to determine whether an equation of 72 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS this type is generally applicable to solutions of electrolytes in various solvents. Since a larger amount of experimental material is available for solutions in liquid ammonia than for solutions in any other solvent, we may consider solutions in this solvent first. Since the more dilute solutions have already been considered and found to conform to the 280 240 <200 160 120 80 40 \ \ 5-0 1.0 0.0 1.0 40 3.0 2.0 Log C. FIG. 11. Comparison of Experimental Values with Equation 11 for KNH2 in NH3. mass^action law as a limiting form, it follows that the equation will be applicable to the more dilute solutions in any case. It remains, there- fore, to determine whether the equation likewise applies to the more concentrated solutions. Kraus and Bray,6 who have examined the applicability of this equa- tion to a large number of non-aqueous solutions, including solutions in ammonia, have concluded that the experimental values may be repre- • Kraus and Bray, lac. cit. FORM OF THE CONDUCTANCE FUNCTION 73 sented by an equation of this type within the limits of experimental error. In general, it has been found that the more consistent the ex- perimental data are among themselves, the more nearly do they adjust themselves to Equation 11. The results for inorganic electrolytes dis- solved in ammonia are summarized in Table XXVII. TABLE XXVII. CONSTANTS OP THE CONDUCTANCE FUNCTION FOR INORGANIC ELECTROLYTES IN NH3 AT — 33°. Electrolyte lO4^ m D KNH2 1.20 1.18 0.095 Agl 2.90 0.70 0.009 NH4C1 12.0 0.84 0.127 KN03 15.5 0.96 0.25 NaN03 23.0 0.89 0.32 NH4Br 23.0 0.82 0.24 LiN03 26.0 0.86 0.34 Nal 28.0 0.83 0.43 AgN03 28.0 0.83 0.36 NH4N03 28.0 0.86 0.39 KI 42.0 0.94 0.62 The values of A0 are not given in this table, but they will be found in Table XXII. By means of the constants in these tables the equivalent conductances of the various electrolytes may be calculated at any de- sired concentration within the limits of experimental error up to approxi- mately normal concentrations. It is obvious that a comparison of the ionization of different electrolytic solutions may be made by means of the constants given above. The relative ionization of two salts will vary as a function of the concentration, since the constants for the two elec- trolytes will not, as a rule, have the same value. The values of the constant K have already been considered and need not be further dis- cussed here. The values of the constant D are seen to lie within fairly narrow limits. Excepting the constants for potassium amides and silver iodide, the values of D lie between 0.127 and 0.62. and most of the values lie between 0.24 and 0.43. There is no fixed relation between the values of D and of K, although in general an electrolyte with a large value of K has a large value of D. Thus, potassium amide, silver iodide and ammonium chloride have the smallest values of K and likewise they have the smallest values of the constant D. So, also, potassium iodide, which has the highest value of the constant K, likewise has the highest value of the constant D. Apparently, the constants K and D are not 74 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS entirely independent of each other, or, in other words, they depend in a corresponding manner upon some property of the electrolyte. The values of ra lie between 0.70 and 1.18 and, for the most part, they lie between 0.82 and 0.96. The general form of the curve, as we shall presently see, is determined largely by the value of the constant ra. It follows, consequently, that the curves for the various electrolytes will in general be similar. No definite relation appears to exist between the values of the constant ra and the constants D and K. In many cases, however, as we shall see later, electrolytes having a small value of K and D have a relatively large value of ra. Silver iodide is an exception to this rule. The constants for a number of organic electrolytes are given in Table XXVIII. TABLE XXVIII. CONSTANTS OF EQUATION 11 FOR ORGANIC ELECTROLYTES IN NH3 AT —33°. Solute Ao 104# ra D Cyanacetamide 260 0.045 1.24 0.026 Benzenesulphonamide 208 1.39 1.00 0.029 Methylnitramine 256 8.4 0.85 0.080 Metanitrobenzenesulphonamide 231 12.5 0.76 0.103 Nitrourethaneammonium 262 21.6 0.76 0.22 Trinitraniline 234 30.0 0.73 0.38 They have been arranged in the order of increasing values of K. It is at once evident that there is no relation between the various constants and the value of A0. On the other hand, there is apparently a rough parallelism between the constants K and D. The order of the K and D constants, in other words, is identical. The order of the constant ra appears to be the reverse of that of the constants D and K; that is, as K and D increase, ra decreases. Aside from solutions in liquid ammonia, the equation has been found to hold for solutions in sulphur dioxide,7 amyl and propyl 8 alcohols and phenol.9 In the case of the sulphur dioxide solutions the equation holds within the limits of experimental error. In that of the alcohol solu- tions, the deviations appear to be considerable at certain points, but it is possible that these are due either to experimental errors or to a lack of proper adjustment of the constants. The constants found are as follows: 7 Kraus and Bray, loc. cit. •Keyes and Winninghoff, J. Am. Chem. Soc. 38, 1178 (1916). •Kurtz, Thesis, Clark University (1921). FORM OF THE CONDUCTANCE FUNCTION 75 TABLE XXIX. CONSTANTS OF EQUATION 11 FOR SOLUTIONS IN DIFFERENT SOLVENTS. Solvent Solute m K D AO Sulphur dioxide ..... KI 1.14 8.5 X 10'4 0.403 207. Iso-amyl alcohol ____ Nal 1.2 5.85 X 1Q-4 0.374 7.79 Propyl alcohol ..... Nal 0.75 38.3 X 10~4 0.208 20.1 Phenol ............. (CH3)4NI 1.28 2.3 X 10~4 0.69 16.67 Comparing the ionization in ammonia and sulphur dioxide, in view of the much lower value of the constant K, dilute solutions in sulphur dioxide are ionized to a much smaller extent than are solutions in am- monia. On the other hand, in the more concentrated solutions, the ioniza- tion values again approach each other, since the value of D for sulphur dioxide is relatively large and the value of m is much greater than that in ammonia. The conductance curves of solutions in sulphur dioxide, phenol and amyl alcohol pass through a minimum while that of solu- tions in propyl alcohol resembles the curve for aqueous solutions. In the case of a great many solutions whose ionization is relatively low, the limiting value of the equivalent conductance in dilute solutions cannot be determined. Under these conditions, the value of K remains indeterminate. Nevertheless, if the ionization is relatively low, the ap- plicability of Equation 11 may be tested approximately. It is apparent that, when the ionization is low, the constant K becomes negligible in comparison with the term involving the constant D. Also, the value of A becomes small in comparison with that of A0, so that for purposes of approximation the value of A may be neglected in comparison with that of A0. Under these conditions Equation 11 reduces to the form: (12) CA2 = D A02 — m (CA) ™ 9 For the sake of brevity we may write: (13) DA02 — m=P. If we take the logarithm of both sides of this equation, we obtain the linear equation: (14) log CA2 = m log CA + log P. In order to test the applicability of the equation to solutions of very low ionization, therefore, it is only necessary to plot the logarithms of the values of CA and of CA2, both of which may be obtained from experi- mental data. If the equation holds, the points will lie upon a straight 76 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS line, the slope of which gives the value of the constant m and the inter- cept on the axis of CA2 the value of P. In Figure 12 are shown plots of Equation 14 for a number of organic electrolytes dissolved in hydrobromic and in hydriodic acids and in 3-0 3-5 2.5 i.o Log(cA) FIG. 12. Illustrating the Applicability of Equation 11 to Solutions of Binary Elec- trolytes in Solvents of Low Dielectric Constant. hydrogen sulfide. These solutions are well adapted to the purpose of testing the applicability of the equation, since the ionization of electro- lytes in these solvents is extremely low. It is evident that, except in the case of a few very concentrated solutions, the equation holds within the limits of experimental error. The curves, in general, have approximately FORM OF THE CONDUCTANCE FUNCTION 77 the same slope, which follows from the fact that the value of m is ap- proximately the same for these solutions. The greater the value of the exponent m, the steeper the curve on the plot. A great many solutions of this type have been measured and the results have been compared with the equation. The deviation in no case appears to be very great, from which it may be concluded that the equation holds to a considerable degree of approximation. The values of the constants m and P for various solutions are given in Table XXX.10 Many of the substances which appear in this table are not ordinarily classed as typical electrolytes. They are, in general, basic compounds TABLE XXX. VALUES OF THE CONSTANTS OF EQUATION 12 FOR VARIOUS SOLUTIONS. Liquid Hydrochloric Acid (HC1). Tempera- Solute Formula ture m P Triethylammonium chloride (C2H5)3N.HC1 —100° 1.42 5.75 Acetamide CH3CONH2 —100° 1.40 5.53 Methylcyanide CH3CN —100° 1.44 4.17 Resorcinol C6H4(OH)2 —89° 1.18 3.89 Hydrocyanic acid HCN —100° 1.46 3.33 Toluic acid CH3 . C6H4COOH — 96° 1.52 1.58 Diethylether (C2H5)2O —100° 1.51 1.38 Propionic acid C2H5COOH — 96° 1.47 1.21 Acetic acid CH.COOH —96° 1.42 1.09 Benzoic acid C6H5COOH — 96° 1.42 0.94 Butyric acid C3H7COOH — 96° 1.45 0.85 Methylalcohol CH3OH —89° 1.61 0.71 Formic acid HCOOH — 96° 1.55 0.67 Ethylalcohol C2H5OH —89° 1.70 0.50 Butylalcohol C4H9OH —89° 1.62 0.38 Liquid Hydrobromic Acid (HBr). Triethylammonium chloride (C2H5)3N.HC1 —81° 1.51 4.03 Thymol CH3 . C3H7 . C6H3OH — 80° 1.57 3.60 Methylcyanide •. . . CH3CN —81° 1.53 2.48 Acetamide CH3CONH2 —81° 1.48 2.29 Acetone (CH3)2CO —81° 1.63 1.88 Metacresol m-CH3.C6H4OH —80° 1.54 1.70 Orthonitrotoluene o-CH3 . C6H4NO2 —81° 1.50 0.99 Benzoic acid C6H5COOH — 80° 1.67 0.82 Acetic acid CH3COOH — 80° 1.66 0.78 10 Kraus and Bray, loc. cit. 78 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS TABLE XXX.— Continued. Liquid Hydrobromic Acid (HBr). Tempera- Solute Formula ture m P Metatoluic acid ........... m-CH3 . C6H4COOH — 80° 1 .65 0.77 Paratoluic acid ........... p-CH3 . C6H4COOH — 80° 1.62 0.76 Butyric acid ............. C3H7COOH —80° 1.66 0.71 Orthotoluic acid .......... o-CH3C6H4COOH — 80° 1.60 0.65 Diethylether .............. (C2H5)20 —81° 1.63 0.59 Paracresol ............... p-CH3.C6H4OH —80° 1.66 0.55 Resorcinol ............... C6H4(OH)2 —80° 1.40 0.52 Orthocresol ............... o-CH3.C6H4OH —80° 1.68 0.45 Methylalcohol ............ CH3OH —80° 1.80 0.41 Allylalcohol .............. C2H3.CH2OH —80° 1.79 0.39 Ethylalcohol .............. C2H5OH —80° 1.80 0.35 Amylalcohol .............. C^OK —80° 1.84 0.27 Normal propylalcohol ..... n-C3H7OH —80° 1.77 0.27 Phenol ................... C6H5OH —80° 1.61 0.27 Liquid Hydriodic Acid (HI). Triethylammonium chloride (C2H5)3N.HC1 —50° 1.58 2.69 Ethylbenzoate ............ CC)H5COOC2H5 —50° 1.62 2.09 Diethylether ........ ...... (C2H5)20 —50° 1.66 1.26 Liquid Hydrogen Sulfide (H2S). Triethylammonium chloride (C2H5)3N.HC1 —81° 1.58 2.06 Nicotine ................. C10H14N2 —81° 1.63 1.20 Mercuric Chloride (HgCl2). Caesium chloride ......... CsCl 282° 1.20 14.5 Potassium chloride ........ KC1 282° 1.21 14.3 Ammonium chloride ....... NH4C1 282° 1.22 14.3 Sodium chloride ........... NaCl 282° 1.29 13.7 Cuprous chloride .......... CuCl 282° 1.33 13.6 Liquid Iodine (I2). Potassium iodide ....... ... KI 140° 1.44 13.5 Ethylamine (C2H5NH2'). Silver nitrate ............. AgN03 0° 1.42 4.68 Ammonium chloride ....... NH4C1 0° 1.57 1.97 Lithium chloride .......... LiCl 0° 1.54 1.80 Amylamine (Cg Silver nitrate . ............ AgN03 25° 1.67 1.97 FORM OF THE CONDUCTANCE FUNCTION 79 TABLE XXX.— Continued. Aniline (C6H5NH2). Tempera- Solute Formula ture m P Ammonium iodide NH4I 25° 1.44 2.19 Silver nitrate AgN03 25° 1.42 2.02 Pyridine hydrobromide . . . . C5H5N.HBr 25° 1.51 1.91 Aniline hydrobromide C6H5NH2.HBr 25° 1.44 1.29 Lithium iodide Lil 25° 1.33 1.04 Methyl Aniline (C6H5NHCH3). Pyridine hydrobromide C5H5N.HBr 25° 1.64 1.19 Aniline hydrobromide C6H5NH2.HBr 25° 1.59 0.59 Acetic Acid (CH3COOH). Lithium bromide LiBr 25° 1.43 2.60 Pyridine C5H5N 25° 1.56 1.86 Dimethylaniline C6H5N(CH3)2 25° 1.48 1.53 Aniline C6H5NH2 25° 1.52 1.32 Propionic Acid (C2H5COOH). Lithium bromide LiBr 25° 1.74 0.84 Aniline C6H5NH2 25° 1.79 0.37 Pyridine C5H5N 25° 1.76 0.32 Bromine (Br2). Trimethylammoniumchlo- ride11 (CH3)3NHC1 18° 1.62 0.55 Iodine12 I2 25° 1.74 0.17 containing either oxygen or nitrogen and in all likelihood they owe their electrolytic properties to the formation of complexes with the solvent, in which oxygen and nitrogen exhibit basic properties. For a given value of m the ionization is in general the greater the greater the value of P. It is apparent that among these electrolytes the typical salts are the most highly ionized. In solutions in the halogen acids and hydrogen sulphide, the substituted ammonium salts, or their derivatives, are more highly ionized than are other substances. In general, also, the typical salts have values of the constant m smaller than those of electrolytes which have a lower ionization. There are, however, a few exceptions, such, for example, as resorcinol in hydrochloric acid, which has a value "Darby, J. Am. Chem. Soc. 40, 347 (1918). "Plotnikow ana Rokotjan, Ztschr. f. phya. Chem. 84, 365 (1913). 80 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS of m of only 1.18. Correspondingly, resorcinol in hydrobromic acid has a constant of only 1.40, which is distinctly lower than that of other sub- stances dissolved in this solvent. It is interesting to note that the value of the constant m never exceeds 2. The highest value of this constant is 1.80 for methyl and ethyl alcohols in hydrobromic acid. It appears prob- able that the values of m for these two substances in hydrogen iodide will be found greater than in hydrogen bromide. In fused mercuric chloride the different typical salts exhibit a very similar behavior. The constant P differs only inappreciably for different electrolytes and the values of the constant m, for the most part, fall within very narrow limits. In the amines the constant m increases and the constant P decreases as the organic radical becomes more complex. The same is true in the case of acetic and propionic acids, where the constant m for propionic acid is much greater than for acetic acid. Judging by the relatively low value of the constant m for liquid iodine, this substance is a fairly good ionizing agent. 2. Geometrical Interpretation of the Conductance Function. The conductance function: — Y may be interpreted most readily by graphical methods. It will be under- stood that y = T— and that the following equations may at once be con- A0 verted to equations in which CA and A appear as variables in place of CY and Y- In speaking of the ionization, it is not intended to convey the impression that the conductance ratio necessarily measures the ioniza- tion, but rather it is introduced as a convenient variable for the purpose of discussion. If we differentiate the above equation, we have: (15) ____ , '' d(Cy) dv The coefficient , * ., which is the tangent to the Y> CY-curve, is a measure of the change of the ionization as a function of the ion concen- tration at any point on the curve. It is evident that if the term ~ ..„ . approaches zero as CY approaches zero, the tangent will ap- proach the value — ^ as a limit, where K is the limit which K' ap- FORM OF THE CONDUCTANCE FUNCTION 81 preaches at zero concentration. At higher concentrations the tangent will decrease; that is, the ionization will increase less rapidly for a given increase in the ion concentration, because both K' and -^ ,.~ > in- crease with the concentration. If we introduce A and CA as variables, Equation 15 has the form: dA A* /CA dJC' -2'' d(CA) • The plot of A against the specific conductance in dilute solution will therefore be a curve convex toward the axis of specific conductances, and as the concentration decreases it will approach a line whose tangent is — provided the conditions mentioned in the preceding paragraph are K. fulfilled. In order to follow up the form of the curve at higher concentrations, we may introduce the conductance function 11. On differentiating this function we have: (17) " A2 Since K' approaches K at low concentrations, it follows that the tangent approaches the value — -=• as a limit. At higher concentrations, the tangent decreases, since K' decreases. Ultimately the form of the curve depends upon the value of m. If m is less than 1, then the tangent will always have a negative value; in other words, the equivalent conduct- ance will always decrease with increasing values of the specific con- ductance. On the other hand, when m is greater than unity, the tangent will become zero, when: (18) J.\. that is, at this point the conductance passes through a minimum value after which it increases with increasing values of the specific conduct- (CA\m -r— 1 + K, and denoting by C' and A' the values of the concentration and the equivalent conductance at the minimum point, we have: (19) D(m-D) 82 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS where y' ='r~' This e(lua^on gives the value of the specific conductance, A0 or the ion concentration, at the minimum point. The value of the ioniza- tion follows from the equation: Y' _ When m equals 1, we have a limiting case in which Equation 18 reduces to: dA A2 mK (21) Kft rr It is evident that since -^ decreases as the concentration increases, the tangent approaches a value zero at high concentration. The ionization, therefore, approaches a constant value which may be obtained by writing m = 1 in Equation 11; we have: or, neglecting K, (22) ^ „ = D or Yf = YT^- The ionization of such solutions, therefore, approaches the value -z — . as a limit. If an electrolyte has a very small value of K and a relatively large value of D, while the value of m is nearly unity, the conductance will vary only very little with concentration at higher concentrations. This is the case with the cyanides in liquid ammonia, more particularly with the cyanides of gold and silver. The value of m is a little less than unity for the first substance and a little greater than unity for the second.13 For the ion concentration Cy — 1, Equation 11 reduces to: and since K may be neglected at this concentration, we have: (23) The constant D, therefore, measures the ratio of the ionized to the un- ionized fraction at the concentration CY = 1. We shall see that, for a " Kraus and Bray, loc. cit., p. 1360. FORM OF THE CONDUCTANCE FUNCTION 83 given substance in different solvents or in the same solvent at different temperatures, the value of D is practically constant, while the values of m and K vary. It follows, therefore, that the y, Cy-curves for all such solutions pass through the point Cy = 1, Y = n _i_ i • ^is relation is of importance in interpreting the influence of temperature on the conduct- ance of solutions. The further discussion of the relation between the conductance and the concentration is greatly simplified by introducing the function K' and examining the manner in which K' varies as a function of the ion concen- tration. Differentiating, we have the equations: A0W (24) ^-JMPtJP* If D were zero, that is, if the mass-action law held, we should have: . or K' = constant. On the other hand, when the D term is present, K' will always increase with the concentration. The form of the K', CA-curve is determined mainly by the constant m. When m = 1, we evidently have: (26) = Dm or In this limiting case, therefore, K' varies as a linear function of the specific conductance CA. The form of the curves for values of m greater and less than unity may readily be determined by means of the second differential coefficients. W^e have: (27) 3^T5=D«(»-1) When m < 0, (28) and the K, Cy-curve is everywhere concave toward the axis of Cy. When 84 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS and the curve is everywhere convex toward the Cy-axis. In the limiting case, m = 1, and (30) and K is a linear function of Cy. From Equation 24, it follows that when m < 1, dK' <31> c!Lmo d(CA)= °° and when m > 1, In the first case the K', Cy-curve approaches the limit K asymptotic to the axis of K', while in the second case it approaches the limit asymptotic to a line parallel to the axis of Cy. The curvature of both curves increases as the concentration de- creases.1* For the radius of curvature of the K', Cy-curve we have the equation: 2(2-w») , mV*JH/3 (CY) " [Dm(m — I)]3/2 (m — I)2/3 The exponent 2— m of the first term of the right-hand member of this equation is positive for all values of m less than 2. Since no solutions are known for which m is greater than 2, we need not consider greater values of m. It is evident, therefore, that, due to the first term, the radius of curvature increases with Cy for all values of m. For m > 1, the coefficient 2m — 1 is positive and the radius of curvature increases with Cy due to this term also. When m < 1, 2 — m > 2m — 1 so long as m is greater than zero. It follows, therefore, that the first term overbalances the second and that the curvature, for all values of m between zero and 2, decreases with increasing concentration, becoming infinite in the limit. For m = 1, R = oo, and the curvature is zero. For m < 1, the curvature is negative; that is, the curve is concave toward the Cy-axis. While for m > 1, the curvature is positive, and the curve is convex toward this axis. For given values of D and K and for different values of m we have a family of curves passing through the points Cy = 0, K' = K and Cy = 1, K' — D -}- K. Such a system of curves is shown in Figure 13. The con- 14Kraus, J. Am. Chem. Soc. £2, 6 (1920). FORM OF THE CONDUCTANCE FUNCTION 85 stants assumed are: D = 1.703, K = 0.001, and A0 = 129.9 for all curves, while ra = 0.52 for Curve I,m = 1.50 for Curve II, and ra = 1 f or Curve III. The greater the value of ra, the less rapidly does K' increase at the lower concentrations. For a value of m = 0, the curve degenerates into a horizontal straight line, corresponding to the mass-action constant K' = K + D. .8 1.6 1.4 1.2 0.4 0.1 CUPVlfy /fa*t 0.1 0.2 0.3 0.4 0.5 0.6 Ion Concentration (Cy). 0.7 0.8 09 FIG. 13. Showing Typical K' Curves for Different Values of m According to Equation 11. It is evident that a given percentage deviation of K' with respect to K will be found at different values of the ion concentration. If we con- sider two solutions for which the value of K' has increased by a given percentage amount over K in both cases, then the ion concentrations of the two solutions are related according to the equation: (34) K If D/K for the two solutions is of the same order, then the ratio of the ion concentrations will depend upon the values of ra. The smaller the value of ra, the lower will be the ion concentration at which a given change in K will be found. This is also obvious from Figure 13. For 86 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS a given rise in the curve above the value of K, the ion concentration will be the smaller, the smaller the value of ra. The value of the ion concen- trations corresponding to any given value of Kf are found by drawing a horizontal line and reading off the concentrations at the points of inter- section. In Table XXXI are given the values of ra, D/K, and the ion TABLE XXXI. VALUE OF D/K AND OF ra AND CONCENTRATIONS AT WHICH GIVEN DEVIA- TIONS FROM THE MASS- ACTION LAW OCCUR FOR SOLUTIONS IN NH3. ; Electrolyte D/K X 10-2 m K'~ K ~ A A CX10* CyXlQ4 CX104 KNH2 ............. ........ 7.91 1.18 2.76 8.82 8.97 65.0 Agl ........................ 0.345 0.70 0.86 1.14 6.38 18.03 NH4C1 ............ . ...... . . 1.06 0.84 1.10 1.19 5.70 7.99 KN03 ...................... 1.35 0.89 1.35 1.46 6.89 10.80 NaN03 .................... 1.39 0.89 1.33 1.42 6.52 8.06 NH4Br .............. : ...... 1.04 0.82 0.89 0.92 4.85 5.70 LiN03 ..................... 1.31 0.86 1.06 1.10 5.33 6.32 Nal ....................... 1.54 0.83 0.63 0.64 3.33 3.66 AgN03 ..................... 1.29 0.83 0.78 0.80 3.38 3.80 NH4N08 .................... 1.39 0.86 0.98 1.02 4.92 5.64 KI ........................ 1.43 0.94 2.03 2.12 8.91 10.50 Cyanacetamide .............. 55.8 1.24 0.83 15.4 2.53 120.0 Benzenesulphonamide ........ 2.09 1.00 2.40 6.34 9.59 64.8 Methylnitramine ............ 0.941 0.85 1.32 1.52 7.08 12.04 Metanitrobenzenesulphonamide 0.825 0.76 0.58 0.61 3.62 4.49 Nitrourethaneammonium ..... 1.02 0.76 0.44 0.45 2.74 3.03 Trinitraniline ............... 1.27 0.73 0.22 0.22 1.45 1.49 concentrations Cy and the total salt concentrations at which the increase over the values of K amounts to 5 and 20 per cent respectively. For approximately the same value of D/K the value of Cy, for which a given increase occurs in the value of the mass-action function, decreases as m decreases. Thus, in the case of benzenesulphonamide, methyl- nitramine, metanitrobenzenesulphonamide, and trinitraniline, the value of m decreases from 1.0 to 0.73, while the value of Cy for a 5% increase in the function decreases from 2.40 to 0.22. Similarly, in the case of sodium and potassium iodides, the values of ra are respectively 0.83 and 0.94, and the values of the ion concentrations for a 5% increase in the func- tion are 0.63 and 2.03 respectively. The deviations from the simple mass-action law, at a given concentration therefore appear smaller in the case of potassium iodide than in that of sodium iodide. For the same FORM OF THE CONDUCTANCE FUNCTION 87 value of the constant m, a given deviation occurs at the lower concen- tration, the greater the value of D/K. Thus, sodium iodide and silver nitrate both have a value of the exponent m = 0.83, while the values of D/K are 1.54 and 1.29 respectively. Correspondingly, the values of the ion concentrations for a 5% increase of the function are 0.63 and 0.78 respectively. The value of D/K for typical electrolytes in ammonia lies in the neighborhood of iOO. For weak electrolytes the value of D/K appears to be larger, as for example for cyanacetamide and potassium amide. In the case of silver iodide, however, which appears to be a very exceptional electrolyte, the value of D/K is extremely small. As we shall see below, the value of D for a given electrolyte is relatively independent of the nature and condition of the solvent. At higher temperatures, the dielectric constant of the solvent decreases and with it there is a large decrease in the value of the constant K, while the constant D remains practically fixed. At higher temperatures, therefore, the value of D/K will increase. This tends to increase the deviations from the simple mass-action relation. On the other hand, the value of m increases with increasing temperature and decreasing dielectric constant, and this tends to make the percentage deviations from the simple mass-action relation smaller. The observed effect will be the resultant of these two. From the known form of the conductance curve in solvents of very low dielec- tric constant, it is evident that ultimately the effect due to the increase in the value of D/K overbalances that due to the increase in the value of m. Corresponding to the K' ', Cy-curves, we have the y, Cy-curves. These curves pass through the common points y = 1> 181.0 3590.0 3350.0 5970.0 25110.0 11910.0 14620.0 Fcalc. 181.0 5880.0 8530.0 16300.0 44900.0 9260.0 14600.0 The electrolyte employed for comparison is sodium iodide, except in the case of water, epichlorhydrin, ethylene chloride and ammonia, in which the electrolytes were sodium chloride, tetraethylammonium iodide, tetra- propylammonium iodide and potassium nitrate, respectively. So far as solutions in water are concerned, the ionization values correspond very closely for different binary electrolytes, so that it is a matter of indifference whether one or another typical binary electrolyte is em- ployed as reference electrolyte. At the higher concentrations, it is true, the value of y is somewhat lower for sodium chloride than for potassium chloride. However, this does not affect the comparisons appreciably; if anything, the comparison is somewhat more favorable with sodium chloride than with potassium chloride as reference electrolyte. If Equation 38 were applicable, the calculated values of F should everywhere correspond with the observed values. At an ionization of 70% the calculated values of F are in all instances too small. The dis- crepancy is greatest in the case of ethylene chloride at 70% ionization, which, according to calculation, should be 569 liters, whereas the meas- ured dilution is 11,290. In general, the lower the dielectric constant of FORM OF THE CONDUCTANCE FUNCTION 95 the medium, the greater the discrepancy between the observed and cal- culated values, although there are some marked exceptions. Further- more, the order of the deviations varies as the ionization of the electro- lyte varies. This is particularly noticeable in the case of ammonia and isobutyl alcohol, where the observed and calculated values very nearly agree at 95% ionization, but diverge largely at an ionization of 70%. On the other hand, in other cases, the deviation changes sign. For example, at 70% ionization the observed value for ethyl alcohol is 125.9 and the calculated value 39.2, whereas at 95% ionization the observed value is smaller, being 3590, and the calculated value 5880. That Walden's relation cannot hold generally may most readily be shown by graphical means. If we take logarithms of both sides of Equation 39, we have: log V2 — log Vx = 31og^. 82 If the values of y f°r an electrolyte in different solvents are plotted against values of log V, then obviously for any given value of y the abscissas on the curves will differ by 3 log — . In other words, the curve £2 for an electrolyte in any one solvent may be derived from that in any other solvent by merely displacing the curve along the axis of log V by p an amount equal to 3 log — . An inspection of Figure 3, where values E2 of y f°r different solvents are plotted as functions of log V, shows at once that this condition is not fulfilled, for, if the curve for water were displaced parallel to itself, it would not coincide with the curves for solutions of typical electrolytes in other solvents, such as ethyl alcohol, ammonia and ethylene chloride. Indeed, in order to test the applicability of Walden's relation it is not even necessary to know the value of A0, since it follows readily from Equation 39 and from the equation y =—r- A0 that if the conductances themselves are plotted as functions of log V, it must be possible to derive the curve for an electrolyte in any one solvent from that in any other solvent by displacing the curve parallel to itself in some direction, this direction being determined by the values of A0 and of the dielectric constant 8. Those familiar with the properties of electrolytic solutions will at once recognize that this condition is not fulfilled. Actually, it is not to be expected that any simple relation will exist between the ionization y and the dielectric constant of the solvent, for, 96 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS as we have seen, the value of y is expressed approximately as a function of the concentration by means of Equation 11. As was pointed out above, the constant D is practically independent of the dielectric con- stant, while ra increases and K decreases with increasing values of this constant. As a result, the relative ionization of an electrolyte in two solvents will vary with the concentration in a more or less complex manner, and in two solvents the order of the ionization values may be reversed as the concentration changes. The important conclusion to be drawn from the behavior of solutions of electrolytes in different solvents is that the conductance function is of the same general form in all solvents. A single empirical equation is capable of expressing the relation between the conductance and the concentration in all cases, practically within the limits of experimental error. Whether or not this equation represents precisely the relation between the conductance and the concentration is relatively unimportant, so long as the deviations from this equation show no decided systematic trend. In aqueous solutions, the weak electrolytes follow the mass- action law in conformity with the ionic theory. The strong electrolytes, however, do not fulfill this condition. It follows from the foregoing con- siderations that the conductance curve for strong electrolytes in water dif- fers from that of electrolytes in other solvents only as regards magnitude of the observed effects and not as regards the nature of the phenomena involved. Any theory which has to account for the relation between the conductance and the concentration of electrolytes in water must equally account for the relation between these quantities in non-aqueous solvents. Various theories have been proposed to account for the change of the equivalent conductance as a function of the concentration in the case of strong electrolytes. The simplest of these is that the degree of ioniza- tion is actually measured by the conductance ratio, in which case it is necessary to account for the change in ionization as a function of the concentration. Unfortunately, a general theory of other than dilute solutions does not exist at the present time. A comprehensive method of treating concentrated solutions is therefore lacking. The problem of equilibrium in a system of charged particles has not been solved, and the question therefore remains open as to whether or not the change in ionization may be accounted for. On the other hand, the assumption may be made that the speed of the ions changes as a function of the concentration, as a consequence of which the conductance ratio does not correctly measure the degree of ionization. Certain writers have as- sumed that typical electrolytes are completely ionized in solution and that consequently the change in the conductance is due entirely to a FORM OF THE CONDUCTANCE FUNCTION 97 change in the speed of the carriers. It should be stated, however, in this connection, that no theory has thus far been proposed which ade- quately accounts for the change in the carrying capacity of the ions as a function of the concentration, particularly in solvents of low dielectric constant. Any such theory must not only account for an initial diminu- tion in the speed of the ions, but it must also account, in many cases, for a subsequent increase in the speed with increasing concentration. In fact, such a theory must account for the various forms of the con- ductance curves in different solvents and for the change in the form of the curves as the condition of the solvent is altered. Incidentally, it is to be noted that the order of the changes in the speed of the ions on this assumption is very great. It is true that, in aqueous solutions, the speed does not vary greatly from the most dilute solutions up to normal concentration, but in solutions in solvents of low dielectric constant it is not only necessary to account for a decrease in speed but in many cases for an increase in speed which, over a limited range of concentration, is, at times, as great as a thousandfold. It seems very difficult to account for a change of speed of this magnitude on the basis of our present knowledge of the properties of the carriers in different media. In this connection it should be borne in mind that, superimposed on these hypothetical changes in the speed of the ions, there is a change due to the viscosity of the solution which effect appears in every respect to be normal in character. Furthermore, solutions of weak electrolytes, both in water and non-aqueous solvents, conform to the mass-action law up to fairly high concentrations. If the speed of the ions changes with the concentration, then such a simple relation is not to be expected. A third hypothesis has been proposed, namely: that the ionization reaction differs from that which is commonly assumed. Certain writers have made the assumption that, in non-aqueous solutions, the electrolyte is associated, the association changing with concentration, and that only the associated molecules are capable of ionization. They assume, for example, in the simplest case, that the following reactions take place: = (MX)2 As the concentration increases, the amount of the polymer increases and this increase might be sufficient to provide for an actual increase in the number of ions present. If this hypothesis is correct, the current in such solutions is carried chiefly by complex ions and consequently transfer- ence numbers in such solutions should be abnormal. Reliable trans- ference numbers in solvents of low dielectric constant are not available, 98 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS but from the data for solvents of somewhat higher dielectric constant it may be inferred that the transference numbers are approximately normal. Furthermore, since it appears that the deviations from the mass-action law in aqueous solutions are of the same character as in non-aqueous solutions, it follows that similar intermediate ions would have to be assumed to be present in solutions of the strong binary elec- trolytes in water. If such were the case, not only should the trans- ference numbers be abnormal, but they should vary as a function of the concentration. Now, while it is true that many transference numbers do vary with the concentration, a considerable variation takes place only at relatively high concentrations, and only at such concentrations where the viscosity of the solution has increased sufficiently to materially affect the motion of the ions through the solution. It would seem that trans- ference measurements should yield data corroborating this last hypothesis if it were correct. So far as available data are concerned, the hypothesis is not substantiated. 4. The Form of the Conductance Curve in Dilute Aqueous Solu- tions. The applicability of the conductance function to aqueous solu- tions is uncertain. That the Storch equation holds approximately for aqueous solutions at higher concentrations has long been known. In the case of Equation 11 this would yield for m values of approximately 0.5, and for D values in the neighborhood of 2. With such large values of the constant D and small values of the constant m, it becomes very difficult to determine the value of the constant K. At concentra- tions sufficiently low, so that the effect of the D term might be neglected, the ionization is so nearly complete that it becomes practically impos- sible to demonstrate whether or not the mass-action law is approached as a limiting form. Kraus and Bray have shown that Equation 11 may be applied with considerable exactitude to solutions in water up to 10~3 normal, provided a value of A0 is chosen which is lower than the experi- mentally determined values of the equivalent conductance at very low concentrations. More recently, Washburn and Weiland21 have con- cluded from their very accurate conductance measurements on KC1 up to 2 X 10~5 normal that the mass-action law is actually approached as a limit. Their results, however, do not appear to be conclusive, since, in extrapolating for the value of A0, they assume the mass-action law to hold.22 If the mass-action constant is calculated with a value of A0 based on the assumption that the mass-action law holds, then the results must necessarily conform to the assumption made. The curve obtained "Washburn and Weiland, J. Am. Cher*. Soc. W, 106 (1918). »» Kraus, J. Am. Cfhem. Soc. 4%, 1 (1920). FORM OF THE CONDUCTANCE FUNCTION 99 is shown in Figure 14, in which values of the mass-action function K' are plotted against those of the concentration. The form of this function is entirely different from that which has been found to hold in solutions in non-aqueous solvents and it is obvious, moreover, that the function is a comparatively complex one. At higher concentrations, and practically down to 1.5 X 10"4 normal, the K', C-curv£ is everywhere concave toward the axis of concentrations. At this low concentration, however, the curve changes its form, and approaches a value asymptotic to a line parallel to the axis of concentrations. In order to establish the mass- action law as a consequence of experimental observations it must be Concentration X FIG. 14. Showing Variation of K' with Concentration for Aqueous Solutions of KC1 at 18° According to Washburn. shown that, over a measurable concentration interval, points on the curve necessarily lie upon a horizontal straight line. As this has not been done, it is evident that Washburn's conclusions remain in doubt. The manner in which the curve for the mass-action function ap- proaches the axis depends upon the value of the constant m in the general equation. For values of m greater than unity, the curve ap- proaches the axis asymptotic to a line parallel to the axis of concen- trations; while for values of m less than unity, it approaches the axis asymptotic to the axis of K' . In the case of water, therefore, for which the value of m appears to be less than unity, we should expect that the K! curve would be everywhere concave toward the axis of concentrations. 100 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS The conductance of potassium chloride solutions between the concen- trations of 10'* and 2 X 10~5 normal may be represented well within the limits of experimental error, by means of the Equation 11 23 in which the constants have the value: ra = 0.52, D — 1.703, A0 = 129.9, and K = 10 X 10-4. Washburn's value for K is 200 X lO'4. Actually, this represents an upper probable limit for the value of the constant K. The value 10 X 10~* would appear to be too small. Salts in the alcohols have values of the mass-action constant considerably greater than this. Since, in general, the value of the mass-action constant increases with the dielectric constant, we should expect that the value of this constant in the case of aqueous solutions would be greater than in the alcohols. It should be noted, however, that the experimental results might still be represented within the limits of experimental error if a value con- siderably greater than 10 X 10~4 were assumed for the mass-action con- stant. It is possible, therefore, that the salts in water may have a value of the mass-action constant as high as 100 X 10'*. On the other hand, so far as the actual data are concerned, it cannot be definitely demon- strated that the mass-action law is approached as a limiting form in aqueous solutions of strong electrolytes. Even the value of 200 X 10~4 for potassium chloride appears to be distinctly lower than the value of the constants for certain much weaker electrolytes in aqueous solution, as, for example, acids of intermediate strength. In the case of the strong acids and bases, sufficient data are not available to determine the order of magnitude of the limit which the function K' approaches. If the data relating to hydrochloric acid are correct, the ionization of this acid in a 10~4 normal solution is as low as that of potassium chloride at the same concentration, assuming that the value of A0 for hydrochloric acid is 380.0. Actually this value of A0 is somewhat too low and the value 382.0 is probably more nearly correct. It would appear, therefore, that the strong acids may approach a value of the mass-action constant as low or lower than that of the salts; or, in other words, values lower than 200 X 10~4. No data are available from which the ionization of the strong bases may be calculated at low concentrations. The limiting values which the ionization constants of the strong acids and bases approach at low concentrations is of considerable practical importance, since the hydrolysis of salts depends upon the relative values of these constants and that of water. If the values which the mass- action constants of the bases and acids approach at low concentrations are sufficiently small, then the salts of these acids and bases will be »Kraus, Joe. cit. FORM OF THE CONDUCTANCE FUNCTION 101 hydrolyzed to an appreciable extent at very low concentrations. In case the limits approached differ for the acids and the bases, the meas- urement of the conductance of very dilute salt solutions will be affected by hydrolysis. It appears not impossible that the bases may approach values of the mass-action constant lower than those of the acids. In liquid ammonia solutions the ionization constants of the bases are much lower than those of the acids. We might, therefore, expect that at con- centrations approaching 10~5 normal the conductivity of the salt might be appreciably affected by hydrolysis. This is almost certainly the case with silver nitrate. The ionization constant of this base is approxi- mately 2.5 X 10~4 at 25°. This value is based on the solubility of a saturated solution of silver oxide in water whose ionization has been determined to be approximately 0.64. At 10~3 normal the conductance of the silver nitrate solution would be affected to the extent of 0.7 per cent due to hydrolysis. Until more accurate data are available on the ionization of the strong acids and bases at low concentrations, the inter- pretation of conductance measurements with salts at low concentrations remains in doubt. 5. Solutions of Formates in Formic Acid. It is evident, from the considerations of the foregoing sections, that, as the concentration of an electrolyte increases, the value of the function K' increases. In other words, as the concentration of the electrolyte increases, the conductance falls less rapidly than required by the simple mass-action relation. As we have seen, if the simple mass-action law holds, then a plot of the reciprocal of the equivalent conductance against the specific conductance, or the ion concentration, yields a linear relation between the experi- mentally determined points. Deviations from the mass-action law are then, obviously, such that at high concentrations the points diverge from a straight line toward the axis of specific conductances. In general, therefore, these curves are concave toward the axis of specific con- ductances. There are indeed a few cases in which the curves are convex toward the axis of specific conductances, or, in other words, in which the deviations from the mass-action relation are in the opposite direction. This has been found to be the case with aqueous solutions of certain weak organic acids whose viscosity is very high. Presumably this form of the curve is due to the rapidly increasing viscosity of the solution at higher concentration. The same form of curve has been found by Schlesinger and his associates for solutions of formates in formic acid.24 •* Schlesinger and Calvert, J. Am. Chem. 8oc. S3, 1924 (1911) ; Schlesinger and Martin, J. Am. Chem. Soc. 36, 1589 (1914) ; Schlesinger and Coleman, J. Am. Chem. Soc. 38 271 (1916) ; Schlesinger and Mullinix, J. Am. Chem. Soc. 41, 72 (1919) ; Schlesinger and Reed, J. Am. Chem. Soc. 41, 1921 (1919) ; Schlesinger and Bunting, J. Am. Chem. Soc. 11. 1934 (1919). 102 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS According to Schlesinger, solutions of the formates in formic acid present an anomaly in that, while they are highly ionized, differing but little in this respect from aqueous solutions, the simple law of mass-action is obeyed up to concentrations as high as 0.3 normal. If this interpreta- tion is correct, it will be necessary to revise all commonly accepted notions relative to the causes underlying the deviations from the simple mass- action law, since in these solutions we would have a case in which the law of mass-action is obeyed up to high concentration for solutions of strong electrolytes. We may, therefore, examine the results obtained Specific Conductance of Sodium Acetate in Water. 10. 20. 30. 40. SO 60. 70 .029 0. S. 10. 15. ZO. £S. 30. 35. Specific Conductance of Sodium Formate in Formic Acid. FIG. 15. Comparison of Conductance Curves in Formic Acid and in Water. in formic acid with some care in order to determine whether or not solu- tions in this solvent may be brought into line with solutions in other solvents. It is at once apparent that measurements with solutions in formic acid may lead to difficulties of interpretation, owing to the fact that the conductance of the pure solvent is very high. It is not possible to carry the measurements to very low concentrations ; and if such measure- ments are carried out, the results will always be more or less in doubt. In Figure 15, the upper curve represents a plot of I/A against the specific conductance for solutions of sodium formate in formic acid, according to Schlesinger. It will be observed that, between a concen- tration of C = 0.0667 and C = 0.297, the points lie upon a straight line within the limits of experimental error. At lower concentrations the curve deviates from a straight line, being concave toward the axis of FORM OF THE CONDUCTANCE FUNCTION 103 ion concentrations, while at higher concentrations it is convex toward this axis; in other words, the experimentally determined points lie upon a curve which has an inflection point somewhere between the concentra- tions given above, probably in the neighborhood of 0.1 normal. Schles- inger is inclined to attribute the deviation of the points in the more dilute solutions to the presence of impurities. So far as the conductance of the solvent is concerned, since sodium formate has an ion in common with formic acid, it is to be expected that the ionization of formic acid itself will be repressed by sodium formate, so that the conductance of the pure solvent itself will not enter. He believes, however, that there are present in the solvent impurities, as a result of which the measured con- ductance is higher than that due to the electrolyte. On the other hand, it is known that the salts of the fatty acids yield ions which move very slowly and whose solutions exhibit an extremely high viscosity. The form of the curve in the case of the formates in formic acid is similar to that of certain acids in water. Further light may be thrown upon this question by considering the conductance curves of salts of organic acids in water, whose solutions likewise exhibit a high viscosity. The lower curve in Figure 15 represents a plot of I/ A against the specific conductances for sodium acetate in water at 18°. An inspection of the figure shows at once that the curve for sodium acetate in water is in all respects similar to that of sodium formate in formic acid. Between the concentrations 0.1 and 0.5 normal, the points lie upon a straight line within the limits of experimental error. In the more dilute solutions, the experimentally determined points lie upon a curve concave toward the axis of concentrations and in the more concentrated solutions on a curve convex toward this axis. In the case of sodium formate in formic acid, the concentration interval over which the points lie upon a straight line is 0.0667 to 0.297, corresponding to a concentration ratio of 4.45, while in the case of sodium acetate in water the corresponding concen- tration interval is 0.1 normal to 0.5 normal, whose ratio is 5.0. If we hold that the law of mass-action applies to solutions of sodium formate in formic acid, we might equally well hold that this law applies to solu- tions of potassium acetate in water. Our knowledge of the behavior of aqueous solutions, however, is such that it is at once evident that the linear form of the curve between 0.1 and 0.5 normal is due to the fact that, owing to the high viscosity of the solutions at higher concentra- tions, the conductance as measured is smaller than it otherwise would be. On the other hand, in the more dilute solutions the form of the curve in the case of sodium acetate is entirely similar to that of other binary electrolytes in water. It is difficult, therefore, to escape the con- 104 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS elusion that in the case of solutions of the formates in formic acid, likewise, the approximately linear form of the curve over a limited con- centration interval is due to the existence of an inflection point and that the causes underlying the course of the curve are the same as those in solutions of sodium acetate in water. It appears probable, therefore, that solutions of the formates in formic acid do not constitute an excep- tion to the well-known behavior of strong electrolytes in solvents of high dielectric constant. From this point of view these solutions are normal in their behavior. 6. The Behavior of Salts of Higher Type. Up to this point, the electrolytes considered have been of the binary type. In the case of salts of higher type the interpretation of conductance measurements becomes much more difficult and uncertain, since it is possible, and even probable, that ionization may take place in several stages, as indeed it does in the case of weak acids and bases. For example, a salt of the type MX2 may ionize according to the equations: MX2 = MX+ + X- MX+ = M++ + X- MX2 = M++ + 2X-. If ionization takes place only according to the last equation, then the degree of ionization may be calculated from conductance measurements. But if ionization takes place according to the first two equations, then it is not possible to determine the number of carriers in the solution at a given concentration. In the case of weak dibasic acids, ionization often takes place according to the first two equations, the constants of the two reactions being such that one reaction is practically completed before the other reaction has begun. With salts this does not appear to be the case. In any case, if the concentration is sufficiently low, we should expect that, ultimately, there would be present in the solution only the ions M++ and X-. Since the ion M++ carries two charges, its carrying capacity will be approximately twice as great as that of an ion carrying only a single charge. The molecular conductance of such an electrolyte should therefore approach a value approximately twice that of a binary electro- lyte, or its equivalent conductance should approach a value of the same order as that of binary electrolytes. An examination of the conductances given in Table III indicates that this is the case. The limiting value of the equivalent conductance for salts of different type is throughout of the same order, and we may conclude, therefore, that at low concen- FORM OF THE CONDUCTANCE FUNCTION 105 trations the carrying capacity of an electrolyte is determined by the number of charges associated with the ionic constituents. In solutions of salts of the type of copper sulphate, reaction may take place according to the equation: CuSO, = Cu+* + S04-. This reaction is a binary one, similar to that of the binary salts, but the molecular conductance of such a salt should be twice that of a binary salt. Such has been found to be the case. This behavior of salts of higher type appears to be quite general and is not confined to aqueous solutions. In Table XXXIV are given conductance values for solutions of strontium and barium nitrates in ammonia. It will be observed that in both cases the limiting value of the molecular conductance is much higher than that of binary electro- lytes and is, in fact, approximately twice that of these electrolytes. We may assume, therefore, that in these solutions we have ultimately a reaction corresponding to the type: It is apparent, however, that at a given concentration the number of carriers present in solutions of these electrolytes is much lower than it is in solutions of typical binary electrolytes. Owing to the low value of the ionization, the values of A0 for electrolytes of this type have not been determined with any degree of certainty. TABLE XXXIV. CONDUCTANCE OF TERNARY SALTS IN NH3 AT — 33°. Sr(N03)225 Ba(N03)226 V Arnol V Amol 286.2 145.0 91.1 101.3 1283.0 207.0 1407.0 2006 5441.0 275.8 14950.0 3194 20360.0 359.3 58750.0 4225 61660.0 449.0 116500.0 4985 151100.0 514.2 Similar results have been obtained with solutions of ternary electro- lytes in various other solvents, such as acetone, pyridine, and the like. In many cases, however, the solubility of these salts is relatively low and their ionization at ordinary concentrations is often extremely small. They do not, therefore, lend themselves to a quantitative study of the "Franklin and Kraus, Am. Chem. J. 23, 292 (1900) 38 Franklin and Kraus, J. Am. Chem. Hoc. 27, 200 (1905). 106 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS relation between the conductance and the concentration. In the case of aqueous solutions, however, sufficient data are available to make it possible to obtain a general notion as to the manner in which the con- ductance varies as a function of concentration. Assuming a reaction of the type MX2 = M- + 2X-, and assuming the mass-action law to apply, we obtain the equation: In Table XXXV are given values of the function K' calculated according to the above equation at a series of concentrations for calcium chloride dissolved in water at 18°. TABLE XXXV. VALUES OP THE MASS-ACTION FUNCTION FOR CaCl2 SOLUTION IN H20 AT 18°. C .... ID'3 5X10-3 2X10-2 10'1 5X10-1 .954 .910 .849 .764 .686 1.88X10'5 1.7X10'4 1.62X10'3 1.88X10'2 2.6X10'1 I v:.: It will be observed that the mass-action function for this salt increases very greatly with the concentration. On the whole, the increase is much more marked than it is for binary electrolytes. The value of the func- tion, moreover, is much lower throughout than it is for solutions of binary electrolytes. At 5 X 10'1 normal the value of K' is only 0.26, which is approximately one-half that of potassium chloride, while at 10'3 normal the value is 1.88 X 10~5. The mass-action function, therefore, falls off very rapidly as the concentration decreases. In the case of copper sul- phate solutions we have the equation: Values of the mass-action function for this electrolyte at different con- centrations are given in Table XXXVI. At higher concentrations the value of the function K' for this salt is smaller than that for calcium chloride, but the constant decreases much less rapidly as the concentra- tion decreases and at lower concentration the value of the function is much greater than that of calcium chloride. On the whole, the function appears to undergo a smaller change with the concentration in the case of copper sulphate than in that of uni-univalent electrolytes. However, it FORM OF THE CONDUCTANCE FUNCTION 107 is to be borne in mind that the value of A0 for this electrolyte is much less certain than that for the uni-univalent salts. TABLE XXXVI. VALUE OF THE MASS- ACTION FUNCTION FOR CuS04 IN H20 AT 18°. C ..... 10-3 5X10'3 2X10'2 lO'1 1.0 y%.... 86.2 70.9 55.0 39.6 30.9 K ..... 5.4X10'3 8.6X10-3 1.34X10'2 2.6X10'2 1.38X10"1 As the salts become more complex, the value of the mass-action func- tion becomes smaller and decreases more rapidly as the concentration decreases. For potassium ferrocyanide, assuming the reaction equation: K4FeCN6 = 4K+ + FeCN6~~, the mass-action function has the form: CU-Y) Values of the function at different concentrations are given in Table XXXVII for this salt, as well as for lanthanum sulphate. The constant for the ferrocyanide is throughout small and at low concentrations approaches values of an entirely different order of magnitude from that at the higher concentrations. In the case of lanthanum sulphate, the change in the constant is even more pronounced, as may be seen from an inspection of the table. TABLE XXXVII. VALUES OF THE MASS- ACTION FUNCTION OF AQUEOUS SALT SOLUTIONS. K4FeCN6 C 2X10-3 1.25X10'2 5.0X10'2 1.0X10'1 3.0X10'1 4.0X10'1 y% 85.8 71.0 68.7 53.2 48.8 45.3 K .52X10'10 1.5X108 1.03X10-6 0.920X10'5 4.33X10'4 0.925X10'3 La2(S04)3 C ........... 2X10'3 10'2 5X10'2 Y% ......... 51.4 33.9 26.2 K .......... 1.28X10'12 0.67X10-10 1.03X10'8 It is obvious that, in solutions of electrolytes of higher type, the mass-action function varies the more the higher the type of the salt. The value which the function appears to approach at very low concen- 108 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS trations becomes extremely small and it is uncertain whether or not the function approaches a limiting value other than zero. The interpreta- tion of the results, moreover, is rendered uncertain owing to the possible formation of intermediate ions. It might be expected, however, that, in the limit, the intermediate ions will disappear and the function will correspond to the usual mass-action function. Although the curves become quite complex for salts of higher type, it appears, nevertheless, that the conductance curves at higher concen- trations have the same general form as for salts of simpler type, and that they vary in a similar manner as the nature of the solvent varies. In the following tables are given values for the conductances of Cu(N03)2 and K2Hg(CN)4 in ammonia.27 TABLE XXXVIII. CONDUCTANCE OF TERNARY SALTS IN NH3 AT — 33°. Cu(N03)2 K2Hg(CN)4 FA FA 1.5 98.3 2.0 198.8 4.9 82.9 5.0 182.7 9.9 78.2 19.6 159.8 19.9 80.9 49.8 169.2 323.0 151.8 590.0 298.9 1300.0 213.7 4545.0 493.1 11190.0 417.0 22450.0 498.0 It will be observed that, in both cases, the conductance passes through a minimum value at concentrations in the neighborhood of 0.1 normal. In other words, an increase in the conductance with the concentration at the higher concentrations is not confined to binary electrolytes, but is more or less typical of all electrolytes. It appears, therefore, that the general form of the conductance function is the same for electrolytes of different types. What the precise form of the equation may be, however, has not been determined, since the A0 values are unknown and the prob- lem is complicated owing to the possible formation of intermediate ions. * Franklin, Ztschr. f. phys. Chem. 69, 272 (1909). Chapter V. The Conductance of Solutions as a Function of Their Viscosities. 1. Relation Between the Limiting Conductance A0 and the Viscosity of the Solvent. One of the factors upon which the conductance of a solution depends is the viscosity of the solution itself. If conductance is due to the motion of charged particles through a medium, then the speed of the particles will obviously depend upon the resistance which the particles experience in their motion; that is, upon the viscosity of the medium. Unless the solutions are concentrated, their viscosities will not differ materially from that of the pure solvent. We should therefore expect that the viscosity of the pure solvent would determine the motion of particles under otherwise given conditions. We shall accordingly examine the relation between the conductance and the viscosity of solu- tions in different solvents. In very dilute solutions we may expect that the motion of a given particle will be practically independent of that of other particles of the electrolyte which may be present in the solution. In the limit, therefore, the A0 values will be determined by the nature of the moving particles and by that of the solvent medium in which they move. In Table XXXIX 1 are given fluidity and A0 values for solutions in a number of solvents, together with the values of the ratio A0/F. TABLE XXXIX. FLUIDITY AND A0 VALUES FOR ELECTROLYTES IN DIFFERENT SOLVENTS. Solvent Water Ammonia Sulphur dioxide Benzonitrile . Temp. 18° —33° —10° 25° Epichlorohydrin 25° Propylalcohol 18° Acetone 18° Methylethylketone 25° Pyridine 18° Isobutylalcohol 25° Acetoaceticester 18° Isoamylalcohol 25° Ethylenechloride 25° 1 These values are taken from Kraus and Bray (Zoo. cit., p. 1383), excepting those for water and the viscosity data for sulphur dioxide for which see Fitzgerald, J. Phya. Chem. 16, 621 (1912). 109 ? = l/< P A0 \0/F Electrolyte 93.9 111.0 1.173 Nal 391.0 301.2 0.770 " 233.4 199.0 0.854 KI 80.0 49.0 0.613 Nal 97.1 62.1 0.649 (C2H5) 1.0 0.8 0.6 o.o 1.0 4.0 S.O 2,O 3.0 Concentration. FIG. 16. Viscosity of Aqueous Solutions at Different Concentrations. In glycerine solutions,7 ammonium iodide, potassium iodide, and rubidium iodide exhibit negative viscosity effects. Lithium chloride, on the other hand, as in water, exhibits a viscosity increase withc increasing concentration. In glycerine solutions, the negative viscosity effect dis- appears in the neighborhood of 75°. It is obvious that, if the viscosity of a solution changes with concen- tration, the speed of the carriers, to which the conductance of the solu- tions is due, will likewise change with the concentration. If this is the case, then the conductance ratio, y = -r-, no longer measures correctly AQ 'Davis and Jones, Ztachr. }. phys. Chem. 81, 68 (1913). 114 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS the degree of ionization. It has been proposed to take account of the change of conductance due to the viscosity effect in direct proportion to the fluidity change of the solution.8 In that case the degree of ionization of the electrolyte is given by the expression: /Af\\ & FO (40) Y = 2C7' where Fa is the fluidity of the pure solvent and F that of the solution. Other writers * have proposed an equation of the form: (41) Y = ^ where p is a constant, and A and A0 are ionic conductances. If p were equal to unity, the conductance of the solution would be corrected in direct proportion to the fluidity change. Difficulty arises in determining the value of p. It has been suggested that the value of this constant may be derived from the manner in which the speed of an ion in dilute solution changes as a function of the temperature. As we shall see presently, the change in the A0 values of the ions is not in general directly proportional to the fluidity change of the solvent, but is in most cases smaller. It has been shown that a relation of the type (42) A = KFP holds very nearly.10 The values of the constant p for different salts are given in Table XLII. TABLE XLII. VALUE OF THE VISCOSITY-TEMPERATURE EXPONENT p FOR DIFFERENT IONS. Univalent Ions. Ion Cl- K+ NH4+ N03- Ag+ Na+ CH3COO p 88 .887 .891 .807 .949 .97 1.008 A 65.4 64.7 64.4 61.8 54. 43.5 34.6 Divalent Ions. Ion 1/2S04~ 1/2 C A" 1/2 Ba" 1/2 Ca" p 0.944 .931 .986 1.008 A 68.7 63.8 55.9 52.1 )usfleld and Lowry, Phil. Trans. [A] 20k, 289 (1903) ; Noyes and Falk, J. Am. •Washburn, J. Am. Chem. 8oc. S3, 1463 (1911). "Johnston, J. Am. Chem. Soc. SI. 1010 (1909). THE CONDUCTANCE OF SOLUTIONS— VISCOSITIES 115 Since p is in general less than unity, it follows that the conductance of the ions changes less rapidly than does the viscosity of the solvent for a given increase in temperature. As a rule, the lower the conductance of the ion, the greater the value of the exponent p. For most slowly mov- ing ions the exponent appears to approach the value unity as a limit. This is exemplified in the case of the acetate and the calcium ions. The lower the conductance of an ion, therefore, the more nearly does the conductance change in direct proportion to the fluidity change of the solvent. But while the value of p in Equation 42 h^s thus been evalu- ated, there is no good reason for believing that the exponent p in Equa- tion 41 will have the same value. It obviously is not possible to deter- mine the manner in which correction should be applied for the change in the conductance of solutions due to concentration change, unless we know the manner in which the ionization at these concentrations varies as a function of concentration. In other words, the nature of the cor- rection as found will depend upon the assumed nature of the conductance function. We have the equation: where /(C) is some function of the concentration of the solution. As we have seen, in solutions at higher concentrations, the function K' follows approximately the relation: where n has a value in the neighborhood of 1.5 for aqueous solutions. Assuming this equation to hold at higher concentrations, we may deter- mine the nature of the viscosity correction on the basis of this assump- tion. In order to determine the nature of the correction, therefore, we may determine the value of the constants n and D at lower concentra- tions, where the viscosity change is negligible, and thereafter extrapolate this function to higher concentrations. In other words, by means of Equation 9a we may calculate the value of y at higher concentrations and compare it with the directly measured value and with the fluidity of the solution at that concentration. Or, conversely, the experimentally determined conductance values at higher concentrations may be multi- plied by an assumed correction factor and the corrected values compared with the values calculated by means of the above equation. If the assumptions made are applicable, then the two values should correspond. 116 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS The simplest correction would be that in which the conductances were assumed to change in direct proportion to the fluidity change of the solution. This method of correction has been applied to solutions of potassium iodide dissolved in water at O0.11 In Figure 17, lower curve, are plotted values of log'(CA) and of log[C(A0 — A)], both for the measured (rep- 0.5 Log (cA) for LiCl. I.O 1-5 s I " 3 iS 0.0 5 T.o 2.0 3.0 X* o I 4 $ T.o Log (cA) for KI. 3.0 FIG. 17. Showing Influence of Viscosity Correction on the Conductance Curves of KI and LiCl in Water at 0°. resented by crosses) and the corrected (represented by circles) con- ductance values of potassium iodide dissolved in water at 0°. If Equa- tion 9a holds and if the assumed viscosity correction is applicable, then the corrected points should lie upon a straight line.12 This, apparently, is the case. The conductance curve of potassium iodide in water at 0° is a very exceptional one in that at higher concentrations it passes through a slight minimum and maximum, after which the conductance decreases very rapidly with increasing concentration. This form of the curve is due 11 Kraus, J. Am. Chem. Soc. 36, 35 (1914). 12 Equation 9a may be written : n log (CA) = log [C7(Ao A) ] + log ZM< THE CONDUCTANCE OF SOLUTIONS-VISCOSITIES 117 to the viscosity change of the solution at higher concentrations. As we have seen, the fluidity passes through a maximum, after which it de- creases sharply. If the values of the conductance as calculated from jji Equation 9a are multiplied by the fluidity ratio •=-, then these calculated values fall upon a curve (B) exhibiting a slight maximum and minimum, g 60 a r i \ \ 1.30 Log (Concentration). FIG. 18. Showing the Influence of Fluidity Change on the Conductance Curve of KI in Water at 0°. which practically coincides with the curve of measured conductances, as may be seen from Figure 18. It is apparent that in the case of solu- tions of potassium iodide in water — and, in fact, this has been shown to be true for aqueous solutions of all electrolytes exhibiting a negative viscosity effect — the speed of the ions changes in direct proportion to the fluidity change of the solution. The peculiar form of the conductance curve, as we have it in solutions of the potassium iodide, is due to the variation of the viscosity effect. 118 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS In solutions of electrolytes in water which exhibit a positive viscosity effect, the conductance appears to change less than the viscosity of the solution. If we treat the conductance curve of lithium chloride in a manner similar to that employed in the case of potassium iodide, we obtain as plot not a straight line, but a curve lying below the straight line resulting from Equation 9a. In other words, the conductance values appear to be overcorrected. This result is illustrated in Figure 17, upper curve, in which A is the uncorrected curve, B is the curve in which the conductance is corrected in direct proportion to the fluidity change, while C is a curve in which correction has been applied to the lithium ion only. We may conclude, therefore, that, in aqueous solutions, the conductance may be corrected for the viscosity change in direct propor- tion to the fluidity change in the case of salts which exhibit a negative viscosity effect, but that, in solutions of salts which exhibit a positive viscosity effect, the correction made should be smaller. Just what cor- rections should be applied is difficult to determine at the present time. We have seen that in non-aqueous solutions the viscosity effect is much larger than it is in aqueous solutions. We should therefore expect that the conductance of non-aqueous solutions would be affected to a much greater extent than that of aqueous solutions. It appears, how- ever, that in solutions of electrolytes in non-aqueous solvents the con- ductance changes much less than the fluidity of the solvent. The relation between the conductance and the viscosity is illustrated in Figure 19, in which are plotted the conductance and fluidity values of solutions of potassium iodide in liquid ammonia at different concen- trations. Branch B is extrapolated on the assumption that Equation 9a holds. There is also indicated on this figure the calculated conductance of these solutions, Branch D, on the assumption that the conductance changes in direct proportion to the fluidity of the solvent. It will be observed that the conductance, as corrected in this way, is much too low to correspond with the experimental conductance curve represented by circles. It is evident, therefore, that in non-aqueous solutions the con- ductance change is smaller than corresponds to the viscosity change. This is further borne out by the fact that Equation 11 appears to hold for solutions of many electrolytes up to concentrations at times as high as 2 normal. It is obvious that the viscosity of the solutions at these concentrations must be much greater than that of the pure solvent, and consequently it follows that the correction to be applied for the viscosity change is probably the smaller the greater the viscosity change; that is, the lower the dielectric constant of the solvent. On the other hand, it has been found, in the case of all solutions in non-aqueous solvents, that, THE CONDUCTANCE OF SOLUTIONS— VISCOSITIES 119 at sufficiently high concentrations, the conductance curve ultimately falls, and falls the more rapidly the higher the concentration. There appears to be no exception to this behavior. There can be little question but that the final decrease in the conductance is due to a large increase in the viscosity of the medium. This is illustrated in Figure 20, where the conductance of solutions of silver nitrate in methylamine 13 is repre- sented as a function of the concentration. The maximum lies a little 19* 160 128 •§ 1" 0.96 '— £ - i.i 0.8 I/>K (concentration). FIG. 19. Showing the Influence of Fluidity Change on the Conductance of Solutions of KI inNHaat— 33.5°. above normal concentration at — 33° and is displaced toward higher concentrations at higher temperatures. 3. Relation between Viscosity and Conductance on the Addition of Non-Electrolytes. The addition of a non-electrolyte to a solution of an electrolyte in most cases increases the viscosity of the solution.1* The conductance change on the addition of a non-electrolyte is in the same direction as that of the viscosity change, but in most cases the con- ductance change is smaller than the corresponding viscosity change. » Fitzgerald, Joe. cit., p. 640. 14 In a few instances, however, where the added non-electrolyte forma a stable complex with one of the ions in solution, the addition of a non-electrolyte results in a viscosity decrease. An example of this effect is found in solutions of certain of the heavy metals in water whose viscosity is reduced on the addition of ammonia. [Blanchard, J. Am. Chem. Soc. 26, 1315 (1904).] In these cases the addition of a non-electrolyte causes a decrease in the viscosity only so long as it combines with the electrolyte to form the complex. Beyond this point the viscosity in general increases with further addition of non-electrolyte. 120 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS The experimental material available is very incomplete. So far as any conclusion may be drawn, however, the conductance change is the more nearly proportional to the fluidity change, the smaller the molecules of 4S 40 1* 10 0123 Log V. FIG. 20. Conductance of Silver Nitrate in Methylamine at Different Temperatures. the added non-electrolyte. It has been found that the relation between the conductance and the viscosity on the addition of a non-electrolyte may be expressed by an exponential equation of the form A0 = KF^, where A0 is the limiting conductance of the electrolyte in solutions con- THE CONDUCTANCE OF SOLUTIONS-VISCOSITIES 121 taining the non-electrolyte and F is the fluidity of the solution. The smaller the conductance change of the electrolyte for a given fluidity change, the smaller is the value of the exponent p. In Table XLIII are given values of the exponent p for aqueous solutions of a number of electrolytes in the presence of non-electrolytes. TABLE XLIII. CHANGE OF CONDUCTANCE OF ELECTROLYTES DUE TO ADDED NON-ELECTROLYTES. Non- Raf- Gly- Ace- Methyl Electrolyte Sucrosef finose* cerolf tone$ Ureaf Alcohol* Mol. Wt 342.1 594.4 92 58 60 32 p for KC1 0.66 0.675 0.83 0.93 0.95 1.2 t 20° 25° 20° 25° 25° 25° Methyl Methyl Non-Electrolyte Sucrosef Raffinose* Raffinose* Alcohol* Alcohol* Electrolyte HC1 CsCl LiCl CsCl LiCl p 0.55 0.676 0.669 0.8 1.1 °*° 25° 25° 25° 25° Non-Electrolyte AcetoneJ Glycerol§ Urea§ Pyridine§ Electrolyte HC1 CuS04 NaOH LiN03 v . 1.0 1.0 1.0 1.0-1.3 t . . 25° 15° 25° * Clark, Thesis, Univ. of 111. (1915). See also, Washburn, "Principles of Physical Chemistry," 2 Ed., p. 260. t 5holm, Finskct Vetenslcap. Soc. Forhandl. 55, A No. 5, p. 75 (1913) ; Washburn, loc. cit. t Ryerson, Thesis, Univ. of 111. (1915). § Green, J. Chem. Soc, 93, 2049 (1908). It will be seen from the table that, in general, the higher the molecu- lar weight of the added non-electrolyte, the smaller is the value of the exponent p. This is most clearly shown in the case of potassium chloride, for which electrolyte the data are more extensive than for others. The exponent in the presence of sucrose and raffinose is in the neighborhood of 0.67, while in the presence of urea it is 0.95 and in the presence of methyl alcohol 1.2. The molecular weight of the added elec- trolyte is thus a governing factor in determining the manner in which the conductance of an ion varies due to viscosity change. That some transpositions in the order of the exponent and in that of the molecular weight of the added non-electrolyte will occur is to be expected, since specific influences may make themselves felt. It is noticeable that in the case of methyl alcohol the exponent has a value greater than unity. 122 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS The significance of this result remains uncertain. It is to be expected, however, that, on the addition of an electrolyte whose molecular weight is lower than the mean of that of the solvent molecules, effects may occur which cannot well be predicted on the basis of our present knowledge of the viscosity relations in such mixtures. It is interesting to note that, in the presence of non-electrolytes of high molecular weight, the coeffi- cient for different electrolytes has very nearly the same value. Thus, in the presence of raffinose the values of the exponent for lithium, potas- sium and caesium chlorides are very nearly identical. Since these salts have a common anion, it may be inferred that the influence of the vis- cosity effect due to non-electrolytes of high molecular weight is the same for the lithium, potassium and caesium ions. This is apparently not so nearly true in the presence of non-electrolytes of low molecular weight, but even here, in some instances at any rate, the exponent does not differ greatly for different salts. It would seem that the influence of the vis- cosity change on the .conductance of an ion, due to the electrolyte itself, differs markedly from that due to the addition of a non-electrolyte. At the present time, sufficient data are not available to enable us to draw conclusions with any considerable degree of certainty. 4. The Influence of Temperature on the Conductance of the Ions. As is shown in Table XLII, with increasing temperature the conductance of the ions increases, and this increase is the more nearly proportional to the increase in the fluidity of the solvent, the lower the conducting power of the ion. In the case of the acetate ion, the conductance is everywhere proportional to the fluidity of water from 0° to 156°, which is the entire interval over which the viscosity of the solvent has been measured. In the following table are given the ratios of the fluidity of water to the conductance of the acetate ion from 0° to 156°. 15 TABLE XLIV. RATIO OP THE FLUIDITY OF WATER TO THE CONDUCTANCE OF THE ACETATE ION AT DIFFERENT TEMPERATURES. Temp 0° 18° 25° 50° 75° 100° 128° 156° -T .... 2.73 2.72 2.73 2.72 2.71 2.72 2.71 2.71 ACH3COCT It is evident that, in dilute solutions, the conductance of the acetate ion, and presumably therefore its speed, is directly proportional to the fluidity of the solvent. Since the conductance of the acetate ion is proportional to the fluidity " Johnston, loc. cit. THE CONDUCTANCE OF SOLUTIONS— VISCOSITIES 123 of water up to 156°, we may assume, in the absence of experimental data, that it remains proportional at higher temperatures. In order, therefore, to compare the conductance of the different ions with the fluidity of water, we may compare the conductance of these ions with that of the acetate ion whose values are known up to 306°. The ratio of the conductances of the various ions to that of the acetate ion is given in Table XLV.16 TABLE XLV. INFLUENCE OF TEMPERATURE ON THE CONDUCTANCE OF VARIOUS IONS RELATIVE TO THAT OF THE ACETATE ION. Ion Conductance at temperatures: — 0.0° 18° 25° 50° 75° 100° 128° 156° 218° 306° K+ 1.99 1.87 1.83 1.72 1.66 1.58 1.54 1.50 1.32 1.18 Na+ 1.28 1.26 1.25 1.22 1.20 1.19 1.19 1.18 1.15 1.11 NH4+ .... 1.98 1.86 1.83 1.72 1.66 1.59 1.55 1.52 1.37 1.30 Ag+ 1.62 1.57 1.54 1.51 1.49 1.45 1.43 1.42 1.29 .. Cl- 2.02 1.89 1.85 1.73 1.67 1.59 1.54 1.51 1.32 1.18 N03- 1.99 1.78 1.73 1.55 1.46 1.37 1.30 1.25 1.21 .. H+ 11.82 9.08 8.58 6.95 5.88 4.95 4.23 3.68 2.79 1.82 OH- 5.17 4.95 4.71 4.24 3.75 3.38 3.07 2.81 2.08 1.62 In determining the conductance of the various ions, it is of course necessary to assume values for the transference numbers of one pair of ions. In the case of potassium chloride, the transference number is very nearly 0.5 and at higher temperatures it appears to approach this value as a limit. It has been assumed, therefore, that at temperatures above 100° the transference number of the potassium and chloride ions is 0.5. This assumption, moreover, is justified by the fact that, as the tem- perature increases, the transference numbers of all ions appear to approach one another. In the above table the ionic conductances at the higher temperatures are based upon this assumption. The relation between the ionic conductances and the temperature is shown in Figure 21, where the conductances relative to the acetate ion are plotted as ordinates and the temperatures as abscissas. Since the con- ductance of the acetate ion is proportional to the fluidity of the solvent, it follows that the ordinates will be proportional to the ratio of the ionic conductances to the fluidity of the solvent. On examining the figure, it will be seen that the greater the value of the conductance of an ion, the less does the conductance increase as the temperature increases. Ai That is, the ratio - — decreases with increasing temperature and de- ac "Kraus, loc. cit. 124 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS creases the more, the greater the value of the ratio. In other words, these ratios appear to approach unity, as a limit at high temperatures. The conductances of all ions, therefore, appear to approach that of very slowly moving ions. For example, at 0° the conductance of the hydrogen ion is 11.82 times that of the acetate ion, while at 306° it is only 1.82 times that of this ion. At 0° the conductance of the potassium ion is 1.99 times that of the acetate ion, while at 306° it is only 1.18 times that of this ion. At 0° the conductance of the sodium ion is 1.28 times that of the acetate ion, whereas at 306° it is only 1.11 times that of the same 12 H+ 6 OH- t Nor 100° 200' Temperature. 3«> d FIG. 21. Showing the Relative Change of Ionic Conductances with Temperature. ion. It is evident, therefore, that as the temperature increases the speeds of the different ions approach a common value. With the exception of the nitrate ion, the curves for the ionic conductances do not intersect. At low temperatures, however, the relative conductance of the nitrate ion, with respect to that of the acetate ion, decreases much more rapidly than it does for other ions having the same conducting power. At 0° the ratio of the conductance of the nitrate ion to that of the acetate ion is 1.99, whereas at 25° it is only 1.73. In the case of the potassium ion at the lower temperature, the ratio is also 1.99, but at 25° it is 1.83. These results have an important bearing on our conceptions as to the nature of the conducting particles, particularly as regards the effect of temperature on the speed of these particles. As has been shown by THE CONDUCTANCE OF SOLUTIONS— VISCOSITIES 125 means of transference experiments, the ions are hydrated in water. In order to account for the fact that the speeds of the different ions at higher temperatures approach one another, it might be assumed that the hydrates break down at higher temperatures, but this assumption would not be in harmony with certain facts. Since the conductance of the slowly moving ions changes in direct proportion to the fluidity of the solvent as the temperature increases, it is reasonable to assume that the relative dimensions of the ion complex remain practically constant. If, therefore, the speed of the more rapidly moving ions approaches that of the more slowly moving ions at higher temperatures, it points to a slow- ing up of the more rapidly moving ions as the temperature increases. This corresponds to a greater relative resistance to their motion, which can only be interpreted as due to an increase in the dimensions of the ion-complex. In other words, as the temperature increases, the hydra- tion of the more rapidly moving ions increases, which tends to reduce their speed relative to that of more slowly moving ions. If the hydration of the ions is due primarily to electrical forces acting between the ions, which are charged, and the surrounding solvent mole- cules, which have an electrical moment, then we should expect that, as the dielectric constant of the medium decreases, the size of the complex will increase, since in a dielectric medium the force is inversely propor- tional to the dielectric constant. For this reason we should expect the relative speeds of ions in non-aqueous solvents of low dielectric constant to approach one another much more nearly than they do in water. This appears to be the case. Moreover, this is also in harmony with the fact that in the case of very large ions, in other words, in the case of ions which have a low conducting power, the conductance in different sol- vents, as well as at different temperatures, is very nearly proportional to the fluidity of the solvent. We may conclude, therefore, that the hydra- tion of the ions increases, or, including non-aqueous solvents, that the solvation of the ions increases with the temperature because of a decrease in the dielectric constant of the medium. It is not to be assumed, how- ever, that the dimensions of the ions in different solvents are controlled entirely by the dielectric constant. The solvent may combine chemi- cally with a given ion to form a complex, which ion in turn may have associated with it additional solvent molecules, due to electrical inter- action between this ion and the solvent. We should expect this to be the case with silver ions which form an extremely stable complex with ammonia. Even in aqueous solutions, the silver ion forms a complex Ag(NH3)2+ with ammonia. This may account for the relatively low conducting power of the silver ion in liquid ammonia solution. Whereas, 126 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS for example, the conductance of the lithium ion in ammonia is 3.36 times that of the lithium ion in water, that of the silver ion in ammonia is only 2.15 times that in water. So, also, we find that the ammonium ion in ammonia has a conductance of only 2.03 times that of the ammonium ion in water, indicating the formation of relatively large complexes. In this connection it may be pointed out that the ammonium salts form with ammonia saturated solutions whose vapor pressures are extremely low. For example, the vapor pressure of a saturated solution of ammonium nitrate in ammonia is one atmosphere at 26°. If the complexity of the ions increases with the temperature, we should expect that at higher temperatures the viscosity would be in- creased more largely for a given addition of salt than at lower tem- peratures. This, again, corresponds with observations on the viscosity of solutions. The change of viscosity due to a given addition of salt increases as the temperature rises, and this increase appears to be the greater the higher the temperature. It is to be noted, also, that the increase in viscosity due to the addition of electrolytes is much greater than that due to the addition of non-electrolytes, except in the case of non-electrolytes which have very large molecules. In general, as has already been pointed out, the viscosity effect is the greater the lower the dielectric constant of the solvent. In solvents of very low dielectric constant, the viscosity of some solutions becomes so great, at high con- centrations, that they often become practically solid. 5. The Influence of Pressure on the Conductance of Electrolytic Solutions. As we have seen, the conductance of the ions is a function of the viscosity of the solution. As the hydrostatic pressure on a solu- tion is increased, its viscosity changes, the sign and magnitude of this change being dependent upon the nature of the solvent medium and upon the concentration of the solution in question. The effect of pres- sure on the viscosity of solutions in water, as well as the effect upon water itself, has been measured by Cohen.17 In Figure 22 are shown the percentage changes of viscosity for pure water at different pressures and temperatures. From an inspection of the figure it will be seen that with increasing pressure the viscosity of water decreases markedly. As the temperature rises, however, the viscosity effect diminishes and it is evident that at higher temperatures the effect changes sign. From the form of the curves at 15° and 23° it is evident that at higher pres- sures the curves for the viscosity effect will pass through a minimum and that ultimately, therefore, the viscosity change will change sign, the viscosity increasing with increasing pressure. In non-aqueous solvents "Cohen. Wied. Ann. J5, 666 (1892). THE CONDUCTANCE OF SOLUTIONS— VISCOSITIES 127 the viscosity increases with increasing pressure, as was found by Ront- gen 18 and Warburg and Sachs 19 for ether and benzene, and by Cohen for turpentine. In general, the viscosity effect in non-aqueous solvents is greater than that in water, and, as we shall see below, the effect is the greater the greater the viscosity of the medium. The pressure-viscosity effect in solutions is a function of the con- Pressure in Atmospheres. O ZOO MOO 000 800 1000 Fia. 22. Showing the Influence of Pressure on the Viscosity of Water at Different Temperatures. centration, as was shown by Cohen. In Figure 23 are shown curves for the viscosity change of solutions of sodium chloride in water at 2° and 14.5°. The broken line curves relate to the lower temperature. The concentrations of the various solutions are indicated on the figure. With increasing concentration of the solution, the viscosity decrease, due to a given increase in pressure, diminishes and ultimately changes sign; that is, with increasing pressure, the viscosity of the solution increases. The lower the temperature, the greater the influence of a given pressure "Rontgen, TFied. Ann. 22, 510 (1884). » Warburg and Sachs. TFied. Ann. 22, 518 (1884), 128 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS change upon the viscosity, but at higher concentrations the effect of temperature diminishes greatly. Pressure in Atmospheres. 0% FIG. 23. Showing the Influence of Pressure on the Viscosity of Aqueous Sodium Chloride Solutions at Different Concentrations. The change in the viscosity of a solution with pressure will obviously have an influence upon the conductance of the solution. The viscosity THE CONDUCTANCE OF SOLUTIONS— VISCOSITIES 129 effect, however, is not the only one involved. As Tammann has shown,20 the conductance-pressure coefficient is the resultant sum of four effects; namely, the volume change of the solution due to pressure change, the change in the mobility of the ions due to the viscosity change of the solution, the change in the ionization of the electrolyte, and finally the change in the conductance of the solvent medium, which, as a rule, is due to a small quantity of electrolyte present as impurity. The conductance- pressure coefficient, therefore, is given by the equation: X Y' Ap where X is the conductance of the solution due to the electrolyte, V that due to the solvent medium, y is the ionization of the electrolyte and y' that of the solvent medium, and cp is the ionic resistance; that is to say, the reciprocal of the ionic mobility. In the equation, therefore, the first term of the right-hand member measures the conductance change due to the volume decrease of the solution; the second term measures the conductance change due to the viscosity change of the solution; the third, the conductance change due to the ionization change of the electrolyte; and the last term, the conductance change due to the ionization change of the solvent medium. By suitably choosing the condition of the solu- tion, it is possible to minimize the value of various of the terms enter- ing into this equation, and thus make apparent the effect of the various factors on the conductance of the solution due to pressure change. Let us examine first the typical form of the conductance-pressure curves in the case of aqueous solutions of 0.01 N KC1. In Figure 24 21 are represented values of the ratio of the resistance of the solution, 7?p, under a pressure of p kilograms per square centimeter to the resistance Rp=i under a pressure of one atmosphere at a series of temperatures. It will be observed that as the pressure increases the resistance of the solu- tion decreases initially. As the temperature rises, the value of the decrease due to a given pressure change diminishes. At high pressures the isotherms exhibit a minimum. • The higher the temperature, the lower the pressure at which the minimum occurs. It is evident that at suffi- ciently high temperatures the minimum will disappear and the resistance of the solution will increase throughout with increasing pressure. This has been found to be the case with strong electrolytes, such as sodium chloride in aqueous solution. In solutions of strong binary electrolytes, the ionization at a con- centration of 0.01 N is so high that but little change is to be expected in " Tammann, Ztschr. f. pTiys. CJiem. 27, 458 (1898). "Korber, Ztschr. f. phys. Chem. 67, 222 (1909). 130 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS its value as a result of pressure change. The third term of the right- hand member of Equation 43 may therefore be neglected. The fourth term, likewise, may be neglected at this concentration, since the con- ductance of the pure solvent is negligible in comparison with that of the solution. The observed conductance change of solutions, under these conditions, therefore, is due to the first two terms. The value of the first Pressure. 1000 1500 2000 1.02 1.0! 1.00 0.99 0.98 0.97 3,095 ^0.94 0.93 0.9? 091 090 0.89 0.88 057 500 3500 v\ \ \ 5000 99-50* 78.88° 59.200 39.40° 19.18° 0.01° FIG. 24. Showing the Influence of Pressure on the Resistance of 0.01 N Aqueous KC1 Solutions at Different Temperatures. term of the right-hand member may be calculated from the data of Amagat on the compressibility of pure water, since the compressibility of an 0.01 N solution will not differ appreciably from that of pure water. If the first term of the right-hand member is transposed, we have the equation: Q Pressure. 500 1000 1SOO 2000 2500 3000*2 / Sal Kl NaBr KBr Naa KCl Litl H a A // / / j / // // / 7 ' // / y y / / / / / 3^ ;LX /, y // / V s^ ^ /s / ^ \ • — - / \\ \ ^ -~-—~ - — — . : — • — i \ \ \ v-- ^__ Fia. 27. Showing the Influence of Pressure on Aqueous Solutions of Various the Resistance Coefficients for Electrolytes. 134 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS solutions of various electrolytes at a concentration of 0.01 N at a tem- perature of 19.18°, while in Figure 27 24 are shown values of -^ as cal- culated from the measured values of g—-, according to Equation 44. As stated above, the curve for sodium chloride corresponds with the viscosity curve of pure water as determined by Cohen. It will be seen, however, that the curves for other electrolytes differ from that of sodium chloride and that, therefore, in these cases the pressure effect upon the ions is not directly proportional to the viscosity change of the solution. In the case of potassium chloride the conductance evidently increases slightly more than corresponds to the viscosity change of the solution, while for lithium chloride and hydrochloric acid the conductance increase due to increasing pressure is enormously greater than the viscosity change of the solution. On the other hand, in the case of potassium bromide, sodium bromide, potassium iodide, and sodium iodide the conductance change of the electrolytes is much smaller than the corresponding vis- cosity change of the solution. Manifestly, the change in the speed of the ions with pressure change is dependent not only on the viscosity of the solvent medium, but also on other factors. What these factors are, we do not know with certainty, but it appears probable that the speed of the ions is affected by a change in their effective size. Such an effect will obviously be a property of the ions themselves, which is in accord- ance with Korber's observations. However we may interpret these results, it is obvious that the speed of the ions in a dilute aqueous solution is not determined primarily by the viscosity of the solution, although the viscosity is an important factor. According to Equation 43, the value of the ratio -^L varies as a function of concentration. In Figure 28 *5 are shown values of the ratio TT-^- for sodium chloride in water at 19.18° at a series of concentrations. At the highest concentrations the resistance of the solution increases throughout with increasing pressure. This is in accord with Cohen's observations on the viscosity of sodium chloride solutions, which, at higher concentrations, exhibit a marked viscosity increase. As the con- centration of the solution decreases, the curves exhibit a minimum. Initially, with increase in pressure, the resistance of the solution decreases, »* Korber, loc. cit.f p. 227. » Ibid., loo. cit., p. 234. THE CONDUCTANCE OF SOLUTIONS— VISCOSITIES 135 Pressure. 500 1000 1500 2000 2500 3000 Kg Cm- 0.00ln, FIG. 28. Showing the Influence of Pressure on the Resistance of Sodium Chloride Solutions at Different Concentrations at 19.18°. while at higher pressures the resistance of the solution increases. In this case, again, the general form of the curve corresponds to the viscosity 136 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS effects of the solution. As the concentration decreases, the minimum point is displaced toward higher pressures, and the curves approach one another. Thus the curves at 0.1 N and 0.01 N differ but little. This is due to the fact that below a concentration of 0.1 N the ionization of the electrolyte is so great and the concentration so low that the viscosity effects could not differ materially from those in pure water. At lower concentrations, namely at 10~3N and 10~4N, the minimum disappears and the pressure effect becomes very large, the curves becoming the steeper, the lower the concentration of the solution. This divergence of the curves at very low concentrations is due to the effect of pressure on the conductance of the solvent medium; namely, to the fourth term in Equation 43. In the limit, these curves approach the dotted curve shown in the figure, which is that of the solvent medium. We have still to consider the case in which the third term of Equation 43 becomes an effective factor. This will obviously be the case with solutions of weak electrolytes. The ionization of an electrolyte, if the mass-action law holds — and this is in general the case with weak electro- lytes in aqueous solutions — is determined by the value of its ionization constant K. According to the Planck equation, we have: (44&) d log £ __ Az; dp RF According to Tammann, the value of At> is negative, so that as the result of pressure increase the value of the ionization constant K increases and with it the value of the ionization y. In the case of weak electrolytes, at intermediate concentrations and lower temperatures, the first three terms of Equation 43 have the same sign, and consequently the resist- ance of solutions of weak electrolytes should decrease with increasing pressure much more largely than that of solutions of strong electrolytes under otherwise the same conditions, and the decrease should be the greater the weaker the electrolyte and the greater the value of Ai>. The first investigations in this direction were carried out by Fanjung.26 Measurements on 0.1 N acetic acid were carried out by Tammann up to pressures of approximately 4000 kilograms per square centimeter. In Rv the following table are given values of the ratio -5-*- for acetic acid Hp=i at 20.140.27 In the case of ammonia, which has approximately the same ionization constant as acetic acid, the pressure effect is even greater than in that of 28 Fanjung, Ztachr. 1. pTiys. Chem. 14. 673 (1894). "Tammann, Wied. Ann. 69t 770 (1899). THE CONDUCTANCE OF SOLUTIONS— VISCOSITIES 137 acetic acid, since the value of Av for ammonia is more than twice that of acetic acid. TABLE XLVI. RELATIVE RESISTANCE OF 0.01 N SOLUTIONS OP ACETIC ACID IN WATER AT 20.14° AT DIFFERENT PRESSURES. cm.2 1 500 1000 1500 2000 2500 3000 3500 4000 1.000 0.855 0.738 0.650 0.582 0.526 0.487 0.447 0.410 The influence of pressure upon the conductance of electrolytes is brought out more clearly by representing the conductance-pressure coeffi- FIG. 29. Conductance-Pressure Coefficients for Electrolytes of Different Types as a Function of Concentration at a Pressure of 500 kg./cm.a. Curve 1, Weak Electrolytes. Curve 2, Moderately Strong Electrolytes. Curve 3, Strong Electrolytes. cient as a function of the concentration of the solution, the pressure remaining constant. In Figure 29 28 Curve 1 represents the pressure "Tammann, Ztachr. f. phys. Chem. Tl, 729 (1895). 138 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS coefficient of weak electrolytes as a function of their concentration at a pressure of 500 kg./cm.2 The curve actually corresponds very closely with that of acetic acid in water at this pressure. As Tammann has shown, it follows from the Planck equation that at low concentrations and for relatively small values of the constant K the ionization change, due to increasing pressure, increases with increasing concentration, until a prac- tically constant value is reached. The conductance-pressure coeffi- cient increases with increasing concentration of the weak electrolyte up to a concentration of about 10~3 normal for electrolytes whose con- stant is below 10"*. At higher concentrations the ionization change due to pressure change remains practically constant. However, at higher concentrations the value of - -r— decreases, while the value of — T^ v Ap q) Ap decreases and ultimately changes sign, as follows from Cohen's observa- tions on the viscosity of aqueous salt solutions. Therefore, the con- ductance-concentration curves, and consequently the curves for the coeffi- cient, exhibit a very flat maximum. In the case of solutions of strong electrolytes, the term --T? has inappreciable values at concentrations below 10~2 normal, and has only very small values at much higher con- centrations. In dilute solutions, therefore, the pressure coefficient has very nearly a constant value, independent of concentration. At higher concentrations, however, the value of the coefficient decreases, owing to the diminution in the value of ~T— and owing to an ultimate change in the sign of the viscosity effect at higher concentrations of the electrolyte, as was found by Cohen. Electrolytes of intermediate strength exhibit a type of curve intermediate between these two extreme types, as repre- sented by Curve 2. In this case the value of the coefficient increases with increasing concentration of the solution at lower concentrations owing to the increasing ionization of the electrolyte. Ultimately, how- ever, the effect of the viscosity change makes itself felt, the curve passes through a maximum, and thereafter falls with increasing concentration. At very low concentrations the viscosity-pressure coefficient has actually been found to increase and approach large values due to the effect of the fourth term in the right-hand member of Equation 43. This increase in the coefficient, as was shown by Tammann,29 is due to the increased ionization of the solvent medium. The limiting value which the coefficient ^-r- approaches at low con- » Tammann, Zt&cTvr. f. phys. Chem. 27, 464 (1898). THE CONDUCTANCE OF SOLUTIONS— VISCOSITIES 139 centrations, assuming that the conductance of the solvent is zero, or has been otherwise corrected for, differs for different electrolytes, and is, in RP general, the greater, the greater the value of -5 — . Thus the limit ap- /tp=i preached for hydrochloric acid at a pressure of 3000 kilograms per square centimeter is approximately 17 per cent, while that of sodium chloride is approximately 8 per cent and that of potassium chloride 9 per cent. Since in dilute solution the effect due to - T- is the same as that in pure v Ap water, it follows that these differences are due to differences in the vis- cosity effect as illustrated in Figure 28. In the case of hydrochloric acid, the value of y -r— passes through a flat maximum at a concentration in the neighborhood of 0.5 normal. In non- aqueous solutions the order of the viscosity effects differs from that in aqueous solutions, chiefly owing to the fact that with in- creasing pressure the viscosity of the solvent medium increases and con- sequently the speed of the ions is reduced with increasing pressure. In *f> Figure 30 30 are shown values of the ratio ^ for solutions of 0.002 N Kp=i tetramethylammonium iodide and 0.1 N malonic acid in ethyl alcohol. As was the case with water, the curve for weak electrolytes lies below that for strong electrolytes. With increasing temperature, however, the order of the curves is reversed with respect to their order in water; that Rv is, the ratio decreases both in the case of strong and weak electro- Kp=i lytes. The curves are very nearly linear for solutions of strong electro- lytes but are convex toward the axis of pressures for solutions of weak electrolytes. This form of the curve is accentuated in solutions in sol- vents of high viscosity ; as, for example, amyl alcohol, for which values of Rv ^— are represented in Figure 31.31 In this case, the curves for malonic acid at higher temperatures exhibit a minimum, while the curves for tetramethylammonium iodide are distinctly convex toward the axis of pressures. It is evident that at pressures beyond 3000 kilograms per square centimeter the curve for malonic acid in ethyl alcohol would likewise pass through a minimum. The observed phenomena in non- »» Schmidt, Ztschr. f. phys. Ghent. 75, 319 (1910). 11 /bid., loc. cit.f p. 320. 140 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS aqueous solutions may be accounted for in the same manner as those for aqueous solutions. The difference in the form of the curves for various electrolytes in the two cases arises chiefly as a result of the difference 1.B 1.7 1.6 1.3 1.0 0.8 0.7 \*> 60° 20° 60° 1000 2000 Pressure in kg. /cm.2 JOOO FIG. 30. Showing the Influence of Pressure on the Resistance of 0.002 N Solutions of Tetramethylammonium Iodide (above) and 0.1 Malonic Acid (below) in Ethyl Alcohol at Different Temperatures. in the sign and magnitude of the viscosity pressure effect and in the value of the ionization of the dissolved electrolytes. In solvents of lower dielectric constant, the typical salts behave like electrolytes of inter- mediate strength. At a given pressure, with increasing concentration of THE CONDUCTANCE OF SOLUTIONS— VISCOSITIES y 141 1.0 C.Q 60° 60* 1000 2000 Pressure in kg./cm.J 3000 Fia. 31. Showing the Influence of Pressure on the Resistance of Solutions of Tetra- methylammonium Iodide (dotted) and Malonic Acid (continuous) in Amyl Alcohol at Different Temperatures. the electrolyte, the ratio — ^-, due to the increased ionization of the V1 electrolyte, increases from values less than unity to greater values which are in general less than unity. At still higher concentrations, however, 142 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS the increasing viscosity effect overbalances the effect of increased ioniza- tion and the curve passes through a maximum. In solutions of weak electrolytes the ratio p increases rapidly with increasing concentration of the electrolyte, due to increased ionization, and, for very weak electro- lytes, particularly at low temperatures, passes through unity to greater values. Here, again, at sufficiently high concentrations, the curve may pass through a maximum, owing to the ultimate predominance of the viscosity effect. From his measurements, making the assumption that the Planck equation holds as well as certain other assumptions, Schmidt has calculated the value of — — , the viscosity ratio, due to pressure, for potassium iodide, sodium iodide and tetramethylammonium iodide in alcohol. He found that this ratio increases markedly with the pressure. In the case of potassium iodide and sodium iodide the increase is very nearly the same, being from 1.0 to 2.34 for 0.02 N solutions and a pres- sure change from 1 to 3000 atmospheres. In the case of tetramethyl- ammonium iodide the ratio — — increases somewhat more than for the other two electrolytes measured. This indicates that the viscosity effect in alcohol, similar to that in water, is a property of the ions. It appears, however, that the effects in the case of different ions are much more nearly the same in non-aqueous solutions than in water. This is as might be expected, since in solvents of low dielectric constant the ionic conductances themselves differ much less than in water. Schmidt has also calculated the value of the ionization y at different pressures and has found that the ionization increases with increasing pressure. That the pressure effect is intimately related to the viscosity of the solution is clearly indicated by the fact that the order of the effects in different solvents corresponds to the order of the viscosities of these solvents. The higher the viscosity of the solvent, the greater is the ratio r>— for a given pressure change. In the majority of solvents Schmidt found that this ratio might be expressed as a function of the pressure by the equation: RV (45) log •=. pp} where |3 is a constant. This equation was found to be particularly ap- plicable at higher temperatures. In other cases it was necessary to add THE CONDUCTANCE OF SOLUTIONS-VISCOSITIES 143 a quadratic term to the right-hand member of the equation. In the case of non-associated liquids the value of p may be expressed in terms of the viscosity of the solvent by means of the equation: (46) ft = 0.000106 + 0.00561 cp, where q> is the viscosity of the solvent. In the following table are given values of the viscosity q>, together with the measured values of p and those calculated according to Equation 46.32 TABLE XLVII. RELATION BETWEEN THE VISCOSITIES OF DIFFERENT SOLVENTS AND THE PRESSURE EFFECTS. Normal solvents. Solvent (p p p calc. Anisaldehyde 0.056 0.03420 0.03420 Benzylcyanide 0.022 0.03234 0.03229 Nitrobenzene 0.020 0.03217 0.03218 Furfurol 0.017 0.03204 0.03201 Benzaldehyde 0.016 0.03194 0.03196 Acetic anhydride 0.010 0.03178 0.03162 Acetone 0.003 0.03106 0.03123 Associated solvents. Glycerine 7.0 0.03300 0.0393 Isoamyl alcohol 0.042 0.03178 0.03342 Ethyl alcohol 0.012 0.03095 0.03173 Methyl alcohol 0.006 0.03078 0.03140 The calculated and observed values of P agree very well for the non- associated solvents, but in the case of the associate^ solvents there is a wide discrepancy between the two. A very simple relation thus exists between the viscosity and the pressure effect in the case of normal sol- vents, while in the case of associated solvents the relation is much more complex. This is as might be expected, for in associated solvents a change in the complexity of the solvent molecules doubtless accompanies any pressure change. It is clear that the difference in the nature of the pressure effects in water and in non-aqueous solvents is chiefly due to the difference in the viscosity effects in these cases. w Schmidt, loc. cit., p. 334. Chapter VI. The Conductance of Electrolytic Solutions as a Function of Temperature. 1. Form of the Conductance-Temperature Curve. The limiting value of the conductance is a function of the viscosity of the solvent, and consequently of the temperature also. The conductance of the more slowly moving ions is very nearly proportional to the fluidity of the solvent over such ranges of temperature for which viscosity data are available. The conductance of the more rapidly moving ions increases relatively less with the temperature than does that of the more slowly moving ions, and this effect is the more marked the greater the con- ductance of the ions. In considering the conductance of solutions at higher concentrations, it is necessary to take into account another factor, namely the change in the ionization of the electrolyte. The observed conductance change is therefore the resultant effect due to the change in the viscosity of the solution and to the change in the ionization of the electrolyte. While, with increasing temperature, the viscosity decreases and the conduct- ance consequently increases, the ionization in general decreases and the conductance of the electrolyte decreases in consequence. Since these two factors affect the conductance in opposite directions, it follows that the resultant effect of temperature on the conductance will depend on the relative magnitude of the ionization and the viscosity effects; and, in general, with increase in temperature the conductance of a solution may either increase or decrease. At ordinary temperatures, the conductance of many solutions increases with the temperature, and it was formerly assumed that a positive temperature coefficient was a characteristic property of electrolytic solutions. We now know, however, that this is not the case and that the temperature coefficient of solutions may be either positive or negative and that, in a given solvent, the temperature coefficient is a function of the temperature as well as of concentration, and that the sign of the temperature coefficient may change with tem- perature as well as with concentration. Considering, first, the conductance as a function of temperature, the concentration remaining fixed, it is found that, in general, the con- ductance increases with the temperature at low temperatures; but as the 144 SOLUTIONS AS A FUNCTION OF TEMPERATURE 145 temperature rises, the temperature coefficient decreases. The conductance curve is therefore concave toward the axis of temperatures. If the tem- perature is carried sufficiently high, the conductance passes through a maximum after which it decreases, the negative temperature coefficient increasing as the temperature rises. Experiments of this kind were first carried out by Sack,1 who found that, in solutions of copper sulphate, -60 ' O 2O 46 % 6O 6O /OO Temperature. FIG. 32. Conductance-Temperature Curves for Various Electrolytes in Liquid Ammonia. the conductance passes through a maximum in the neighborhood of 128°. For solutions of strong binary electrolytes in water, however, the maxi- mum lies at much higher temperatures. Before proceeding to a detailed discussion of aqueous solutions, we may consider solutions in other solvents. The conductances of a con- siderable number of solutions in ammonia have been measured and a maximum has been found in all cases.2 The form of the curves will be *Sack, Wied. Ann. d. Phys. tf, 212 (1891). 2 Franklin and Kraus, Am. Chem. J. tk, 83 (1900). 146 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS evident from Figure 32. As a rule the maximum lies in the neighborhood of 25° C but the temperature of the maximum is a function of concen- tration and with increasing concentration the maximum is displaced toward lower temperatures. The curves for different electrolytes are similar, indicating that the underlying phenomenon is the same in all cases. As the critical temperature is approached, the conductance ap- proaches a very low value, and it appears as though the curve would cut the axis of temperatures at a point near the critical temperature. The conductance, however, does not, in fact, fall to zero at the critical point, but has appreciable values at temperatures much above that point. The phenomenon in the neighborhood of the critical point will be discussed in detail in another section and need not be further considered here. It may be stated, however, that the property of forming conducting solu- tions with electrolytes is not peculiar to the liquid state but is one com- mon to fluid systems. The .form of the conductance-temperature curve is the same in all sol- vents. The conductance of a considerable number of solutions in sul- phur dioxide has been measured 3 at higher temperatures and the curves obtained have a form which corresponds with those of ammonia solu- tions. In solutions of KI in methylamine the form of the curve differs slightly in that, at very high temperatures, the conductance appears to approach the axis of temperatures asymptotically. In the alcohols,4 as well as in water,5 the conductance-temperature curves are of the same general type. 2. Conductance of Aqueous Solutions at Higher Temperatures. In order to proceed with the discussion of this subject, it is necessary to have some notion as to the degree of ionization of the electrolyte in solu- tion. The degree of ionization of non-aqueous solutions at higher tem- peratures is unknown. In other words, we do not have a sufficient num- ber of measurements at a series of temperatures and concentrations to enable us to determine the value of A0 at these temperatures. For aqueous solutions, however, a large amount of material is available, having been obtained by A. A. Noyes and his associates,6 and from these data the effect of temperature on the ionization of salts becomes ap- parent. In the following table are given values of the equivalent conductance for potassium chloride at a series of temperatures and at the concentra- tions 0.08 and 0.002 normal. 1 Walden and Centnerszwer, ZtscTir. }. phys. Chem. 39, 542 (1902) «Kraus, Phy8. Rev. 18, 40 and 89 (1904). 8 Noyes, Carnegie Publication, No. 63, pp. 47, 103, and 266. •Noyes, loc. cit. SOLUTIONS AS A FUNCTION OF TEMPERATURE 147 TABLE XLVIII. CONDUCTANCE OF KC1 IN H20 AT HIGHER TEMPERATURES. Concentration * 0° 18° 25° 100° 140° 156° 218° 281° 306° 0.08 N. A 72.3 113.5 — 341.5 455 498 638 723 720 0.002 N. A 79.6 126.3 146.4 393 534 588 779 930 1008 It will be noted that at the higher concentration the conductance passes through a maximum somewhere between 281° and 306°. In the more dilute solution, a maximum has not been reached below 306°. This behavior is quite general in aqueous solutions and is found also in non- aqueous solutions. The lower the concentration, the higher the tem- perature of the maximum. For solutions of sodium chloride, the conductance-temperature curve is similar to that of potassium chloride, although for this salt the maxi- mum has not been reached at 306°, even at a concentration of 0.08 normal. We have seen that, with increasing temperature, the conduct- ance of the sodium ion increases relatively more than that of the potas- sium ion. As a consequence, the maximum in the conductance curve is shifted to higher temperatures. In general, the higher the conductance of the electrolyte, the lower the temperature of the maximum and the lower the concentration at which the maximum will appear at a given temperature. For silver nitrate, the maximum lies somewhat lower than it does for potassium chloride, as may be seen from the following table: TABLE XLIX. CONDUCTANCE OF AgN03 IN H20 AT HIGH TEMPERATURES. Concentration t 18° 100° 156° 218° 281° 306° 0.08 N A 96.5 294 432 552 614 604 The lower temperature of the maximum for silver nitrate is due, partly, to the abnormal manner in which the conductance of the nitrate ion changes as a function of the temperature and, partly, to the more rapid decrease in the ionization of silver nitrate with increasing tem- perature. The higher types of salts exhibit maxima which are more pronounced and which occur at lower concentrations and lower temperatures. In Table L are given values for barium nitrate and magnesium sulphate at 0.08 normal. 148 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS TABLE L. CONDUCTANCE OF Ba(N03)2 AND MgS04 IN H20 AT HIGH TEMPERATURES. Barium Nitrate. Concentration Temp. 18° 100° 156° 218° 281° 0.08 N A 81.6 257.5 372 449 430 Magnesium Sulphate. Temp. 18° 100° 156° 218° 0.08 N A 52 •«. 136 133 75.2 It will be observed that the maximum lies below 281° for barium nitrate, while for magnesium sulphate the maximum lies between 100° and 156°. The more complex the salt the lower the temperature and the lower the concentration at which the maximum appears. As we shall see presently, this is due chiefly to the fact that the ionization of salts of higher type falls off more rapidly with the temperature than does that of the binary salts. For strong acids, the maxima lie at temperatures considerably below those of the binary salts. For hydrochloric acid the maximum lies in the neighborhood of 240° and for nitric acid in the neighborhood of 200° at a concentration of 0.08 N. The conductance-temperature curve of sulphuric acid, which is a dibasic acid, has a peculiar form, which has an important significance. Below are given values of the equivalent conductance for sulphuric acid at a series of temperatures at concentrations 0.002 and 0.08 normal. TABLE LI. CONDUCTANCE OF H2S04 AT HIGH TEMPERATURES. Concentration 18° 25° 50° 75° 100° 128° 156° 218° 306° 0.002 N 353.9390.8 501.3 560.8 571.0 551 536 563 637 0.08 N 240 258 306 342 373 408 440 488 474 It will be observed that, at the higher concentration, sulphuric acid exhibits a relatively flat maximum at a temperature of about 250°, while at the lower concentration it exhibits a maximum at about 100° and a minimum at about 160°, after which the conductance again increases and presumably passes through a maximum at a temperature above 306°. At still lower concentration the maxima and minima become more pro- nounced. As Noyes and Eastman 7 pointed out, this behavior of sul- phuric acid appears to be due to the fact that ionization takes place in two stages according to the equations: * Noyes, Joe. cit., p. 270. SOLUTIONS AS A FUNCTION OF TEMPERATURE 149 H2S04 = H+ + HS04- HS04- = H+ + S04- At the higher concentrations, the second ionization process has taken place to only a small extent and the form of the curve is largely due to the change in the ionization according to the first process, the maximum point occurring when the increased conductance of the ions due to tem- perature is just counterbalanced by the decreased conductance due to decrease in ionization. At the lower concentration the second ionization process is likewise involved. The second ionization corresponds to that of the weaker acid and the ionization according to this process falls off more rapidly with rising temperature, thus giving rise to the initial maximum. When the ionization according to the second process has been largely depressed, the curve thereafter depends chiefly upon the ionization according to the first equation. The ionization of strong electrolytes, apparently without exception, decreases with increasing temperatures; but at lower temperatures the rate of decrease is relatively small. In the case of the weak acids and bases the ionization increases between 0° and 40°, and thereafter de- creases rapidly at higher temperatures. In the following table are given values for the ionization constants of ammonium hydroxide and acetic acid.8 The values represent averages for a number of concentrations. In general, the ionization constant is independent of concentration up to 0.1 normal. TABLE LII. IONIZATION CONSTANT X 10~8 FOB AMMONIUM HYDROXIDE AND ACETIC ACID. 18° 25° 218° 306° NH4OH 17.2 18.1 1.80 0.093 CH3COOH 18.3 1.72 0.139 Initially there is a slight increase in the ionization constant, after which there is a sharp decrease at higher temperatures. Between 218° and 306° the constant of ammonium hydroxide changes slightly more than that of acetic acid. Similar results have been obtained in the case of other weak acids. For example, the ionization constant of diketo- tetrahydrothiazole 9 at 0°, 18° and 25° is respectively 0.0711 X 10'6, 0.146 X 10-6 and 0.181 X 10~6. Between 0° and 25° the constant of am- monium hydroxide varies between 13.91 and 18.06 X 10~6. It appears • Noyes, Joe. tit., p. 234. • /bid., Joe. cit., p. 290. 150 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS that the change in the value of the constant is greater for the weaker electrolyte. The ionization constant for water itself is a function of the tem- perature. At ordinary temperature the constant has been variously determined, the values at 18° lying between 0.68 and 0.80, the lower value being probably the more nearly correct. In the following table are given values of the ionization constant of water at various temperatures up to 306 °.10 TABLE LIII. IONIZATION CONSTANT OF WATER AT DIFFERENT TEMPERATURES. 0° 18° 25° 100° 156° 218° 306° KWX 1014 ... 0.089 0.46 0.82 48. 223. 461. 168. The ionization constant of water thus increases very rapidly at lower temperatures and passes through a maximum not far from 218°. The large value of the ionization constant of water and the relatively low values of the ionization constants of the acids and bases at higher tem- peratures lead to a relatively large hydrolysis of the salts of anything but the strongest acids and bases, and it is not improbable that even salts of the strong acids and bases ultimately suffer hydrolysis at low concentrations at the highest temperatures. The increase in the ionization constant of the weak acids between 0° and 40° may be related to the molecular changes which water under- goes within this temperature interval. Within this interval the density and specific heat of water are abnormal and within this temperature interval, also, the viscosity effects in solution, as well as the viscosity effects under pressure, exhibit abnormal relations, as has already been pointed out. An adequate explanation of these various phenomena, how- ever, appears not to exist. The ionization of different electrolytes in water at temperatures from 18° to 306° are given in Table LIV at concentrations of 0.01 and 0.08 normal. An examination of this table shows that the ionization of all electrolytes decreases markedly with the temperature, the decrease being the greater the higher the temperature and the higher the concentration. The ionization-temperature curves of different binary electrolytes corre- spond closely with one another, with the exception of the strong acids and silver nitrate. In the case of the last named salt, however, the ionization values at the highest temperatures are subject to large errors, 10 Noyes, loc. cit., p. 346. SOLUTIONS AS A FUNCTION OF TEMPERATURE 151 S S3 $ 3 £3 co eo So -S *£ii *J5 * *£• *£* * *° * "°° * " *H2 "^ *53 ***• " " *° "' 00 t^ 4s- t>» t>» CO ^ *O ^i . 00 . "to ' * Oi "I-H 00 00 t» 00 • oo • -co "»d ' * o K i - .:.:..:•*:* " ' " ' co ^ Ttjcot^^-j^c^oo^-tp^. . ^ -^j ^ N ^ 8 * *S5 *S2 oo oo •CO « . «00 'OS • . «OJ «>^ "-J *t>. *o * •*£ *co *oo *i-i *os ' i-t pc«oo coco iei ; »o ; »d i-J ^c^i I £i *H *cooo I«3 Io' Ico OS OS OS OS OS OS OS 00 00 00 GO 00 co ; * OS "OS * 00 "06 S :S3 1 . °°- OS (N ^ . ^ C^ !>. ^ . ^ t>. SS *S "fe "S "on "e§ a 2 a 31s i— iCO'— lOOr- ir-iOO'-iQOi-Hi-tOO'— ii-iOOr-HCO'-'QO'-'CO'— iGO'-iOO'-iOO'-HGO'-iOO o.o. op p op o. p p op p p p p p op po op p p op op p p o'o'oooooooooo'oooooooooooo'oooo'ooo °-c ) 1 1 y^» *i v - o i Is s 11 S W ffl ^^ 55 ^;. Accordingly, the approximate constants given above have been adopted for the purpose of illustrating the effect of temperature upon the ionization and con- ductance of an electrolyte. The constant D is assumed to be inde- pendent of temperature. This condition is approximately fulfilled in solvents having dielectric constants lower than 25. The lower curves Z25 ZOO 175 ,00 75 50 45 £•0 £00 ISO § 100 so 1.0 0.0 T.o 3.0 Log V. FIG. 33. Illustrating the Influence of Temperature on the Ionization and the Con- ductance of Electrolytes in Solvents of Relatively Low Dielectric Constant. in Figure 33 represent the values of the ionization at different tempera- tures, the lower curves corresponding to the higher temperatures. In order to secure a plot on which the ionization and conductance values may be conveniently represented at all concentrations, the logarithms of the concentrations, instead of the concentrations themselves, have been plotted as abscissas. It will be observed that the ionization curves inter- sect at a concentration of 3.6 normal, corresponding to the value log C = 0.556. Actually, the intersections do not occur at a point, since the I ionization is given by the equation y = , JD -f- and the constant K 158 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS decreases slightly as the temperature increases. The value of K, how- ever, is so small that this effect is scarcely appreciable. At concentra- tions greater than 3.6 normal, the ionization increases with the tempera- ture, and this increase is the greater the greater the value of m. In general, the increased conductance due to increased ionization in these regions is masked by the rapidly increasing effects of viscosity. In the ' neighborhood of normal concentration the viscosity effect becomes suffi- ciently great to overbalance the conductance increase due to increased ionization and the conductance-temperature curves pass through a maxi- mum in this region, after which they fall off very rapidly. Nevertheless, it is to be noted that, in all cases for which measurements are available at different temperatures in very concentrated solutions, the conductance increases markedly with the temperature and this increase is the greater the higher the concentration. In Table LVIII are given values of the conductance of concentrated solutions of different salts in methylamine and ethylamine at a series of temperatures.13 What is striking in these results is the high value of the temperature coefficient at high concentration, as, for example, in solutions of silver nitrate in methylamine at V = 0.2456. Between —33.5° and —15° the conductance increases 91 per cent or 4.92 per cent per degree. The same holds true for solutions of silver nitrate in ethylamine, where the conductance increases nearly 100 per cent between — 33.5° and — 15° at 0.4083 N, while, between — 15° and 0°, the conductance of solutions of ethylammonium chloride increases 6.76 per cent per degree at 0.17 N. It is true that the viscosity in these concentrated solutions must differ greatly from that of the solvent and the viscosity may change much more rapidly with the temperature in the case of the concentrated solu- tions than in that of the more dilute solutions. Nevertheless, it appears not improbable that the high value of the temperature coefficients of concentrated solutions is in part due to the increased ionization at these high concentrations. As the concentration decreases below 3.6 N, the ionization decreases with increasing temperature. Those solutions for which m is less than unity exhibit an increase in ionization throughout with decreasing con- centration, while those solutions for which m is greater than unity exhibit first a decrease and then an increase, so that the ionization curves pass through minima in the neighborhood of 0.1 N. These minima are the more pronounced the greater the value of m. In very dilute solutions, again, the ionization curves approach one another, corresponding to the fact that at low concentrations the ionization in all cases approaches unity. 18 Fitzgerald, J. Phya. Chem. 16, 621 (1912). SOLUTIONS AS A FUNCTION OF TEMPERATURE TABLE LVIII. 159 CONDUCTANCE OF CONCENTRATED SOLUTIONS IN METHYLAMINE AND ETHYLAMINE. Salt AgNOg V 0.2456 Methylamine — 33.5° 3.237 — 15° 6.180 0° 9.262 + 15° 13.05 It 0.4790 14.33 20.56 25.67 30.8 n 0.9348 22.61 28.92 34.15 38.77 11 2.084 24.32 29.48 32.97 34.95 11 5.449 21.80 25.18 26.81 27.41 11 10.63 20.04 22.19 22.74 22.19 KI 0.6094 31.12 38.17 42.90 46.49 « 1.190 32.97 38.52 41.74 43.96 M 2.320 28.49 31.45 33.90 33.39 AgNO, 0.4083 Ethylamine. 2.135 3.989 5.824 8.072 u 0.7968 5.310 7.753 10.09 12.11 tt 0.9928 5.67 8.44 10.55 12.52 u 1.981 5820 7.625 9082 1025 tl 3.953 4.320 5.400 6.141 6.719 (( 7886 2.683 3.181 3454 3690 tt 15.73 1.677 1.818 1.939 1.939 11 3139 1.212 1.277 1.285 1 188 LiCl ' 0.4215 1.586 2.080 n 0.8224 __ 2.001 2.447 2.661 ti 1.604 1.279 1.763 1.911 1.835 tt 3.131 0.8484 0.9915 0.976 0.8052 C2H6NH3C1 .... u n tt tt tt 0.1666 0.3253 0.6346 0.7676 1.497 2.922 2.293 3.692 2.606 1.285 0.7197 3.851 5.090 4.675 2.921 1.261 1.450 5.242 5.820 5.294 2.992 1.181 2.440 6.616 6.406 5.630 2.886 1.064 If the values of the ionization given by the lower curves in the figure are multiplied by the corresponding A0 values, the conductance curves shown in the upper part of the figure are obtained. At low concen- trations, where the ionization decreases only little with rising tempera- ture, the increased conductance, due to temperature rise, more than counterbalances the decreased conductance due to decreased ionization, and the conductance therefore increases with increasing temperature. In very concentrated solutions, also, the conductance increases with the temperature since the change in ionization here is relatively small. At 160 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS intermediate concentrations, however, where the change in ionization is large, the conductance-concentration curves at different temperatures intersect one another in a more or less complicated manner, indicating that the conductance-temperature curves in this region exhibit maxima. 100 100 C *.003| C«|.0 50 C..3J -50 -JO - Temperature. + 10 FIG. 34. Conductance-temperature Curves, illustrating the Relation between Con- ductance and Temperature for Solutions of Electrolytes at Different Concentra- tions in Solvents of Relatively Low Dielectric Constant. The temperature- conductance curves are shown in Figure 34 for concen- trations from 1.0 to 0.001 normal. At 0.001 normal the conductance increases throughout with increasing temperature. As the temperature rises, however, the conductance change due to a given temperature change becomes smaller and smaller and at this concentration the curve is very near a maximum at a temperature .of + 10°. At a concentration of 0.0031 normal, the conductance curve exhibits a very flat maximum at a SOLUTIONS AS A FUNCTION OF TEMPERATURE 161 temperature of — 10°. As the concentration of the solution increases, the maximum is shifted toward lower temperatures as indicated by the dotted curve. At 0.01 normal the maximum lies in the neighborhood of — 30°, while at 0.031 normal the maximum is still further displaced in the same direction. At 0.1 normal the maximum remains at practically the same value, but at 0.31 normal the maximum is displaced toward higher temperatures, being very flat in this case and lying somewhere in the neighborhood of — 10°. At 1 normal the maximum has arisen to temperatures above + 10° and the conductance increases markedly over the entire temperature range from — 50° to + 10° • The maximum occurs at the lowest temperature at a concentration in the neighborhood of 0.1 N. These curves represent, in general, the behavior of solutions at different temperatures. They correspond very closely with the values obtained by Franklin14 for solutions of KI in S02. The maximum in the conductance-temperature curves shifts from higher to lower tem- peratures with increasing concentrations, reaches a minimum, and there- after again shifts from lower to higher temperatures with increasing con- centration. In certain cases the effect of viscosity is such that it just counterbalances the effect of increased ionization over a considerable temperature interval. Ammonium sulphocyanate dissolved in sulphur dioxide is an example of this type, the conductance being practically independent of temperature at a concentration of approximately 0.1 normal. At concentrations greater than 0.1 normal the temperature coefficient of ammonium sulphocyanate solutions in sulphur dioxide is positive and is the greater the greater the concentration of the solution, while at lower concentrations the temperature coefficient is negative and initially increases with decreasing concentration. Ultimately, however, the sign of the coefficient must change. The fact that solutions in all solvents, without exception, exhibit maxima in the conductance-tempera- ture curves at intermediate concentrations indicates that at the tem- peratures in question the constant m has reached a value near or greater than unity. Curves of this type have been observed in solu- tions in ammonia, sulphur dioxide, water, methyl and ethyl amine, and methyl and ethyl alcohols. It is not to be doubted that the phenomenon is a general one. That the temperature coefficient of solutions becomes positive at very high concentrations is indicated by practically all data available for solutions at high concentrations. In general, it has been found that the higher the concentration the greater the value of the tem- perature coefficient, or rather that the temperature coefficient passes through a minimum or negative value at intermediate concentrations. " Franklin, loc. cit. 162 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS This result, however, does not become apparent in solutions of high dielectric constant, since the effects in question become marked only when the constant ra approaches a value of unity or greater. With increasing concentration, the temperature of the conductance maximum decreases, passes through a minimum and thereafter again increases in the more concentrated solutions. This course of the curve V = 16.3 V * 8-14 V-S.I7 20° Temperature. +0* FIG. 35. Showing the Conductance as a Function of the Temperature for Solutions of Cobalt Chloride in Ethyl Alcohol at Different Concentrations. is illustrated in Figure 35, in which are plotted the temperature-con- ductance curves for cobalt chloride, CoCl2, in ethyl alcohol.15 The course of the maximum is here indicated by the broken line. The lowest point of the maximum temperature is approximately 31° and at a an 400 1300 200 IOO 00 Temperature °C. FIG. 39. Representing the Conductance of Ammonium Chloride in Methyl Alcohol as a Function of the Temperature in the Critical Region. 60 50 40 30 237 239 241 243 245 TEMPERATURES 247 249 251 FIG. 40. Representing the Cpnductance of Potassium Iodide in Methyl Alcohol above the Critical Point at Various Concentrations of the Solvent. 174 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS TABLE LXIII. CONDUCTANCE OF KI IN CH3OH AS A FUNCTION OF THE DENSITY OF THE SOLVENT. Density \i X 106 of Solvent 245° 250° 0.251 45.6 37.2 0.220 28.8 22.6 0.208 21.2 . 16.83 0.178 8.0 6.0 0.163 3.7 2.8 0.127 1.44 1.2 from 1.44 to 45.6, or approximately 50 times. At 250° the increase in the conductance is not so great, since for the same concentration change the conductance increases only from 1.2 to 37.2, or 30 times. The A, ^-curves indicate a fairly rapid decrease in the conductance immedi- ately above the critical temperature. As the temperature rises these curves appear to approach a horizontal straight line. The lower the concentration, the less does the conductance change with the temperature. At a given temperature, the addition of a given amount of solvent increases the conductance the more the greater the density of the solvent. In other words, the A,C-curves at constant temperature are strongly convex toward the axis of concentrations. It is to be borne in mind that the conductance of a solution is a function of the number of carriers and the speed with which these car- riers move. Unless the nature of the carriers changes very greatly, we should expect that the speed of the carriers would be the greater the lower the density of the solvent, since the viscosity of a gas increases with its density. Since, now, the conductance of a solution increases very rapidly with the density and since this increase is the greater the greater the density of the solvent, it is difficult to escape the conclusion that the increase in the conductance of these solutions is due to an increase in the number of carriers present in them. According to the commonly accepted theory of electrolytic solutions, the change in the conductance of solutions as a function of the concen- tration is due to a change in the relative number of carriers; that is, to a change in the ionization of the electrolyte. Because of various difficulties which have arisen in accounting for the properties of strong electrolytes, some writers have suggested that strong electrolytes in solution are completely ionized. The study of the properties of non- aqueous solutions and of solutions at higher temperatures yields no apparent support for such an hypothesis. If the salts in solvents of low SOLUTIONS AS A FUNCTION OF TEMPERATURE 175 dielectric constant are completely ionized, then it becomes exceedingly difficult to account, on the one hand, for the very low value of the con- ductance of these solutions at certain intermediate and low concentra- tions and, on the other hand, for the very rapid increase in the conduct- ance of these solutions at higher concentrations. So, in the case of solutions in the neighborhood of the critical point, it is difficult to account for the rapid decrease in the conductance of the solution as the critical point is approached on the basis of this hypothesis. Again, in the case of solutions above the critical point, the large increase in the conductance of the solution as the concentration of the solvent increases is with diffi- culty accounted for on the assumption that the electrolyte is completely ionized, unless, at the same time, an hypothesis is introduced according to which the speed of the ions through the solvent medium is enormously increased by an increase in the concentration of the solvent. For such an hypothesis there is an entire lack both of experimental facts and of theoretical support. On the other hand, if the fundamental elements of the usual theory of electrolytes are accepted, we are forced to the conclusion that the ion- ization of electrolytes is a complex function of the concentration and that, at very high concentrations, in the case of solvents of low dielectric con- stant, the ionization increases with the concentration. While theoretical support is lacking for this assumption, no theoretical principle's are con- tradicted by such an hypothesis. Furthermore, if we assume that the ionization of electrolytes is a function of the concentration and is approxi- mately measured by the conductance ratio -T-, the influence of tempera- A0 ture, of concentration, and of the viscosity of the solvent may be readily accounted for without contradicting known facts and without intro- ducing any further hypotheses for which a theoretical foundation is lacking. In other words, on the basis of the ionization hypothesis, it is necessary to make only a single assumption whose correctness remains uncertain, whereas in the case of other hypotheses a number of assump- tions are necessary. Unless other and more conclusive facts can be adduced in support of the hypothesis that the strong electrolytes are completely ionized in solution, this hypothesis is clearly untenable at the present time. Chapter VII. The Conductance of Electrolytes in Mixed Solvents. 1. Factors Governing the Conductance of Electrolytes in Mixed Solvents. Since the properties of electrolytic solutions are functions of the properties of the solvent, it follows that in the case of mixed solvents the properties will be functions of the concentration of the solvents in the mixture. We may have mixtures in which either one or both of the solvents are capable of forming electrolytic solutions with ordinary salts. In the case of water, mixtures are, as a rule, obtained only with other solvents which have the power of forming electrolytic solutions. In the case of certain non-aqueous solvents, however, mixtures may be obtained with solvents not capable of forming electrolytic solutions with ordi- nary salts. The addition of a second solvent component to a solution of given concentration will in general affect the conductance in that the speed of the ions and the ionization of the electrolyte will be influenced by the addition of the second solvent. The conductance will therefore be a more or less complex function of the relative concentration of the two solvents. The effect of the addition of a second solvent will depend upon the concentration of the electrolyte as well as upon its nature. In certain solutions, the formation of an electrolytic solution depends upon an interaction between the dissolved substance and the solvent. When such is the case, the conductance of the solution is often greatly affected by the addition of a second solvent component. Such is the case with solutions of the acids in non-aqueous solvents on the addition of water. The addition of a small amount of water to a solution of an acid in an alcohol, for example, has an enormous influence upon the properties of the resulting solution. Similar results are obtained in non- aqueous solutions of salts which exhibit a pronounced tendency to form hydrates, as, for example, calcium chloride. If we assume that the nature of the ions remains fixed and inde- pendent of the nature of the second solvent, then we should expect the speed of the ions to be a function of the viscosity of the medium. The viscosity of a mixture of two solvents varies continuously with the rela- tive concentration of the solvents. The viscosity curves may exhibit either a minimum or a maximum or they may vary continuously between 176 ELECTROLYTES IN MIXED SOLVENTS 177 the values of the two pure media as extremes. If the viscosity of the two solvents differs greatly, then in general the viscosity of a mixture will lie intermediate between that of the two pure components. If the two sol- vents have approximately the same viscosity and particularly if both solvents are associated liquids, the viscosity curve will as a rule exhibit a maximum. Cases in which the viscosity curve passes through a mini- mum are rather exceptional. The viscosity of a mixture of two solvents will in all cases be of the same order of magnitude as that of the two components. If the nature of the ions remains fixed, therefore, the speed of the ions may be ex- pected to vary approximately in proportion to the fluidity change. In adding a second solvent to a solution of an electrolyte in another solvent, an interaction may take place between the electrolyte and the added solvent. In this case, the nature of the ions will change and with it, in general, their speed. In some instances, the change in the speed of the ions due to this cause is relatively large. In general, it may be expected that the ionization of a salt in a mixture of two solvents, particularly in dilute solutions, will have a value inter- mediate between those of the same electrolyte in the pure solvents. For we have seen that the ionization of a salt is a function of the dielectric constant of the medium, and the dielectric constant of a mixture of two solvents is in general intermediate between those of the pure components. Here again, however, we have to take into account the interaction between the electrolyte and the components which form the solvent medium. If interaction takes place between the second solvent and the electrolyte, then a new complex is formed whose ionization may differ greatly from that of the same electrolyte in the first solvent and, in fact, all of whose chemical properties may differ greatly from those of the original electro- lyte in the first solvent. A considerable number of examples of this type are found in aqueous solutions. When, for example, ammonia is added to a solution of a silver salt in water, a complex is formed between the silver ion and ammonia, which apparently has the composition Ag(NH3)2+ and whose properties are distinct from those of the normal silver ion in water. So, we find that salts of this ion are much more soluble than those of the normal silver ion, particularly in the case of the halides. Similar complexes are formed in the case of many other salts dissolved in water in the presence of ammonia, as, for example, salts of copper, zinc, cobalt, nickel, etc. The distinctive properties of the complex affect all the characteristic properties of the resulting elec- trolytic solution. So the addition of ammonia to a solution of a silver or a copper salt in water decreases the viscosity of the solution, until all 178 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS the metal has been transformed to the complex. This behavior is due to the fact that the solutions of this complex possess a negative viscosity relative to that of pure water, while solutions of the original salt possess a positive viscosity with respect to pure water. In non-aqueous solutions, we find similar relations; that is, inter- action often takes place between the second solvent component and the electrolyte. Thus, the ionization of solutions of a large number of salts appears to be greatly affected by the addition of a small amount of water. This is particularly the case with electrolytes which exhibit a marked tendency to form complexes with water. If a salt, which exhibits a marked tendency to form hydrates, is dissolved in a medium, with which this salt has little tendency to form a solvate complex, then the salt will be relatively little ionized when dissolved in this solvent. On addition of water to such a solution, the salt apparently forms a complex with water, whose ionization in the original solvent is much greater than that of the anhydrous salt. Solutions of potassium chloride or iodide, for example, are highly ionized in acetone and their ionization, and consequently their conductance, is but little affected by the addition of water. On the other hand, lithium chloride, which shows a pronounced tendency to form complexes with water, is ionized to only a relatively slight degree in pure acetone. On the addition of water to a solution of a lithium salt in acetone, the conductance is greatly increased. Similar results have been obtained in the case of calcium chloride. 2. Conductance of Salt Solutions on the Addition of Small Amounts of Water. In Table LXIV are given values of the conductance of solu- TABLE LXIV. CONDUCTANCE OF SALTS IN ANHYDROUS PROPYL ALCOHOL AT 25 °.1 Nal CX103 0.0623 0.1581 0.3902 0.6591 1.498 2.310 5.890 13.26 27.77 53.40 Ca(N03)2 Anhydrous C X 103 Amoi 19.94 19.36 18.36 17.72 16.30 15.40 13.23 11.28 9.815 8.400 0.363 0.792 1.617 3.326 5.908 7.247 14.320 24.930 43.290 5.140 3.834 2.894 2.184 1.798 1.688 1.258 0.976 0.772 *Kraua and Bishop, J. Am. Chem. Soc. 43, 1568 (1921). ELECTROLYTES IN MIXED SOLVENTS 179 tions of calcium nitrate and sodium iodide in propyl alcohol. In the case of calcium nitrate the values given are the molecular conductances whose limit at low concentration should be approximately twice that of the equivalent conductance. It will be observed that while sodium iodide is highly ionized, calcium nitrate is ionized to only a relatively small extent. At a concentration of approximately 10~3 molal, the ionization of cal- cium nitrate is less than 15 per cent, whereas at the same concentration sodium iodide is very largely ionized. If the equivalent conductances are plotted against the concentrations, the curve of sodium iodide approaches a limiting form asymptotically, whereas that of anhydrous calcium nitrate is convex toward the axis of concentrations, the increase in conductance being the greater the lower the concentration of the electrolyte. The addition of 0.185 mols of water per liter to the calcium nitrate solution, whose concentration was 0.045 N, raised the conductance from 0.772 to 2.036, and an additional 0.346 mols raised the conductance to 2.991. It is evident, therefore, that the addition of water to a solution of anhydrous calcium nitrate in propyl alcohol causes a large increase in the ionization of the salt. This follows, since the viscosity of the solvent is not materially affected by the addition of small amounts of water. It is true that, if a complex is formed on the addition of water to a solution of calcium nitrate, the speed of the ion may be affected by the addition of water, but it seems likely that, if anything, the speed of the complex will be lower than that of the original ion. However this may be, it is very unlikely that the speed of the complex could vary greatly from that of the anhydrous ion and the resulting change in the conductance must therefore be due to a change in the ionization of the electrolyte as a result of the formation of a complex with water. TABLE LXV. CONDUCTANCE OF Mg(N03)2.6H20 IN ANHYDROUS PROPYL ALCOHOL AND IN PROPYL ALCOHOL CONTAINING 0.7 PER CENT WATER AT 25°. Anhydrous Solvent Solvent + 0.7% Water CX103 Amoi. CX103 A 0.394 12.422 .298 17.774 0.865 10.730 1.950 9.062 1.942 8.932 3.758 7.326 3.483 7.774 6.339 6.188 6.406 6.408 11.670 5.096 9.804 6.026 19.460 4.400 19.89 4.674 30.410 3.921 36.12 3.866 49.560 3.555 180 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS In Table LXV are given values for the conductance of magnesium nitrate hexahydrate in anhydrous propyl alcohol and in propyl alcohol containing 0.7 per cent of water. The original salt having been hydrated, it is probable that the complex hydrate was to some extent present in the solution. Nevertheless, the value of the molecular conductance is of the same order of magnitude as that of anhydrous calcium nitrate in propyl alcohol and the conduct- ance curve is of the same general form. On the addition of water, the conductance of the magnesium nitrate is markedly increased, particularly in the more dilute solutions. The curve for the conductance in the presence of water twice intersects the curve for the conductance in the anhydrous solvent. This effect may in part be due to a change in the speed of the ions, owing to the presence of water, and in part to a more or less complex equilibrium which must exist between the dissolved electrolyte and the water. Those salts which have only a slight tendency to form stable com- plexes with water are, as a rule, ionized more highly in such solvents as acetone and the alcohols than are salts which exhibit a pronounced ten- dency to form stable complexes with water. Correspondingly, the addi- tion of water to a solution of a salt, which has little tendency to form complexes with water, has very little influence upon its ionization. The effect is scarcely observable in solutions of such salts as potassium and sodium iodides. In the case of lithium chloride dissolved in ethyl alcohol there is a slight increase in the ionization upon the addition of water. In Table LXVI are given values for the conductance of solutions of lithium chloride in ethyl alcohol in the presence of water.2 It is evident from an inspection of this table that the conductance of lithium chloride in ethyl alcohol is increased slightly upon the addition of water. The effect is somewhat more marked at higher concentration. TABLE LXVI. CONDUCTANCE OF LiCl IN C2H5OH IN THE PRESENCE OF WATER AT 25°. 0 A 517'7 A J31.8 « Goldschmidt, Ztschr. /. phya. Chem. 89, 138 (1914). Dilution of pjMols per Liter .2w Electrolyte 1 2 10 V 18.8 19.7 24.2 20 32.2 32.8 33.1 640 ELECTROLYTES IN MIXED SOLVENTS 181 3. The Conductance of the Acids in Mixtures of the Alcohols and Water. In aqueous solutions, the acids and bases occupy a unique posi- tion in that their solutions possess properties which, as a rule, differen- tiate them sharply from solutions of typical salts. The acids and bases in water are the only electrolytes which apparently conform to the mass- action law in this solvent. Furthermore, the ionization of different acids and bases differs greatly, while that of salts of the same type is prac- tically the same at all concentrations. So, also, the speed of the hydrogen and hydroxyl ions is much greater than that of the ordinary ions at ordi- nary temperatures. In the case of acids, at any rate, many facts indicate an interaction between acid and water whereby a complex positive ion is formed. In Table LXVII are given conductance values for solutions of hydro- chloric acid in methyl alcohol in the presence of varying amounts of water.8 TABLE LXVII. CONDUCTANCE OF HYDROCHLORIC ACID IN METHYL ALCOHOL IN THE PRESENCE OF VARYING AMOUNTS OF WATER AT 25°. A., The effect of adding water to a solution of hydrochloric acid in methyl alcohol is to greatly decrease the conductance of the solution and this effect is relatively independent of the concentration of the solute. It appears, therefore, that the ionization of hydrochloric acid is not materially affected by the addition of water, but that the speed of the hydrogen ion is greatly reduced. It is true that on the addition of water to methyl alcohol the viscosity is increased, but the viscosity change due to the small amounts of water added in the case of these solutions is inconsiderable and cannot account for the large decrease in the conduct- ance of these solutions. Apparently, therefore, the change in conduct- ance is due to a slowing up of the hydrogen ion, since it is known that the chloride ion is normal in its behavior in mixtures of alcohol and water. The values given for the limiting value of the equivalent con- ductance are approximate, since the extrapolation function employed in determining these values is uncertain. » Goldschmidt and Thuesen, Ztschr. f. phya. Chem. 81, 32 (1913). Mols of H20 per Liter Cone, of 0 0.1 0.2 0.5 1.0 2.0 Electrolyte J 115.4 99.6 91.3 81.6 78.1 67.1 0.10 (171.9 141.7 129.3 120.8 116.7 97.8 0.0015625 192. 157. 143. 135. 130. 107. 0.00 182 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS Apparently, when water is added to a solution of hydrochloric acid in methyl alcohol, a complex is formed with water which moves with a much lower speed than does the normal hydrogen ion in pure methyl alcohol. It will be noted that the speed of the normal hydrogen ion in methyl alcohol is exceptionally high. The A0 values for typical salts in this solvent lie in the neighborhood of 100. The hydrogen ion must therefore move with a speed roughly three times that of the chloride or potassium ion. Solutions of hydrochloric acid in ethyl alcohol exhibit a similar behavior on the addition of water.4 Values of the equivalent conduct- ance of hydrochloric acid in ethyl alcohol in the presence of varying amounts of water are given in Table LXVIII. TABLE LXVIII. CONDUCTANCE OF SOLUTIONS OF HYDROCHLORIC ACID IN ETHYL ALCOHOL IN THE PRESENCE OF WATER AT 25°. Mols of H20 per Liter 0 0.028 0.05 0.1 0.2 0.5 1.0 2.0 3.0 Dilution 74.2 63.2 58.5 52.6 47.4 42.8 41.8 42.4 44.4 1280 35.0 32.0 30.4 27.5 24.2 21.3 21.4 23.3 26.1 10 89.4 75.1 69.3 62.0 56.0 50.5 48.5 48.2 49.5 oo The conductance curve passes through a minimum for a solution contain- ing approximately two mols of water per liter. This minimum is slightly affected by the concentration of the acid. At lower concentrations the minimum occurs at a slightly higher concentration of water. The shift in the minimum point, following a change in the concentration of the acid, may in part be due to a change in the viscosity of the solution due to the addition of acid. On the other hand, it is possible that the ioniza- tion of the salt is materially affected by the presence of water, particu- larly at the higher concentrations. It may be assumed, however, that at very low concentrations of acid, the ionization is not materially changed due to the addition of water. If this is true, and the acid is highly ionized, the A0 values should follow a curve corresponding approxi- mately to that of the most dilute solution. In other words, the A0 values should pass through a minimum somewhere between 1 and 2 normal with respect to water, which has been found to be the case. This indi- cates that the addition of water results in an initial decrease in the speed of the ions up to a concentration of about 2 normal, and there- after in an increase on further addition of water. « Goldschmidt, Ztschr. f. phya. Chem. 89, 132 (1914). ELECTROLYTES IN MIXED SOLVENTS 183 This is further indicated by results at higher concentrations of water. In the following table are given values for the conductance of hydro- chloric acid in mixtures of water and ethyl alcohol at 25° for larger amounts of water.5 TABLE LXIX. CONDUCTANCE OP SOLUTIONS OF HYDROCHLORIC ACID IN ALCOHOL IN THE PRESENCE OF WATER AT 25°. Equivalent Conductances at Dilutions CH20 F = 12 F = 48 F=oo 0.0 34.3 43.6 67. 6.83 37.2 43.0 51. 13.85 60.3 65.8 75.5 27.68 115. 121. 130. 41.57 207. 218. 230.5 The values for the pure solvent do not agree with those given in Table LXVIII. It is possible that the values in this case are low owing to the presence of traces of water.6 However, it is evident that, in the presence of water at higher concentrations, the conductance increases with addition of water. This may be due, in part, to an increased ionization, but it appears probable that it is also in part due to an increase in the speed of the hydrogen ion. That a complex between water and the hydrogen ions is initially formed is likewise indicated by other prop- erties of these solutions such as the catalytic effects due to the hydro- gen ion.7 In the case of the weaker acids, on addition of water, the conductance curve is modified the more the weaker the acid. In Table LXX are given values for the conductance of sulphosalicylic acid in ethyl alcohol.8 In solutions of sulphosalicylic acid, there is a marked decrease in the con- ductance on addition of small quantities of water up to normal concen- tration, but the effect is not as great as it is in solutions of hydrochloric acid. TABLE LXX. CONDUCTANCE OF SULPHOSALICYLIC ACID IN C2H5OH AT 25° IN THE PRESENCE OF WATER. V = 160. CHQ .... 0 .003 .019 .1 .2 .5 1.0 49.0 49.0 45.4 37.0 32.8 29.9 29.5 "Kailan, Ztsclw. /. phys. Cliem. 89, 678 (1914). • Kailan, loc. cit. 7 Goldschmidt and Thuesen, loc. cit.f p. 62. 8 Goldschmidt, Ztschr. f. phys. Chem. 89, 139 (1914). 184 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS In the following table are given values for the conductance of picric acid in methyl alcohol in the presence of water.9 TABLE LXXI. CONDUCTANCE OF PICRIC ACID IN CH3OH AT 25° IN THE PRESENCE OF WATER. Concentration of Water Cone. 0 .5 1. 2. of Acid 9.32 12.7 16.3 23.4 0.1 56.73 63.7 70.2 75.7 0.0015625 In this case, the conductance effect due to addition of water is the reverse of that in solutions of stronger acids. The conductance increases throughout as the concentration of water increases. It is evident that the ionization of picric acid is much smaller than that of the stronger acids. The increase in the conductance at the higher concentration is much more marked than it is at the lower concentration, indicating that at higher concentration, at least, an increase in the ionization due to the addition of water is a primary factor in causing an increase in the con- ductance of the solution. It may be presumed that the speed of the hydrogen ion is independent of the nature of the acid, and that conse- quently the A0 values for picric acid decrease with increasing amounts of water, until fairly high concentrations are reached. In the following table are given approximate values of A0 for picric acid dissolved in methyl alcohol in the presence of water.10 TABLE LXXII. CHANGE OF A0 FOR PICRIC ACID IN METHYL ALCOHOL WITH VARYING AMOUNTS OF WATER. CH20 0 .5 1. 2. A 182 108 98 90 These values of A0, while only approximate, nevertheless cannot differ greatly from the true values and clearly indicate that the increase in the conductance of picric acid is due to an increased ionization of the acid as a result of the presence of water. In solutions of weaker acids, the effect of water on the ionization of the acid is even more pronounced. In the following table are given values for trichlorobutyric acid: 11 • Goldschmidt and Thuesen, loc. cit.f p. 35 10 Ibid., loc. tit. n/6id., loc. cit.f p. 37. ELECTROLYTES IN MIXED SOLVENTS 185 TABLE LXXIII. CONDUCTANCE OF 0.2 N TRICHLOROBUTYRIC ACID IN CH3OH IN THE PRESENCE OF WATER. 0 10 2.0 A 0.446 0.825 1.283 In a 0.2 normal solution of this acid the conductance is increased 100 per cent on the addition of one mol of water. In other words, the ioniza- tion is increased somewhat over 100 per cent by this addition of water. In this respect the acids behave in a manner similar to that of typical salts which have a great tendency to form hydrates. The effect of water on the ionization of the weaker acids is clearly shown in the increased value of the ionization constants of these acids on addition of water. In Table LXXIV are given values of the ioniza- tion constant 12 for trichloroacetic acid in absolute alcohol and in alcohol containing 0.622 mols of water at different dilutions. Excepting at the highest concentrations, the constant varies but little with the concentra- tion of the acid. TABLE LXXIV. IONIZATION CONSTANT OF TRICHLOROACETIC ACID IN ALCOHOL IN THE ABSENCE AND IN THE PRESENCE OF WATER. K X 10-6 V Pure Alcohol CR Q = 0.622 N 5.5 5.03 31.1 11. 4.74 29.3 22. 4.45 28.6 44. 4.45 27.6 88. 4.50 27.6 176. — 28.4 It is evident that, due to the addition of 0.622 mols of water, the ionization constant of trichloroacetic acid is increased approximately six times. Corresponding to this increase in the value of the ionization con- stant of the acid, the conductance of the acid is obviously greatly increased. The effect of water on the conductance of different electro- lytes is shown in Figure 41. The great percentage increase in the con- ductance of trichloroacetic acid will be noted in contrast to a smaller increase in the case of picric acid and lithium chloride and a large decrease in that of hydrochloric acid. "Braune, Ztschr. f. phys. Chem. 85, 170 (1913). 186 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS It seems fairly clear that, on the addition of water to a solution of an acid in alcohol, a complex is formed between the acid and the added water. The hydrogen ion of this complex moves with a speed much lower than that of the normal hydrogen ion in alcohol or in pure water. In the case of the weaker acids, the ionization of the hydrated acid is i.o Mols of Water. 3.0 FIG. 41. Illustrating the Influence of Water on the Conductance of Different Electrolytes in Ethyl Alcohol. much greater than that of the unhydrated acid. In solutions of salts in non-aqueous solvents, there is, as we have seen, a similar increase in ionization on the addition of water in the case of those salts which exhibit a pronounced tendency to form complexes with water. In these cases, therefore, the process of ionization is intimately connected with the formation of a more or less definite complex, and since these complexes are formed on the addition of a small amount of water to solutions in ELECTROLYTES IN MIXED SOLVENTS 187 anhydrous solvents, there is all the more reason for believing that these complexes exist when the salts are dissolved in pure water. 4. Conductance in Mixed Solvents over Large Concentration Ranges. A considerable number of systems have been studied in which salts have been dissolved in mixtures of two solvents miscible in all propor- tions. In these solutions the conductance has not been studied for small additions of either component. As a rule, the concentration was varied by intervals of 25 per cent. In such cases, the change in the viscosity of the medium, as well as that in the ionization of the electrolyte, makes itself felt. When the two solvents have approximately the same dielectric con- stant and the dissolved salts are ionized to practically the same extent in the two solvents, then the conductance of solutions in mixtures of these solvents is determined primarily by the viscosity of the mixtures. In other cases, where the viscosity change is small and the ionization of the salt in the two solvents differs greatly, the form of the curve is largely dependent upon the ionization change brought about by the change in the composition of the mixture. In Figure 42 are shown values of the fluidity of mixtures of acetone with water, methyl and ethyl alcohol at 0°.1S In Figure 43 are shown fluidity curves for mixtures of methyl alcohol with water and ethyl alcohol/4 and nitrobenzol with methyl and ethyl alcohols,15 at 25°. The values are given in Table LXXV. In the case of these curves the precise TABLE LXXV. THE FLUIDITY OF MIXTURES AS A FUNCTION OF THEIR COMPOSITION. Solvent Per Cent B = 0 A B 0 25 50 75 100 H2O Acetone . . . 56.24 34.12 33.03 58.80 244.1' CH3OH C2H5OH Acetone . . . Acetone . . . 122.2 53.88 153.9 96.08 187.4 147.0 222.2 200.4 244.1 [ 244.1J H20 CH3OH 112.3 76.18 67.72 83.6 144.4 H20 C2H5OH .. 112.3 55.22 41.56 47.21 87.4 C6H5N02 CH3OH ... 54.29 84.4 110.9 142.3 166.4 C6KLN02 C2H5OH .. 54.3 73.3 82.7 88.2 87.4 C2H5OH CH3OH ... 87.36 105.5 124.9 147.3 164.4 values are represented only for the pure solvents and the mixtures hav- ing compositions of 25, 50 and 75 per cent, smooth curves having been "Jones, Bingham and McMaster, ZtscJir. f. phys. CJiem. 57, 193 (1906). "Jones and Veazey, Conductivity and Viscosity in Mixed Solvents, Carnegie Reports, p. 190 (1907). "Jones and Veazey, Ztsctir. f. phys. Chem. 62, 49 (1908). 188 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS drawn through these points. At intermediate concentrations the true curves may vary considerably from the curves as drawn, particularly at concentrations in the neighborhood of the axes. Nevertheless, the curves show in a general way the relation between the fluidity and the com- position of these mixtures. The fluidity curves of all mixtures in which 25 50 IS too Per? FIG. 42. Representing the Fluidity of Mixtures of Acetone with Various Solvents at 0° as a Function of Composition. water is one component are characterized by a pronounced minimum, which lies roughly at a composition of 50 per cent. When the fluidity of the second solvent differs greatly from that of water, the minimum is displaced in the direction of the solvent having the lower fluidity. In mixtures of solvents of the same type, such as methyl and ethyl alcohols, as well as in mixtures of the alcohols and nitrobenzol, or the alcohols and acetone, the curves approach more -or less closely to straight lines, the viscosity of the mixture being throughout intermediate between that of ELECTROLYTES IN MIXED SOLVENTS 189 the two components. When the two components have nearly the same fluidity, the fluidity curve exhibits a slight minimum. It is apparent that the fluidities of mixtures in general differ con- siderably from those of the pure components and it is to be expected that the conductance of solutions in such mixtures will be materially affected by the viscosity change of the solvent. In those cases in which the elec- SO 7S /CO B FIG. 43. Fluidity of Various Mixtures at 25°. trolyte is largely ionized, it is to be expected that the conductance of a solution in a mixture of two solvents will vary approximately in accord- ance with the fluidity of the mixture. At higher concentrations a similar correspondence between the conductance and the fluidity is to be expected when the ionization of the electrolyte is the same in the two solvents. In general, this will be the case when we have solvents which have the same dielectric constant, and an electrolyte which does not exhibit a marked tendency to form solvates. In other cases, when the ionization is 190 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS largely dependent upon the formation of solvates between the electrolyte and one or the other of the solvent components, the ionization of the salt in the mixture, rather than the fluidity of the mixture, will determine the form of the conductance curve and this will be the more true, the more nearly the fluidity curves are linear functions of the composition. In Figure 44 are shown conductance curves for solutions of tetra- ethylammonium iodide in mixtures of water 16 with methyl and with 100 50 o A. Per Cent of Component B. FIG. 44. Conductance of Tetraethylammonium Iodide in Solvent Mixtures at 25° at 7 = 800. ethyl alcohol, nitrobenzol 17 with methyl and with ethyl alcohol, and methyl with ethyl alcohol.16 The data from which the curves are drawn are given in Table LXXVI. Comparing the conductance curves with the fluidity curves, it is clear that in these solutions of tetraethylammonium iodide there is a close correspondence between the two. The conductance curves for mixtures of methyl alcohol, ethyl alcohol and nitrobenzol correspond very closely with the fluidity curves. So, also, in mixtures of water with ethyl and 18 Jones, Bingham and McMaster, loc. cit.f p. 257. " Jones and Veazey, loc. cit., p. 44. ELECTROLYTES IN MIXED SOLVENTS 191 TABLE LXXVI. CONDUCTANCE OF TETRAETHYLAMMONIUM IODIDE IN MIXED SOLVENTS AT 25° AT A DILUTION OF 800 LITERS. Solvent Per Cent B A B 0 25 50 75 100 H20 CH3OH . .. 100.6 67.03 55.17 62.50 105.3 H2O C2H5OH ... 100.6 54.53 38.68 35.51 41.46 C6H5N02 CH3OH . . . 31.44 47.91 63.54 80.53 105.3 C6H5N02 C2H5OH ... 31.34 37.88 41.87 43.51 41.46 C2H5OH CH3OH . . . 41.46 55.20 69.44 84.22 105.3 methyl alcohols, a pronounced minimum is found in both conductance curves. Finally, in mixtures of nitrobenzol and ethyl alcohol, the con- ductance curve exhibits a slight maximum corresponding with the maxi- mum in the fluidity curve. In general, salts which show little tendency to form stable complexes with water, in other words, those salts which exhibit a negative viscosity in aqueous solutions, yield conductance curves closely resembling those for tetraethylammonium iodide. It may be noted, however, that the conductance for tetraethylammonium iodide in methyl alcohol is abnormally high, being in fact somewhat greater than that of the same salt in water. In general, the conductance of salts in methyl alcohol is somewhat lower than that of salts in water, even though the viscosity of water is greater than that of methyl alcohol. The curves for solutions of other binary salts do not differ materially from those of tetraethylammonium iodide. In the case of electrolytes of this type, the ionization in a given solvent is near the maximum and is not appreciably affected by the addition of a small amount of another solvent. Moreover, the ionization of typical salts in these solvents does not differ greatly at concentrations approaching 10~3 normal. The form of the conductance curves, therefore, is determined primarily by the fluidity of the solvent mixtures. TABLE LXXVII. CONDUCTANCE OF SOLUTIONS OF POTASSIUM IODIDE IN MIXTURES OF ACETONE WITH METHYL AND ETHYL ALCOHOLS AND WATER AT 0°. Per Cent Acetone 0 25 50 75 100 H20 78.0 47.8 37.5 44.1 120.01 CH3OH 71.7 83.9 94.1 106.5 120.0^7 = 1600 C2H5OH 28.6 40.1 61.3 84.8 120.0J H20 76.7 44.6 36.3 41.6 100.41 CH3OH 65.7 74.1 82.7 93.1 100.417 = C2H5OH 22.0 35.5 52.2 72.0 100.4J 192 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS In Table LXXVII are given values for the conductance of potassium iodide at 0° in mixtures of acetone with methyl and ethyl alcohols and water 18 at the concentrations V = 1600 and V = 200. The results are shown graphically in Figure 45. It is apparent that in solutions of potas- sium iodide in mixtures containing acetone, the general form of the con- ductance curves corresponds with that of the fluidity curves. However, the deviations from the fluidity curves in these solutions are considerably V--ZQO as so Per Cent Acetone. too FIG. 45. Conductance of Potassium Iodide in Acetone Mixtures at Oc V = 200 and V = 1600. at Dilutions greater than in solutions of tetraethylammonium iodide in mixtures of the alcohols and water. This is doubtless due to the relatively low ionizing power of acetone and its selective action upon different electro- lytes, as well as upon the exceptionally high value of the fluidity of pure acetone with respect to that of the other solvents. The concentration change from a dilution of 1600 to 200 has only an immaterial influence upon the form of the curves. The ionization of acetone solutions of salts which exhibit a marked tendency to form complexes with water, or other solvents, is very low. Under these conditions, the change in the ionization of the electrolyte due " Jones, Bingham and McMaster, loo. cit., p. 193. ELECTROLYTES IN MIXED SOLVENTS 193 to the addition of a second solvent becomes apparent. In Table LXXVIII are given values for the conductance of lithium bromide in mixtures of acetone with methyl and ethyl alcohols and water.19 TABLE LXXVIII. THE CONDUCTANCE OF LITHIUM BROMIDE IN MIXTURES OF ACETONE WITH METHYL AND ETHYL ALCOHOLS AND WATER AT 0°. Per Cent Acetone 0 H20 56.12 CH3OH 57.63 C2H5OH 20.79 H2O 47.25 CH3OH 35.92 C2H5OH 10.55 The results are shown graphically in Figure 46. An examination of the curves shows a very complex behavior on the part of these solutions compared with that of solutions of potassium iodide in the same solvents. In mixtures of acetone and methyl alcohol, at the lower concentration, 25 50 75 100 35.71 28.34 31.65 70.891 60.38 67.02 84.15 70.89 U r=1600 29.21 50.98 66.28 70.89J 28.82 21.70 24.00 11.911 35.03 34.27 29.77 11.9UT* r = 10 14.72 19.23 19.16 11.91 CH50H CHjOH too V* JO O 2ST SO 75 100 Per Cent Acetone. FIG. 46. Conductance of Lithium Bromide in Acetone Mixtures at 0° at V = 10 and V = 1600. » Jones, Bingham and McMaster, loc. cit., p. 257. 194 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS the conductance curve exhibits a pronounced maximum. The curve for ethyl alcohol mixtures exhibits a pronounced inflection point, while that for water merely exhibits a minimum corresponding to the minimum in the fluidity curve of the mixtures of acetone and water. At the higher concentration, the curve for water initially rises steeply to a very flat maximum and minimum, after which it rises with increasing concentra- tion of water, the curve corresponding roughly to the fluidity curve of the mixtures within the region of these compositions. The conductance of solutions in mixtures of acetone and methyl alcohol rises sharply for initial additions of methyl alcohol, after which it remains practically constant until the axis of the pure methyl alcohol is reached. With ethyl alcohol the conductance likewise increases markedly for the initial addi- tions. Thereafter, the curve passes through a maximum, after which it gradually diminishes to the final value of the conductance in pure ethyl alcohol. It is only in solutions in which the percentage of ethyl alcohol has fallen as low as 25 per cent that the curves begin to approach in form the fluidity curves of the mixtures. For mixtures containing larger amounts of acetone the form of the curve is due largely to the change in the ionization of the electrolyte. On the addition of a second solvent to acetone, the ionization of lithium bromide is greatly increased. In the water mixtures, the viscosity is increased so greatly for small additions of this solvent that the conductance diminishes. In the case of methyl alcohol, however, the fluidity is only slightly reduced by the addition of alcohol and consequently the conductance curve rises initially due to the increased ionization of the salt. At higher concentrations of alcohol, however, the increasing viscosity of the solvent finally makes itself felt and the conductance again falls. At the higher concentration of the salt, the addition of water causes a sufficient increase in the ionization of the electrolyte to overbalance the decrease due to the decreasing fluidity of the mixture. Initially, therefore, the conductance curve for lithium bromide in the mixture increases with the addition of water, passing through a slight maximum, after which the curve approximates the fluidity curve of the solvent. As a rule, higher types of salts are ionized to a much smaller extent than are binary electrolytes, particularly the salts of metals which exhibit a pronounced tendency to form solvates with water. In Table LXXIX are given values for the conductance of calcium nitrate in mixtures of acetone with methyl and ethyl alcohols and water.20 The relation between the conductance and the composition of these mixtures is shown graphically in Figure 47. It is evident that solutions of calcium nitrate in mixtures containing acetone present a very complex *> Jones, Bingham and McMaster, loc. tit., p. 193. ELECTROLYTES IN MIXED SOLVENTS 195 25 50 75 100 80.0 66.2 76.7 10.361 82.6 79.2 64.2 10.36 \V = 1600 31.6 38.0 36.2 10.36J 55.0 42.2 31.3 4.44] 17.76 13.82 8.10 4.44 \V = 10 6.01 6.00 4.80 4.44J TABLE LXXIX. CONDUCTANCE OF SOLUTIONS OF CALCIUM NITRATE IN MIXTURES OP ACETONE WITH METHYL AND ETHYL ALCOHOLS AND WATER AT 0°. Per Cent Acetone 0 H20 128.3 CH3OH 77.2 C2H5OH 18.81 H90 89.8 CH3OH 18.98 C2H5OH 5.13 relation between conductance and composition. This is particularly true of the acetone-water mixtures. Solutions of calcium nitrate in acetone are ionized to a very slight extent, even at high dilutions. The limiting equivalent conductance of binary electrolytes in acetone has a value of approximately 170. The limiting value of the equivalent conductance of tsro HtO V= 1600 50 7S Per Cent Acetone. 100 FIG. 47. Conductance of Calcium Nitrate in Acetone Mixtures at 0° at V = 10 and V = 1600. 196 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS calcium nitrate is obviously of the same order. Even at a dilution of 1600 liters, therefore, calcium nitrate is ionized less than 10 per cent. The addition of hydroxy-compounds, which tend to form stable complexes with calcium salts, causes an enormous increase in the conductance of solutions of this salt in acetone, even though the amount of the second component added is relatively small. The curves as drawn are only rough approximations and it is not improbable that the initial conduct- ance increase is even greater than indicated in the figure. Owing to the increased ionization of calcium nitrate on the addition of water, there- fore, the conductance rises enormously, even though the speed of the ions is greatly depressed on the addition of water. As a consequence, the con- ductance curve on addition of water passes through a pronounced maxi- mum at a composition at or above 75 per cent of acetone. On the addition of further amounts of water, the conductance curve follows, roughly, the fluidity curve of the solvent mixture. The addition of methyl alcohol likewise results in an increase in ionization, although this increase is much lower than in the case of water. The conductance curve, therefore, passes through a comparatively flat maximum at a composition in the neighborhood of 25 per cent of acetone. The ionization of calcium nitrate dissolved in a mixture of methyl alcohol and acetone therefore has not reached a value corresponding to that of a normal electrolyte, even when as much as 75 per cent of methyl alcohol has been added. The addition of ethyl alcohol causes a marked increase in the conductance, although considerably less than that due to methyl alcohol. The curve passes through a distinct maximum, after which the conductance de- creases, chiefly owing to the decrease in the fluidity of the mixture. At the higher concentration, the curves are greatly modified. Again, the ionization of the electrolyte is greatly increased on addition of the second solvent, as is indicated by a marked increase in the conductance of the solutions. In the case of water, the curve exhibits a marked inflec- tion point in the neighborhood of the composition containing 50 per cent of alcohol and water. At these higher concentrations, therefore, solu- tions of calcium nitrate in mixtures of acetone and water exhibit an ionization much below that of normal electrolytes. The curve, on addi- tion of methyl alcohol, shows a continuous increase in the conductance throughout its course. That for ethyl alcohol shows a slight increase only, the curve exhibiting a very flat maximum. At the higher concen- trations of the salt, therefore, the addition of ethyl alcohol causes only a relatively small increase in the conductance of calcium nitrate. Actu- ally, however, the ionization is considerably increased on the addition of ethyl alcohol, since the fluidity of the ethyl alcohol mixture is much lower than that of pure acetone. ELECTROLYTES IN MIXED SOLVENTS 197 Extensive data are available which show that the examples given above are typical of the behavior of solutions of electrolytes in mixed solvents. The data do not have sufficient precision to make it possible to determine the values of AO in the mixtures, fof which reason it is necessary to consider only the general outline of the conductance curves. It is evident that, in the case of solutions of salts which are highly ionized, the conductance curves parallel the fluidity curves. If, however, the electrolyte is only slightly ionized in one of the solvents, the addition of the second component may cause a large shift in the conductance values due, primarily, to a large change in the ionization of the electrolyte. It should be noted that, whenever the fluidity of the solvent medium changes, whether under the action of pressure or temperature, or whether through a change in the viscosity of the medium due to the presence of the electrolyte itself or due to the presence of a non-electrolyte, the con- ductance is affected by the viscosity change, and, while the conductance may not change in direct proportion to the fluidity change of the medium, nevertheless the effect of fluidity change is very marked. These facts are in entire accord with our notions as to the nature of the conduction process. On the other hand, it is clearly evident that the conductance is likewise dependent upon some other factor, namely the ionization. The ionization is a function, in the first place, of the dielectric constant of the solvent medium, as well as of the concentration of the electrolyte. In the second place, however, the ionization is greatly affected by inter- action between the dissolved electrolyte and the solvent medium. Ap- parently, complexes are formed between the dissolved electrolyte and the solvent, which are largely ionized. Certain solvents, such as acetone, for example, appear to have a very small tendency to form complexes. When salts, which exhibit a marked tendency to form complexes, are dissolved in solvents of this type, the resulting ionization . is relatively low. This effect is marked in the case of salts of the alkali metals. Salts of sodium, potassium, rubidium and caesium are very largely ionized in all solvents, apparently without exception, whereas the salts of lithium exhibit a markedly lower ionization in many solvents, as for example in acetone. As is well known, lithium salts exhibit a great affinity for hydroxy-solvents, and apparently the formation of a complex is a necessary condition for ionization in the case of salts of this type. In comparing the ionizing power of different solvents, therefore, it is necessary to select such electrolytes as exhibit the least tendency to form complexes. This has in general been done by various writers on this subject. Nevertheless, it should be borne in mind that the possibility always exists that a given electrolyte in a given solvent may exhibit exceptional properties. Chapter VIII. Nature of the Carriers in Electrolytic Solutions. 1. Interaction between the Ions and Polar Molecules. The results given in the preceding chapter indicate that an equilibrium exists between the ions, and possibly the un-ionized fraction, of a dissolved electrolyte and the molecules of an added non-electrolyte of the polar type. If reactions of this type take place between a non-electrolyte and an elec- trolyte, both of which are present in relatively small amounts in the solvent medium, then there is all the more reason for believing that reaction takes place between the electrolyte and the non-electrolyte when the latter is present in large excess. Apparently, the ions in solution do not consist merely of the charged groups present in the original salt, but rather of these groups associated with the solvent. Where the ions possess great tendency to form definite complexes with the solvent, as is the case, for example, with the calcium ion in water and the silver ion in ammonia, a portion of the solvent is present in the form of a definite chemical compound. In addition to this, however, an ion may con- ceivably be associated with a further amount of solvent as a result of the charge on the ion and the electrical moment of the solvent molecules. 2. Hydration of the Ions in Aqueous Solution. It has been defi- nitely established that in aqueous solutions certain ions are hydrated ; * that is, in passing through the solution they carry water with them. Since the conductance values of all ions in water are of the same general order of magnitude, it follows that all ions are in all likelihood hydrated, save, perhaps, the highly complex ions. If the ions are hydrated, then, in the course of a transference experi- ment, water will be transferred toward one electrode or the other. If N^ represents the number of molecules of water associated with the anion and N the number of molecules of water associated with the cation and if T is the fraction of the current carried by the anion, that 1Lobry de Bruyn, Rec. Trav. Ohim. 22, 430 (1903) ; Morgan and Kanolt, J. Am Chem 800. 28, 572 (1906) ; Bucbbock, Ztachr. f. phtfs. Chem. 55, 563 (1906) ; Washburn, J Am Chem. Soc. 31, 322 (1909) ; Washburn and Millard, J. Am. Chem. /S'oc. 37, 694 (1915). 198 CARRIERS IN ELECTROLYTIC SOLUTIONS 199 is, if this is the true transference number of the anion, and if T^ is the true transference number of the cation, then according to Washburn 2 the net transfer of water per equivalent of electricity passing through the solution will be: (47) V IA/ V 14/ which are likewise equivalent. From these eight equations the concentrations of the eight different molecular species may be determined for any con- centrations Cj. and C2 of the total acids and the total bases in solution. In this case, interaction with the solvent is assumed not to take place. In a mixture of two electrolytes with a common ion we have the reaction equations : M!+ X X- = K^U.X M2+ X X- = #2M2X and the condition equations: M,X + Mx = Cx M,X + M2 = C2 MXX + M2X + X = Cx + C2. In this case the solution of the problem is comparatively simple. In a mixture of two electrolytes having an ion in common, assuming the mass-artion law to hold, the ionization of the electrolytes in the mix- ture will be the same as that in the original solutions before mixing, if the concentrations of the qommon ion in these solutions, before mixing, are equal. Such solutions are said to be isohydric.1 This result is a consequence of the law of mass-action. Let M±+, M2+ and X~ be the concentrations of two solutions having in common the ion X~. It is obvious that the concentration of the common ion in these two solutions will be equal to M/ for the first solution and M2+ for the second solution. Let a volume Vt liters of the first solution be mixed with a volume of V2 liters of the second solution. If the concentrations of the ion X~ in the two original solutions are equal, then we obviously have: Mx+ = M2+ = X-. 1 Arrheniua, Ann. d. Phj/s. S0f 51 (1887) ; Ztachr. /. phys. Chem. 2,284 (1888) ; t&id., 5, 1 (1890). 220 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS In the mixture, therefore, assuming that no displacement of the equi- librium takes place, we should have for the concentration of the ions Mx+ the value 1+ * , for that of the common ion — * * J" v 2 — - and for V, + V2 Y! -j- V2 y that of the un-ionized fraction M^,, * y . If the law of mass-action 1 I 2 holds, we have the equation: If M!+ = M2+, the expression for the concentration of the common ion becomes : and the equilibrium equation reduces to: M±+ x xx- _ In other words, if the concentration' of the common ion is the same in the original solutions, then, if these solutions are mixed in any proportion, assuming no change in the equilibrium to take place, the concentrations of the ions in the mixture will be such as to fulfill the conditions necessary for equilibrium. The correctness of this principle may readily be tested in the case of weak acids. Since the conductance in solutions of the acids is due chiefly to the conductance of the hydrogen ion, it follows that two acids will have the same concentration of the hydrogen ion when the solutions have the same specific conductance. Therefore, a mixture of two solu- tions fulfilling these conditions will have the same specific conductance as the original solutions. If the anions have different conductance values, the specific conductance of isohydric solutions will differ in proportion to the conductance of these anions, and the specific conduct- ance of a mixture of the solutions will be the arithmetic mean of that of the components. This principle has been extensively tested by the conductance as well as other methods and has been shown to hold true for mixtures of weak acids and bases. It has been found, however, that even in solutions which do not con- form to the law of mass-action, that is, in solutions of strong electrolytes, HOMOGENEOUS IONIC EQUILIBRIA 221 a similar condition holds. If, for example, solutions of sodium chloride and potassium chloride have the same ion concentration, then, on mixing, the concentration of the ions in the mixture will be the same as that in the original solutions. Apparently, then, the isphydric principle holds, even in the case of electrolytes which do not obey the law of mass-action. This principle has been employed very extensively for the purpose of calculating the concentrations in mixtures of strong electrolytes. If the electrolytes in a given mixture do not obey the law of mass-action, then it is obviously impossible to calculate the equilibrium in the mixture unless we know the law governing this equilibrium. The isohydric prin- ciple is an empirical relation which has been assumed to govern the equilibrium in mixtures. In order to test the correctness of this prin- ciple, it is obviously necessary to determine the concentrations of the ions in the mixture by some independent means. The law of equilibrium for a given electrolyte in a mixture must reduce in the limit to that of a solution of the electrolyte in the pure solvent. It has been shown that, for a strong electrolyte, Equation 11 holds very nearly. According to this equation, the ratio of the product of the concentrations of the ions divided by the concentration of the un-ionized fraction varies as an exponential function of the ion concen- tration. It is clear that this relation conforms to the principle of iso- hydric solutions. In a mixture of electrolytes, the equation might take the form: u where P^ is the value of the ion product, Cu is the concentration of the un-ionized fraction, and C^ is the total concentration of the positive or negative ions in the mixture. Indeed, it is apparent that an equation of the form: (51) ??-=F(ZC) Lu will conform to the isohydric principle,1 where F(2C^) is any explicit function of the total ion concentration of the mixture. For, on mixing two solutions whose ion concentrations are C* and C^", the equilibrium will be unaffected by the relative volumes of the solutions mixed, pro- >Arrhenius, Ztschr. f. phys. Chem. 31, 218 (1899). 222 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS vided that C/ and C/' are equal. Equation 51, therefore, is the analyti- V V cal expression of the isohydric principle. In the limit, as the second com- ponent in the mixture disappears, the equation reduces to that for the first salt alone. In the case of mixtures of electrolytes without a com- mon ion the same expression applies. Equation 51 is not the only function which might be assumed to hold for the mixture which reduces to the form of Equation 11 in the case of a solution of a single electrolyte. We might assume for the mixtures a function of the form: Pt (52) -^-=F(P.)9 ^u where again P^ is the ion product. In the limit the concentrations of the positive and negative ions become equal for the solution of a single salt, and consequently this equation reduces to the form of Equation 11. The isohydric principle, or more generally, the iso-ionic principle, is a consequence of the law of mass-action, but, when the law of mass-action fails to hold, there is no reason for assuming that Equation 51 rather than Equation 52 is correct, for both reduce to the same limiting form in the case of a solution of a single electrolyte. We may, therefore, inquire which of the two functions corresponds most nearly with the experimental values. In order to test the functions in the case of mixtures, it is obviously necessary to measure some property of these mixtures by independent means, as, for example, the conductance of a mixture of electrolytes. Assuming that the conductance of the ions in the mixture is the same as that of the same ions in pure solutions, it is possible to calculate the specific conductance of the mixture, if the form of the conductance func- tion for the pure electrolytes is known, and if a function is assumed for the mixture. If the assumed function is correct, then the calculated specific conductance for the mixture should correspond to the measured specific conductance of the mixture within the limits of experimental error. If the calculated and observed values do not correspond, it fol- lows that the function assumed for the mixture is not correct. That an equilibrium actually exists in the mixture appears to be beyond question, although the exact nature of the reaction may be somewhat in doubt. Bray and Hunt 2 have measured the specific conductance of mixtures of sodium chloride and hydrochloric acid in water at 25°. They have likewise calculated the specific conductance of the mixtures, assuming aBray and Hunt, J. Am. Chem. Soc. S3, 781 (1911). HOMOGENEOUS IONIC EQUILIBRIA 223 the isohydric principle; that is, assuming Equation 51. The results are given in Table LXXXIII, in which the concentrations of sodium chloride and hydrochloric acid are given in the second and third columns re- spectively, and the measured specific conductance is given in the fourth column. In the fifth column is given the specific conductance calculated on the assumption of the iso-ionic principle, namely Equation 51, while in the seventh column is given the value of the calculated specific conduct- ance, assuming Equation 52. In the sixth and eighth columns are given the percentage deviations between the measured and calculated values. TABLE LXXXIII. MEASURED SPECIFIC CONDUCTANCE OF MIXTURES OF NaCl AND HC1 COM- PARED WITH VALUES CALCULATED ACCORDING TO EQUATIONS 51 AND 52. Concentration (Approx.) millimols No. NaCl HC1 Specific Conductance n Calculated Equa- Calculated Measured tion 51 % Dif. Equation 52 % Dif. 1 2 3 4 5 6 100 100 100 100 100 100 100 50 20 10 5 2 47.25 29.14 18.06 14.36 12.52 11.41 48.21 29.62 18.31 14.50 12.59 11.45 2.1 1.6 1.4 1.0 0.6 0.3 Mean — 1.15% 7 20 50 21.75 21.89 — 0.7 8 20 20 10.157 10.27 — 1.1 9 20 10 6.253 6.307 — 0.9 10 20 4 3.889 3.919 — 0.8 11 20 2 3.101 3.118 — 0.6 12 20 1 2.709 2.721 — 0.4 Mean — 13 14 15 16 5 5 5 5 12.5 5 2 1 5.651 2.632 1.621 1.011 5.678 2.650 1.630 1.016 Mean —0.57% 47.09 28.82 17.84 14.18 12.39 11.35 Mean + 0.85% 21.65 + 0.4 10.13 + 0;3 6.221 3.870 3.094 2.702 Mean +0.33% 5.646 + 0.1 2.634 —0.1 1.619 + 0.1 1.010 + 0.1 Mean + 0.05% Comparing the measured values of the specific conductance with those calculated on the basis of Equation 51, it is seen that the deviations from the iso-ionic principle are consistently larger than any conceivable experi- mental error. In the case of 0.1 normal solutions of sodium chloride, the 224 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS mean error is 1.15 per cent; for 0.02 normal solutions, 0.75 per cent; and for 0.005 normal sodium chloride solutions, the mean deviation is 0.57 per cent. At the lower concentrations the agreement is measurably better than at the higher concentrations, a result which is perhaps not unexpected, since at concentrations as high as 0.1 normal viscosity effects unquestionably come into play. The agreement between the measured and calculated values based on Equation 52 is markedly better than that of values based on Equation 51. In the case of the 0.1 normal solutions of sodium chloride, the mean deviation is 0.85 per cent. In the mixtures of sodium chloride of concentration 0.02 and 0.005, the mean deviations are respectively 0.33 and 0.05 per cent, values which fall very nearly within the limits of experimental error. In calculating the specific con- ductances of the mixtures according to Equation 52, 424 was assumed for the value of A0 for hydrochloric acid and 127 for that of sodium chloride. These values may be somewhat in error, but it is to be noted that the calculated specific conductances are affected to only a very small extent by the value assumed for A0. It must be concluded from these results that the isohydric principle is not applicable to mixtures of strong electrolytes. In the case of the mixtures of hydrochloric acid and sodium chloride, at any rate, Equation 52 yields results which corre- spond quite closely with the observed values at low concentrations. It is uncertain, however, that a similar correspondence will be found in the case of mixtures of other electrolytes. For the present, therefore, the form of the function which should be assumed in the case of mixtures of strong electrolytes remains doubtful. 2. Hydrolytic Equilibria. Water itself is ionized to a slight extent into hydrogen and hydroxyl ions. There therefore exists in water an equilibrium which, if the law of mass-action holds, is expressed by the equation: where KW is the ionization constant of water. The concentration of the hydrogen and hydroxyl ions in pure water has been determined by Kohlrausch from the conductance of very pure water. At 18° this method yielded the value 0.80 X 10~7 for the concentration of the hydrogen and hydroxyl ions in pure water. The ionization constant has also been determined from the electromotive force of gas cells, from the rate of certain esterrification reactions and from the hydrolysis of certain salts in water. In these latter methods, an electrolyte has, in general, been present, which naturally introduces an uncertainty as to the effect of HOMOGENEOUS IONIC EQUILIBRIA 225 the electrolyte on the ionization constant of water. The results of the various methods are summarized in the following table. TABLE LXXXIV. THE HYDROGEN-ION CONCENTRATION (X 107) IN PURE WATER AS DETER- MINED BY VARIOUS INVESTIGATORS. Investigator Method of Determination 0° 18° 25° Arrhenius ...... Hydrolysis of sodium acetate by ester-saponification ................. 1.1 Wijs ........... Catalysis of ester by pure water ........ 1.2 Nernst ......... Electromotive force of gas cell ...... 0.8 Lowenherz ..... Electromotive force of gas cell ......... 1.19 Kohlrausch and Heydweiller . . Conductance of pure water ....... 0.36 0.80 1.06 Kanolt ........ Hydrolysis .................... 0.30 0.68 0.91 When a salt is dissolved in water, interaction takes place between the ions of the salt and the ions of water with the resultant formation of un-ionized molecules of acid, or of base or of both, depending upon the strength of the acid and the base. Assuming the law of mass-action to hold in the mixture for both acid and base, and assuming that the salt is highly ionized and that its ionization function is known and is the same in the mixture as it is in a solution of the salt alone, the con- centration of the various constituents in the mixture may be obtained from a solution of the reaction equations: H+ X X- = # (53) M+ X OH- = and the condition equations: MX + HX + X- = Ca, (54) MX + MOH + M+ = C6, M+ + H+ = X- + OH-, where Ka, K^ and KW are the ionization constants of acid, base, and water, respectively, and Ca and C^ are the total concentrations of acid and of base, and the other symbols represent the concentrations of the various constituents concerned in the reaction. Let us assume that the acid is stronger than the base, in which case H+ is greater than OH~. Let Y represent the fraction of base present in the form of ions. Since 226 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS M* differs from X~, ys is not identical with the ionization of the salt, but, unless the hydrolysis is great, the value of ys will not differ appre- ciably from that of the salt at the concentration in question. Let h represent the total fraction of base present in the un-ionized condition, in which case h is the hydrolysis coefficient. A solution of the above equations leads to the equation: (55) The concentrations of the various constituents are given by the follow ing equations: C- Kbh (l-h) Kh K (56) OH- = Kbh _ _ MOH = hCb If YS, together with the reaction constants, are known, the concen- trations of the constituents may be calculated. The equations may be generalized by introducing the ionization function KS for the salt by means of the equation: (57) M+ X X- = £SMX. This leads to the equation: (58) HOMOGENEOUS IONIC EQUILIBRIA 227 These equations are independent of the concentration of the various reacting constituents so long as the assumed conditions are fulfilled. In many instances they may be greatly simplified for practical purposes. If the concentration of the salt is not extremely low and if the acid is stronger than the base, the concentration of the hydroxyl ions may be neglected in comparison with that of the M+ ions, and the term - — -r Kbh may be dropped out of the equations. If the hydrolysis is small, the concentration of the hydrogen ions may be neglected in comparison with that of the M+ ions. The equation, then, reduces to the form: Kw v v r* ft i,\2 i v n /t it\° KaKb Lb (l~h) Kbtb(l—h) If acid and base are present in equivalent amounts, the hydrolysis of the salt is expressed by the equation: (!-*)« KaKb ' KbCb(l-h) and the hydrogen ion concentration by: (61) KwKa Kwy8Cbd-K) These equations are generally applicable, provided the concentration of the hydrogen ions is relatively small in comparison with that of the ions of the salt. In the case of a solution of a strong acid and a weak base, the second term in Equation 60 is evidently determinative of the degree of hydrolysis of the salt, while in solutions in which both the acid and base are very weak and the total concentration of the base is high, the first term is chiefly determinative of the hydrolysis. In the case of acids and bases of intermediate strength, and particularly at fairly low con- centrations, both terms must be taken into account in determining the hydrolysis of a salt. In very dilute solutions of salts of relatively strong acids and bases, it is possible that conductance measurements may be appreciably affected by hydrolysis. This is particularly true if the limiting values of the ionization constant approached by acid and base differ. It is obvious that the actual concentration of acid and of base in solution is very low, 228 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS and the values of the ionization functions to be introduced for acid and base are therefore not the values for these ionization functions at ordi- nary concentrations of acid and base, but rather the values approached at very low concentrations. Actually, we do not know the limiting value which the ionization functions approach in aqueous solutions of strong acids and bases. Consequently, conductance measurements with dilute salt solutions remain in doubt so long as the values of the ionization functions remain unknown. It is fairly certain that in the case of salts of weaker bases, such as the silver salts, for example, the conductance must be measurably affected at concentrations below 10~3 normal. Ac- cording to Bottger,3 the ionization constant of silver oxide at 25° is 2.5 X 10~4. Assuming for the ionization constant of water the value 0.91 X 10~14 and assuming that the ionization of the salt is practically complete, we obtain the following values for the hydrolysis of silver salts at 25°. TABLE LXXXV. HYDROLYSIS OF SILVER SALTS AT DIFFERENT CONCENTRATIONS AT 25°. C 10-3 10-* 10-5 h 1.9 X10-4 6.0 X10-4 1.9 X10-4 Cond. inc 5.7 X 10'4 1.8 X 10'3 5.7 X 10'3 As a result of the replacement of Ag+ ions by H+ ions in the solution, the conductance is increased approximately in the ratio of one to three. In the third line of the above table are given values of the increase in the conductance due to the hydrolysis of the salt. It is seen that even at 10"3 normal the conductance of a silver salt is affected to the extent of 0.057%, while in a 10~4 normal solution the conductance correction amounts to 0.18%. That the hydrolysis of salts of the weaker bases becomes appreciable at higher temperatures is indicated by the work of Noyes and Melcher 4 with the salts of silver and of barium. In the case of silver nitrate, at higher temperatures, a deposit of silver was formed over the inner walls of the platinum-lined bomb. This pre- sumably was the result of a precipitation of silver oxide, which is unstable at these temperatures and decomposes to metallic silver and oxygen. The extent of the hydrolysis of salts of strong acids and bases is very uncertain. At the higher concentrations, these electrolytes appear to be ionized somewhat more strongly than typical salts. Washburn has de- duced the value of 0.02 as the limit approached by the ionization con- stant of potassium chloride at low concentrations. But this value really " Bottger, Ztschr. }. phys. Chem. 46, 602~(1903). « Noyes, Carnegie Publication, No. 63, p. 94, HOMOGENEOUS IONIC EQUILIBRIA 229 represents an upper limit and it is possible that the true value may be much below this limit. The high value of the ionization, however, ren- ders any precise determination of the limiting value of the mass-action function uncertain, and, indeed, if conductance data alone are considered it is even uncertain that a definite limit greater than zero is approached.4* The strong acids and strong bases are ionized to practically the same extent at higher concentration ; and if the ionization functions in the case of these two types of electrolytes approach the same limits at low con- centrations, the conductance of a salt as measured will be found some- what lower than the true value if hydrolysis becomes appreciable. On the other hand, if the functions of acid and of base approach values which differ considerably, then the result will be to increase the conductance of the solution above that of the unhydrolyzed salt. If, for example, the ionization constant of the acid relative to that of the base were 10~3, then, at a salt concentration of 10~5 N, the hydrolysis would have a value of 0.95 X 10"3 or approximately 0.1 per cent, which would raise the con- ductance of the solution approximately 0.3 per cent. In view of the entire lack of experimental data relating to the limiting values of the ionization constants of the strong acids and bases, conductance measure- ments with salts at concentrations below 10~* normal cannot be inter- preted with certainty. In solutions of salts of weaker acids and bases, hydrolytic equilibria appear to be fairly well established. This lends support to the view that the ionization constants of the weaker acids and bases, as well as that of water, are not materially affected by the presence of larger amounts of salt. The agreement of the values for the ionization constant of water as determined from a measurement of the conductance of solutions of salts of weak acids and bases, with that as determined by other methods, indicates that the fundamental assumptions underlying the theory of hydrolytic equilibria are substantially correct. In these equi- libria, the ionization of the salt is involved. If, as some assume, the salts are completely ionized at all concentrations, then the ionization y of the salt should vanish from the hydrolysis equation, which would materially affect the values obtained for the ionization constant of water. At the present time, however, data making such a comparison possible are not sufficiently precise to enable us to draw any certain conclusions. Among other typical equilibria involving electrolytes are those in which a strong acid or a strong base is partitioned between two weaker " Naturally, if this view were adopted, it would be necessary to recast our notion* relative to the nature of electrolytic equilibria. 230 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS bases or Weaker acids.5 A considerable number of equilibria of this type have been investigated and, in general, the results confirm the assump- tion that the strong base or acid is distributed between the weaker acids or bases in conformity with the law of mass-action. Equilibria similar to hydrolytic equilibria in aqueous solutions have been found to exist in solutions in non-aqueous solvents. Such equi- libria are to be expected in the case of all distinctly acid solvents which are capable of yielding a hydrogen ion. This, therefore, includes solu- tions in all acids, such as hydrocyanic acid, formic acid, acetic acid, etc. It likewise includes solutions in hydrogen derivatives whose acid prop- erties are extremely weak, such as ammonia, for example. Franklin6 has shown that equilibria of the hydrolytic type exist in solutions in liquid ammonia. In the case of salts of very weak bases, such as mercury for example, ammono-basic salts are precipitated when the neutral salt is dissolved. These precipitates are redissolved on the addition of an acid, while precipitation is facilitated by the addition of an ammono-base, such as potassium amide. While equilibria of the hydrolytic type thus exist in ammonia solutions, the evidence indicates that it is only in the case of extremely weak bases that hydrolysis takes place to an appreciable extent. The concentration of hydrogen ions in ammonia is without doubt of an exceedingly low order. This is indicated by the fact that salts whose ammono-bases are practically insoluble in liquid ammonia, such as calcium and barium nitrates, for example, yield clear solutions when dissolved in ammonia, even at high concentrations. Furthermore, as is well known, solutions of the alkali metals, as well as of metals of the alkaline earths, in liquid ammonia, are comparatively stable. It is to be expected that such would not be the case if the con- centration of tjhe hydrogen ions were appreciable. Schlesinger7 has shown that solutions of salts in formic acid are appreciably hydrolyzed. He found that on passing a current of air through solutions of chlorides in formic acid free hydrochloric acid is carried over. That hydrolysis may occur in solutions in other solvents, such as hydrocyanic acid, for example, is indicated by the high value of the residual specific conductance of the pure solvents. It is, of course, possible that in these cases the conductance is in a measurable degree due to the presence of impurities, but the high value obtained in many instances is probably due to the presence of hydrogen ions. It is prob- able, moreover, that the higher the dielectric constant of the medium, the greater the concentration of hydrogen ions due to the solvent. No •Thiel and Roemer, Ztschr. f. phys. Ohem. 61, 114 (1908). •Franklin, J. Am. Chem. 8oc. £7, 820 (1905). » Schlesinger, J. Am. Chem. Soc. 33, 1932 (1911). HOMOGENEOUS IONIC EQUILIBRIA 231 systematic study- has been made of reactions of the hydrolytic type in non-aqueous solvents. Certain solvents, such as sulphur dioxide, acetone and bromine, for example, appear to be of a non-polar type. In these cases it is to be expected that equilibria of the hydrolytic type do not exist. In the case of polar solvents, however, we may expect equilibria of the hydrolytic type even though hydrogen ions are not involved. Mercuric chloride may serve as an example of this type of solvents. This salt, when fused, dissolves typical binary salts and yields solutions which conduct the current with considerable facility. If a salt of the type of potassium nitrate, for example, were dissolved in mercuric chloride, reaction might be expected to take place, with the formation of potassium chloride and mercuric nitrate in the solution. This reaction is obviously of the hydro- lytic type. Indeed, we see that reactions of the type MX + NY = NX + MY, which take place in mixtures of fused salts, are of the hydrolytic type. We have here, however, an extreme case in that, in all likelihood, the ionization of the solvent itself is extremely high, whereas in the case of ordinary hydrolytic reactions the ionization of the solvent is exceedingly low. There is reason for believing that examples exist of equilibria of the hydrolytic type intermediate between those of water and those of mixtures of fused salts. Chapter X. Heterogeneous Equilibria in Which Electrolytes Are Involved. 1. The Apparent Molecular Weight of Electrolytes in Aqueous Solu- tion. If an electrolyte is dissolved in a solvent in equilibrium with a second phase, the thermodynamic potential of the solvent is displaced, and a displacement in equilibrium results. On the addition of an elec- trolyte to water, therefore, we should expect a change in the solubility of substances in this solvent; or, in case water itself appears as a second phase, we should expect a displacement in the freezing point, boiling point, etc. The earlier experiments on the freezing point of aqueous salt solutions indicated a fairly close agreement between the ionization as determined by conductance measurements and that as determined from freezing point measurements. These data have been examined and collected by Noyes and Falk.1 In solutions of the binary salts the agreement is, on the whole, fairly close in dilute solutions, although in the more concentrated solutions deviations, which exceed possible experimental errors, make their appearance. In solutions of potassium chloride the two methods yield practically identical results up to concentrations as high as 0.1 normal. In order to calculate the molecular weight of a substance from the freezing point of its solution, the laws governing the equilibrium in the mixture must be known. Since the general case has been worked out only for dilute solutions, it is obvious that the ionization of electrolytes, and the molecular condition of substances in general, may not be deter- mined from freezing point determinations at higher concentrations. Washburn and Maclnnes2 showed that, while the freezing point curve for potassium chloride corresponds very nearly with that of a solution of sugar in water up to fairly high concentrations, those for solutions of lithium chloride and caesium nitrate exhibit deviations at fairly high dilutions. The deviations in the case of the last named salts lie in oppo- site directions from the theoretical curve of ideal solutions. They found, 1 Noyes and Falk, J. Am. C hem. 8oc. S3, 1437 (1911). 'Washburn and Maclnnes, J. Am. Chem. Soc. 33, 1686 (1911). 232 HETEROGENEOUS EQUILIBRIA 233 however, that at lower concentrations the curves for the three salts ap- proach that of an ideal system, assuming the ionization to be given by the conductance ratio -T-. Ao More recently the methods for determining the temperature of solu- tions in equilibrium with ice have been greatly refined, and molecular weight determinations are available at very low concentrations. In Table LXXXVI, under ^ are given values of the ionization for potassium chloride at low concentrations as determined by Adams 3 and by Bed- ford.4 Under yc are given values of the ionization at the same concen- trations as determined from conductance measurements. TABLE LXXXVI. COMPARISON OF THE IONIZATION VALUES FOR POTASSIUM CHLORIDE FROM FREEZING POINT AND CONDUCTANCE MEASUREMENTS. C X 103 Yi (Adams) y^ (Bedford) yc 2 0.969 .... 0.971 5 0.961 0.959 0.956 10 0.943 0.939 0.941 20 0.922 0.915 0.922 50 0.888 .... 0.889 100 0.861 .... 0.860 An examination of this table shows that the ionization values as deter- mined by the freezing point method correspond within the limits of error with those as determined by the conductance method. The temperature of the conductance measurements, in this case, was 18°, while that of the freezing point measurements was necessarily in the neighborhood of 0°. It is known, however, that at fairly high dilutions the ionization of salts varies only little between .0° and 18°. The results are therefore com- parable. In Table LXXXVII are given values of the ionization as determined from freezing point and conductance measurements for solutions of potas- sium nitrate, potassium iodate, sodium iodate, and for equi-molar mix- tures of potassium chloride and potassium nitrate, and potassium iodate and sodium iodate.5 Examining the results given in the following table, it is evident that, in the case of potassium nitrate, the ionization values by the two methods •Adams, J. Am. Chem. Soc. 37, 482 (1915). * Bedford, Proc. Roy. Soc. (A) 83, 454 (1910). • Hall and Harkins, J. Am. Chem. Soc. S8, 2658 (1916). 234 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS TABLE LXXXVII. COMPARISON OF THE IONIZATION VALUES OF SALTS AS DERIVED FROM FREEZING POINT AND CONDUCTANCE MEASUREMENTS. Potassium Nitrate C X 103 Yi (Adams) Yc 2 0.967 0.970 5 0.958 0.953 10 0.937 0.935 20 0.908 0.911 50 0.848 0.867 100 0.787 0.824 I Potassium lodate C X 103 Y; (Hall & Harkins) YC 2 0.940 0.965 5 0.929 0.946 10 0.916 0.928 20 0.890 0.903 50 0.835 0.860 100 0.764 0.819 Sodium lodate C X 103 Y; (Hall & Harkins) YC 2 0.950 0.960 5 0.934 0.939 10 0.915 0.917 20 0.890 0.890 50 0.832 0.842 100 0.772 0.801 Equal Molecular Mixtures of KCl and KNOS C X 103 Y; (Hall & Harkins) 10 1.94 20 1.914 50 1.868 100 1.827 200 1.773 Equal Molar Mixtures of KI03 and NaI03 C X 103 Y- (Hall & Harkins) 10 20 50 100 1.912 1.890 1.834 1.768 HETEROGENEOUS EQUILIBRIA 235 agree at concentrations below 20X10"3 N. At higher concentrations, how- ever, the freezing point method yields lower values than the conductance method. In the case of potassium iodate, the agreement is not so good. At the lower concentrations the value of the ionization as determined by the conductance methods is about 1.5 per cent higher than that deter- mined by the freezing point method. The limiting value of the conduct- ance of the iodates is much less certain than is that of the chlorides and 'nitrates, and it is possible that the ionization values, as determined by this method are in error owing to an error in the value of A0. If the value of A0 were increased by 1.5 per cent, the conductance values for potassium iodate would agree up to a concentration of 0.05 normal. In solutions of sodium iodate, the discrepancies exceed the limit of experi- mental error, of the conductance measurements, at any rate. It is pos- sible that here, also, an error in the value of A0 would tend to harmonize the results. As regards the freezing point of equi-molar mixtures of two electro- lytes, it is interesting to note that the values of i for the mixtures are practically the mean of those for the pure substances at the same concen- tration. In Table LXXXVIII are given values of i for salts of higher type,6 together with values of y^ and Yc» where reliable values of Y ars available. TABLE LXXXVIII. IONIZATION OP SALTS OF HIGHER TYPE AS DETERMINED BY THE FREEZING POINT AND CONDUCTANCE METHODS. CX103 i (Hall & Harkins) y- (Hall & Harkins) ~ 5 10 20 50 100 200 500 5 10 20 50 100 200 Magnesium Sulphate, MgS04 1.708 1.614 1.520 1.394 1.303 1.214 1.099 0.708 0.614 0.520 0.394 0.303 0.214 0.099 Potassium Sulphate, K2S04 2.830 0.915 2.772 0.886 2.701 0.851 2.567 0.784 2.451 0.726 2.327 0.664 0.741 0.669 0.596 0.506 0.449 0.403 0.905 0.872 0.832 0.771 0.722 0.673 •Hall and Harkins, loc. cit. 236 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS Barium Chloride, BaCl2 5 2.847 0.924 10 2.790 0.895 0.883 20 2.730 0.865 0.850 50 2.647 0.824 0.798 100 2.585 0.793 0.759 200 2.535 C.768 0.720 Cobalt Chloride, CoCl2 5 2.858 0.929 10 2.802 0.901 20 2.749 0.875 50 2.687 0.844 Lanthanum Nitrate, La(N03)z 5 3.694 0.898 10 3.578 0.859 0.802 20 3.440 0.813 50 3.261 0.754 0.701 100 3.149 0.716 200 3.063 0.688 500 3.002 0.667 The agreement between the ionization values as determined from conductance and freezing point measurements, in the case of the salts of higher type, is not as close as in that of the binary salts. The devia- tions in the more dilute solutions are in the neighborhood of one per cent, for the uni-divalent salts. In solutions of potassium sulphate the ioniza- tion values by the freezing point method are slightly higher than those by the conductance method, except at a concentration of 0.2 normal, where the conductance method gives a slightly higher value. On the whole, for this salt the agreement is fairly close and it is possible that the discrepancies which remain may be due to error in the value of A0 employed. In the case of barium chloride, the ionization values by the freezing point method at the lower concentrations are slightly over one per cent higher than those by the conductance method. At the higher concentration the difference in the values increases to five per cent at 0.2 normal. The differences at the lower concentrations may arise from uncertainties in the values of A0, but at the higher concentrations there is evidently a definite divergence between the two curves. Accurate con- ductance values for cobalt chloride are not available. The values of i, however, do not differ greatly from those of barium chloride or potassium sulphate. In solutions of lanthanum nitrate, the ionization values as deter- HETEROGENEOUS EQUILIBRIA 237 mined by the freezing point method are approximately seven per cent greater than those determined by the conductance method. Comparison, however, can be made only at two concentrations. The discrepancies in the values appear to be greater than might be expected from any possible errors in the assumed value of A0. In the case of magnesium sulphate, there is a marked divergence between the values of the ioniza- tion as determined by the two methods. However, as the concentration decreases, the ionization curves, as given by the two methods, approach each other. Considering these results broadly, it may be concluded that the freez- ing point and the conductance methods give values for the ionization which fall very nearly within the limits of experimental error at concen- trations approaching 10~3 normal for solutions of the binary salts, and that in the case of solutions of salts of higher type the differences between the values, as determined by the two methods, do not, in general, exceed one per cent at low concentrations for salts of the uni-divalent type. For salts of the di-divalent type, the discrepancies between the values, as determined by the two methods, are markedly greater, lying in the neighborhood of 5 per cent, and the same is true of lanthanum nitrate. In general, however, in the case of salts of higher type, the divergence of the values determined by the two methods diminishes as the concen- tration decreases. Considering the results of freezing point determinations, it is a strik- ing fact, the significance of which cannot be ignored, that, as the concen- tration decreases, the molecular depression of the freezing point increases and approaches a limiting value, which, in the case of salts of different types, corresponds with the ionic structure of these salts and which is in agreement with the fundamental ionic reactions assumed by the ionic theory. So the value of i for the binary salts approaches a value of 2, for ternary salts 3, for quaternary salts 4, etc. While the significance of the agreement between the results of freezing point and conductance meas- urements remains uncertain, the fundamental importance of the fact that the limits approached in the two cases are substantially the same should not be overlooked. The difference between the results by the two methods at the higher concentrations are readily explainable, since the calculation of the num- ber of molecules present in a mixture is based upon the assumption that the laws of dilute solutions hold. Even in the case of non-electrolytes, the laws of dilute solutions fail to hold at concentrations as low as 0.1 normal, and it is therefore a priori probable that the laws of dilute solu- 238 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS tions in electrolytic systems will fail at concentrations below this value. Furthermore, in the case of salts of higher type, it is not improbable that intermediate ions are formed, as a result of which a divergence will arise between the results as determined by conductance and by osmotic methods. Nernst 7 has called attention to the fact that, since the law of mass- action in its simple form does not hold for solutions of strong electrolytes, the laws of dilute solutions cannot be applied to these mixtures. As a consequence, if the ionization is correctly determined by, the conductance method, the ionization as determined by osmotic methods, assuming the laws of dilute solutions to hold, should differ from that determined by conductance measurements. It appears, however, that in the case of certain electrolytes, such as potassium chloride, osmotic methods and conductance methods lead to the same value of the ionization, and, in the case of other electrolytes, the two methods lead to very nearly the same value at concentrations approaching 10~3 normal. Yet, in the neighborhood of 10~3 normal, strong electrolytes do not conform to the simple law of mass-action. Those who would use the results of osmotic methods to substantiate the correctness of the results of conductance methods thus find themselves in a dilemma, for, if the two methods lead to identical values of the ionization, then, if the results of osmotic meas- urements are looked upon as correct, the interpretation of conductance measurements must be in error, while, if the results of conductance meas- urements are accepted in their usual sense, the laws of dilute solutions are inapplicable. That the concordance of the ionization values deter- mined by conductance and osmotic methods at low concentrations is an accidental one is very improbable. It appears, rather, that this agree- ment is the expression of a fundamental property of such solutions. The significance of this agreement, however, remains uncertain. This ques- tion will be discussed further in the next chapter. The molecular weight of electrolytes in aqueous solutions has like- wise been determined from the measurement of the elevation of the boil- ing point. The precision of such measurements is necessarily much lower than that of the freezing point depression and need not be discussed in detail here. The molecular weight of electrolytes in aqueous solutions has also been determined from vapor pressure measurements.8 The experimental difficulties attending the use of this method are very great and it is doubtful if the precision of such determinations equals that of T Nernst, Ztschr. f. pJiys. Chem. 38, 494 (1901). "Lovelace, Frazer and Sease, J. Am, Chem. SQC. $3, 102 (1921). HETEROGENEOUS EQUILIBRIA 239 the freezing point method. The results obtained agree well with those obtained by the freezing point method.8* 2. The Molecular Weight of Electrolytes in Non-Aqueous Solutions. A great many measurements have been made of the molecular weight of electrolytes in various non- aqueous solvents. With a few exceptions, the boiling point method has been employed. The resulting data suffer, consequently, from the inaccuracies inherent in this method. Measure- ments at low concentrations appear to be entirely lacking. In general, in solvents of fairly high dielectric constant, where the ionization is com- parable with that in water, the molecular weights as determined lie below the normal values and indicate ionization. In solvents of fairly low dielectric constant, usually below 20, the apparent molecular weight rarely indicates ionization at higher concentrations. The most extensive molecular weight determinations in a non-aqueous solvent have been made by Walden and Centnerszwer 9 with solutions in sulphur dioxide. In Table LXXXIX are given values of the van't Hoff factor i for various electrolytes dissolved in sulphur dioxide at dilutions from 1 to 16 liters. An inspection of the table shows that, at a dilution TABLE LXXXIX. VALUES OP i FOR ELECTROLYTES DISSOLVED IN SULPHUR DIOXIDE. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. KJ ..................... 0.42 KCNS .................. 0.41 NaJ ........................ NH4J ................... 0.41 NH4CNS ................ 0.29 RbJ .................... 0.52 N(CH3)H3C1 ............ 0.28 N(CH3)2H2C1 ........... 0.87 N(CH3)3HC1 ............ 1.12 N(CH3)4C1 .............. 1.16 N(CH3)4Br .............. 1.30 N(CH,)4J ............... 1.26 N(C2H5)HSC1 ........... 0.43 N(C2H5)2H2C1 ........... 0.70 N(C2H5)3HC1 ........... 1.15 N(C2H5)J .............. 1.61 N(C7H7)H3C1 ........... 0.44 S(CH3)3J ............... 0.84 0.55 0.49 0.57 0.53 0.40 0.61 0.38 0.79 1.00 1.08 1.10 1.20 0.50 0.69 1.06 1.39 0.51 0.97 4 0.63 0.60 8 0.74 0.68 16 0.86 0.71 0.64 0.71 0.82 0.73 0.82 0.85 0.49 0.62 0.81 0.76 0.82 0.86 0.99 0.96 0.96 1.05 1.03 1.02 1.01 0.97 0.95 1.16 1.18 1.23 0.62 0.68 0.71 0.70 0.76 0.78 1.06 1.05 1.06 1.27 1.17 1.11 0.59 0.72 0.80 1.03 1.06 1.08 ••According to Heuse (Thesis, Univ. of 111., 1914), the agreement between the con- ductance and the vapor pressure method does not hold for KC1 at 25°. . See also Wash- burn, "Principles of Physical Chemistry," Ed. 2, p. 268. • Walden and Centnerszwer, Ztschr. /. phys, Chem, 39, 513 (1902), 240 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS of 16 liters, a few salts have a value of i greater than unity, while the greater proportion of the salts has a value of i less than unity. At higher concentrations the curves exhibit a very complex form. In the case of most of the substances which have a relatively high value of i at lower concentrations, the value changes but little until a concentration of 0.2 normal is reached, when the value of i begins to increase rapidly with increasing concentration. In the case of salts having a low value of i at the lower concentrations, the value of i, in general, decreases with increasing concentration, particularly as normal concentration is ap- proached. Certain of the electrolytes exhibit an exceptional behavior in that the curves of the i values intersect those of the majority of the electrolytes. It is evident that molecular weight determinations in sul- phur dioxide are uncertain in their significance. On the whole, the curves exhibit a definite trend as the concentration decreases indicating that the value of i will ultimately rise above unity. It is to be borne in mind that the ionization of salts in sulphur dioxide is relatively low, being in general less than 20 per cent in the neighborhood of 0.1 normal. Further- more, even in the case of aqueous solutions, freezing point and con- ductance methods lead to divergent results at higher concentrations. If the divergence of a solution of an electrolyte from the simple laws of dilute solutions is in any considerable measure due to the electrostatic action of the charged particles upon one another or upon the solvent me- dium, then it is to be expected that as the dielectric constant of the sol- vent is smaller, the divergence at a given concentration will be greater, since the force due to a charged particle varies inversely as the dielectric constant. It seems not improbable, also, that, in the case of certain sol- vents, polymerization may take place to a considerable extent at higher concentrations. This would greatly complicate the behavior of these solu- tions and would make it impossible to interpret either the results of conductance or of osmotic measurements. The molecular weights of a number of electrolytes in liquid ammonia at its boiling point have been determined by Franklin and Kraus 10 from the boiling point measurements. Owing to the exceptionally low value of the boiling point constant of liquid ammonia, about 3.4, measurements below 0.1 normal were not made. As a consequence, the determinations relate almost entirely to concentrations at which it might be expected that the laws of dilute solutions would not hold. In general, in the neighbor- hood of 0.1 normal, the observed elevation of the boiling point corre- sponds approximately with a normal value of the molecular weight of the dissolved electrolyte. At higher concentrations, the molecular eleva- » Franklin and Kraus, Am. Chem. J. 20, 836 (1898). HETEROGENEOUS EQUILIBRIA 241 tion of the boiling point increases in the case of all the salts measured. It is obvious that in these solvents the concentration at which the meas- urements were carried out is too high to admit of a comparison with the results of the conductance method. In comparing the results of the conductance method with that of other methods of determining the degree of ionization of salts in non-aqueous solvents, it should be borne in mind that, according to conductance measurements, the deviations from the law of simple mass-action increase greatly as the dielectric constant of the medium decreases. If, then, the deviations from the laws of dilute solutions lead to a lack of correspondence between the results of the osmotic and the conductance methods, the discrepancy between the results of the two methods should be the greater, the greater these deviations. It might be expected, therefore, that, in solvents of low dielectric con- stant, the discrepancies would prove to be very great. In solvents of fairly high dielectric constant, molecular weight deter- minations by osmotic methods yield values for the ionization which are comparable with those resulting from conductance measurements, and the ionization increases as the concentration decreases. In making such comparisons, however, it should be borne in mind, not only that the ex- perimental errors are great in the osmotic determinations, but, also, that the conductance values are more or less uncertain, and that the values of A0 are often subject to considerable errors. In the following table are given values of the ionization YC as determined from conductance meas- urements and Y£ as determined from the elevation of the boiling point for solutions of (C2H5)4NI in a number of solvents.11 TABLE XC. VALUES OF i FOR SOLUTIONS IN DIFFERENT SOLVENTS. CH3OH CH3CN V 3 6 12 V 10 15 Tc 0.38 0.45 0.52 YC 0.48 0.54 yb 0.24 0.29 0.38 y& 0.49 0.57 C2H5OH C2H8CN V 30 V 30 Yc 0.41 YC 0.53 Y6 0.30 Y& 0.54 "Walden, Zttchr. }. phys. Chem. 55, 281 (1906). 242 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS While the correspondence between the two methods is not very exact, nevertheless it is evident that the relations in these solvents are similar to those found in aqueous solutions. In pyridine the values of i are in general less than unity, as may be seen from the following table. TABLE XCI. VALUES OF i FOR SOLUTIONS IN PYRIDINE. AgN03 (C2H5)4NI V= 128 7= 16 32 i— 0.77 0.75 0.91 i— 0.73 0.82 The molecular weight of sodium iodide in acetone has been deter- mined by McBain and Coleman.12 The values obtained are very nearly normal from 0.9 to 0.04 normal concentrations. If anything, the mole- cular weights are slightly larger at the lower concentrations. At these concentrations, the conductance method indicates an ionization varying from 17 to 43 per cent. It is evident that in this solvent the results of conductance and of osmotic measurements are not in agreement. In acetone, however, the deviations from the law of simple mass-action are large, and there is evidence that polymerization of the dissolved salts takes place, presumably with the formation of complex ions.12a This renders the interpretation of results in the more concentrated solutions difficult. Phenol is the only non-aqueous solvent in which the molecular weights of salts have been determined at relatively low concentration. Riesen- feld,13 from the freezing point of a saturated solution of potassium iodide in phenol, whose concentration is 0.0045 normal, obtained a value of 170, for the molecular weight of potassium iodide, which corresponds closely with the normal value of 166. The equivalent conductance of solutions of potassium iodide in phenol at these concentrations is of the order of 1.0. Hartung14 has measured the molecular weights of a number of salts in phenol by the freezing point method. These include tetramethyl- ammonium iodide, sodium acetate, aniline hydrochloride, dimethylamine hydrochloride, as well as several organic salts of alkali metals. The concentrations run to dilutions, in some cases, as low as 0.01 normal. In the following table are given the values obtained for i for solutions of tetramethylammonium iodide and sodium acetate in phenol. With aniline hydrochloride, i has a value of unity at a concentration of 0.02 N "McBain and Coleman, Trans. Faraday Soc. 15. 45 (1919). "•Serkov, Ztschr. f. phys. Chem. 78, 567 (1910). « Riesenfeld, Ztschr. /. phys. Chem. 41. 346 (1902). "Hartung, Ztschr. /. phys. Chem. 77, 82 (1911). HETEROGENEOUS EQUILIBRIA 243 and decreases to values less than unity at higher concentrations. In the case of dimethylamine hydrochloride i has a value of 1.18 at V = 23, and decreases to a value in the neighborhood of unity at a dilution of TABLE XCII. MOLECULAR WEIGHTS OF SALTS IN PHENOL. Tetramethylammonium Iodide. M = 201.1 V M(obs.) t 92.7 135.5 1.48 38.9 143.5 1.40 22.9 150.2 1.34 12.3 163.9 1.23 8.18 171.5 1.17 5.70 177.6 1.13 4.75 182.6 1.10 4.08 185.4 1.08 3.52 188.8 1.07 3.05 189.0 1.06 2.67 190.0 1.05 2.40 191.1 1.05 2.10 191.5 1.06 1.73 188.9 1.07 1.59 185.3 1.08 Sodium Acetate. M = 82.1 V M(obs.) t 41.8 46.6 1.75 29.5 48.8 1.66 20.5 54.0 1.51 16.3 57.5 1.43 13.3 59.9 1.37 11.4 61.8 1.33 9.68 63.5 1.30 8.70 65.0 1.27 7.62 66.5 1.23 6.86 67.1 1.22 5.89 68.0 1.20 5.12 69.5 1.19 4.43 70.2 1.16 3.85 72.0 1.14 3.37 73.5 1.11 2.98 76.7 1.06 2.65 78.4 1.04 2.37 81.0 1.01 2.15 82.9 0.99 2.0 83.0 0.99 244 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 2 liters. As may be seen from the table, the value of i for tetramethyl- ammonium iodide in the neighborhood of 0.01 N is approximately 1.50, while that for sodium acetate is even higher than that of tetramethyl- ammonium iodide, being 1.75 at V = 41.8. Phenol has a dielectric constant of 9.68 and the high values obtained for i are unexpected. The conductance of solutions of tetramethylam- monium iodide in phenol at 45° has been measured by Kurtz.14a The constants for these solutions are m = 1.28, D = 0.69, K = 2.3 X 10~* and A0 = 16.67. Solutions of tetramethylammonium iodide in phenol thus exhibit an ionization not very different from that found for solutions of typical salts in other solvents, having a dielectric constant in the neighborhood of 10. While the ionization is marked at the lower con- centrations, the value is much lower than corresponds to the value of i found by Hartung. Thus, at a concentration 0.01 N, the ionization from the conductance values is 0.194 in contrast to 0.48 from freezing point determinations. It is evident that there is a wide discrepancy between the values of the ionization as determined by the two methods. It is particularly striking that the values of i found for salts of weak organic acids are higher than those for typical electrolytes. Since phenol is an acid sol- vent, it is probable that a solvolytic reaction takes place when a salt is dissolved in phenol according to the equation: PhOH + MX = MOPh + HX. If this were the case, we should expect the greatest values of i in the case of salts of weak acids and bases, which would account for the high values found for solutions of tetramethylammonium iodide and sodium acetate. Lacking further experimental material, however, the question must be left open. The results obtained from molecular weight determinations indicate that, in solvents of intermediate dielectric constant, the values of y^ approach those of yc at low concentrations. At high concentrations the divergence is often great and the variation of the i values depends greatly on the nature of the electrolyte. In solvents of dielectric constant lower than 20, the values of y by the two methods are not in agreement. This is not surprising, since these solutions may be expected to show large divergences from the laws of ideal systems. So far as may be judged from the available material, however, at very low concentrations, y • and 7_ approach a common limit in non-aqueous solutions. The corre- i/ "a Kurtz, Thesis, Clark Univ. (1920). HETEROGENEOUS EQUILIBRIA 245 spondence found between the values of y^ and Yc m aqueous solutions appears, therefore, to be a property of electrolytic solutions in other solvents also. 3. Solubility of Non-Electrolytes in the Presence of Electrolytes. The solubility of non-electrolytes in water is, in the majority of cases, depressed by the addition of an electrolyte. The effect of the added electrolyte on the solubility depends upon the nature of the substance in question, as well- as upon that of the added electrolyte. If reaction takes place between the two, the solubility is naturally influenced by this reaction. For certain substances, the solubility is very nearly a linear function of the concentration of the added salt, in which case it may be expressed by the equation: (62) S = S0 + BS0C where S0 is the solubility of the non-electrolyte in pure water, S is the solubility in the presence of the salt at the concentration C, and B is the solubility coefficient, which is a constant if the solubility varies as a linear function of the concentration. In general, however, the solubility function is not a linear one. The change in the solubility for a given addition of electrolyte is, as a rule, the greater the smaller the amount of electrolyte added. The solubility is more accurately expressed by the equation: q .(63) log -=- = PC,15 where p is a constant. O0 In the following table are given values for the solubility of hydrogen in aqueous solutions of different electrolytes.18 In pure water, the solu- TABLE XCIII. SOLUBILITY OF HYDROGEN IN AQUEOUS SOLUTIONS OF ELECTROLYTES AT DIFFERENT CONCENTRATIONS AT 25°. C= 0.5 1 2 3 4 CH3COOH ......... 0.0192 . 0.0191 0.0188 0.0186 0.0186 CH,C1COOH ...... 0.0189 0.0186 0.0180 ........ HN03 ............. 0.0188 0.0183 0.0174 0.0167 0.0160 HC1 ............... 0.0186 0.0179 0.0168 0.0159 ____ H2°4 ............. 0.0185 0.0177 0.0163 0.0150 0.0141 KOH .............. 0.0167 0.0142 ........ NaOH ............. 0.0165 0.0139 0.0097 0.0072 0.0055 "Rothmund, Ztschr. f. Electroch. 7, 675 (1901) ; Ztschr. f. phys. Chem. 69, 524 (1909) ; Nernst, ibid., 38, 494 (1901). "Geffcken, Ztschr. f. phys. Chem. 49, 257 (1904). 246 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS bility of hydrogen at 25° is 0.01926. The results are shown graphically in Figure 48. An examination of the table shows that solubility depres- sion is a specific property of the electrolyte. The depression due to chloroacetic acid is slightly greater than that due to acetic acid. Nitric, hydrochloric and sulphuric acids cause a small, but markedly greater, depression of the solubility. On the other hand, sodium and potassium hydroxides cause a marked depression of the solubility. The solubilities may be compared by means of the solubility coeffi- o.ooo in zn 3* Concentration of Added Electrolyte. FIG. 48. Solubility of Hydrogen in Water at 25° in the Presence of Electrolytes at Varying Concentrations. cient for the percentage equivalent solubility change, as defined by the equation : (64) B' = 100 S0 — S X S0 ^ C' In Table XCIV are given the values of the percentage equivalent solubility depression of hydrogen, corresponding to Table XCIII. If the solubility varied as a linear function of the concentration of the salt, the equivalent percentage solubility depression would be a constant. As may be seen by reference to Figure 48, the curves are convex towards the axis of concentrations, which corresponds to a decrease in the solubility coefficient. In Table XCV are given values of the relative percentage solubility depression for nitrous oxide and in Table XCVI those for oxygen at 25° and 15°. It will be observed, in the first place, that the percentage solubility effect is in certain cases a function of the tempera- HETEROGENEOUS EQUILIBRIA 247 TABLE XCIV. EQUIVALENT PERCENTAGE SOLUBILITY DEPRESSION FOR HYDROGEN IN WATER AT 25°. C= 0.5 1 2 3 4 CH3COOH 1.0 1.0 1.0 1.0 CH2C1COOH 3.7% 3.4 3.3 HN03 4.8 4.9 4.8 4.4 4.2 HC1 7.3 7.0 6.4 5.8 H2S04 8.0 8.1 7.7 6.7 2 KOH 26.6 26.4 NaOH 28.6 27.9 24.8 20.9 17.9 TABLE XCV. RELATIVE PERCENTAGE SOLUBILITY DEPRESSION OF NITROUS OXIDE AT 25° AND 15.° t = 25° t = 15° 0.5 1 2 3 4 0.5 1 2 3 4 HN03 ....— 1 —1 —1.1 .. ..000 HC1 +5.7 + 4.4 + 3.1 . . . . + 5.9 + 5.1 +4.0 . . H2^°4 .... 9.4 8.7 7.2 6.3 5.5 11.3 10.2 8.6 7.5 6.9 NH4C1 ... 12.4 10.9 12.8 11.2 CsCl 16.8 17.5 KJ 17.8 17.2 19.5 18.6 KBr 19.5 18.3 20.8 19.4 LiCl 19.8 18.7 20.8 19.9 RbCl 20.5 18.7 21.3 19.7 KC1 20.6 20.0 .. .. .. 23.6 20.6 KOH .... 26.9 26.6 28.3 28.1 TABLE XCVI. RELATIVE EQUIVALENT PERCENTAGE SOLUBILITY DEPRESSION OF OXYGEN AT 25° AND 15°. t = 25° t = 15° c = 0.5 1 2 3 4 5 0.5 1 2 3 4 5 HN03 .... 4 4 4 8.3 7.4 6.6 HC1 7.8 6.8 6.3 10.4 8.9 1 0 fi in 7 Q A 81 7 K 1 O O 1 A *7 n n O O O O 2 lo. U J.U./ 9.4 0.4 .1 7.5 lo.8 10.7 9.9 8.8 8.0 NaCl 30.0 27.6 24.3 ^ 30.3 28.4 25.1 KsSO, 2 35.7 32.8 .. 38.0 34.7 .. .. KOH 36.4 33.1 397 35.5 NaOH .... 37.7 33.8 28.6 . . f f , . 41.3 36.4 30.6 t m f t f f 248 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS ture, while in other cases the solubility effect is relatively independent of temperature. In the presence of nitric acid, the coefficient for oxygen increases from 4 to 8 per cent, as the temperature falls from 25° to 15°. In the presence of hydrochloric acid the coefficient increases slightly, while in the presence of sulphuric acid the coefficient changes but little. In the presence of sodium chloride, the coefficient is practically identical at the two temperatures. The solubility of nitrous oxide appears to vary less than that of oxygen as the temperature changes. The order of the electrolytes in terms of their solubility effect is practically the same for different gases. Indeed, in many cases, the solubility coefficients for different gases are very nearly the same for the same electrolyte. An inspection of the tables will show that, in general, the order in which the electrolytes appear is the same. In certain cases, however, the solubility effects show an influence due to the nature of the dissolved gas. For example, in a 1.0 normal solution, the solubility coefficient for hydrogen in the presence of nitric acid is 4.9, that of oxygen is 4, and that of nitrous oxide is — 1 per cent. The negative sign indicates that the solubility is increased on addition of the electrolyte. The solubility effect is smallest in the case of the acids and is greatest in that of the bases. The solubility coefficients for the salts are, in general, slightly smaller than those for the bases. In Table 1T XCVII are given values of the percentage equivalent solu- bility depression for a variety of substances in the presence of different electrolytes. A comparison of the results collected in this table shows that the order of electrolytes as regards their effect on the solubility of different substances is practically identical throughout. This is particu- larly true in the case of those substances where reaction with the -electro- lyte is not to be expected. The smallest effect for typical salts is ob- served in the case of ammonium nitrate. However, any general relation between the nature of the electrolyte and the nature of the solubility effect cannot be established. The action is specific in character. With a few exceptions, the addition of an electrolyte to a solution of a non-electrolyte in water causes a depression in the solubility of the non-electrolyte. This effect, which has been called a "salting out" effect, is not, however, characteristic of electrolytes alone. For example, the percentage equivalent solubility depression of hydrogen in water in the presence of sugar at normal concentration is 32. Similarly, the equivalent depression of hydrogen at the same concentration at 20° is 9.2 for chloral hydrate. The depression for sugar is greater than that for most salts, while that for chloral hydrate is greater than that for the "Euler, Ztschr. f. pliys. CJiem. 1$, 310 (1904). HETEROGENEOUS EQUILIBRIA 249 § I 8'*OOO t>»O5 § • - '-"H J !« j H H rr, *? ^ ^ «3 [IX rt^ « rHCSlOO5rH*Tfl'*»OOO (Nl^- 52 PQ ^g H rH-rH'-rHrH''-*'*rH«OOt• O5 ". " rH (N C^l (/ If S, is a constant, as it is if the laws of ideal solutions hold, and if tv K! is a constant, then it follows from Equation 66 that (69) Ml*XX- = K1Su = K, where X~ is the concentration of the common ion in the solution, and K is a constant. For an electrolyte in solution in equilibrium with its solid phase, the product of the concentrations of the ions remains con- stant, provided that the laws of dilute solutions hold. According to these considerations, the solubility of a given electrolyte may be depressed to a value which corresponds to the concentration of the un-ionized fraction in a solution of the pure electrolyte in equilibrium with its solid phase. The foregoing relations are based on the assumption that the laws of dilute solutions are applicable. As we have seen, this condition is not fulfilled in solutions of strong electrolytes. The effect of the presence of strong electrolytes upon the solubility of other strong or weak elec- trolytes can, therefore, be determined 'by experiment only.2** The con- centration of the various molecular species in the mixture cannot be deter- mined, even though the solubility of the first electrolyte is known, unless a law is assumed governing the equilibrium of the various electrolytes present in the mixture; and the results obtained for the concentration of the ionized and the un-ionized fraction of the first salt in the mixture, as calculated, will depend upon the laws assumed as governing the equi- librium in the mixture. We shall first examine the effect of strong and weak electrolytes upon the solubility of weak electrolytes; that is, electrolytes which conform to the simple mass-action law. Such determinations have been made by Kendall.22 In Table CII is given values for the solubility of a number of weak acids in the presence of other acids, both weak and strong. The results are shown graphically in Figures 49 and 50. Considering first the .solubility of orthonitrobenzoic acid and salicylic acid in th< m It is evident from Equation 69 that KI and 8U might vary in such a manner tha their product would remain constant, in which case the ion product would remain con stant. It is very improbable, however, that such a compensation actually occurs. "Kendall, Proc, Roy. Soc. 85 A, 218 (1911). HETEROGENEOUS EQUILIBRIA 257 TABLE GIL SOLUBILITY OP WEAK ACIDS IN THE PRESENCE OF OTHER ACIDS. A. Salicylic Acid in the Presence of Formic Acid. Solubility, Solubility, Formic acid, gravimetric, volumetric, per cent. mols per liter. mols per liter. 0.00 0.01631 0.01634 0.24 0.01531 0.46 .... 0.01474 0.625 0.01484 1.25 0.01496 2.5 0.01536 5.0 0.01716 10.0 0.02101 B. Solubility of Hippuric Acid in the Presence of Formic Acid. Solubility, Solubility, Formic acid, gravimetric, volumetric, per cent. mols per liter. mols per liter. 0.00 0.02045 0.02048 1.25 0.02014 2.5 0.02078 5.0 0.02275 10.0 0.02661 C. Solubility of Salicylic Acid in the Presence of Acetic Acid. Acetic acid, Solubility, gravimetric, per cent. mols per liter. £ 0.00 0.01631 0.625 0.01691 1.25 0.01745 2.5 0.01846 5.0 0.02059 D. Solubility of Salicylic Acid in the Presence of Hydrochloric Acid. Hydrochloric Solubility, Solubility, acid, gravimetric, volumetric, normal. mols per liter. mols per liter. 0.01631 0.01634 0.0179 0.01290 0.0357 .... 0.01238 0.125 0.01214 0.25 0.01194 0.5 0.01123 258 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS TABLE GIL— Continued E. Solubility of o-Nitrobenzoic Acid in the Presence of Hydrochloric Acid. Hydrchloric Solubility, Solubility, acid, gravimetric, volumetric, normal. mols per liter. mols per liter. 0.04320 0.04360 0.0179 0.03681 0.0357 .... 0.03390 0.125 0.02980 0.25 0.02922 0.5 0.02846 presence of hydrochloric acid, it will be observed that the solubility de- creases greatly on the initial addition of hydrochloric acid, after which the solubility decreases slightly, practically as a linear function of the concentration. In the presence of the weaker acids, the initial decrease O.04 O.OJ 0.01 O-NlTROBENZOC AoO IN HCt SALICYLIC ACID IN HG. 0.0 6.S O.I 0.2 O.3 Concentration of Added Acid. FIG. 49. Solubility of Moderately Strong Organic Acids in Water in the Presence of Hydrochloric Acid at 25°. is relatively slight, and this decrease is the smaller the weaker the added acid. The solubility of salicylic acid in the presence of acetic acid increases from the beginning. In the case of the organic acids the solu- bility eventually increases, practically as a linear function of the con- centration of the added acid. The results are in harmony with the HETEROGENEOUS EQUILIBRIA 259 assumption that the initial depression in the solubility of the acid is due to the depression of its ionization. Acetic acid is so weak that, even at fairly high concentrations, it has no appreciable effect on the ionization of salicylic acid, and consequently the resulting curve merely measures the increase in the solubility of the un-ionized fraction. In the case of hippuric and salicylic acids in formic acid, the added acid is sufficiently strong to practically completely repress the ionization of salicylic acid present in solution. In these cases, therefore, there is an initial decrease in the solubility, while finally, when the ionization is completely repressed, the solubility is increased, owing, presumably, to the increased solubility of the un-ionized molecules of the first acid on addition of the second. By extrapolating the linear solubility curves backwards, until they inter- Per Cent of Added Acid. O I e y 4 s 6 7 s 9 to o.ois 02 O.Olf FIG. 50. Solubility of Weak Organic Acids in Water in the Presence of Other Organic Acids at 25°. sect the axis of solubility, the intercepts on this axis correspond approxi- mately to the solubility of the un-ionized fraction in pure water. It will be noted that the solubility of salicylic acid and of orthonitro- benzoic acid is depressed according to the requirements of the mass-action law not only on addition of weak acids, but also on addition of hydro- chloric acid. In this case, the solubility of the un-ionized fraction in the more concentrated solutions decreases slightly with increasing concen- tration of hydrochloric acid. The initial depression effect is marked, particularly in the case of orthonitrobenzoic acid, which is a fairly soluble acid. Apparently, the addition of a strong acid to a solution of a weak acid, as well as the addition of a weak acid to a solution of a weak acid, does not greatly alter the ionization constant of weak acids. The ioniza- tion constant of salicylic acid at 25° is 1.02 X 10~3; that of hippuric acid is 2.22 X 10-4; and orthonitrobenzoic acid 6.16 X 10"3. 260 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS Kendall and Andrews 22a have recently extended the investigation of the solubility of acids in the presence of weak acids. They have meas- ured the solubility of acids of varying strength and solubility in the presence of both strong and weak acids up to high concentrations. They include hydrogen sulphide, carbonic acid, boric, oxalic, succinic, trichloro- acetic, m-nitrobenzoic, 3-5-dinitrobenzoic, benzoic, picric and (3-naph- thalene sulphonic acids in the presence of hydrochloric acid ; and suberic, mandelic, succinic, oxalic, tartaric and boric acids in the presence of acetic acids up to concentrations of 10 normal added acid. They have also measured the solubility of boric, benzoic and salicylic acids in the presence of nitric acid. The solubility of all acids on addition of a strong acid is initially decreased. On addition of larger amounts of the strong acid the solu- bility, with a few exceptions, passes through a minimum. At high con- centrations of the added acid, the solubility increase is very marked in some cases while, in a few, the minimum is lacking. The initial decrease appears to be due to a repression of the ionization of the saturating acid. The stronger the acid, the greater is the initial depression, while in the case of very weak acids the initial depression is wanting. The minimum solubility of an acid is much lower than corresponds to the concentration of its un-ionized molecules in pure water. This is ascribed to the depres- sion of the solubility because of hydration effects accompanying the addi- tion of the strong acid. It may be noted that the maximum depression of hydrogen sulphide and carbonic acids is very low, amounting to only a few per cent. The final rise in the solubility curve is ascribed to the formation of compounds between the two acids at high concentrations. This view is supported by the results of conductance measurements which indicate the formation of complexes. This accounts for the widely divergent effect of strong acids on different weak acids at higher concen- trations. The solubility curves for weak acids in the presence of acetic acid exhibit a great variety of form. Here, the common ion effects at low concentration of added acid are approximately as might be expected. The effect of strong and weak acids on the un-ionized fraction of weak acids does not differ greatly from that observed in the case of non-elec- trolytes. For example, the solubility of hydrogen in water is only very slightly depressed due to the addition of acetic acid, but somewhat more strongly due to the addition of hydrochloric acid. In a normal solution of hydrochloric acid, the solubility depression in the case of hydrogen is 7 per cent and that in the case of the undissociated fraction of orthonitro- benzoic acid 10 per cent. The percentage depression in the case of sali- "• Kendall an9 Concentration of added salt in equivalents per liter. FIG. 56. Solubility of Lanthanum lodate in Water in the Presence of Other Electrolytes. It will be sufficient to consider, here, the solubility of a ternary elec- trolyte of the type MX2, which ionizes according to the equation: As we have already seen in connection with the solubility of binary elec- trolytes in the presence of other electrolytes, the experimental results in the case of fairly dilute solutions are. in reasonably good agreement with the assumption that the concentration of the un-ionized fraction of the salt, as well as the ion product, remains constant on the addition of other electrolytes. If a similar assumption is made in the case of a ternary electrolyte, it leads to the following equations for the solubility of the salt in the presence of an electrolyte with a common univalent ion, a common divalent ion, and without a common ion. With a common univalent ion, (71) S- - where K is the ionization constant of the reaction given above. In this equation the solubility appears as an explicit function of the concentra- 276 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS tion of the common ion X~. In order to determine the concentration of the common ion in the mixture, it is obviously necessary to know the ionization functions for the various electrolytes concerned. While these functions are not known, a fair approximation could probably be obtained by assuming one of the functions given in Chapter IX. This would necessarily involve the further assumption that intermediate ions are not present. On the addition of a common divalent ion, the solubility is given by the equation: (7*\ I'2) — 2 M++ > while, on the addition of a salt without a common ion, M~Y- "» -- ~' — ' where Kf is the constant of the reaction MY2 = M" + 2Y-. Since different electrolytes of the same type are ionized to practically the same extent in water, it follows that, in the mixture containing a salt without a common ion, the equivalent concentrations X~ and M++ will not differ greatly from each other. The first two terms of Equation 73, therefore, will remain constant on the addition of a salt without a common ion. The last term of this equation, however, will obviously increase as the concentration of the ion Y~, due to the addition of a salt NY, increases. It is evident, therefore, that according to this equation the solubility of a ternary salt should be increased upon the addition of a salt without a common ion. On the other hand, comparing Equations 71 and 72, it is evident that the addition of a common univalent ion will cause a much greater solubility depression than will the addition of a common divalent ion, since the concentration of the univalent ion appears in the denominator with the exponent 2, while that of the divalent ion appears in the denominator with the exponent %. Roughly, this is in agreement with observations. As may be seen by reference to Figure 53, the addition of a salt with a common univalent ion causes a much greater depression than does the addition of a salt with a common divalent ion. As we have already seen, the solubility of a binary salt decreases as the reciprocal of the concentration. of the common ion. The solubility curve of a binary electrolyte, therefore, should lie intermediate between HETEROGENEOUS EQUILIBRIA 277 that of a ternary electrolyte in the presence of a common univalent ion and in that of a common divalent ion. Harkins34 has calculated solubility curves on the assumption that (74) Sm (S + C)n = 1, where ra and n are the number of ions resulting from the dissociation, while S is the solubility of the salt and C is the concentration of the added salt. The curves calculated on these assumptions correspond roughly with the observed curves. An exact correspondence is not to be expected, since the assumptions made in calculating these curves are obviously only roughly fulfilled. The equations given above obviously do not account for the form of the curves at higher concentrations, particularly for the increase in the solubility of a ternary salt on the addition of larger amounts of a salt with a common divalent ion. According to Harkins this increase is due to the formation of an intermediate ion MX* according to the reaction: M« + X- = MX*. On this assumption the solubility on the addition of a salt with a com- mon univalent ion is given by the equation: (75) S where K^ is the constant resulting from the reaction: MX* + X- = MX2. It is evident, from this equation, that, if intermediate ions MX* are formed, then, on the addition of an electrolyte NX, the solubility depres- sion will be smaller than in the case where no intermediate ions are formed. From this equation, it follows, also, as may readily be seen by differentiating with respect to the concentration of the common ion X", that with increasing concentration the solubility must decrease irre- spective of the values of the constants K and K±. If a salt of the type MY2 is added, the solubility is given by the equation: (76) S = MX, + XM Here K2 is the equilibrium constant resulting from the reaction: M++ + X- = MX+. "Harkins, Joe. cit. 278 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS It is evident that: (77) K = K1K2. An inspection of the above equation shows that, owing to the formation of the intermediate ion MX+, the value of whose concentration is given by the second term of the right-hand member, the solubility is increased due to the formation of the intermediate ion. With increasing value of M++, this term may become sufficiently great to overbalance the effect of the last term of the right-hand member. This is more readily seen on differentiating Equation 76 with respect to the concentration of the common ion M++, which leads to the equation : tm dS _£y*MX2W 1 1 \ dM++" M++% \2K2 2M+V* The solubility will be a minimum when: (79) 1 Obviously, the concentration of the common divalent ion M++ at the minimum point of the solubility curve is equal to the equilibrium con- stant K2. If this constant is small, then the minimum point will lie at a low concentration; whereas, when this constant is large, the minimum •point will lie at high concentrations. In other words, when K2 is large the fraction of salt present in the form of intermediate ions MX+ is relatively small; whereas when Kz is small this fraction is relatively large and the minimum point accordingly appears at low concentrations. It may be noted, in this connection, that the solubility curves of lead salts exhibit a pronounced minimum at relatively low concentrations. That for lead iodate in the presence of lead nitrate is in the neighborhood of 0.04 N ; that for lead chloride in the presence of lead nitrate is at approxi- mately the same concentration. Silver sulphate, in the presence of potas- sium sulphate, exhibits a minimum in the neighborhood of 0.1 N. Cal- cium sulphate exhibits minima in the neighborhood of 0.15 N in the presence of salts with a common S04~~ ion. In the case of salts with a common Ca+* ion, this minimum does not appear. The difference in the behavior of calcium sulphate in the presence of a common positive or negative divalent ion may be due to various causes, since in this case there is involved the formation of two different types of complexes. Considering the behavior of uni-divalent salts, it is evident that those salts which exhibit a pronounced tendency to form complexes, such as lead salts for example, likewise exhibit a pronounced minimum in the solubility curve in the presence of a common divalent ion. HETEROGENEOUS EQUILIBRIA 279 The simple explanation offered above must obviously not be pressed too far, particularly in the more concentrated solutions. On the addi- tion of a salt of the type MY2, there is a possibility that complexes of the form MXY may result. In all likelihood, however, at low concen- trations, these are not present to a large extent. While solutions of highly soluble salts, as well as solutions of non- electrolytes, exhibit a great variety of properties which bring out clearly the individual characteristics of the various substances involved, in solu- tions of difficultly soluble salts, the solubility curves show remarkable regularities, indicating that the observed behavior of these solutions lies in properties common to electrolytes in general, at these concentrations. The solubility effects are readily explained on the assumption that the concentration of the un-ionized fraction, as well as the ion product, remains substantially constant on the addition of a second electrolyte. The great decrease in the concentration of the un-ionized fraction, which many investigators have assumed to be correct, is doubtful. It appears probable that this result follows from a failure of the applicability of the isohydric principle to mixtures of electrolytes. The solubility in- crease observed in the case of salts of higher type on the addition of salts with a common polyvalent ion makes it appear probable that intermediate ions are present in relatively large amounts in solutions of salts of higher type at higher concentrations. Heterogeneous equilibria from a thermodynamic point of view will be discussed in another chapter. Chapter XI. Other Properties of Electrolytic Solutions. 1. The Diffusion of Electrolytes. If a concentration gradient exists in an electrolytic solution, diffusion will take place. The rate of diffusion of an ion is the greater the greater its mobility. However, in view of the fact that the ions of an electrolyte are oppositely charged, the dif- fusion of these ions will not be independent of one another. Nernst1 has derived an expression for the diffusion coefficient in dilute solutions of electrolytes. The diffusion coefficient is thus given by the equation: (80) D = 2UV u + v XRT, in which U and V are the ionic mobilities. If the electrolyte is not completely ionized, the neutral molecules also will diffuse, and their rate of diffusion will, in general, differ from that of the ions. The diffusion coefficient of various electrolytes has been measured by Arrhenius and more extended measurements are due to Oholm.2 In Table CX are given values for the diffusion coefficients of different electrolytes in water at 18°. TABLE CX. DIFFUSION COEFFICIENTS OF ELECTROLYTES IN WATER AT 18°. Cone. NaCl KOI LiCl KJ HOI CH2COOH NaOH KOH 0.01 .... .... 1 .170 1 .460 1.000 1.460 2 .324 0.930 1.432 1.903 0.02 .... 1 .152 1 .431 0.980 1.428 2 .285 0.910 1.404 1.889 0.05 .... .... 1 .139 1 .409 0.971 1.412 2 .251 0.895 1.386 1.872 0.10 .... .... 1 .117 1 .389 0.951 1.391 2 .229 0.884 1.364 1.854 0.20 .... 1 .098 1 .367 0.929 1.380 2 .202 0.871 1.342 1.843 0.50 .... 1 .077 1 .345 0.919 1.372 2 .188 0.856 1.310 1.841 1.00 .... 1 .070 1 .330 0.920 1.366 2.217 0.833 1.290 1.855 2.00 1 .320 0.928 . . . , . . 1.259 1.892 2.8 .... 1.064 1.434 t 3.6 1 .338 , . , . . . t . 9 , > > 4.2 . . 0.956 . . . . . . . . , . 5.5 1 .065 . . . . 1.549 . . . . . . . . » Nernst, Ztschr. f. phi/a. Chem. 2, 613 (1888). » Oholm, Ztachr. }. phya. Chem. 50, 309 "(1905); Meddel. Vet.-Akad's. Nobelinstitut, Vol. «, No. 22 (1911). 280 OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 281 It will be observed that in the more dilute solutions the diffusion coefficient is the greater, the greater the conductance of the electrolyte. Thus, at 0.01 normal, the diffusion coefficient of HC1 is 2.324, of KOH 1.903, of KC1 1.460, and of LiCl 1.000. As the concentration increases, the diffusion coefficient in the more dilute solutions decreases. This may be accounted for if we assume that as the concentration increases the ionization decreases, and that the diffusion coefficient of the neutral molecules is smaller than that of the ions. At higher concentrations the influence of viscosity change must be taken into account. In the case of most salts, the viscosity increases with increasing concentration, and it is to be expected that, owing to this factor, there will be a decrease in the diffusion coefficient at higher concentrations. The increase in the value of the diffusion coefficient at very high concentrations cannot be accounted for in this way. If, however, the ions are hydrated, then it is not improbable that at the higher concentrations, where the number of salt molecules becomes comparable with that of the number of water molecules, the degree of hydration of the ions decreases, as a result of which their mobilities may be expected to increase. Of particular significance are the results obtained by Arrhenius8 for the diffusion of electrolytes in the presence of other electrolytes. If the diffusing electrolyte has a rapidly and a slowly moving ion, the dif- fusion of the rapidly moving ion is hindered, owing to the drag exerted upon it by the charge on the more slowly moving ion. If, now, another electrolyte is added, the rate of diffusion of the first electrolyte will be in- creased, since the diffusion of the oppositely charged ion may be compen- sated by the diffusion of another ion in the opposite direction. For exam- ple, the diffusion coefficient of a 0.52 N solution of HC1 in water at 12° is 2.09, while that of the same electrolyte in 3.43 N solution of NH4C1 is 4.67, and in a 0.375 N solution of KC1 3.89. Evidently, on adding am- monium chloride to the hydrochloric acid solution, the rate of diffusion is greatly increased due to the fact that the motion of the Cl~ ions in the direction of the concentration gradient is compensated by a motion of the NH4+ ions in the opposite direction. This phenomenon is quite general, as may be seen from Table CXI. The influence of the added electrolyte on the diffusion coefficient is extremely marked. For example, the addition of 0.028 N KC1 to a 1.04 N solution of HC1 raises the diffusion coefficient from a value of 2.09 to 2.27, or approximately ten per cent. Effects such as these afford perhaps the strongest grounds we have for believing that electrolytes are ionized. On the other hand, they do not enable us to determine to what extent •Arrhenius, Ztschr. /. phyg. Chem. 10, 51 CL892). 282 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS TABLE CXI. DIFFUSION COEFFICIENTS OF ELECTROLYTES IN THE PRESENCE OF OTHER ELECTROLYTES IN WATER AT 12°. Diffusing Electrolyte 1.04-n HC1 0.52-n HC1 0.55-n HNCX 0.54-n NaOH 0.98-n KOH 0.49-n KOH Added Electrolyte None 0.67-n NaCl 0.1-n NaCl 0.75-n KC1 0.25-n KC1 0.085-n KC1 0.028-n KC1 0.75-n BaCl2 0.085-n BaCl2 2-n NH4C1 0.25-n NH4C1 None 0.042-n KC1 0.375-n KC1 3.43-n NH4C1 None 0.1-n KN03 0.5-n KN03 0.5-n NaNOs None 0.25-n NaCl 0.067-n NaCl 0.25-n Na2S04 1-n NaN03 1-n NaC2H302 0.2-n NaN03 0.2-n NaC2H30, 3-n NaCl 1-n NaCl None 0.1-n KC1 1-n KC1 None 0.05-n KN03 0.5-n KN03 0.5-n KC1 Diffusion Coefficient at 12° 2.09 3.51 2.50 4.22 3.08 2.51 2.27 4.12 2.46 4.50 2.99 2.09 2.46 3.89 4.67 1.91 2.59 3.70 3.39 1.15 1.90 1.51 1.80 2.20 1.78 1.80 1.60 1.98 2.30 1.72 1.92 2.57 1.70 1.91 2.54 2.57 ionization has taken place in a given solution. These facts, while they do not enable us to distinguish between partial and complete ionization, supply abundant evidence that salts are ionized to a large extent. OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 283 2. Density of Electrolytic Solutions. According to the ionic theory, the properties of dilute solutions of electrolytes are additive functions of the concentrations of the ions and of the un-ionized molecules. If Ji is the value of a given property of such solutions and (81) then: (82) kn = Ay + B(l — Y), where Jt0 is the value of the property at zero concentration, jc is its value at the concentration C, y is the ionization of the electrolyte at this con- centration, and A and B are constants relating to the ions and the un- ionized molecules respectively. Ajt is evidently the percentage equivalent property change due to the electrolyte at the concentration in question. In applying this equation, it is tacitly assumed that the property is inde- pendent of any interaction between the ions and the un-ionized molecule, otherwise a term should be added involving the concentration and the equation would no longer be linear. Equation 82 may evidently be written: (83) Arc = B + A'y, where (84) A' = A — B. Ajt is thus a linear function of y, and from the known values of An the values of y may be obtained. Such additive properties lend themselves to a determination of YJ and a comparison with the value of y as derived from conductance measurements might be expected to thus serve as a check on the correctness of these values. A simpler method of com- parison consists in plotting the measured values of A:t against those of y as derived from conductance measurements.4 If the two methods yield concordant values of y, the graph should be a straight line. Unfortunately, this method of checking the results of conductance measurements is restricted in its application owing to the fact that in many cases the value of a given property for the un-ionized fraction does not differ appreciably from the sum of those of its constituent ions. This appears to be the case, for example, with many of the optical properties of electrolytic solutions. Many properties of atomic and molecular complexes depend upon the * « Heydweiller, Ann. d. Phya. 37, 739 (1912) ; ibid., SO, 873 (1909) ; Magie, Physical Kevvew 25, 171 (1907). 284 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS number and the distribution of the charges within these complexes. If these complexes are relatively stable, as we know the ion complex to be, then the properties of the complexes will be relatively independent of the manner in which two or more of them are grouped together. We should not, therefore, expect any considerable change in those properties of elec- trolytes which depend primarily upon the distribution of the charges on the ions; for the ionic complexes exist practically unchanged in the un-ionized molecules whatever their state; that is, whether in solution or as liquid, solid, or, perhaps, even vapor. Only such properties as depend on the field due to the ions may be expected to exhibit a marked differ- ence for the ions and the un-ionized molecules. In the un-ionized state the two ions form an electrical doublet with a closed field, while in the ionized state the field is open. Those properties, therefore, which depend upon the field in the immediate neighborhood of the ions should give evi- dence of the existence of the ions and of the un-ionized molecules, should these molecules be present in solution. Foremost among the properties of this class we should expect the den- sity of solutions to be included. It is well known that the solution of salts in water is accompanied by a marked volume contraction, which is the greater the lower the concentration of the solution. According to Drude and Nernst,5 a volume change is to be expected as a result of the action of the ionic charge on the molecules of the surrounding medium. Obviously, other effects may come into play, such as the hydra- tion of the ions, etc. The density of aqueous solutions has been studied from this point of view by Heydweiller.6 He found that, with a few exceptions, the density change of electrolytic solutions may be represented as a linear function of the ionization corresponding to Equation 82. It is true that the pre- cision of the density measurements is not always great and often the concentration range over which the equation has been tested is not large. Then, again, the lowest concentrations up to which the relation has been tested is not much below 0.1 N. It is a remarkable fact, however, that for a number of electrolytes the density may be expressed as a linear function of the ionization over large concentration ranges, as, for example, in the case of zinc chloride, calcium chloride and potassium hydroxide. The constant B is the equivalent percentage density change due to the un-ionized salt. If it be assumed that the un-ionized molecules in the solution occupy the same volume as they do in the pure condition as salts, then the value of the constant B may be calculated from the known den- • Drude and Nernst, Ztschr. f. pJiys. Chem. 15, 79 (1894). • Heydweiller, loc. cit. OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 285 sity of the salt. In Table CXII are given values of BC, so calculated, together with values of B& as experimentally determined by Heydweiller for different salts in water. TABLE CXII. COMPARISON OF EXPERIMENTAL AND CALCULATED VALUES OF B. Salt Be Bc Salt Be BC NH4I 8.38 8.55 LiN03 3.71 4.02 NaCl 3.36 3.15 LiCl 2.06 2.17 NaN03 4.88 4.74 Nal 10.45 10.77 KN03 5.21 5.30 1/2 CaI2 .... 11.55 11.70 1/2 K2S04 . .. 5.73 5.45 1/2 BaBr2 . . . 11.80 11.75 KC103 6.73 7.00 1/2 BaI2 15.56 15.58 AgN03 13.28 13.04 1/2 CdN03 . . 9.21 9.15 From an inspection of the table it appears that the values of Be and # are in remarkably good agreement. The differences probably do not G exceed the experimental error. The values calculated in this way, how- ever, do not in all cases agree as well as those appearing in the above table. In the case of salts which show a marked tendency to form hydrates, Heydweiller has employed the density of the hydrated salt rather than that of the anhydrous salt and has obtained excellent agree- ment between the observed and the calculated values of the constant B, while in another group of electrolytes the values of B as calculated are not in close agreement with those as measured. This is illustrated in the following table. TABLE CXIII. COMPARISON OF EXPERIMENTAL AND CALCULATED VALUES OF B. Salt Bp Br Salt fl fl \j c NH4C1 0.42 1.83 KC1 2.94 3.71 NH4Br 4.45 5.69 KBr 6.65 7.48 NH4NO, 2.60 3.39 KI 10.56 11.20 1/2 N2H8S04 . 2.49 2.87 KCNS 3.70 4.57 Lil 9.53 10.10 1/2 K2Cr04 . . 5.83 6.16 LiBr 5.84 6.19 RbCl 6.24 7.79 CsCl 10.36 12.62 While there is a marked deviation between the values of B as derived from the experimental curves and as calculated from the density of these 286 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS salts, nevertheless, the parallelism existing between the two sets of values is unmistakable. The constants A are the equivalent percentage density changes due to the ions. This property should be an additive one. If this is true, the difference in the values of the constant A for salts with a common ion should be constant. Heydweiller has calculated the value of the constants A for different ions. To illustrate how nearly the additive condition is fulfilled by the experimental values of the constants, the fol- lowing values are given. Table CXIV-A relates to a series of sodium salts and Table CXIV-B to a series of nitrates. In the first column is given the symbol of the negative ion of the salt, in the second column the experimentally determined value of the constant A, in the third column the value of the constant Aa for the anion, and in the last column the difference A — Aa = for the cation. similar values are given for those salts. In the case of the nitrates A. C2H302 . F Sodium Salts A Aa 4.44 3.04 4.56 3.16 7.33 5.95 5.95 4.54 4.38 3.02 8.08 6.68 11.52 10.27 4.88 3.40 7.09 5.77 7.72 6.38 C103 .... N03 .... Cl Br I OH 1/2 S04 . 1/2 Cr04 TABLE CXIV, SHOWING THE ADDITIVE NATURE OF A. 1.40 1.40 1.38 1.41 1.36 1.40 1.25 1.48 1.32 1.34 Mean 1.38 H .... B. Nit A . . 347 .rates Aa — 1.05 — 0.35 1.38 10.02 — 0.98 2.10 6.32 1.33 3.61 5.43 3.63 2.02 4.38 6.54 10.34 Li . . 420 Na ... . . 5.95 Ag .... .. 14.61 NH4 ., K . . 3.61 . . 6 72 Rb ... . . 10.75 1/2 Mg 1/2 Zn 1/2 Cd 1/2 Cu 1/2 Ca 1/2 Sr 1/2 Ba 1/2 Pb . 5.82 .. 8.09 .. 9.94 ., 8.14 ., 6.57 . . 8.98 . .(10.76). . . 14.87 4.52 4.55 4.57 4.59 4.59 4.62 4.43 4.49 4.48 4.51 4.51 4.55 4.60 (4.22) 4.53 Mean 4.54 It will be noted that the values of the constants A and Aj show remark- CL K, ably small variations. They thus fulfill the condition of additivity. Only a few electrolytes, such as magnesium sulphate, sodium car- OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 287 bonate, and sulphuric acid, exhibit density changes which do not vary as linear functions of the ionization. The cause of the variation in these cases is uncertain, but may be due to the formation of complex ions, to hydrolysis, etc. The volume changes of electrolytic solutions in methyl alcohol have likewise been examined.7 The results obtained correspond very closely with those obtained in the case of aqueous solutions. The density change due to ionization, which is obviously equal to the difference A — B, is considerably greater in methyl alcohol solutions than it is in water. This is not surprising, since the dielectric constant of this solvent is much smaller than that of water. We should expect that, if the density change is the result of the action of the field due to the charge on the surrounding solvent molecules, the density change would be the greater the smaller the dielectric constant of the medium. In order to finally establish the additive nature of the density changes of electrolytic solutions, it will be necessary to extend the measurements to much lower concentration. Methods exist for measuring the densities of dilute solutions with sufficient precision to make it possible to extend the measurements to concentrations approaching 10~3 N. Until this is done, the results of density measurements must remain more or less in doubt. The concordance of the results so far obtained, however, would appear to justify further efforts along these lines. Some measurements have been made by Rohrs8 on the density of solutions in ethyl alcohol and acetone. The interpretation of the results is uncertain owing to the small change in the ionization over the con- centration intervals for which measurements were made. 3. Velocity of Reactions as Affected by the Presence of Ions. The speed of many reactions, such as the inversion of sugars and the hydroly- sis of esters, for example, is greatly increased on addition of acids. Ostwald 9 showed that the catalytic effect of different acids is the greater the stronger the acid. It appeared, at first, that the catalytic effect of the acids provided an independent method for estimating the concentration of the hydrogen ions in an acid solution. Further investigations,10 how- ever, showed that the catalytic action is likewise dependent upon other factors, such as the presence of other substances and especially electro- lytes. Thus, the catalytic action due to a strong acid should be reduced on the addition of a salt of this acid. While such a reduction takes place 7 Ruthenberg, Inaugural Dissertation, Rostock (1913). •Rohrs, Ann. d, Phys. 57, 289 (1912). 9 Ostwald. J. prakt. Chem. 28, 449 (1883) ; 29, 385 (1884) ; 31, 307 (1885). "Arrhenius, Ztschr. f. phys. CJiem. 5, 1 (1890). 288 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS in the case of the weaker acids, in that of the stronger acids the catalytic action is actually increased. It is now commonly accepted that the un-ionized acid molecules, as well as the ions themselves, influence the rate of these reactions. Ac- cording to this hypothesis, the reaction constant is given by an equation of the form: (85) K = KiCh+KnCn, where K^ and Kn are the velocity constants for the ions and the un-ion- ized molecules respectively and C^ and Cn are the concentrations of the ions and the un-ionized molecules. The constant Kn is in general deter- mined by adding, to a dilute solution of an acid, a salt of the same acid. Under these conditions, the ionization of the acid is practically repressed to zero and it is assumed that the residual catalytic action is due entirely to the un-ionized acid molecules. The results of many experiments on a great variety of reactions are, on the whole, in good accord with this hypothesis. It should be noted, however, that the ratio of the constants Kn to K- is a function of the strength of the acid, as well as of other factors. The weaker the acid, the smaller is, in general, the value of this ratio. In the case of the strong acids, the value of this ratio may be unity or even greater. In the following table are given values of the inversion coefficient for aqueous solutions of cane sugar, according to Ostwald, at 25°. The concentration of the acids was in all cases 0.5 N and the values given for the constants are relative to that of hydrochloric acid taken as unity. t TABLE CXV. INVERSION COEFFICIENTS FOR DIFFERENT ACIDS. Hydrochloric acid 1.000 Trichloroacetic acid 0.754 Nitric acid 1.000 Dichloroacetic acid 0.271 Chloric acid 1.035 Monochloroacetic acid . . . 0.0484 Sulphuric acid 0.536 Formic acid 0.0153 Benzenesulphonic acid 1.044 Acetic acid 0.0040 It is clear that the catalytic action of the acids is intimately related to their strength. For the purpose of investigating the effect of the neutral molecules upon reactions, solutions in non-aqueous solvents are in many respects better adapted than those in water, since the ionization of the acid in OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 289 these solutions is much smaller than in water. Numerous experiments have therefore been carried out in methyl and ethyl alcohols. In the following table are given values of the esterification constant for different acids in methyl alcohol, according to Goldschmidt and Thueson,11 at 25°. The numerical values for 0.05 HC1, 0.1 picric acid and 0.1 trichlorobutyric acid are given in the second, third and fifth columns respectively, while in the fourth and sixth columns are given the values for picric acid and trichlorobutyric acid of the strength given in the presence of 0.15 picrate and 0.1 butyrate respectively. TABLE CXVI. ESTERIFICATION CONSTANTS IN METHYL ALCOHOL FOB DIFFERENT ACIDS IN THE PRESENCE OF OTHER ACIDS AS CATALYZERS. Catalyzing acids Esterifying acid HC1 C6H3N307 Picrate C4C13H602 Butyrate Phenylacetic acid . . 2.23 0.265 0.047 0.0167 0.00102 Acetic acid 4.86 0.590 0.100 0.0375 0.00172 n-Butyric acid 2.23 0.277 0.0535 0.0177 0.00097 i-Butyric acid 1.55 0.196 0.0353 0.0129 0.00074 i-Valeric acid 0.583 0.0735 0.00144 0.00475 0.00029 From this table it may be seen that the catalytic action of an acid is the greater the stronger the acid. Nevertheless, the catalytic action of an acid is not proportional to the concentration of the hydrogen ion. The ratio between the velocity constants for 0.05 N hydrochloric acid and 0.1 N picric acid varies between 7.78 and 8.91 for the different acids, while the ratio of the ion concentrations is 6.56. So, also, the ratio of the hydrogen ion concentrations for 0.1 N and 0.01 N picric acid is 3.64. The ratio of the esterification constants between these concentrations is 3.90. It will be observed that, on the addition of sodium picrate to picric acid, the velocity constant varies approximately in the ratio of 1 to 6, while, on the addition of trichlorobutyrate to butyric acid, the velocity constant changes in the ratio of 1 to 18. It should be stated in this con- nection that the values given for the constants of picric acid and tri- chlorobutyric acid in the presence of other salts represent practically the minimum limiting values which are independent of the concentration of the added salt. In other words, the salt added is sufficient to completely repress the ionization of the acid. Accordingly, the residual catalytic action of the acid must either be due to the un-ionized molecule or to some other agency. The weaker the acid, the smaller, relatively, is the "Goldschmidt and Thueson, Ztschr. f. phya. Chem. 81, 30 (1913). 290 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS catalytic power of the neutral molecule. The values of the constants K- and K may be determined from a series of measurements. In the case of the examples given above the following values of K^C^ were obtained for trichlorobutyric acid as catalyzer at concentrations of 0.1 and 0.05 N. TABLE CXVII. VELOCITY COEFFICIENTS FOR THE HYDROGEN ION OF TRICHLOROBUTYRIC ACID IN THE ESTERIFICATION OF DIFFERENT AdDS. Con- centration Phenyl- of Acid acetic Acetic n-Butyric i-Butyric i-Valeric 0.1 0.0157 0.0358 0.0167 0.0122 0.00448 0.05 0.0109 0.0247 0.0114 0.00826 0.00304 Ratio .... 1.44 1.45 1.47 1.48 1.47 It is seen that the ratio of the velocity coefficients calculated for the ions between 0.1 and 0.05 N is 1.46. According to conductance measure- ments the ratio of the ionization of this acid at these two concentrations is 1.42. Taking into account the numerous possible sources of error, the agreement appears fairly satisfactory. Kn In the following table are given values of K and — - for hydrochloric K* acid, acetic acid, and the chloro- substitution products of this acid.12 TABLE CXVIII. T7- VARIATION OF THE RATIO -=^ FOR DIFFERENT ACIDS. Ki Acid | *» x? ** 1 Hydrochloric acid 780 1.77 Dichloroacetic acid 220 0.50 5.1 X 10'2 a-p-Dibromopropionic acid 67 0.152 1.67 X 10~2 Monochloroacetic acid 24.5 0.055 0.155 X 10'2 Acetic acid 1.5 0.0034 0.0018 X 10'2 Similar results have been obtained by Taylor and by Ramstedt.13 It is clear that the value of Kn increases with the strength of the acid. As "Dawson and Fowls, J. Ghent. Soc. 10& 2135 (1913). "Taylor, Meddel K. Vet.-Akad's. Nvbelinstitut, Vol. 3, No. 1 (1913) ; RamsteIdem, Ztschr. f. phys. Chem. 63, 370 (1908). 294 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS Wave Length. 3660 700 800 SCO 100 80 SO 31,6 25 20 16 12,6 10 S 43 S + I 1 ,xo 4- X + t 1 0 1 • • •f Wave Length. 4000 100 200 300 4400 100 so €3,1 SO 20 16 12.6 10 FIG. 57. Absorption Curve of Tri- FIG. 58. Absorption Curves of Aqueous chloroacetic Acid in Water(. ) and in Petroleum Ether (X), and of Po- tassium Trichloroacetate in Water (+), and Barium Trichloroacetate in Water(o) as a Function of the Wave Length. Solutions of NH4(.), K(-f), Ba(X), and Ca(o) Trichloracetates. OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 295 It will be observed, from this table, that the values of the extinction coefficients for chromic acid and potassium bichromate are identical within the limits of experimental error. The absorption here is due to the negative ion. It will be noted that the absorption, moreover, is independent of the concentration, which indicates that the negative ion in the un-ionized molecules possesses the same optical properties as in its free state; that is, in its conducting state. The absorption coefficients of the chromate ion are not affected by the presence of acid, but they are slightly affected by the presence of bases. In the following table are given values of the extinction coefficients for potassium bichromate in the presence of varying amounts of potassium hydroxide for the wave length X = 486. TABLE CXX. ABSORPTION COEFFICIENTS OF SOLUTIONS OF POTASSIUM BICHROMATE IN THE PRESENCE OF POTASSIUM HYDROXIDE. Wave Length A = 486. Cone. Base 0 1/2000 1/100 1/1 f 50 89.9 84.3 83.7 81.7 V 100 89.0 84.0 83.0 82.3 [200 89.0 83.6 82.0 81.4 It will be observed that, on the addition of potassium hydroxide, the absorption of potassium bichromate is affected to a small but measurable extent. Hantzsch has shown that this is due to the formation of other chromophore groups. In different solvents, the chromates have identical values of the ab- sorption coefficients, as may be seen from the following table. TABLE CXXL ABSORPTION COEFFICIENTS OF SODIUM CHROMATE IN METHYL ALCOHOL AND IN WATER. A, = 486. V H20 CH3OH 2000 229 231 5000 227 233 The results obtained from a study of other chromophore groups are similar to those obtained in the case of the chromates, and need not be given here. 296 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS Hantzsch 21 has also studied the absorption of salts of certain organic chromophore groups. In certain of these salts, marked changes have been found and Hantzsch has been able to show that in these cases the change is due to a shift in the equilibrium between two chromophore groups. In the case of salts of certain organic chromophores, however, small differences have been found for which an adequate explanation has not thus far been given.22 In the following table are given values for the equivalent extinction coefficients for different salts of acetyloxindon. TABLE CXXII. EXTINCTION COEFFICIENTS FOR DIFFERENT SALTS OF ACETYLOXINDON IN WATER. X = 436. Concentration: 1/100 1/250 1/1250 1/2500 1/5000 Thickness of layer: 1 mm. 1 cm. 2 cm. 5 cm. 10 cm. Sr . ......... 400 388 390 384 Li ............ .. .. 347 350 358 350 Salt Na .............. 388 385 390 382 380 Cs .............. 383 391 387 380 390 Tl ............... 389 385 381 390 394 In aqueous solutions, the absorption spectra of the different salts of this acid are very nearly identical with the exception of the lithium salt, whose values appear to be a little low. In the case of all salts, the extinc- tion coefficient is independent of the concentration. While the extinction coefficients for the oxindon salts in aqueous solu- tions are the same for all cations, with the possible exception of lithium, in solutions in ethyl alcohol a marked difference has been found. In Table CXXII are given values of the extinction coefficients of different salts in ethyl alcohol. It will be observed that here, again, the value of the co- efficient is independent of the concentration, but that it varies with the na- ture of the positive ion. This variation is unquestionably far in excess of any probable experimental error. The difference might be ascribed to a difference in the optical properties of the un-ionized molecules, and it is known that in these solutions the ionization of these salts is relatively low. However, over the concentration ranges in question, the ionization for a given salt varies considerably, which makes it difficult to account for the constancy of the coefficient at different concentrations. While Hantzsch is » Hantzsch, Ber. 43, 82 (1910). Ztfic/w. /. phya. Chem. 8}f 321 (1913). OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 297 TABLE CXXIII. EXTINCTION COEFFICIENTS FOB SALTS OF ACETYLOXINDON AT DIFFERENT CONCENTRATIONS IN ETHYL ALCOHOL. X = 436. Concentration: 1/100 1/1000 1/1000 1/2500 1/5000 Thickness: 1cm. 1cm. 2cm. 5cm. 10cm. Ca . 214 220 226 217 Sr 230 227 232 231 Ba 230 238 240 236 Li 259 263 255 250 258 a 325 330 328 325 322 K 339 338 333 325 340 Rb 329 327 329 343 341 Cs 390 409 393 383 395 Tl 325 328 337 330 inclined to account for these variations on the basis of a slight rearrange- ment in the chromophore group, somewhat similar to that established in the case of the salts of the oximidoketones, a thoroughly satisfactory ex- planation of this behavior of the above solutions does not exist. From the foregoing, it appears that, in solutions of salts which have stable chromophores, the absorption spectra are independent of the con- dition of the salt, and accordingly we may conclude that, whether an ion is combined or uncombined, the absorption spectrum remains unchanged. Where changes occur, reactions are to be looked for, the nature of which, however, has not been established in all cases. 5. The Electromotive Force oj Concentration Cells. The properties of a solution are determined by the values of the variables which fix its state. If the solution is subject to the action of external forces, its prop- erties will vary accordingly. Under such conditions the thermodynamic potential of the dissolved substance suffers a change and electromotive forces naturally arise under suitable arrangement of solutions and elec- trodes. Such, for example, is the case when solutions are subjected to centrifugal action.23 We shall, however, confine ourselves here to a con- sideration of electromotive forces arising as a result of concentration dif- ference. Wherever we have a surface of discontinuity between two electrolytes, or between an electrolyte and a metal, an electromotive force will in general arise. For a system under the action of external forces, the condition for «• Tolman, Proo. Am. Acad. tf, 109 (1910). 298 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS equilibrium requires that the total potential shall be the same throughout the system. The total potential is defined by the equation: (88) M' = M + P, where M' is the total potential of a given molecular species, M is its thermodynamic potential, and >P is the potential due to the external forces. The thermodynamic potential may be expressed as a function of the concentration by means of the equation: (89) M = RTlogC + i + J, where i is a function independent of concentration, while J is a function which, in general, involves all the independent variables of the system. For a concentration cell operating between the concentrations Cx and C2, we have: (90) (M+ + M-) 2 — (M+ + M-) ± = — W, where M+ and M~ are the thermodynamic potentials of the ions of a given electrolyte and W is the work performed by the cell when one equivalent (or mol) of the electrolyte is carried from the first solution to the second. Introducing Equation 89, and writing for W its value in electrical units, we have: (91) -rEF = RT log£^ + (2J.)2- (27^, Uj O1 where 2,7- = J+ + J~> F is the electrochemical equivalent, E the elec- tromotive force, and r the number of equivalents of electricity flowing per equivalent of electrolyte transferred. The value of r depends upon the number of charges v associated with a molecule of the electrolyte and the nature of the electrode process. For a concentration cell with transference, (92) ' r — v/N, where N is the transference number of the ion to which the electrodes are impermeable. For cells without transference, N = 1. The electro- motive force E is that due to the transfer of the electrolyte alone, and, if other processes are involved, the measured electromotive force must be corrected for these processes before introducing into Equation 91. At higher concentrations, in view of the fact that the ions are hydrated, solvent will be carried from a solution of one concentration to that of another. This process involves work and the electromotive force, as measured, must be corrected accordingly. In general, since the relative OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 299 hydration of the ions is not known at the concentrations in question, such corrections cannot be made. The same considerations hold true of the reactions in which the electrolyte is concerned, such as the formation of intermediate or complex ions, complex molecules, etc. The electromotive force of a concentration cell may likewise be expressed in terms of the concentrations of the un-ionized fraction, which leads to the equation: (93) -rEF = RTloS^+J^-JUi. If the conditions of dilute systems are fulfilled, then: (94) J* = J- = Ju = Q, in which case the electromotive force of the cell may be calculated, if the concentration of the ions or of the un-ionized molecules is known. Equation 93, in this case, reduces to: (95) This is the equation first developed by Nernst.24 When the conditions for a dilute system are no longer fulfilled, the function J is involved in the expression for the electromotive force. This function thus measures the change in the potential of the electrolyte due to interaction between the various molecular species present in the mixture. The form of this function is not known, except in so far as it has been determined experimentally. The electromotive force of concen- tration cells has in many cases been employed for this purpose, since it affords a convenient and direct measure of the change in the potential of the electrolyte. In order to determine the true form of the function, however, it is necessary to know the concentrations C+ and C" or C . Except as the concentration of the ions may be determined from con- ductance measurements, no method appears to be available whereby the concentrations of the ions and of the un-ionized molecules in an electro- lytic solution may be determined. For practical purposes, the equation is often written: C Q2 (96) — rEF = RT log ^ + ZJ^ — 27 . «Nernst, Ztachr. f. phya. (Them. 2t 613 (1888). 300 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS If the electromotive forces have been determined experimentally, they may be expressed as a function of the total salt concentration Cg by means of this equation. In this case, the function «/,&i includes not only the change in the potential of the electrolyte due to the internal forces of the system, but it also includes a term which takes into account the change in the expression due to the substitution of GS for C+ and C~. The electromotive force of concentration cells for a great many elec- trolytes has been measured by various investigators.25 Only a few examples of the results obtained will be given here to show, in a general way, the manner in which the potential of an electrolyte varies with the concentration. In Table CXXIV are given values of the electromotive force of concentration cells with hydrochloric acid as electrolyte between silver chloride electrodes.26 The concentration of the concentrated solu- tion is in this case throughout 0.1 N. The concentration of the dilute solution is given in the first column, in the second column is given the value of the electromotive force as measured, in the third and fourth C • C columns are given the values ~ and -~, as determined from conduc- S2 C^2 tance measurements, and in the fifth and sixth columns the values of the same ratios as calculated from Equations 93 and 96, assuming ,7 = 0. TABLE CXXIV. ci cu COMPARISON OF VALUES OF — - AND — — FOE HC1 AS DERIVED FROM Liz C^2 CONDUCTANCE AND ELECTROMOTIVE FORCE MEASUREMENTS. (Cal.) (Cal.) Cii CUi Ci! Cu1 Concentration — ^— -^- ^— of dilute sol. E.M.F. Li2 ^uz Li* Luz 0.02 0.07617 4.78 7.76 4.57 20.9 0.01 0.10913 9.49 17.3 8.82 77.7 0.002 0.18711 46.7 112.5 41.8 1744.0 ci It will be observed that the calculated values of the ratio ~ do not Ciz differ greatly from those derived from conductance measurements, but "Linhart, J. Am. Chem. Soc. 39, 2601 (1917) ; ibid., Ifl, 1175 (1919) ; Ellis, ibid., S8, 737 (1916) ; Noyes and Ellis, ibid., 39, 2532 (1917) ; Lewis, Brighton and Sebastian, ibid., 39, 2245 (1917) ; Allmand and Polack, J. Chem. Soc. 115, 1020 (1919) ; Randall and Cushman, J. Am. Chem. Soc. 40, 393 (1918) ; Harned, ibid., 37, 2460 (1915) ; Loomis, Essex and Meacham, ibid., 39, 1133 (1917) ; Loomis and Acree, Am. Chem. J. 46. 632 (1911) ; Maclnnes and Beattie, J. Am. Chem. Soc. 42, 1117 (1920). »Tolman and Ferguson, J. Am. Chem. Soc. 34, 232 (1912). OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 301 cu that, on the other hand, the calculated values of the ratio -~^ differ enormously from those measured. The value of the ratio -^, as deter- Lu* mined from conductance measurements, may be somewhat in error owing to uncertainties in the value of A0. Since the value of 1 — y is relatively small, it is obvious that a small error in the value of A0 will have a large effect on the value of the ratio determined from conductance measurements. Nevertheless, it is evident that the electro- motive force as measured is much greater than that calculated according to Equation 95. In the case of other electrolytes similar results have been obtained. C- In the following table are given values of -^ as calculated from the °t2 electromotive force of potassium chloride concentration cells.27 The concentrations of the solutions are given in the first two columns, the values found and calculated for the ion ratios are given in the last two columns. TABLE CXXV, C '• COMPARISON OF THE RATIO -^, AS DETERMINED FROM ELECTROMOTIVE % FORCE AND CONDUCTANCE MEASUREMENTS. C ' C- 0.5 0.05 8.85 8.09 0.1 0.01 9.16 8.33 0.05 0.005 9.30 8.64 0.01 0.001 9.62 9.04 It is evident that the ion ratios as determined by means of conductance measurements are considerably greater than those calculated from the measured electromotive forces, assuming Equation 95 to hold. As the solutions become more dilute, the two values approach each other slowly. The explanation of these phenomena has been the subject of much discussion. The observed fact is that, assuming the laws of dilute solutions to hold, the electromotive force of a concentration cell as "Maclnnes and Parker, J. Am. Chem. Soc. S7, 1445 (1915). 302 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS measured is smaller than that which would be calculated from the con- centrations of the ions and larger than that calculated from the con- centrations of the un-ionized fraction. One obvious explanation is that the conditions assumed to hold in applying the Nernst equation are not fulfilled, for this equation obviously can apply only to solutions which are sufficiently dilute so that the deviations from ideal systems lie within the experimental error. The behavior of solutions of strong electrolytes clearly shows that this condition is not fulfilled. The Nernst equation, therefore, should not apply. On the other hand, it is possible that the ionization measured by means of the conductance ratio -r- is not correct. If this is true, the A0 concentrations of the ions are not known and it is therefore not possible to calculate the electromotive force of a concentration cell from Equa- tion 95. In this case, we still have to take account of the fact that solutions of strong electrolytes do not fulfill the conditions of dilute solutions. Consequently, it is not possible to calculate from the electro- motive force of concentration cells the concentrations of the ions in solution ; for it may readily be shown, from electromotive force measure- ments, that the law of mass action does not apply to solutions of strong electrolytes and that, consequently, the laws of dilute solution do not apply. The ratios of the concentrations of the ions, therefore, cannot be calculated by means of the Nernst equation. It has been suggested that strong electrolytes are completely ionized even at fairly high concentrations. In that case the function J 8 in Equation 96 measures the change in the potential of the electrolyte due to interaction between the ions. Granting this assumption, the function Js has a negative value at relatively low concentrations. With increas- ing concentration the value of J diminishes, passes through a minimum, and thereafter increases, passing through a value 0 and becoming posi- tive at very high concentrations.28 A considerable number of measurements have been made on the electromotive force of concentration cells in which other electrolytes have been added to the solution of the electrolyte surrounding one electrode. Poma and Patroni 29 have measured the electromotive force of copper electrodes in solutions of copper salts, to which various electrolytes with a common ion had been added. Poma 30 measured the potential of the hydrogen electrode in acid solutions in the presence of other elec- 28 The manner in which J varies is discussed further in the next chapter as is also the relation of this function to the activity. 29 Poma and Patroni, Ztschr. f. phys. Chem. 87, 196 (1914). 80Pojna, Ztschr. /. phys. Chem. 88, 671 (1914), OTHER PROPERTIED OF ELECTROLYTIC SOLUTIONS 303 trolytes, both with and without a common ion. The results of Poma indicate a considerable change in the electromotive force due to the addition of another electrolyte. The effect varies with the concentra- tion and also with the nature of the added electrolyte. At the higher concentrations of added salt, at any rate, the effect is greatly dependent upon the nature of the added electrolyte, the electromotive force due to the addition of a given amount of electrolyte being the greater the greater the tendency of the salt to form hydrates. The sign of the electromotive force, moreover, was found to depend upon the nature of the added electrolyte. The results of Poma do not seem to be in good agreement with the results of other investigators who have investigated the electromotive force of similar cells. The potential of the hydrogen electrode in solu- tions of hydrochloric acid in the presence of varying amounts of alkali metal chlorides has been investigated by Chow,31 who found that, keep- ing the total ion concentration constant, the potential of the electrode in the mixture may be calculated according to Equation 95, the total concentration of hydrogen and of chlorine being employed for the con- centrations of the ions. According to this result, the function J§ remains constant in the mixture, provided the total concentration of the mixed electrolytes is maintained constant. Similar results have been obtained by Earned.32 The results of Harned indicate that at low concentra- tions the function Jl(! has the same value for the mixture as it has for o the pure electrolyte at the same total salt concentration. At higher con- centrations, according to Harned's measurements, the potential of the electrolyte depends upon the nature of the added electrolyte. It was also found that the potential of the hydrogen electrode in hydrochloric acid suffers nearly the same change due to the addition of equivalent amounts of potassium chloride and sodium bromide. As yet, experimental data in this direction are not sufficiently exten- sive to warrant generalizing the conclusions drawn from the investiga- tions referred to above. 6. Thermal Properties of Electrolytic Solutions. It is only recently that the technique of thermal measurements has been refined to a point where data obtained with electrolytic solutions are sufficiently precise to make an inter-comparison of the various thermal properties of such solutions generally possible. Even now, accurate data are available for only a limited number of systems, as a result of which but few general "Chow, J. Am. Chem. Soc. &, 497 (1920). "Earned, J. Am. Chem. SQC. 42, 1808 (1920) ; i&itf,, 37, 2460 U9J5), 304 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS conclusions may at the present time be reached relative to the manner in which the thermal quantities are dependent upon the various factors governing the condition of a solution. Water, itself, is ionized, and the energy of the ionization reaction corresponds very satisfactorily with the heats of neutralization of strong acids and bases. According to the Ionic Theory, the heats of neutraliza- tion of different strong acids and bases should be the same at low con- centrations, since the neutralization process under these conditions con- sists essentially in a combination of the hydrogen and hydroxyl ions to form water. The most reliable determination of the heats of neutraliza- tion was made by Wormann.33 The mean value of the heat of neu- tralization for hydrochloric and nitric acids with sodium and potassium hydroxides at 18° was found to be approximately 13700 calories. The heat of ionization of water is related to the ionization constant of water by means of the equation: (97) d\ogK_ U dT ~ RT2' where U is the energy change accompanying the ionization of one mol of water. Noyes and his associates 3* have measured the ionization constant of water at a series of temperatures up to 218°. The heat of ionization derived from their results is in good agreement with the value found by Wormann for the heat of neutralization. Thus at 18° Noyes finds that the value 14055 is in agreement with his experimental values. Direct determinations of the heat of neutralization of strong acids and bases at higher temperatures do not appear to exist, so that a compari- son in these regions cannot be made. At higher temperatures the ioniza- tion constant of water passes through a maximum, as a consequence of which it follows that the heat of ionization changes sign. Equation 97 is likewise applicable to the ionization process of elec- trolytes in water. If the ionization values are known at different tem- peratures, the energy change accompanying the ionization process may be calculated, assuming that the energy change accompanying the process remains constant. The equation holds true even though the conditions for dilute systems are not fulfilled, provided the concentrations enter- ing in the equation represent the real concentrations of the molecular species in question. Thermal data of sufficient precision are not avail- able to make it possible to determine to what extent the results of con- ductance measurements at different temperatures are in agreement with thermal data. In a general way, however, the results appear to be in agreement. In the case of the weak acids and bases, the order of * Wormann, Ann. D. Phys. 18, 775 (1905). •« Carnegie Publications, No. 63 (1907). OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 305 magnitude of the energy effects, as derived from conductance-temperature measurements, agrees with those derived from the heats of dilution of solutions of weak electrolytes. The ionization constants of acetic acid and ammonia, for example, have maxima in the neighborhood of ordi- nary temperatures, indicating that the energy change accompanying the ionization process is zero; correspondingly, the heats of dilution of solutions of these substances have small, although uncertain, values. In general, weak electrolytes have a greater heat of dilution than strong electrolytes and, correspondingly, their ionization changes more largely with temperature. The heats of dilution of strong electrolytes unquestionably have very small values. Correspondingly, the ionization of strong electrolytes at ordinary temperatures changes but little with temperature. The ionization of certain salts, such as magnesium sulphate, decreases markedly at higher temperatures; and it is to be expected that solutions of these salts will exhibit an appreciable heat of dilution even at rela- tively low concentrations. Experimental determinations of these quan- tities, however, are lacking. In view of the uncertainty of the thermal data, it cannot be stated that the commonly accepted ionic theory leads to results which are in contradiction with the thermal properties of electrolytic solutions. Recently, careful determinations of the heats of dilution of a number of electrolytes have been made by a number of investigators. Accord- ing to Randall and Bisson,35 the heat of dilution of sodium chloride from 0.28 N to zero concentration amounts to only two calories. At higher concentrations the heat of dilution, although small, is quite marked. The heats of dilution of a number of salts, as well as of mixtures of salts, have been determined by Stearn and Smith,36 and Smith, Stearn and Schneider.37 The heats of dilution for sodium and potassium chlorides were found to be very nearly the same, although varying slightly at high concentrations. At low concentrations, the heat of dilu- tion, in all cases, approaches a value of zero, as might be expected. The heats of dilution are not in all cases of the same sign, since that of strontium chloride is opposite in sign from that of sodium and potassium chlorides. The heats of dilution for mixtures of two electrolytes in general differs markedly from the mean heat of dilution of the con- stituents. Stearn and Smith suggest that this result may be due to the fact that complex compounds, whose formation presumably would be accompanied by an energy change, are formed in mixtures of salts. For sodium and potassium chlorides the heat of dilution is negative, which »8 Randall and Bisson, J. Am. Chem. S — 0, may at once be applied if the equation of state is known, while, if the equation of state is not known, the problem is neces- sarily insoluble, since it is not possible to evaluate the integral in ques- tion. When reaction takes place between various constituents present in the mixture, the condition for equilibrium leads to the equation: (99) 2AT = 0, where (100) .M Here ra is the molecular weight of the constituent and \i is the thermo- dynamic potential defined according to Gibbs.5 The molecular potential M, of a constituent, is given by an equation of the form: (101) M = RTlogx + F(vT xyz..) where F(vT xyz..) is a function of the composition of the system, as well as of volume and temperature, except when the equation of state of 4 van der Waals-Kohnstamm, "Lehrbuch der Thermodvnamik " Vol 2 •Gibbs, Scientific Papers, Vol. 1, pp. 92 et seq. (1912). 326 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS the system fulfills the condition pv = RT, in which case the only manner in which the concentration is involved in the expression for the thermo- dynamic potential is in the logarithmic term of the above equation. In order to evaluate the term F(vT xyz. . ) it is necessary to know the equa- tion of state of the system, since the value of M as given by the equation: ,,02, « = »-. obviously involves the term f pdv , which cannot be evaluated without }v a knowledge of the equation of state. The equations of state for mix- tures of ordinary liquids are comparatively complex, and a general solu- tion of the problem has not been effected, even for liquids of simple type ; while, in the case of mixtures of substances whose equations of state are comparatively complex, even an approximate solution has been little more than attempted. This subject has been treated in detail by van der Waals.6 b. Jahn's Theory of Electrolytic Solutions. Nernst 7 and Jahn 8 attempted to solve the problem of solutions of strong electrolytes by introducing various correction terms. Since the true equation of state for mixtures containing electrolytes is not known, even approximately, it is obvious that these theories necessarily involve assumptions of an arbitrary nature. These assumptions must contain within them the equivalent of an equation of state. In how far these assumptions are allowable may be ascertained by comparing the consequences of these theories with the experimental facts. Jahn set up the conditions for equilibrium, employing as a criterion for equilibrium, the variation of Planck's function: It is on the whole immaterial what function is employed as criterion for equilibrium, provided, always, that it fulfills the conditions of a charac- teristic function.9 These functions involve the energy of the system and, in order that the condition for equilibrium may be solved, it is necessary to have an expression for the energy of the system in terms of its com- position. In the case of ideal systems, Dalton's law may be assumed to hold, in which case the energy of a mixture of substances is equal to the sum of the energies of its constituents. Jahn assumed an equation for • van der Waals-Kohnstamm, loc. cit. 'Nernst, Ztschr. f. phys. Chem. 38, 487 (1901). •Jahn, Ztschr. 1. phys. Chem. 41, 257 (1902). •Gibbs, Scientific Papers 1, pp. 85 et seq. (1906). THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 327 the energy containing cross terms due to forces acting between the dif- ferent molecular species present in the mixture. This assumption, which is necessary for a solution of the problem by this method, is obviously an arbitrary one. Proceeding in this way Jahn obtains, for a system of electrolytes in equilibrium, the equation: (C-)2 (103) log -J- = (a + fa)C + log tfo, where a and (3 are constants. The constancy of the functions ct and (3 however, depends upon the original assumption made with regard to the manner in which the energy of the system is dependent upon its composi- tion, and, if a different assumption had been made, it would have led to a corresponding variation in the resulting equation. Methods of this kind are correct enough thermodynamically, but, in order that they may lead to results which may be tested experimentally, an assumption must be made, and this assumption is, in general, arbitrary in its nature. In this sense, therefore, the results of these methods are to be looked upon as being purely empirical in character, unless evidence of an a priori nature can be adduced in favor of the assumptions made. In all cases, the cor- rectness of the assumptions may be tested by comparing the resulting equations with the experimental values. Taking the equation of Jahn, it is easy to make a comparison with experiment. This equation obviously involves four constants ; namely, a, (3 and K0, together with A0, the limiting value of the equivalent conductance. The equation is a fairly complex one and it is not easy to extrapolate for the value of A0 on the basis of this equation, but it may safely be assumed that, in the case of potassium chloride, the conductance of whose solutions has been measured to 2 X 10'5 normal, the true value of AO does not differ materially from that ordinarily assumed. At higher concentra- tions, at any rate, a slight error in the value of A0 will cause a relatively small change in the distribution of the points. Assuming the value of A0, and calculating the values of the function K' at three concentrations, it is possible to evaluate the constants a, p and K0. The values of a and P being known, the equation may be tested by plotting values of log K against those of (a + py) C. This plot should yield a linear relation, but, in fact, leads to results inconsistent with the experimental values. The value of K' has a maximum in the neighborhood of 0.05 normal, after which it decreases rapidly. The equation as calculated for potas- sium chloride at 18° is as follows: log K' = 2.5935 + (592.8 — 498.7y)C. 328 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS While Jahn's equation has not been tested in the case of non-aqueous solutions, it is easy to see that it cannot hold generally. For example, f or m = 1 in Equation 11, the function K' varies practically as a linear function of the ion concentration. Such an equation will not reduce to the form of that of Jahn. That Jahn's equation should not hold is in no wise surprising, since- the assumptions underlying it are of an arbitrary nature. It is improb- able that the free energy of electrolytic solutions may be determined as a function of concentration without the aid of an equation of state. In other words, the chance of finding the correct equation by mere accident would appear to be vanishingly small. The method of Nernst does not differ materially from that of Jahn and leads to a similar result. c. Comparison of the Thermodynamic Properties of Electrolytes. Inconsistencies in the Older Ionic Theory. While the application of thermodynamic principles yields no information relative to the mecha- nism involved in electrolytic solutions, these principles when combined with other hypotheses lead to consequences which admit of verification. The bearing of thermodynamics on the theory of electrolytic solutions was long neglected and has often been misinterpreted. So, for example, the correspondence between the ionization values as derived from con- ductance and from osmotic measurements was looked upon as lending support to the older ionic theory. As Nernst 10 pointed out, this apparent confirmation of the ionic theory constitutes, in fact, one of the chief obstacles in the path of its acceptance. Insofar as electrolytic solutions constitute systems in which equilibria prevail, thermodynamic principles are applicable. It is evident, how- ever, that the laws of dilute solutions are not applicable to these systems at ordinary concentrations. Aside from a few very general relations, the application of thermodynamic principles alone can furnish us very little information relative to the nature of these solutions. The general problem is to express the potentials of the various constituents in terms of the independent variables of the system; that is, of the concentrations of the various substances present. Since statistical and other methods have not been developed to a point where they enable us to determine the equation of state of these systems, the problem at the present time can be attacked only by experimental methods. Fortunately, the potentials of electrolytes in solution may be determined readily and with a rela- tively high degree of precision. The values of the potentials as thus determined may be treated by graphical or other empirical methods; and, while the theoretical relation between the potentials and the concentra- «• Nernst, Ztschr. f. phys. Chem. 38f 493 (1901) ; Jahn, iUd., 38, 125 (1901). THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 329 tions of the constituent electrolytes remains undisclosed, the form of the function may be determined. At the same time, the values of the poten- tials of different electrolytes may be compared and relationships brought to light which are of practical importance, even though their theoretical significance may not be apparent. Our knowledge of electrolytes from this point of view is restricted to aqueous solutions. In view of the fact that many properties of electrolytic solutions are greatly modified in solvents of lower dielectric constant, and since the similarity in the be- havior of dilute aqueous solutions of different electrolytes is not often found in other solvents, any generalization of the results obtained in aqueous solutions must be made with caution. The Thermodynamic Method. The significance of the results ob- tained from an examination of the thermodynamic properties of electro- lytic solutions will be better understood if treated without reference to detailed methods. Let us assume that we have a solution in which the following reaction takes place: Mi + Mi +••••-= NI'^I' + **'**' + '" The condition for equilibrium in such a solution is: (104) SnAf = Sn'JIf' . The potential sum for the constituents on either side of the reaction equa- tion may be expressed by a function of the form: (105) 2nM - F(C1}C2). . .C/AV • •), where C1}C2,. . .C/A',. . . are. independent variables. If any of these variables are not independent, a relation will evidently exist among them by means of which they may be eliminated. So long as we are dealing with a solution of a single electrolyte, the potential may obviously be expressed as a function of the concentrations of the ions and the un-ion- ized fraction; that is, we have: (106) Since a relation exists between the concentrations C+, C~ and C 7 it is obvious that one of these variables is not independent. Since, in general, it is not possible to determine the concentration of the ions and of the un-ionized fraction in a solution of an electrolyte, the total concentration of the salt may equally well be employed for practical purposes, in which case: (107) 330 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS If the value of the potential sum *2nM may be experimentally determined at different concentrations, the form of the function F(CS) is empirically known. If the experimental values of DnJlf are correct, then the values of F(CS), as determined by different methods, must necessarily be in agreement. This result has been verified by Lewis and Randall,10* as we shall see below. When mixtures of electrolytes are employed, the expression for the potential obviously becomes a function of a greater number of variables. In the case of a salt in the presence of another salt with a common ion, the potential becomes a function of two variables; and in that of a salt without a common ion, of three variables. We should not expect, therefore, that the values obtained for the potential sum in mixtures could be directly compared with those obtained for the same electrolytes in a pure solvent. The methods which have been adopted by investigators in this field, however, have consisted essentially in expressing the potential of an electrolyte in a mixture as a function of a single variable. This method consists in introducing a variable defined by an equation of the form: (108) Cm =F(C1, C2,...). This function is given such a form that the value derived for the poten- tial sum in the mixture, on introducing Cm as variable, corresponds with that of a solution of the pure substance when the same variable is intro- duced. If such a function exists, then we are led to conclude that the potential sum for a given electrolyte in solution is dependent, not upon the concentrations of the various substances involved, but upon some other single parameter. The potential of an electrolyte as a function of its concentration may be determined directly by means of the electromotive force of concentra- tion cells. More indirectly, the potential may be obtained from the vapor pressures of these solutions and from other related properties, such as the freezing point, boiling point, etc. If the experimental determina- tions are correct, the values of the potentials derived from the measure- ment of these different properties must necessarily be in agreement with one another. Lewis and Randall " have compared the available experimental data for aqueous solutions in this way, and have found them to be in excellent agreement. This implies the correctness of the methods employed in cal- culating the various thermodynamic quantities, as well as the accuracy loa Lewis and Randall, J. Am. Chem. Soc. 43, 1112 (1921). 11 Idem, loc. cit. THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 331 of the experimental methods, by means of which the data were secured. The practical application of thermodynamic principles to electrolytic solutions is largely due to G. N. Lewis.12 In recent years numerous other writers have occupied themselves with this subject.13 The writers on this subject have commonly employed the activity function of Lewis,1* which is defined by the equation: where a is the activity and io is a function independent of the concentra- tion of the constituent in question. The ratio of the activity of a sub- stance to its concentration is termed its activity coefficient and is thus defined by tfie equation: (110) a=£. In a solution of an electrolyte we have an equilibrium of the type: n+AS + n-Az~ = A', where A' represents a molecule of substance which dissociates into n+ positively charged ions A^ and ri~ negatively charged ions A2~. The number of charges on the ions is not indicated. Introducing the values of M from Equation 109 in Equation 104 we may at once derive the expression: (111) log— - =K, - au where a+, cr, and au denote the activities of the positive and negative ions and the un-ionized molecules, respectively, and K is a function inde- pendent of concentration. For the change in the potential of the electro- lyte between any two concentrations of the system, we have the equa- tions: (112) (2n'M')6— (2n'M')a = RT log ^, ua (113) (2nM)6 — (2nM)a = RT log "Lewis, J. Am. Chem. Soc. S}, 1631 (1912). "Bronsted, J. Am. Chem. Soc. 42, 761 (1920) ; Bjerrum, Ztschr. f. Elektrochemie 24, 321 (1918) ; Ztschr. f. Anorg. Chem. 169, 275 (1920); Harned, J. Am. Chem. Soc. & loOo (1920), „ oV«HVA?^roc- Am- Acad' *3> 259 (1907) ; Zt8c*r- /• PhV*- C^em. 61, 129 (1907) ; ibid., 70, — U (1909). 332 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS From Equation 112, the ratio of the activities of the un-ionized mole- cules for any two conditions of the solution may be determined if the potential change is known. Similarly, the ratio of the activity products of the ions may be determined from Equation 113. The actual value of the activity product is not in general determinable. At low concentra- tions, however, as is apparent from Equation 109, the activity a ap- proaches a value equal to that of the concentration C. If the potential can be determined at sufficiently low concentrations, that is, in solutions sufficiently dilute so that the laws of dilute solutions become applicable, the true values of the activity products may be determined. In systems in which a reaction takes place among the constituents the concentra- tions C are not usually determinable, so that the value of the true activity coefficients a remains undetermined. For practical purposes, therefore, a new activity coefficient has been introduced, defined by the equation: where Cs is the total concentration of the electrolyte. Further, instead ol employing the values of the product of the activity coefficients, some function of the product of these coefficients is employed which makes the resulting coefficient more nearly comparable with that of a solution of a single molecular species. For electrolytes, Lewis and Randall have intro- duced a coefficient af) defined by the equation: 1 (115) where af and Cr may be called the reduced activities and the reduced concentrations of the ions.15 In a solution of a binary electrolyte: 15 The nature of the various coefficients may be further elucidated by writing the equations for the potential sum in somewhat more explicit form. We have : (117) 2nM = RT2n log C + Sni0 + ZnJ, where ZnJ = RT 2tt log |. It is evident that this equation is not capable of being employed practically as an inter- polation function, since C is not determinable. If, now, C" is replaced by C gt the total salt concentration of the electrolyte in solution in pure water, (118) 2nM = RT 2n log C8 + 2ni0 + 2nJa If the values of ZnM are known for different values of C , then the variation in the function SwJg over the concentrations in question is likewise known. In Equation 117, "ZnJ measures the change in the value of the potential of a substance in a real system above that in an ideal system at the same concentration. When the reduced concentration THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 333 (116) ro+a-i t/»). V For the solubility of a salt in a mixture containing a salt with a common ion, Bronsted assumes: C" = C0 and C" = C ,, O d where C" and C" are the concentrations of the uncommon and the com- mon ion respectively. This leads to the equation: csct (123) log jf+f = 2* (C(v» - C8W) . so These equations express the solubility of the saturating salt in terms of the total concentration of all the salts in solution. The value of the constant K depends upon the type of salt. For uni-univalent salts, x = approximately 1/3 ; for bi-bivalent salts, 4/3 ; and for tri-trivalent salts, 3. Bronsted shows, in the first place, that the form of the curve is determined by the values of the constants Cg and x. In the presence of salts without a common ion, the solubility of the saturating salt is in- creased due to addition of the second electrolyte; and this increase is the greater, the greater the value of the constant >t. Moreover, the relative increase of the solubility is the greater, the smaller the value of C0 . In 60 the presence of salts with a common ion, the form of the solubility curve depends upon the number of charges on the ions and the number of ions resulting from the different salts. Bronsted shows that solubility curves will, in general, exhibit a minimum. In the case of uni-univalent salts, this minimum will lie at very high jconcentrations ; for bi-bivalent salts, assuming x = 4/3, the minimum concentration is 0.12m; and for tri- THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 339 trivalent salts, assuming x = 3, the minimum is at 0.01 m. Bronsted's equations therefore account for the solubility relations of various salts in a general way, including the minima which have been observed in the case of salts of higher type. Adjusting the value of the constant x to represent the experimental values in the best possible manner, Bronsted has shown that his equations account for the observed solubilities up to 0.1 N, practically within the limits of experimental error. According to Bronsted's equation, the activity of all salts ultimately passes through a maximum. Under these conditions, the solutions will be unstable at the maximum point and the system in these regions should separate into two liquid phases. In the case of salts of higher type, the concentration at which this phenomenon should occur lies in regions where the concentration is fairly low. Bronsted has actually been able to observe separation of a liquid phase in solutions of salts of certain trivalent ions. The results obtained, on comparing the thermodynamic potential of electrolytes in aqueous solution, show that these values as derived by different methods are in excellent agreement. Thermodynamic principles alone are not capable of supplying information as to the nature or number of the molecular species present in electrolytic solutions. The results are naturally in agreement with the assumption that electrolytes are com- pletely ionized and, in view of the fact that in the thermodynamic treat- ment we are restricted to total concentrations and not to actual concen- trations, the results are most simply interpreted on the basis of this hypothesis. This, however, does not preclude the possibility that un- ionized molecules or intermediate ions may exist, or, indeed, that other complexes may be present in these solutions. 3. Theories Taking into Account the Interionic Forces, a. Theory of Malmstrom and Kjellin. A great many investigators have attempted to account for the properties of solutions of electrolytes by taking into account the forces acting between the charges. According to this view, as was pointed out by Thomson 17 and by Nernst,17a the ionization of an electrolyte under given conditions should be the greater the greater the dielectric constant of the medium. Among those who have attempted a solution of the problem by this method are Kjellin 18 and Malmstrom.19 These theories, which are prac- tically the same, lead to an equation of the form: A log C{ = log £ + log Cu + "Thomson, Phil. Mag. [5], S6t 320 (1893). "•Nernst, Ztschr. j. pliya. Chem. 13, 531 (1804). "Kjellin, Ztschr. f. phys. Chem. 77, 192 (1911). 18 Malmstrom, see Kjellin, above. 340 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS where A, B and K are constants and Cu and C^ are the concentrations of the ions and the un-ionized molecules, respectively. For binary electro- lytes A has a value of approximately 1.5, B of 0.3 and K of 1.0. Applied to aqueous solutions of sodium and potassium chlorides, this equation was found to reproduce the results quite closely up to 0.05 N, the con- stants of the equation being fitted to the experimental values. Similar results were obtained with a number of ternary salts. The equation is not applicable to solutions in solvents of lower dielectric constant such as ammonia, even at low concentrations. At high concentrations, in sol- vents of dielectric constant less than 20, it is obviously inapplicable, since, according to this equation, A necessarily increases with concentra- tion. It may be noted that the form of this equation resembles somewhat that of Bronsted's for the solubility of a salt in the presence of other salts. b. Theory of Ghosh. The most comprehensive theory which has been proposed to account for the behavior of solutions of electrolytes is that of Ghosh.20 Ghosh assumes that strong electrolytes are completely ionized, but that only those ions whose energy is sufficiently great to over- come the electrostatic field due to the charges are active in carrying the current. It is difficult to see how Ghosh's activity coefficient differs from the usual ionization coefficient. Apparently, what this author has in mind is that the ionic complexes persist in the neutral molecules. While such an assumption is not fundamental to the older ionic theory, it is nevertheless true that previous investigators 21 in this field have long since recognized that in the neutral molecule the identity of the ionic complexes is not lost. The theory of Ghosh, as well as those of some other writers, would be more readily understandable to most readers if the customary nomenclature had been retained. Ghosh calculates the potential due to the field on the assumption that the ions are distributed in the medium in a definite manner forming a space lattice. He assumes that the space lattice of a salt in solution corresponds to that of the salt in the crystalline state and therefrom cal- culates the distance between the positive and negative charges. In calculating the potential, Ghosh assumes that the ions form doublets so that the work involved in separating the ions is due only to the N pairs of positive and negative ions. This theory has been criticized by Part- ington,22 Chapman and George,23 and more recently by Kraus.24 These 20 Ghosh, Trans. Chem. Soc. 113, 449, 627, 707, 790 (1918). 21 Noyes, Aqueous Solutions at High Temperatures, Carnegie Publication No, 63, p. 350 (1907) . 22 Partington, Trans. Faraday Soc. 15, 111 (1919-20). 23 Chapman and George, Phil. Mag. 41, 799 (1921). "Kraus, J. Am. Chem. Soc. W, Dec., 1921. ..... . . , THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 341 criticisms need not be further considered here but it may be of interest to compare the conductance values calculated according to Ghosh's theory with those experimentally determined. For the conductance of an electrolytic solution Ghosh's theory leads to the following equation: (124) where (125) log A = log AO - DT 2.3026 mR ' Here N is Avogadro's number, 6.16 X 1023, E is the electrostatic unit of charge, 4.7 X 10~10 E.S.U., R is the value of the gas constant in absolute , Epichlorhydrin. 0.0 0.0S 0./S 0.20 O.25" 2.16 2.14- -' 2*0 ^2.06 < be £ a. oo 1.96 /.7B 1.76 /. 70 A66 - /.**• /.62 1.60 0.+ 0.6 1-0 1.9. , Water. FIG. 61. Plot of Ghosh's Conductance Function for Solutions of Potassium Chloride in Water at 18° and Tetraethylammonium Iodide in Epichlorhydrin at 25°. units, and m is a factor depending upon the number of ions n resulting from the ionization of the neutral molecules and upon the number of charges associated with a single ion, as well as upon the manner of dis- tribution of these ions in the solvent medium. It is evident that, for a 342 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS given solvent at a given temperature, the logarithm of the equivalent con- ductance is a linear function of the cube root of the concentration and Ghosh's theory may be readily tested by plotting the experimentally determined values of log A against those of C1/3. If the equation is applicable, the experimental points should lie upon a straight line from which the values of A0 and p may be determined. If the equation is not applicable, the experimental points will evidently show a systematic deviation from a straight line. In Figure 61 are shown the curves for potassium chloride in water and for tetraethylammonium iodide in epichlorhydrin. It is evident from the figure that the experimental points lie upon a curve concave toward the axis of concentrations at low concentrations and convex toward this axis at higher concentrations, with an inflection point between. The experimental points show a systematic deviation from a linear relation and Ghosh's equation therefore is not applicable. In Table CXXXIII the observed and calculated conductance values are compared. TABLE CXXXIII. COMPARISON OF OBSERVED AND CALCULATED VALUES OF A FOR KC1 IN WATER AT 18°. A0=: 132.06 p== 3.620 X 103 !T=:291 D = 81 V 5X104 2X104 104 5X103 2X103 103 5X102 Acaic 130.80 130.35 129.90 129.35 128.40 127.47 126.30 Aobs' 129.51 129.32 129.00 128.70 128.04 127.27 126.24 Aobs'-caic. ... — 1.39 —1.03 —0.90 —0.45 —0.36 —0.20 —0.06 V 2X102 102 50 20 10 5 2 1 ACaic 124.31 122.37 119.97 116.9 112.1 107.4 99.7 92.7 Aob8 126.24 122.37 119.90 115.6 111.8 107.5 101.3 96.5 Aobs,caic. • +0.03 ±0.00 —0.07 —0.3 —0.3 —0.1 +1.6 +3.8 The experimental values have a relative precision not less than 0.05 per cent. It is evident, from the table, that the theoretical values deviate from the experimental values far in excess of any conceivable experimen- tal error, except at a few points in the immediate neighborhood of the inflection point, which is at about 0.01 normal. As may be seen from the curve for epichlorhydrin, the deviations in this solvent are much greater than in water. It is to be noted, too, that the experimental points again lie upon a curve which is of the same type as that of potassium chloride in water; that is, the curve is concave toward the axis of concen- tration at low concentrations and convex toward this axis at high con- THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 343 centrations. It has been shown that this form of the curve is general and that in solutions of non-aqueous solvents the deviations from Ghosh's equation are much greater than in water, and therefore are far in excess of any possible experimental error.25 Ghosh has likewise treated other properties of electrolytic solutions. In view of the fact that his theory fails to account satisfactorily for the relation between the conductance and the concentration of electrolytic solutions, it is unnecessary to consider these properties here. c. Milner's Theory. Of the various theories proposed to account for the properties of electrolytic solutions, that of Milner is perhaps the most noteworthy, since it is comparatively free from arbitrary assumptions. Milner 26 has calculated the virial for a system of positively and nega- tively charged particles by statistical methods, and therefrom has calcu- lated the influence of the ions on the freezing point of solutions.26* He found, in effect, that the virial of a system of charged particles has a finite value, from which the osmotic pressure of the solution may be deduced, and therefrom the freezing point. In the following table are given values of the van't Hoff factor i for potassium chloride in water calculated by Milner, together with the values of i determined by Adams directly from freezing point measurements. TABLE CXXXIV. COMPARISON OF MILNER'S VALUES OP i, WITH THOSE EXPERIMENTALLY DETERMINED. C 0.005 0.01 0.02 0.05 0.1 ?:Milner 1.962 1.947 1.926 1.885 1.838 *Adams 1.961 1.943 1.922 1.888 1.861 As may be seen from the table, the calculated values of i are in excel- lent agreement with those determined by Adams. Milner's values are based on the assumption that the electrolyte is completely ionized, the observed freezing point depression being due entirely to the interaction of the ions. If an ionization value were assumed corresponding to that given by the ratio A/A0, the values of i, as calculated by Milner, would be lower than those observed. Milner has accordingly suggested that, within these ranges of concentration, strong electrolytes are completely ionized. If this is so, the change in the conductance of electrolytes must »Kraus, loc. cit. ™ Milner, Phil. Mag. 23, 551 (1912) ; ibid., 25, 742 (1913). *"» Compare, Cavanagh, Phil. Mag. 43, 606 (1922). 344 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS be due to a reduction in the mean carrying capacities of the ions at higher concentrations. Thus far, the conductance of electrolytic solutions as a function of their concentration has not been accounted for with equal success. Mil- ner 27 has considered this problem, but without arriving at an expression for the conductance as a function of concentration. He has concluded, however, that the decrease of conductance at low concentration must be mainly due to a decrease in the ionic mobilities and not to a decrease in their number. The argument here does not appear to be altogether con- vincing. Milner assumes, for example, that the undissociated molecules are normal in their osmotic behavior. The justification for this assump- tion is by no means obvious. Moreover, experimental facts weigh heavily against the generality of the conclusion reached. Weak electrolytes in water, and, apparently, all classes of electrolytes in non-aqueous solu- tions, approach the mass-action law as a limiting form at low concentra- tions. The difficulty is not alone to account for the failure of the mass- action law in solutions of strong electrolytes in water but, also, to account for the applicability of this law to solutions in other solvents where, judg- ing by the lower value of the dielectric constant, the interionic forces are much greater than in water. Furthermore, according to Milner 's theory, different electrolytes in dilute solutions should exhibit practically identi- cal properties both as regards their osmotic and their electrical properties. This condition is approximately fulfilled in water, but not in solutions in non-aqueous solvents. In these latter solvents, the electrolyte appears to retain its individuality even at exceedingly low concentrations. Any theory which cannot give an account of this fundamental property of electrolytic solutions is obviously incomplete. It is not difficult to see in what manner the conductance would be influenced by interionic action at higher concentrations. According to Milner, the ions are not distributed haphazard throughout the medium, but, on the average, as the result of interaction between the charges, ions having like charges are somewhat farther apart and ions having unlike charges somewhat nearer together than would otherwise be the case. Ordinarily it is assumed that a charged particle moves in a uniform electric field. If, however, the ions are combining and dissociating, or, in any case, if charged particles approach each other sufficiently closely, the surrounding field will be influenced and the speed of the ions will vary for different individuals, depending upon the proximity of other ions. According to this view, the ratio y = -*- is a measure, not of the number - A0 "Milner, PUl. Mag. S5, 214 and 352 (1918). THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 345 of particles actually engaged in the transport of the current, but of the mean conducting power of the ions. It does not necessarily follow, how- ever, according to this view, that all the ions in solution are at all times acting as carriers of the current. Lewis and Randall 28 have recently pointed out that the ionization of an electrolyte cannot be defined without some degree of arbitrariness. This difficulty is not one confined to electrolytic solutions. In all sys- tems, in which reaction takes place among a number of constituents throughout the mass of the mixture, the definition of the concentration of the various constituents concerned becomes uncertain. So long as the system is dilute, the concept of concentration is definite; but, when the concentrations reach such values that the forces acting between the con- stituents become appreciable, the concept embodied in the term molecule becomes indistinct. This difficulty arises of necessity whenever we pass from the purely thermodynamic to the kinetic method of treating systems of real substances. That these various difficulties should arise in solu- tions of electrolytes is not surprising, since these are the only concentrated systems regarding which we have data sufficiently accurate to enable us to observe the deviations from ideal systems with any considerable degree of certainty. That un-ionized molecules exist in aqueous solutions of ternary salts in water appears to be conclusively demonstrated by the fact that transference measurements have shown that complex cations exist. Thus, the transference number of the cadmium ion, in cadmium iodide, according to Hittorff, is greater than unity at high concentrations, and the manner in which the transference number of cadmium chloride varies with the concentration indicates that its behavior is not essentially different from that of cadmium iodide. It must be assumed, therefore, that, in solutions of cadmium salts, ions of the type CdX> exist. If this is true of one electrolyte, the same may well be true of others. Finally, it is not sufficient that a theory of electrolytic solutions shall account merely for a diminution in the conducting power of electrolytes with increasing concentration, for, in solutions in non-aqueous solvents, the conductance increases with increasing concentration at higher con- centrations; and, if the dielectric constant is sufficiently low, the con- ductance increases with increasing concentration even at relatively low concentrations. d. Hertz's Theory of Electrolytic Conduction. P. Hertz 29 has at- tempted to solve the problem of electrolytic conduction by taking into account the interionic forces. He has derived the following equation *Loc. cit. » Hertz, Ann. d, Phya. 37, 1 (1911). 346 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS expressing the relation between the equivalent conductance A and the concentration C of the solution: (126) where u (127) Si(u) = u (128) Ci(u) = j ^^ du, (129) ip(M)=B(Ao — A), and (130) u Here A0, A and £ are constants. A0 is the limiting value which the equivalent conductance approaches as the concentration decreases indefi- nitely. This equation is of the form: (131) £(A0 — A) nrtpkiC1/8). It is evident that, for a given solvent under given conditions, the conductance function will have the same form for different electrolytes according to this theory. If the values of ip (u) and of u are represented graphically, then it should be possible to transform the curve for one electrolyte into that for another by merely altering the scale of plotting. It is obvious that this condition will be very nearly fulfilled in aqueous solutions of strong binary electrolytes, since the ionization of different electrolytes at lower concentrations is practically identical. If Hertz's theory held strictly, the value of the constant A would be predetermined by the nature and condition of the solvent and would be independent of the nature of the electrolyte. The difference in the values of the con- ductance of different electrolytes, therefore, would be accounted for by a difference in the values of the constants A0 and B, and the different con- ductance curves should be transformable one into the other by merely altering the values of these constants; or, if A0 is otherwise determined, by merely altering the value of the constant B. THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 347 Lorenz 30 has tested the applicability of Hertz's function to aqueous solutions of binary electrolytes and has concluded that this function is applicable. As has just been pointed out, this was to have been expected. It should be noted, however, that the value of A, according to Lorenz, differs appreciably for different electrolytes. This result may, in part, be due to the fact that the function has been applied at concentrations where the viscosity effects become appreciable. It is evident that Hertz's function will not be generally applicable to solutions in non-aqueous solvents, certainly not unless the value of A is assumed to differ largely for different electrolytes. Furthermore, it will be entirely inapplicable to solutions in non-aqueous solvents of low dielectric constant at higher concentrations. It is evident from Equation 126 that the factor of u3 is essentially positive so that A0 — A must necessarily increase with increasing concentration. It is known, however, that, in solvents of low dielectric constant, the value of A passes through a minimum, after which the value of A0 — A decreases with increasing concentration. This theory, like others of its kind, is at best restricted in its applicability. As yet it has not been compared with experimental data in a sufficient number of solutions to make it possible to form a clear opinion as to the range of its applicability. In any case, it is in- applicable to solutions in solvents of very low dielectric constant, even though these solutions may be dilute. Here again, as in the case of Milner's theory, the difference in the behavior of strong and weak elec- trolytes remains to be accounted for. 4. Miscellaneous Theories. A great many other theories have been suggested to account for the behavior of electrolytic solutions. In gen- eral, these theories have not been worked out sufficiently to comprehend within their scope more than a limited number of properties of a limited number of systems. Many of them, indeed, are purely qualitative in character. To account for the increase in the conductance of solutions of elec- trolytes in solvents of very low dielectric constant, Steele, Macintosh and Archibald 31 have suggested that at higher concentrations the elec- trolyte polymerizes, and that only these polymerized molecules are capa- ble of ionization. They show that, if a sufficient degree of polymerization is assumed, an ionization curve is obtained somewhat similar in form to that of ordinary electrolytes in aqueous solution. Thus far, this theory is purely qualitative in character and an exact test of its applicability is therefore not possible. We should expect, however, that if only 10 Lorenz and Michael, Ztschr. /. anorg. Chem. 116. 161 (1921): Lorenz and Neu. ibid., 116, 45 (1921) ; Lorenz and Osswald, ibid., 114, 209 (1920). "Steele, Macintosh and Archibald, Phil. Trans. [A] 205, 99 (1905). 348 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS polymerized molecules were capable of ionization, intermediate ions would be present in solution and transference measurements with such solutions, therefore, should yield very abnormal values for the transfer- ence numbers. While certain transference numbers are unquestionably abnormal and while it is indeed very probable that polymerization often occurs in solutions of electrolytes in solvents of both high and low dielec- tric constant, it remains to be shown that the phenomenon is a general one and that it is capable of accounting for the observed properties of electrolytic solutions. Nevertheless, it is highly probable that the effect of polymerization will have to be taken into account in many cases at higher concentrations. It appears, however, that polymerization should lead to a lower rather than to a higher value of the conductance. Trans- ference measurements with the alkali metal halides in acetone yield abnormally high values for the cations, indicating the formation of a complex cation. It is to be noted, however, that the conductance of the halide is the lower the greater its tendency to form complexes. Thus, the conductance of lithium chloride in acetone at higher concentrations is much lower than that of potassium iodide or sodium iodide. That com- plex ions are formed in solutions of cadmium iodide in water was shown by Hittorf, as has already been pointed out. The assumed ionization process in solutions of electrolytes is in a large measure hypothetical. This may account for numerous discrepancies at higher concentrations. Other writers consider solutions of strong electrolytes to be similar to solutions of colloids. Among these are Reychler,32 Georgievics 33 and Wo. Ostwald.34 These theories, however, appear to be little more than analogous, based chiefly upon the similarity between the Storch equation and the adsorption equation. The Storch equation is only an approxima- tion in aqueous solutions which, in other solvents, fails entirely. The osmotic effects in solutions of electrolytes, also, are not in harmony with the view that solutions of strong electrolytes are colloidal in character. Some writers attempt to account for the properties of aqueous solu- tions by taking into account reactions between the solvent and the elec- trolyte. In this connection, it is to be noted that electrolytic solutions are not confined to solvents of the water type. Indeed, such solvents need not necessarily contain hydrogen and, in fact, may be elementary sub- stances, or neutral carbon compounds such as chloroform. In view of this fact, it is highly improbable that the properties of electrolytic solu- tions may be generally accounted for on the basis of chemical processes 82 Reychler, "Etude sur 1'Equilibre de Dissociation," Brochure No. 3, Bruxelles (1917), 83 Georgievics, Ztschr. f. pJiys. Chem. 90, 356 (1915). "Ostwald, Ztschr. Ctiem. Ind. Roll. 9, 189 (1911). THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 349 taking place between the solvent and the dissolved electrolyte. But here, again, there are doubtless many instances where interaction between the electrolyte and the solvent or an added non-electrolyte is a primary factor in the ionization process, particularly at higher concentrations. 5. Recapitulation. In recapitulation, solutions of strong electro- lytes, even at low concentrations, do not conform to the laws of dilute systems. The thermodynamic properties of these solutions can not, therefore, be employed for the purpose of determining the state of the electrolyte in these solutions. The conductance method might be ex- pected to give a measure of the fraction of the ionized and un-ionized molecules present. However, the fact that the relative conductance of the ions of strong acids varies at low concentrations renders the results of the conductance method doubtful. The hypothesis that electrolytes are completely ionized up to fairly high concentrations lacks experimental support. The agreement of the hypothesis with the consequences of thermodynamic principles can not be looked upon as lending material support, since thermodynamics can teach us nothing with regard to the molecular state of a system without a supplementary hypothesis which directly or indirectly involves the equation of state. The fact that the law of mass-action is approached as a limiting form in aqueous solutions of weak electrolytes and in non- aqueous solutions of all electrolytes for which reliable data are available indicates that, if strong electrolytes in aqueous solution are completely ionized, this constitutes only a particular case and the general problem still remains to be solved. Any theory which undertakes to account for the decreased conduct- ance of electrolytes at higher concentrations, on the assumption that the conductance change is due to a change in the speed of the ions, must likewise account for the fact that, in solvents of low dielectric constant, the conductance passes through a minimum value after which it increases. This point may lie at relatively low concentrations. The theories of electrolytic solutions thus far advanced are founded chiefly on observations relating to aqueous solutions. There is great danger, here, that phenomena may be assumed as general which, in fact, are only particular. It is of the greatest importance to analyze the results obtained from a study of the properties of solutions in various sol- vents in order to determine which of these are general, applying to all electrolytic solutions, and which are particular, applying only to solutions in certain solvents or under certain conditions. Aqueous solutions are characterized by the uniformity of the phenomena presented by different electrolytes. In other words, the electrolyte, in aqueous solution, has, 350 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS in a large measure, lost its individuality. This is not true of solutions in other solvents. Here the electrolyte retains its individual character- istics even at very low concentrations. It is interesting to note that, at higher temperatures, certain of the individual properties of electrolytes in aqueous solution disappear while others make their appearance. Thus, the ionic conductances approach one another at higher temperatures, while the ionizatibn values diverge the more the higher the temperature. It is not to be doubted that the properties of aqueous solutions at higher temperatures closely resemble those of non-aqueous solutions under ordinary conditions. It is not unlikely that, in the end, many of the theories, which have been suggested from time to time and found inapplicable, contain certain elements of truth. The error has been introduced in attempting to apply, generally, theories which are applicable only to special cases. It appears probable that, ultimately, it will be necessary to take into account, under various conditions, a change in the speed of the ions with concentration as well as a change in the degree of ionization. At the same time there will doubtless be found many cases in which intermediate ions are formed and in which the electrolyte polymerizes. Yet there is found, in all electro- lytic solutions, a certain unity among the phenomena, which indicates the existence of a comparatively small number of chief governing factors. Chapter XIII. Pure Substances, Fused Salts, and Solid Electrolytes 1. Substances Having a Low Conducting Power. In the preceding chapters, the properties of solutions of electrolytes have been discussed. We shall now consider, briefly, the properties of pure substances in the liquid state. Nearly all substances in the fused condition exhibit a measurable, though often small, conducting power for the electric cur- rent. Even such substances which we ordinarily class as insulators con- duct the current in some degree. What the nature of the conduction process is in these substances has not been shown, but in all likelihood the process is an ionic one; that is, the current is carried by particles of atomic or molecular dimensions. A typical example of this class of con- ductors, or perhaps more properly insulators, is found in the hydrocar- bons. It has been shown that the conductance of substances of this type is materially affected by the presence of small amounts of impurities. The specific conductance of nearly all poorly conducting substances is materially decreased by careful drying and fractionation. Evidently, therefore, in part at least, the conductance of this class of substances is due to the presence of other substances, as a result of which their con- ductance is materially increased. We have, however, no knowledge of the nature of the charged particles by means of which conduction is effected. * In the case of petroleum ether and hexane, it has been found possible to carry the process of purification so far that the effect of impurities is almost entirely eliminated. It has been found that the residual con- ductance in these solvents is chiefly due to the action of radiations from surrounding bodies, as a result of which the solvent itself is ionized.1 The conductance under these conditions was found to be altered by sur- rounding the conductance vessel with screens which absorb the external radiation. The conductance of pure hexane, therefore, is lower than that due to the ions produced by the radiation from surrounding bodies and it is possible that the conductance of this substance is in effect zero. Under ordinary conditions, the conductance of the hydrocarbons is due primarily to impurities. *Jaff6, Ann. d. Phys. 32, 148 (1910). 351 352 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS Recent investigations on the conduction process in solid dielectrics have disclosed the fact that in these media Ohm's law is not obeyed.2 The substances investigated were mica, glass, paraffin, shellac and cellu- loid. Excepting paraffin, for which the conductance was so low that the results were uncertain, the conductance was found to increase with the applied potential. The logarithm of the specific conductance increases approximately as a linear function of the potential gradient. In the case of mica, with which substance measurements were made over a large range of potential, the conductance curves are slightly concave toward the axis of potentials. In the case of glass the conductance increase at higher temperatures was found to be noticeably smaller than at lower tempera- tures. Since Ohm's law does not hold, it must be assumed either that the number of carriers increases with the applied potential or that the mean speed of the carriers increases. It is not improbable that, under the action of the applied potential, carriers of a type differing from those normally present in the dielectric medium may be formed. It is of par- ticular interest to note that in glass, which is an electrolyte at higher temperatures, the above mentioned results indicate a conduction process differing from that at higher temperatures. Compounds of hydrogen with elements which are strongly electro- negative are in general ionized to a slight degree. The most familiar example of this type is water itself, which in the pure state has a specific conductance in the neighborhood of 0.042 X 10~7.2a Other hydrogen de- rivatives of strongly electronegative groups likewise appear to conduct the current in the pure state, some of them much more readily than water. The specific conductance of formic acid appears to lie in the neighborhood of 10~5. In these cases, however, the process of purification has not been carried to such a point that it can with certainty be stated that the residual conductance is entirely or chiefly due to the ionization of the solvent alone. In the case of hydrogen derivatives, in which the hydrogen is not joined to a strongly electronegative group, the residual specific conductance is as a rule relatively low and it is as yet uncertain to what the residual conductance is due. Acetone, for example, may be purified to a point where its specific conductance is of the order of 10~8, but whether this residual conductance is due to acetone itself or to some impurity is unknown. The same obviously holds true of solvents which contain no hydrogen, such as sulphur dioxide, bromine, etc. The hydrogen derivatives of the strongly electronegative groups are 3Poole, PUl. Mag. 42, 488 (1921). "Kohlrausch and Heydweiller, Ann. d. Phys. 83, 209 (1894). PURE SUBSTANCES, FUSED SALTS, SOLID ELECTROLYTES 353 perhaps to be classed as salts. In other words, these compounds should be classed, not with the ordinary hydrocarbons, but rather with the dis- tinctly salt-like substances. These derivatives, when dissolved in water, or other suitable solvents, yield solutions which conduct the current with great facility and which often form compounds with the solvent. Hydro- chloric acid forms a stable complex, ammonium chloride, with ammonia; and with water at low temperature it has been shown to form a complex HC1.H20.3 In water itself, therefore, hydrogen and hydroxyl ions do not consist merely of a hydrogen atom and an OH group associated with the positive and negative charge respectively, but rather of complexes in which the solvent itself is involved. In a sense, therefore, water and ammonia and hydrogen chloride may be considered to be related to salts. However, the typical salts in a fused state exhibit in most instances a conductance much greater than that of the substances which we have just been discussing. With a few exceptions, fused salts conduct the current with extreme facility. Among these exceptions mercuric chloride is one of the most common and striking examples. This salt is itself an electrolytic solvent for other salts, while its specific conductance in the pure state is very low.* Correspondingly, solutions of mercuric chloride in other solvents, as for example water, appear to be only slightly ionized. This class in- cludes the organic tin salts of the type R3SnX. Trimethyltin iodide, for example, is a liquid at ordinary temperatures whose conductance is less than 4 X 10~5. This salt when dissolved in water is ionized nor- mally.5 2. Fused Salts. Inorganic substances which are non-electrolytes in solution, in general, possess only a very low conducting power in the pure state. This, for example, is the case with boric oxide. On the other hand, oxides of the strongly electropositive elements appear to be con- ductors in the fused or even in the solid state. It is, however, the typical salts in their fused state which are of greatest interest. These substances, in general, conduct the current with extreme facility, by means of a purely ionic process, since, as has been shown, Faraday's law applies. In Table CXXXV are given values of the specific conductance \i of sodium nitrate at different temperatures, together with the equivalent conductance A as calculated from the known specific volume, the fluidity of the fused salt F, and the ratio of the conductance to the fluidity ^ .6 JT 'Rupert, J. Am. Chem. Soc. SI, 851 (1909). •Foote and Martin, Am. Chem. J. 41, 45 (1909). 8 Unpublished observations by Mr. C. C. Callis in the Author's Laboratory: •Goodwin and Mailey, Phys. Rev. 25, 469 (1907) ; t&id., 26, 28 (1908). 354 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS TABLE CXXXV. CONDUCTANCE AND FLUIDITY OF SODIUM NITRATE AT DIFFERENT TEMPERATURES. t [i A F K/F 350° 1.173 52.87 42.6 1.24 400 1.384 63.59 54.0 1.18 450 1.562 73.15 65.0 1.12 500 1.716 81.94 77.2 1.06 It will be observed that the specific conductance \i, as well as the equiva- lent conductance A, increases very nearly as a linear function of the tem- perature. Obviously, the equivalent conductance will vary nearly in proportion to the specific conductance, since the density of the fused salt varies only comparatively little with temperature. Between 350° and 500°, the specific conductance increases approximately 60 per cent, which corresponds roughly to an increase of % per cent per degree. The fluidity varies somewhat more than the conductance over the same temperature interval, so that, as the temperature rises, the value of the ratio H de- r creases. It is interesting to note that the value of -^ is near unity, which r differs not greatly from the value of -^ for electrolytic solutions, par- r ticularly in the case of water. This may be taken to indicate that the fused salts are highly ionized. For different fused salts, the conductance is of the same order of magnitude, corresponding to the fact that they have approximately the same fluidity. In Table CXXXVI are given values of the specific con- ductance \i, the equivalent conductance A, and the fluidity F, together with the ratio -^ for different salts. It will be observed that the ratio r TABLE CXXXVI. VALUES OF A AND F FOR DIFFERENT FUSED SALTS. \i A F A/F 350°C. NaN03 .: 1.173 52.88 42.6 1.24 KN03 0.6728 36.54 38.0 0.96 " AgN03 1.245 55.43 45.5 1.22 310°C. LiN03 1.126 44.21 27.2 1.62 250°C. AgC103 1.4743 27.72 -=i is of the same order for the different salts. In the case of the nitrates r the ratio is smallest for potassium nitrate and greatest for lithium nitrate. The order of the ratio •=• corresponds to the order of the atomic volumes, r PURE SUBSTANCES, FUSED SALTS, SOLID ELECTROLYTES 355 Jaeger and Kapma6a have measured the specific conductance and the densities of potassium nitrate, sodium nitrate, lithium nitrate, rubidium nitrate, caesium nitrate, potassium fluoride, potassium chloride, potas- sium bromide, potassium iodide, sodium molybdate, and sodium tung- state over considerable temperature ranges. At a given temperature, the equivalent conductance of the different salts is of the same order of magnitude. For the nitrates the conductance increases in order from caesium to lithium. For the potassium halide salts, the conductance is smallest for the fluoride and greatest for the chloride, while that of the iodide and bromide is intermediate between them. The conductance increases very nearly, although not quite, as a linear function of the temperature. The temperature coefficients vary appreciably, being greatest for potassium fluoride and smallest for caesium nitrate. The conductance of mixtures of fused salts is very nearly a linear function of the composition. In the following table are given values of the conductance of mixtures of sodium and potassium nitrates at 450°, together with the values of F and of -^.7a It will be observed that as the r concentration changes the conductance varies continuously between that of the two components. TABLE CXXXVII. CONDUCTANCE OF MIXTURES OF SODIUM AND POTASSIUM NITRATES AT 450°. 100 molar % KN03 0.973 55.03 60.2 0.915 The fact that in the mixtures of fused salts the conductance is approxi- mately a linear function of the composition shows that no considerable reaction takes place on mixing. This indicates a high degree of ioniza- tion of the fused electrolyte. In Table CXXXVIII are given values of the conductance of mixtures of silver iodide and silver bromide at 550°. 7 Here, again, the conduc- TABLE CXXXVIII. CONDUCTANCES OF MIXTURES OF SILVER IODIDE AND SILVER BROMIDE. %AgBr 0 5 10 20 30 40 60 70 80 90 100 pi.... 2.36 2.40 2.39 2.41 2.43 2.50 2.64 2.67 2.68 2.84 3.00 88 Jaeger and Kapma, Ztschr. f. Anorg. Chem. 113, 27 (1920). T« Goodwin and Mailey, loc. cit. TTubandt and Lorenz, Ztschr. f. phya, Chem. 87, 543 (1914). 0 20 50 80 n .. 1.562 1.389 1.205 1.059 A .. 73.15 67.84 62.56 57.96 F .. 65.7 66.3 63.3 A/F .. 1.12 0.945 0.915 356 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS tance varies continuously between that of the two components. It is true that a few irregularities occur, but these are small and probably lie within the limits of experimental error. The fused salts are characterized by the great similarity in their behavior. As has already been pointed out, the order of magnitude of the conductance is the same for all typical fused salts. In the following table are given values of the conductance of thallium and silver salts at 600° .8 TABLE CXXXIX. CONDUCTANCE OF THALLOTJS AND SILVER SALTS AT 600°. Til 0.840 Agl 2.43 TIBr 1.127 AgBr 3.08 T1C1 1.700 AgCl 4.16 In both cases, the conductance of the salt increases in the order: iodide, bromide, chloride. The conductance of the silver salts is markedly greater than that of the thallium salts. A great many data are available relating to the conductance of fused salts,9 but, in view of the similarity in the behavior of the different fused salts, it is unnecessary to give here in detail the various observations which have been recorded. Thus far, the subject has been studied chiefly from an empirical point of view and we possess but little knowledge of the molecular condition of these substances. The form of the conductance curve of mixtures of sodium and potas- sium nitrate and of silver chloride, iodide and bromide indicates that in these mixtures complex ions are not formed. In some other in- stances, however, there is a probability that complex ions may exist.10 This is the case, for example, with mixtures of potassium chloride and lead chloride. Lorenz has carried out transference measurements which indicate that a complex of the type K2PbCl4 is probably formed in the mixture. 3. Conductance of Glasses. For want of a suitable reference sub- stance, transference measurements with the fused salts have not been carried out, and as a consequence we lack any knowledge as to the pro- portion of the current carried by the two ions in these electrolytes. In a few instances, however, particular systems have been investigated in which the current is carried entirely by either the positive or the nega- • Tubandt and Lorenz, loc. cit. 9 Lorenz. "Electrolyse geschmolzener Salze, Monographien u. Angew. Electrocb," 20 (1905). » Lorenz, Ztschr. /. phya. Chew. 70, 230 (1910). PURE SUBSTANCES, FUSED SALTS, SOLID ELECTROLYTES 357 tive ion. Among those substances which may be classed strictly as fused salts are the glasses. A glass is to be considered as a supercooled liquid which is mechanically rigid. Usually, glasses consist of mixtures of silicates of the alkali metals and the metals of the alkaline earths. What the nature of the compounds is in these systems is not known. Doubt- less, the silica is present in the electronegative constituent. It is well known that ordinary glasses are excellent conductors of the current at high temperatures, the conductance increasing with the temperature. In general, the conductance-temperature curve is exponential in form. In the following table are given values of the resistance of ordinary soda-lime glass at different temperatures.11 TABLE CXL. RESISTANCE OF ORDINARY SODA GLASS AT DIFFERENT TEMPERATURES. Temperature C.... 325 355 404 469 484 500 540 Resistance 9200 1900 687 172 133 89 2.4 It will be observed that, even at temperatures as low as 325°, glass con- ducts the current with measurable facility, while in the neighborhood of its softening point, 540°, it conducts extremely well. To what the great increase in the conductance of glass is due is uncertain. We shall see below that the ionization of a glass varies only little as a function of the temperature and consequently the increased conductance must be due to the increased speed of the ions. The nature of the frictional resist- ance which the ions meet in their motion through a glass is, however, uncertain. At temperatures below 400°, glasses of this type appear to be entirely rigid and consequently the increased conductance is not simply related to the mechanical rigidity of the glass. The conduction process in the case of the glasses is electrolytic in character.1111 If a current is passed through a glass tube from a sodium nitrate anode to a mercury cathode, metal is transferred from the sodium nitrate to the mercury through the glass in accordance with Faraday's law and no change whatever takes place in the glass itself. This indi- cates that the conduction process in such glasses is due to the motion of the sodium ion and is not due to the motion of an electronegative ion. This type of conduction is characteristic of many rigid electrolytic con- ductors. Since positively charged carriers are present within the glass, it is obvious that negative carriers must likewise be present. The nega- tive carriers, however, must form a substantially rigid system, since they take no part in the conduction process. It is also evident that, in the "Darby, Thesis, Clark University (1917). "» LeBlanc and Kerschbaum, Ztschr. f. phys. Chem. 12, 468 (1910). 358 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS case of the glasses, the ions consist of the atoms themselves, since, on passing a current through soda-lime glass, the only material transferred is sodium. This and similar cases are the only ones in which it has been definitely demonstrated that an electrolytic ion consists of a charged atom alone. In the case of glasses, it is possible to substitute the sodium ion by another positive ion.llb Such a substitution is, in effect, a determina- tion of the speed of the ions by the moving boundary method. Substitu- tion may be quite generally effected but, in the case of most positive ions, the glass disintegrates as the process proceeds. In the case of silver, however, a substitution may be carried out to a considerable depth. If sodium is substituted by silver, the weight of the glass is increased in proportion to the difference in the atomic weight of silver over that of sodium. In the following table are given values of the gain in weight of a sample of soda glass, together with the values calculated from the amount of electricity passed as determined in a coulometer.110 The tem- perature is given in the first column. TABLE CXLI. OBSERVED AND CALCULATED GAIN IN WEIGHT OF SODA GLASS ON SUBSTITUTION BY SILVER. Gain in Weight Gain in Weight Temperature Calculated Observed 350° 0.0339 g. 0.0347 g. 350° 0.0396 0.0416 343° 0.0732 0.0762 343° 0.0209 0.0209 By measuring the penetration of the silver boundary into the glass under a given potential gradient, it is possible to determine the volume of the glass which has been affected, and, knowing the composition of the glass, it is possible to determine the fraction of sodium in the glass replaced by silver. This has been done in the case of soda glass with the following results.110 TABLE CXLII. RELATIVE AMOUNTS OF SODIUM REPLACED BY SILVER IN SODA GLASS. | * 1% 278° 76.5 295° 76.8 323° 77.05 343° 82.3 ub Heydweiller and Kopfermann, Ann, d. Phya. 32, 729 (1910). »« Darby, loo. cit. PURE SUBSTANCES, FUSED SALTS, SOLID ELECTROLYTES 359 While these values are not very precise, nevertheless, they clearly indi- cate that about three- fourths of the sodium present in these glasses may be electrolyzed out and replaced by another metal. The effective ioniza- tion of the sodium in soda glass, therefore, is of the order of magnitude of 75 per cent. This is apparently the only direct determination which has thus far been made of the relative amount of a substance actually concerned in the conduction process in an electrolyte. If so large a proportion of the sodium in soda glass is actually concerned in the con- duction process, it is reasonable to assume that the fused salts are very nearly completely ionized. It is interesting to note that, as the tempera- ture rises, the ionization of sodium in glass increases slightly. Since the penetration of the silver is determined solely by the rate of motion of the ions and since the conduction is due entirely to the posi- tive ion, it follows that the depth of penetration should be proportional to the specific conductance or inversely proportional to the specific resist- ance of the glass. This condition is in general fulfilled. From the preceding data it is possible to calculate the speed of the sodium ion in glasses; that is, the speed with which this ion moves under a potential gradient of one volt per centimeter. In the following table are given values of the absolute speed of the sodium ion at different temperatures. TABLE CXLIII. ABSOLUTE SPEED OF THE SODIUM ION IN SODA GLASS AT DIFFERENT TEMPERATURES. 278° 4.52 X 10-8 295° 1.46 X 10-r 323° 3.26 X 10'7 343° 5.9 X 10-6 It will be observed that, as might be expected, the absolute speed of the sodium ion is relatively very low. On the other hand, corresponding to the greatly increased conductance of glass with increasing temperature, the speed of the sodium ion increases largely with temperature. 4. Solid Electrolytes. Solid substances, both crystalline and amor- phous, conduct the electric current with more or less facility. In the case of the insulators, where the conductance is of an extremely low order, it is not unlikely that conductance is due to the presence of traces of impurities. The only substance for which this has actually been shown is crystalline quartz, in which the conductance is due to the pres- ence of traces of sodium as impurity.12 Here the current is carried by » Warburg and Tegetmeier, Ann. d. Phys. 35, 455 (1888). 360 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS the sodium ion which alone is capable of motion in these crystals. The process of conduction appears to be entirely similar to that in glasses. The typical salts, below their melting point, conduct the current, in some cases, with extreme facility. As a rule, the conductance increases with increasing temperature according to an exponential curve. The specific conductance may be expressed fairly well as a function of tem- perature by means of the equation: (132) log [i = a + bt, where a and b are constants. In the following table are given values of the specific conductance of a few salts at temperatures through their melting points.18 TABLE CXLIV. CONDUCTANCE OF SALTS THROUGH THE MELTING POINT. T1C1 AgCl 250° 0.00005 300 0.00024 350 0.0009 400 0.0037 427 (M.P.) ( 0.0067 (1.082 450 1.17 500 1.332 600 1.700 AgBr 200° 240 280 350 400 419 422 425 500 600 0.00052 0.0023 0.0091 0.08 0.38 0.51 M.P. 2.76 2.92 3.08 t 250° 300 350 400 450 455 456 500 600 t 125° 140 144.6 150 250 350 450 550 552 554 600 650 Agl 0.00030 0.0015 0.0065 0.026 0.11 M.P. 3.76 3.91 4.16 0.00011 0.00026 (0.00034 (1.31 1.33 1.78 2.14 2.41 2.64 M.P. 2.36 2.43 2.47 11 Tubandt and Lorenz, Ztschr. f. phys. Chem. 87, 513 (1914). PURE SUBSTANCES, FUSED SALTS, SOLID ELECTROLYTES 361 Temperature. FIG. 62. Specific Conductance of Silver Halides at Various Temperatures Through Their Melting Points. The relation between the conductance and the temperature is shown graphically in Figure 62. In general, the conductance of the solid salt increases with temperature according to Equation 132 up to the melting 362 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS point, where a discontinuity occurs, a large increase taking place on fusion. Silver iodide, however, forms an exception to this rule. This substance exhibits a transition point at 144.6°. Below this temperature the conductance of silver iodide increases with temperature in a manner similar to that of silver chloride and bromide. At the transition point, the specific conductance increases from a value of 3.4 x 10~4 to 1.31. Beyond the transition point, the conductance of silver iodide increases slowly with the temperature, the temperature coefficient being not greatly different from that of fused salts, as may be seen from the figure. It will be observed, furthermore, that at the melting point the conductance of solid silver iodide is markedly higher than that of the fused salt, the conductance on melting decreasing from 2.64 to 2.36. Even at the tran- sition point, at a temperature as low as 144.6, the specific conductance of solid silver iodide is of the order of magnitude of that of fused salts. This is a remarkable phenomenon and shows that the power of con- ducting the current with facility is by no means restricted to the liquid state. Thus far, however, silver iodide is the only solid salt whose con- ductance in the solid state has been found to be comparable with that in the liquid state far below its melting point. The conduction process in solid salts of this type is purely electrolytic, as follows from the fact that Faraday's Law holds true within the limits of experimental error. In the following table are given the observed amounts of silver precipitated on electrolysis, together with the amounts of silver precipitated in a silver coulometer carrying the same current.14 TABLE CXLV. TEST OF FARADAY'S LAW IN SOLID ELECTROLYTES. Ag Ag Dissolved Precipitated Electrolyte Temperature at Anode in Coulometer % Dif. Silver Iodide 540° 0.7212 0.7139 + 1.20 " " 540 0.5642 0.5623 +0.34 150 0.7841 0.7804 +0.48 150 0.7767 0.7706 +0.80 Silver Bromide 400 0.5883 0.5842 + 0.70 Silver Chloride 430 0.3779 0.3751 +0.75 Considering the small amount of silver precipitated or dissolved and the difficulty of carrying out the experiments, the agreement between the observed and the calculated values of the amount of silver dissolved "Tubandt and Lorenz, loo. cit. PURE SUBSTANCES, FUSED SALTS, SOLID ELECTROLYTES 363 at the anode is remarkably good. The applicability of Faraday's Law has been further verified by Tubandt and Eggert.15 There can be little question but that, in the case of these salts, Faraday's Law holds true. By employing solid silver iodide above its transition point in contact with a silver cathode, Tubandt 16 has found it possible to test Faraday's law in the case of other electrolytes than the silver salts and, further- more, has been able to carry out transference measurements in order to determine to what extent the conductance in solid electrolytes is due to the positive and to what extent it is due to the negative carrier. It has been shown that for silver iodide, silver bromide, silver chloride, silver sulphide, above its transition point, and copper sulphide (Cu2S), Fara- day's Law holds and that in these salts the current is carried entirely by the positive ion. These results are very significant in that they show that one set of ions in these solids forms a fixed framework through which the other ions move with considerable facility. In the above salts, the negative ions form the framework through which the positive ions move. In lead chloride, however, the current is carried by the negative ion; the positive ions form the framework through which the negative ions move. These facts have an important bearing on the theory of the structure of solid salts. Silver sulphide has a transition point at 179°. Above the transition temperature, as was shown by actual electrolysis of the salt, Faraday's Law holds and the current is carried entirely by the positive ions. Below the transition temperature, the (3 form of silver sulphide appears to con- duct in part metallically. In the (3 form of silver sulphide, Faraday's Law does not hold, only about 80 per cent of the current being carried by the silver ion. The negative ion in this case is apparently not in- volved in the conduction process, the remainder of the current being carried by a metallic process of conduction. Apparently, therefore, solid electrolytes exist in which the current is carried partly metallically and partly electrolytically. As we shall see in a subsequent chapter, solu- tions of the alkali metals in liquid ammonia likewise conduct the cur- rent by a mixed process. The conductance of a heterogeneous mixture of two solid electrolytes is approximately a linear function of the composition of the mixture. When two solid electrolytes form mixed crystals, however, the conduc- tance of the homogeneous mixture is often much greater than that of the pure constituents. In the following table are given values of the "Tubandt and Eggert, Ztschr. J. anorg. Cliem. 110, 196 (1920) "Tubandt, Ztschr. f. Electroch. 26, 358 (1920). 364 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS specific conductance \i x 106 of mixtures of sodium chloride and potas- sium chloride at 570°. 17 TABLE CXLVI. CONDUCTANCE OF MIXTURES OF SODIUM AND POTASSIUM CHLORIDE AT 570°. %NaCl 0 10 20 30 40 50 60 70 80 90 100 pXlO6 0.87 8.0 16.5 22.0 24.0 24.0 30.0 34.5 40.0 28.0 4.5 The conductance value of 0.87 for pure potassium chloride at 570° has been calculated from the conductance values at somewhat higher temperatures by means of Equation 132. It will be observed that the conductance curve exhibits a maximum in the neighborhood of 80 per cent of sodium chloride, at which point the conductance of the mixture is nearly ten times that of pure sodium chloride and forty times that of pure potassium chloride. Apparently, the maximum lies toward the side of that component which possesses the higher conductance. Other systems of mixed crystals have yielded similar results. Apparently, therefore, it is a general rule that the- conductance of mixed crystals is much greater than that of the pure components. In the case of mixtures of silver iodide with silver bromide and with silver chloride, the conductance-temperature curve of the resulting mix- ture exhibits discontinuities as a result of the peculiar nature of silver iodide.18 Up to 80 per cent of silver bromide, a homogeneous phase re- sults initially, whose conductance curve corresponds with that of silver iodide above the transition temperature of 146.5°. Apparently, then, in these mixed crystals, the silver bromide is present in a condition similar to that of silver iodide above its transition point. The details of the conductance curves of these mixtures need not be discussed further here. It may be noted, however, that a study of the conductance of various solid systems is capable of throwing light on the phase relations in these systems. It will be evident from the foregoing discussion that solid electrolytes exhibit a marked variety of phenomena which have an important bearing on our conceptions of the nature of the conduction process, as well as upon that of the structure of solid salts. The available data are as yet extremely meager, but it may be expected that, as this field is further developed, results of great value will be obtained. 5. Lithium Hydride. The conductance of lithium hydride, both in the solid and in the liquid condition, has been investigated by Moers.19 17 Benrath and Wainoff, Ztschr. f. physt Chem. 11, 257 (1911). u Tubandt and Lorenz, loc. cit. 19Moers, Ztschr. f. anorg. Chem. 113, 179 (1920). PURE SUBSTANCES, FUSED SALTS, SOLID ELECTROLYTES 365 In the following table are given values of the specific conductance of lithium hydride at different temperatures. TABLE CXLVII. SPECIFIC CONDUCTANCE OF LITHIUM HYDRIDE AT DIFFERENT TEMPERATURES. t p t |i 443° 2.124 X10-5 661.5° 2.018 X 1Q-2 507 2.113 X10-4 685 3.206 X 10~2 556 8.447 X 10"4 725 7.59S X 10"2 570 1.491 X 10-3 734 1.125 X 10'1 597 3.225X10-3 754 1.01 638 1.139 X 10-2 The values of the specific conductance may be represented by means of a sum of terms in ascending powers of the temperature. It is interest- ing to note that the same equation applies both above and below the melting point of lithium hydride, which is 680°. Apparently, therefore, there is no discontinuity in the conductance of this hydride at its melt- ting point. This behavior is exceptional. This salt exhibits polarization when a direct current is passed through it, and it has been shown that, on the passage of the current, lithium is deposited at the cathode and hydrogen evolved at the anode. The cur- rent is therefore conducted by either one or both of the ions Li+ and H~. This salt, therefore, presents a very interesting case, not only in that the conductance of the solid is the same as that of the liquid at its melting point, but, also, in that hydrogen appears here as a negative ion. This is the only case so far. observed in which hydrogen has been shown to function in this manner. The behavior of hydrogen in lithium hydride is thus very similar to that of certain metallic elements in their compounds with the alkali metals in liquid ammonia, referred to in a preceding chapter. We saw there that, for example, in a solution containing lead and sodium, lead is dissolved at the cathode and precipitated at the anode. In the pres- ence of very electropositive elements, less electropositive elements tend to take up negative electrons and function as anions. This dual function of many elements, which ordinarily act as cations, is very significant from the standpoint of the constitution of many compounds in which these elements are involved. Chapter XIV. Systems Intermediate Between Metallic and Electrolytic Conductors. 1. Distinctive Properties of Metallic and Electrolytic Conductors. Substances which possess the power of conducting the electric current are, in the main, sharply divided into two classes; namely, metallic and electrolytic conductors. The members of each of these two classes of conducting substances have many properties in common with one another, which properties serve to distinguish the members of one class from those of the other. It is in their optical and electrical properties that the members of the two classes exhibit the greatest contrast. While electrolytic systems, in general, are transparent, metallic systems are non-transparent and exhibit metallic reflection. Electrolytic systems conduct the current with the accompaniment of material effects, while metallic systems conduct the current without attendant material effects of any kind. Nevertheless, the view has been gradually gaining ground that the conduction process in the two systems is similar in that conduc- tion is effected by the motion of charged particles. While we possess a more or less comprehensive theory of the mechanism whereby the transfer of the charge is affected in electrolytic systems., a similar theory does not exist for metallic systems. Such knowledge as we do possess regard- ing the existence of charged particles in metals is founded chiefly on observations on the properties of metals other than those relating imme- diately to the conduction process. There exists little direct evidence showing that the passage of the current through the metals is effected by the motion of charged particles. The great difficulty in the way of a direct attack on the problem of metallic conduction lies in the absence of material effects accompanying the passage of the current. In addition, there has been a complete lack of systems exhibiting properties intermediate between those of metallic and electrolytic conductors. Conducting systems fall sharply into one of two classes; namely, metallic and electrolytic conductors. In recent years, however, a class of solutions has been subjected to investi- gation which appears to bridge the gap between metallic and electrolytic conductors; in other words, which exhibits properties, on the one hand, in 366 SYSTEMS INTERMEDIATE 367 common with those of metallic systems and, on the other hand, with those of electrolytic systems.1 These are solutions of the alkali metals and the metals of the alkaline earth in liquid ammonia and organic derivatives of ammonia. In order to make clear the bearing of these solutions on the problem of metallic conduction, it will be necessary to discuss in some detail the properties of these solutions of the metals in liquid ammonia. 2. Nature of the Solutions of the Metals in Ammonia. The alkali metals are extremely soluble in liquid ammonia, yielding solutions whose external appearance depends upon their concentration. Dilute solutions of the alkali metals, as well as of metals of the alkaline earths, exhibit a fine blue color, whose absorption for all wave lengths is relatively great.1* At higher concentrations, the solutions possess a marked re- flecting power for all wave lengths. Very concentrated solutions exhibit distinct metallic reflection of a color intermediate between that of copper and gold. Among the earlier investigators of these solutions there was much discussion as to whether the metal exists in solution as such or as a compound with the solvent. Cady 2 showed that these solutions are excellent conductors of the electric current and that in concentrated solutions the passage of the current is characterized by the absence of polarization effects at the electrodes. Finally, it has been shown that, in the case of the alkali metals, stable compounds between the metals and the solvent cannot be separated from these solutions.8 While com- pounds between the metal and the solvent may exist in solution, such compounds, if they exist, possess little stability as follows from the low value of the energy changes accompanying the process of solution. In the case of the metals of the alkaline earths, however, it has been shown that compounds may be separated from solution, in which the metal is combined with ammonia. Kraus has prepared the compound Ca(NH3)6 and recently Biltz 4 has prepared the compounds Ba(NH3)6 and Sr(NH3)6. These compounds possess a metallic appearance, resembling that of the concentrated solutions of the metals in ammonia. Kraus has determined the vapor pressure of solutions of sodium in liquid ammonia, from which he calculated the molecular weight of the metal in these solutions. Since the molecular weight can be determined only in dilute solutions, where the properties of the system are approach- ing those of an ideal system, it follows that molecular weight determina- 1 Kraus, J. Am. Chem. Soc. £9, 1557 (1907) ; ibid., SO, 653, 1157 and 1323 (1908) ; iMd., S6, 864 (1914) ; ibid., 43, 749 (1921). la Gibson and Argo, J. Am. Chem. Soc. 40, 1327 (1918). 8 Cady, J. Phys. Chem. 1, 707 (1897). •Kraus, J. Am. Chem. Soc. SO, 653 (1908). «3iltz, Zfschr. f. Electroch. %6, 374 (1920), 368 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS tions are always more or less in doubt. However, if the molecular weights are determined at a series of concentrations, it is possible to draw an inference as to the limit approached, as the concentration of the solution decreases, from the manner in which the apparent molecular weight varies as a function of the concentration. In the following table are given values of the apparent molecular weight of sodium dissolved in liquid ammonia at different concentrations, and in Figure 63 are shown these values plotted as ordinates against the logarithms of the concen- trations as abscissas. TABLE CXLVIII. APPARENT MOLECULAR WEIGHT OF SODIUM IN AMMONIA AT DIFFERENT CONCENTRATIONS. C Apparent Mol. Wt. C Apparent Mol. Wt. 2.903 32.23 0.3665 25.31 1.841 30.70 0.3587 25.27 1.220 29.06 0.2669 23.53 0.9910 28.80 0.2516 23.43 0.9038 28.46 0.2261 23.41 0.5614 26.39 0.1565 21.62 0.5558 26.47 0.1519 21.58 0.4104 25.36 It will be seen that, as the concentration decreases, the calculated value of the molecular weight decreases very nearly as a linear function of the logarithm of the concentration over the ranges of concentration investigated. It is not possible to state what value the molecular weight approaches as a limit, but it is evident that the limit approached has a value less than 23, the atomic weight of sodium. It appears, therefore, that sodium dissolved in liquid ammonia exists in an atomic condition and it is probable that the limit, which the molecular weight approaches, has a value less than the atomic weight of sodium. This indicates the presence of a molecular species other than the sodium atom in these solutions. While similar molecular weight determinations have not been carried out in solutions of metals other than sodium, nevertheless, in view of the similarity of the properties of solutions of the different metals in ammonia, it is highly probable that the state of these metals differs little from that of sodium. 3. Material Effects Accompanying the Current. The criterion for determining whether a given substance is a metallic or an electrolytic conductor is the absence or existence of material effects accompanying the passage of the current. In dilute solutions of the metals in liquid SYSTEMS INTERMEDIATE ammonia, it has been definitely established that material effects accom- pany the current through these solutions. The existence of such effects is readily observed as a consequence of the characteristic color of these solutions. If a current is passed between two platinum electrodes in dilute solution of sodium or potassium in liquid ammonia, it is found that the color in the immediate neighborhood of the cathode is intensi- fied. This result is obviously due to the fact that, as the current passes through the solution, the metallic element as an ion, either simple or complex, is carried up to the cathode. The electrolytic character of the 4" «• If 94 7.9 o-o 0.1 c.e 0.3 0.4 o.s o.e on 0,9 0.9 1.6 u i.i /.s Log V. FIG. 63. Apparent Molecular Weight of Sodium in Liquid Ammonia at Different Concentrations. conduction process in dilute solutions of these metals in liquid ammonia is therefore established; the metal is associated with the positive ion. Taking into consideration the great tendency of the alkali metals to act as positive ions, it is probable that in these solutions the metals are present, in part at least, as charged atoms which do not differ from the positive ions of salts of the same metals dissolved in the same solvent. If positive ions are present in these solutions, then, obviously, nega- tive ions must be present likewise. So far as may be observed, when a current passes through a solution of a metal dissolved in liquid ammonia, no material effect occurs at the anode, save that the concentration of the metal in the immediate neighborhood of this electrode is diminished. 370 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS In dilute solutions, this effect is very pronounced and, in the immediate neighborhood of the anode, the solvent appears to be completely freed from the metal, since the solution becomes colorless and transparent. No reaction of any kind appears to take place at the anode surface, no gas is evolved, nor is any manner of deposit observable. On subjecting a solution of sodium in ammonia contained in a U-shaped tube to ex- tended electrolysis, the metal may be completely removed from the anode limb and transferred to the immediate neighborhood of the cathode surface. In this, no actual loss of the metal occurs, since on reversing the current, or on mixing the solution by shaking, the original solution is reproduced. Apparently, therefore, there is present in these . solutions a negative carrier whose passage into the anode leaves behind it no observable material effect. The nature of the phenomenon is not appreciably altered if another metal is employed in place of sodium. We commonly associate the characteristic metallic properties of a substance with the atoms of this substance; and, in the case of com- pounds, we associate metallic properties with the electropositive con- stituent. A brief consideration, however, will serve to show that this conception is erroneous, and that the electropositive constituent of a compound is entirely nonmetallic in its character. The metals owe their characteristic metallic properties, not to the electropositive constituent present, but, rather, to a common electronegative constituent. If a solu- tion of potassium in liquid ammonia, which has a characteristic color, is placed between two solutions of potassium amide, which are trans- parent, then, on passing a current through this system of solutions, the motion of the color indicates the direction in which the free metal is transported under the action of the current. If the characteristic prop- erties of a solution of potassium in ammonia were due primarily to the presence of an electropositive constituent, then we should expect that the color would move toward the cathode. It has been found, however, that, actually, under these conditions, the color moves toward the anode. As has been shown, potassium in liquid ammonia solutions is associated with the cation and moves toward the cathode. It follows that the transfer of the free metal in the solution, placed between the two solu- tions of potassium amide, is effected by means of the negative carrier. In passing a current through a system of the type described above, there is no indication that anything takes place as the positive ions pass from the potassium solution into the solution of potassium amide, save that the color boundary gradually moves in a direction opposite to that of the positive current, that is, toward the anode. It is probable, there- fore, that the positive ion in a solution of metallic potassium in liquid SYSTEMS INTERMEDIATE 371 ammonia is identical with the positive ion of a solution of potassium amide in this solvent. In other words, there is present in a solution of metallic potassium a positive carrier identical with the positive carrier in potassium amide. The positive carrier, then, in a solution of a metal in liquid ammonia, is nothing other than the normal ion of this metal and its properties in the metal solution differ in no wise from its properties in a solution of its salts. On the other hand, it is evident that, as the negative carrier moves toward the anode from the potassium solution to the potassium amide solution, free metallic potassium, that is, metallic potassium not chemically combined, is carried in the direction of the negative current toward the anode. The metallic properties of the solutions of the alkali metals in ammonia, therefore, must be due, primarily, to the negative carrier, and since free metallic potassium is present in that portion of the solution where blue color is present, it follows that this metal is generated by interaction between the potassium ion of the potassium amide solution and the negative carrier present in the solution of metallic potassium which, under the action of the potential gradient, moves into the potassium amide solution. This negative carrier, which in all like- lihood is identical with the negative electron, is the essential metallic constituent of metallic substances. There evidently exists in a metal solution an equilibrium of the type M+ + e- = Me, where M+ is the metallic ion, e~ is the negative ion (negative electron) and Me is the neutral metallic atom. In the amide solution, as is well known, there exists an equilibrium according to the equation: M+ + NH2- = MNH2. It is evident that, as the negative carrier e~ is carried into the metal amide solution, equilibrium establishes itself between this carrier and the other molecular species present. In other words, the reaction takes place: The total amount of free metal in the solution at any time is e~ + Me. To what extent the metal atoms are ionized into normal positive ions and negative electrons will appear below. 4. The Relative Speed of the Carriers in Metal Solutions. If the conduction process in metals consists essentially in a transfer of charge due to the motion of the negative carriers, since no material effects are observable at the boundaries between different metallic conductors, it 372 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS follows that the negative carrier in all metals is the same. If this is true, and if the negative carrier in the solutions of the alkali metals in ammonia' is the negative electron, then those properties of these solu- tions which depend upon the negative carrier should be the same in solutions of different metals. In how far this is true we shall see pres- ently, since many of the properties of these solutions have been analyzed in terms of their ionic constituents. Since the solutions of the metals in ammonia are ionized, the prob- lem of determining the nature of the conduction process may be attacked in a manner similar to that employed in the case of ordinary electrolytic solutions. It is possible, in the first place, to determine the relative amount of the current carried by the two ions under given conditions. For this purpose, transference measurements might be carried out', the concentration changes resulting when a given quantity of electricity passes through the solution being determined. This experiment is diffi- cult of execution, and consequently recourse has been had to another method, the results of which, although they are not as conclusive as direct transference determinations, nevertheless make it possible to determine the general order of magnitude of the quantities involved. The electromotive force of a concentration cell with liquid junction is given by the equation: from which the value of n, the transference number, may be determined, if the electromotive force E and the concentrations C±YI and C2J2 are known and if the laws of dilute solutions are applicable. Judging by the results obtained in solutions of ordinary electrolytes, this equation yields results which are approximately correct. In the case of a concentration cell which consists of two platinum electrodes placed in metal solutions, having concentrations C± and C2, the work is due to the transfer of n mols of sodium per equivalent of electricity from the concentration Cx to the lower concentration C2. The cell is similar to that of a salt solu- tion with reversible anodes, n is obviously the fraction of the current transported by the positive carrier in the solutions. In Table CXLIX are given values of the electromotive force of con- centration cells at different concentrations — the rdtio of the concentra- tions of the two solutions was approximately 1:2 — together with the transference number n of the cation and the ratio n . n SYSTEMS INTERMEDIATE 373 TABLE CXLIX. E.M.F. OF CONCENTRATION CELLS AND VALUES OF n AND FOB SOLUTIONS OF Na IN NH3. Ca EX103 n 1-^ 0.870 0.080 0.00359 277.6 0.732 0.328 0.0109 90,6 0.335 0.620 0.0231 41.2 0.164 0.72 0.0291 33.4 0.081 0.86 0.0336 28.8 0.040 1.07 0.0385 25.0 0.020 1.38 0.0575 16.4 0.010 1.80 0.0704 13.2 0.005 2.60 0.0980 9.2 0.0024 3.40 0.125 7.0 In Figure 64 are shown values of the ratio ; in other words, the n ratio of the charge transported by the negative carrier to that transported by the positive carrier. On examining the table, it will be seen that, for a given concentration ratio, the electromotive force increases as the con- centration decreases. At higher concentrations, the electromotive force decreases very rapidly with increasing concentration and ultimately be- comes extremely small. Referring to the figure, it is seen that at low concentrations the ratio of the carrying capacities of the two ions ap- proaches a limiting value; that of the negative carrier being approxi- mately seven times that of the positive carrier. As the concentration increases, the relative amount of current carried by the negative carrier increases, at first slowly and then more and more rapidly. In the neigh- borhood of normal concentration, the current carried by the negative carrier is several hundred times as great as that carried by the positive carrier. As we have seen, the positive carrier in a sodium solution is in all likelihood identical with the positive ion of a sodium salt. As Frank- lin and Cady have shown, the speed of this ion varies only little with concentration. The increased carrying capacity of the negative ion at higher concentrations must, then, be due to an increase in the mean speed of the negative carriers. It is a noteworthy fact that the carrying capacity of the negative carrier in dilute solutions is much greater than that of the sodium ion. The speed of the negative carriers in these solutions must therefore be much greater than that of the sodium ion. The speeds of the different 374 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS ions of salts in ammonia solution, as we have seen, do not differ greatly. This indicates that the negative carrier in the metal solutions is of rela- tively small dimensions. ' Nevertheless, if the negative carrier in these solutions were the negative electron unassociated with matter, we should expect a much greater value. It is known, however, that, owing to elec- trostatic action, a charge placed in a fluid medium tends to condense about it an atmosphere of the surrounding molecules. In gases at higher pressures, the speed of the negative carrier is as low as, and often lower 300 sso 200 too SO o.o o.s t.s Log F. 2.0 3.0 FIG. 64. Relative Speed of the Negative and Positive Ions of Sodium in Liquid Ammonia at Different Concentrations. than, that of the positive carrier and it is only at low pressures that the negative carrier in gases loses its envelope of surrounding molecules and acquires a high speed. It is not surprising, therefore, that the nega- tive electron in liquid ammonia should possess a speed comparable with that of ordinary ions. At higher concentrations, however, as is indicated by the increased carrying capacity of the negative ion, the size of the surrounding envelope evidently diminishes and, indeed, it has been shown that some of the negative carriers are completely unassociated with ammonia. If the negative carriers are associated with ammonia, then obviously, SYSTEMS INTERMEDIATE 375 due to the motion of this carrier, ammonia will be carried from the dilute to the concentrated solution. If the vapor pressures of the two solutions are known, we may calculate the work due to the transfer of solvent by the negative carrier, the number of molecules of ammonia associated with this carrier being assumed. The complete expression for the electromotive force is: _ 2nRT . M* where m is the number of molecules of ammonia associated with the negative carrier and p2 and pv are the vapor pressures of the two solu- tions. If we place n = 0 in this equation, that is, if we assume that all the current is carried by the negative carriers, we may calculate a maximum value for m, if the electromotive force of the cell and the vapor pressures of the solutions are known. For a concentration cell between solutions whose concentrations were 1.014 and 0.627 normal, the measured electromotive force was 0.08 X 10'3 volts, and the ratio of the vapor pressures was 1/1.006. This yields for m the value 0.67; that is, a value less than unity. Since m cannot be less than unity, it follows that at least a portion of the current must be carried by carriers not associated with ammonia. It is evident, from the manner in which the electromotive force and the vapor pressure of ammonia solutions vary with the concentration, that at higher concentrations the value calculated for m would be even smaller. The negative carriers in solution, there- fore, consist of negative electrons surrounded with ammonia molecules. As the concentration of the solution increases, the number of ammonia molecules associated with the carriers decreases and ultimately a por- tion of the carriers becomes entirely free from ammonia molecules. The great increase in the relative carrying capacity of the negative carriers at higher concentrations is due to the presence of these free negative electrons. 5. Conductance of Metal Solutions. If the increased carrying capacity of the negative carrier is, in fact, due to an increase in the mean speed of this carrier, the speed of the positive carrier remaining substantially constant, then the equivalent conductance of solutions of the metals in liquid ammonia should increase largely with the concentra- tion at higher concentrations. Since the determinations of the molecular weight, as well as the results on the motion of the boundary between a metal and a metal amide solution, indicate that an equilibrium exists between the positive ions and the negative carriers and the neutral atoms, it is to be expected that the ionization of the metal will vary as a 376 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS function of the concentration. According to these views the state of a metal dissolved in ammonia does not differ materially from that of a salt of the same metal dissolved in this solvent. The only material dif- ference lies in the fact that, whereas in the metal solution the negative electron functions as negative carrier, in the salt solution, a negative ion, that is, a negative electron attached to an atomic complex, serves as negative carrier. We should therefore expect the equivalent con- ductance in dilute solutions to vary as a function of the concentration in a manner similar to that of normal electrolytes. In other words, with decreasing concentration of the solution, the equivalent conductance should increase and approach a limiting value. In Table CL are given values of the equivalent conductance of solu- tions of sodium in liquid ammonia at its boiling point at different con- centrations. The density of the solutions not being known, the dilu- tions given under the column headed V represent the number of liters of pure ammonia of density 0.674, in which one atom of sodium is dis- solved. In the more concentrated solutions the density is considerably lower than that of pure ammonia. TABLE CL. CONDUCTANCE OF SODIUM IN AMMONIA AT — 33.50.5 FA FA 0.5047 82490. 13.86 478.3 0.6005 44100. 30.40 478.5 0.6941 23350. 65.60 540.3 0.7861 12350. 146.0 650.3 0.8778 7224. 318.6 773.4 0.9570 4700. 690.1 869.4 1.038 3228. 1551.0 956.6 1.239 2017. 3479.0 988.6 2.798 749.4 7651.0 1009.0 6.305 554.7 17260.0 1016.0 37880.0 1034.0 In Figure 65 the upper curve represents the equivalent conductance as a function of log V up to a concentration of approximately normal. From an inspection of the table and the accompanying figure, it will be seen that the conductance curve exhibits a minimum in the neighborhood of 0.05 N. At lower concentrations the equivalent conductance increases as the concentration decreases and approaches a limiting value in the neighborhood of 1016. The form of the curve at these concentrations is •Kraus, loc. cit. SYSTEMS INTERMEDIATE 377 similar to that of binary electrolytes in liquid ammonia, the only ma- terial difference being that the conductance has a much higher value. The equivalent conductance of the sodium ion is 130. It follows, then, that the equivalent conductance of the negative carrier in these solutions at low concentrations is in the neighborhood of X886, or 6.8 times that of the sodium ion. We saw in the previous section that the results of measurements of the electromotive force of concentration cells indicate that the carrying capacity of the negative carrier is approximately 7 times that of the positive ion in a sodium solution. This value, therefore, is in excellent agreement with the value 6.8 obtained from conductance Equivalent Conductance, Lower Curve. -! * ! -* s ! ! I ! I 1 \ ^ f ' *• 1 1 \ / V V *-%• — f X O Q l.s 0.0 o.s /.o /.s *& t.s a.o js +.0 *.*• Log V. FIG. 65. Equivalent Conductance of Sodium in Liquid Ammonia at — 33.5° at Different Concentrations. measurements. Evidence has already been presented which indicates that the positive ion in a sodium solution is identical with the positive ion in a solution of a sodium salt. The fact that the conductance of the positive ion, as derived from measurements with the metal solutions, corresponds with that of the sodium ion as derived from measurements with solutions of sodium salts confirms this hypothesis. The positive ion in a solution of sodium in liquid ammonia is therefore the normal sodium ion. If, now, we examine the conductance curve in the more concentrated solutions, we see that below a concentration of 0.05 N the conductance increases with the concentration, the increase being the greater the higher the concentration. This, again, confirms the conclusion derived from a study of the electromotive force of concentration cells. As the concentration increases, the relative carrying capacity of the negative carrier increases. The increase in conductance is due to an increase in the mean speed of this carrier, since at higher concentrations the con- 378 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS ductance increases enormously, which result may be accounted for only on the assumption that the speed of one or both of the carriers increases. Since one of these carriers is the normal sodium ion, it follows that the conductance is due to an increase in the speed of the negative carrier. If these conclusions are valid, then, at high concentrations, the conduc- tance of the metal solutions should approach that of the metals them- selves, for at high concentrations the number of carriers and negative electrons present in the solution becomes comparable with that of the total number of molecules present, in which case we should expect that a considerable fraction of these carriers would be free from ammonia molecules. This is borne out by the results of conductance measure- ments. As may be seen from Table CL, the equivalent conductance in- creases from a value of approximately 475 at a concentration of 0.05 N to a value of approximately 2000 at normal and to approximately 82000 at a concentration of 2 normal. At this concentration the specific con- ductance of the solution is 163.5, the specific conductance of mercury being 1.063X10*, which is about six times that of the metal solution at the concentration in question. The lower curve in Figure 65 shows how the conductance varies with concentration up to 2 N. In the following table are given values of the specific conductance of solutions of sodium in liquid ammonia up to the saturation point of these solutions.6 TABLE CLI. SPECIFIC CONDUCTANCE OF CONCENTRATED SOLUTIONS OF SODIUM IN AMMONIA AT — 33.5°. V n V \i 0.1081 5047.0 0.5099 148.3 0.1331 4954.0 0.7612 20.21 0.1804 2687.0 0.9265 5.988 0.2768 1070.0 1.298 1.269 0.3230 714.0 1.674 0.6465 The results for sodium, together with those for potassium, are shown graphically in Figure 66, where the logarithms of the specific conduc- tance are plotted against the logarithms of the dilution V as defined above. The curve passing through the points is that of potassium; the other, that of sodium. At the highest concentrations, the solutions were saturated, so that the specific conductance was independent of the total amount of ammonia present. The second point for the value V = 0.1331 •Kraus and Lucasse, J. Am. Chem. Soc. }3 (Dec., 1921). SYSTEMS INTERMEDIATE 379 lies just below the saturation point. The specific conductance of the saturated solution is 0.5047 X 104; or, almost precisely one half that of mercury at 0°. That the solutions of the metals in liquid ammonia at these concentrations are metallic admits of no doubt. They exhibit all the properties of metallic substances, both optical and electrical. A brief consideration will show, indeed, that in these solutions the metal possesses an exceptionally high conducting power compared with that of 3.0 CQ I o.s o.o 7.S l.o 2.9 To T.Z 74- 7*6 7.B 0.0 o.a. 0.4- o.e o.& Log V. FIG. 66. Conductance of Concentrated Solutions of Sodium and Potassium in Liquid Ammonia at — 33.5°. many metals. Obviously, if metallic conduction is due to the motion of charged carriers, then two factors influence the conductance; in the first place, the resistance which the carriers experience in their motion, and, in the second, the number of carriers present in a given volume. In comparing the conducting power of different metals, it is not sufficient to merely compare their specific conductances. The concentration factor should also be taken into account. If the specific conductance is divided by the number of gram atoms per cubic centimeter, the ratio yields the atomic conductance of the metal. The atomic conductance of a satu- 380 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS rated solution of sodium in ammonia 6a is 1.1 X 106 The atomic con- ductance of metallic sodium at room temperatures is 5.05 X 106. The conductance of the saturated solution is therefore comparable with that of the pure metal. Values of the atomic conductance of other metals will be found in Table CLIII of the next chapter. The atomic conductance of sodium solutions is about the same as that of osmium and tin and much greater than that of mercury (liquid) and bismuth. 400 0,0 3.0 4.0 2.0 Log V. FIG. 67. Conductance of Dilute Solutions of Potassium , and Lithium and of Mix- tures of Sodium and Potassium in Liquid Ammonia at — 33.5°. The view was expressed, above, that the negative carrier for dif- ferent metals dissolved in liquid ammonia is the same and is, in fact, the negative electron, which carrier presumably effects the passage of the current through all metallic substances. If this view is correct, then, at higher concentrations, where the conductance of the solution is due almost entirely to the negative electron, solutions of different metals in ammonia should exhibit very nearly the same properties. It is to be •• This is based on the value 0.54 for the density of the saturated solution as deter- mined approximately by Dr. Lucasse in the Author's Laboratory. This value may be in error by several per cent. SYSTEMS INTERMEDIATE . 381 expected, of course, that minor variations will be observed, since equiva- lent solutions are not physically .identical. The densities of potassium and sodium solutions, for example, differ; and the amount of ammonia associated with the positive ions in these solutions doubtless differs. Aside from minor differences, we should expect those properties of metal solutions, which depend upon the negative carrier, to be relatively inde- pendent of the nature of the metal. In Figure 67 are shown the conduc- tance curves of dilute solutions of potassium, lithium, and mixtures of sodium and potassium. The uppermost curve is that of potassium, the lowest that of lithium, while the intermediate curve is that of a mixture of sodium and potassium. The curve for mixtures of sodium and potas- sium lies intermediate between that of sodium and of potassium. It is seen that in the case of very dilute solutions of potassium and lithium, the conductance values, as shown, lie below the true values owing to the fact that these metals react with the solvent according to the equation: Me + NH3 = MeNH2 + £H2; that is, the metals react with the solvent to form the amides. This re- moves a portion of the metal from solution and consequently the con- ductance values measured are lower than the true values. From the extensive data presented by Kraus,. however, there can be no doubt as to the cause for the low values observed in dilute solutions in the case of potassium and lithium. At intermediate concentrations, where the formation of amide is not marked, the conductance of the solutions diminishes in the order: potassium, sodium, lithium. At a given con- centration, the difference in the values of the conductance of these metals corresponds approximately to the difference in the conductance of the positive ions of these metals. This shows that in dilute solutions of potassium, sodium and lithium in liquid ammonia, the conductance of the negative carrier is the same ; presumably, therefore, the negative car- riers are identical in the three cases. At higher concentrations, where the conductance of the positive ion becomes negligible in comparison with that of the negative carrier, we should expect the specific conduc- tance of the solutions to be practically the same at the same equivalent concentration. As may be seen from Figure 66, the conductance curves for sodium and potassium possess the same form, and over a considerable range of concentration they are practically identical.7 At higher con- centrations, slight variations occur as might be expected, since the den- sities of these solutions are not the same. The conclusion that the T Kraus and Lucasse, loc. tit. 382 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS negative carrier of the different metals is the same appears, therefore, amply justified. The temperature coefficient of sodium solutions in liquid ammonia has been measured. In Table CLII are given values of the resistance of fairly dilute sodium solutions from the boiling point of liquid ammonia up to 85°C. In the last column are given values of the mean percentage temperature coefficient of these solutions over various temperature inter- vals referred to the resistance at — 33°.7a TABLE CLII. TEMPERATURE COEFFICIENT OF DILUTE SODIUM SOLUTIONS. A(l/fl) t R X * — 33° 124.3 — 13° 85.7 2.25 + 17° 43.4 4.69 + 48° 28.2 5.34 + 85° 15.6 9.00 It is seen that at low temperatures the temperature coefficient of the conductance of these solutions is approximately 2 per cent, and as the temperature increases the temperature coefficient increases markedly reaching a value of 9 per cent for the interval between 45° and 85°. This behavior of the metal solutions in liquid ammonia is in striking contrast to that of normal electrolytes dissolved in this solvent. At ordinary concentrations, the conductance of these solutions passes through a maximum in the neighborhood of room temperatures, the conductance decreasing with increasing temperatures above this point. It is obvious that the factors involved in the temperature coefficients of the metal solutions are very different from those involved in solutions of ordinary electrolytes. It is difficult, in the present state of our knowl- edge, to state to what the high value of the temperature coefficient is due. However, since in fairly dilute solutions the conductance is due primarily to the negative electron more or less associated with ammonia, it is possible that the high value of the temperature coefficient at higher temperatures is due to an increase in the mean speed of the negative carriers as a result of a diminution in the size of the solvent envelope with which the negative electrons are surrounded. While at low concentrations the temperature coefficient of the metal T* Kraus, loc. cit. SYSTEMS INTERMEDIATE 383 solutions is greater than that of ordinary electrolytes, at high concen- trations the temperature coefficient is markedly lower.8 At a dilution V — 0.18, the temperature coefficient is approximately 0.17%. It is evident that at higher concentrations the value of the temperature coef- ficient decreases as the concentration increases. In the neighborhood of the saturation point, the coefficient is not far from zero, and, were it possible to prepare solutions having higher concentrations, it might be expected that the temperature coefficient would even become negative as it is in metals.8* These data on the temperature coefficient of the metal solutions in liquid ammonia serve further to differentiate these solutions from solu- tions of ordinary electrolytes. The behavior of the very concentrated solutions clearly indicates an intimate relation between these solutions and ordinary metallic conductors. The properties of the metal solutions in liquid ammonia, therefore, supply abundant evidence to the effect that conduction in metals is due to the motion of a negative carrier of sub-atomic dimensions, which carrier is the same for all metals. Since the only carrier of sub-atomic dimensions which has been observed is the negative electron, we may infer that the effective carrier in metals, as in these solutions, is the negative electron. 8 Observations by Dr. W. W. Lucasse in the Author's Laboratory. 8» Since this was written, the temperature coefficient of sodium in liquid ammonia has been determined by Dr. Lucasse from a dilution F = 1.7 up to the saturation point The coefficient for the saturated solution is 0.067%. As the concentration decreases, the temperature coefficient increases decidedly reaching a maximum of 3.65% at V = 1 06 after which it decreases more slowly, falling to 2.47% at V = 1.7. Chapter XV. The Properties of Metallic Substances. 1. The Metallic State. With the exception of the elements of the argon group and the strongly electronegative elements of lower atomic weight, elementary substances are metallic. Compounds between strongly electronegative and strongly electropositive elements, as well as compounds between the more electronegative elements, are non- metallic; while compounds between distinctly metallic elements are throughout metallic. Compounds between the less strongly electronega- tive elements and the less strongly electropositive elements are often metallic in the solid state. Thus the compounds of the alkali metals and the metals of the alkaline earths with the elements of the halogen and of the oxygen groups are non-metallic; while compounds of the less electropositive elements, such as lead and iron, with the elements of the oxygen group are often metallic. Within this class are also included certain free electropositive groups, containing both metallic and non- metallic elements, and possibly groups containing only nonmetallic elements. Thus, the free group CH3Hg is metallic,1 while certain of the substituted ammonium groups form stable metallic amalgams.12 There is also evidence that the quaternary substituted ammonium groups are soluble in ammonia in the free state, and that in solution their prop- erties resemble those of the alkali metals.3 The property of metallicity, therefore, is not to be looked upon as an atomic property, since various groups of nonmetallic elements in the free state exhibit metallic properties. The metals thus comprise a major portion of the elementary sub- stances and a large number of compounds between metallic and non- metallic elements. While nonmetallic compounds may, in a large measure, be accounted for through the interaction of the negative elec- trons with atoms, a similar theory of the constitution of metallic com- pounds has not thus far been developed. One of the remarkable facts »Kraus, J. Am. Chem. Soc. 35, 1732 (1913). •McCoy and Moore, J. Am. Chem. Soc. 33, 273 (1911). •Palmaer, Ztschr. f. Elelctroch. 8, 729 (1902) ; Kraus, loc. cit. 384 THE PROPERTIES OF METALLIC SUBSTANCES 385 in connection with inter-metallic compounds is the large number of compounds derivable from a single pair of elementary substances. The constitution of these compounds does not harmonize well with our pres- ent conceptions of valence. The study of these substances is attended with many experimental difficulties and their nature at the present time is little understood. Metallic substances are characterized by certain well-defined prop- erties, chiefly electrical and optical, which are common to all.4 This community of property among metallic substances indicates some com- mon element within their constitution. During the past few decades the view has been gaining ground that the properties of metallic substances are primarily due to the presence of charged particles, presumably nega- tive electrons, which are relatively free to move within the body of the metal. While this theory of the constitution of metals is in good agree- ment with observed facts from a qualitative point of view, it has not been found possible to elaborate a detailed theory of metallic substances which accounts successfully for the major portion of their characteristic properties. 2. The Conduction Process in Metals. Metallic conductors are dif- ferentiated from electrolytic conductors in that the passage of the cur- rent through them is unaccompanied by an appreciable transfer of mat- ter. If a current is passed for an indefinite period of time through a series of metallic conductors, no material effects are observable, either within the conductors themselves or at the boundaries between them. If the conduction process in metals is due to the motion of negative electrons, then there must likewise be present in the metals positively charged constituents or ions which, conceivably, may take part in the conduction process. In all likelihood the amount of matter transferred by these carriers is extremely small, and may under ordinary conditions escape observation. Experiments carried out with amalgams of sodium and potassium indicate that in these systems an appreciable transfer of matter actually takes place.5 Curiously enough, in these amalgams, the electropositive constituent, that is, the alkali metal, was found to be carried toward the anode and not toward the cathode as might have been expected. The data are as yet too meager to warrant drawing * A very complete summary of the literature relating to metallic substances is given by J. Koenigsberger in Handbuch d. Elektrizitat u. d. Magnetismus by L. Graetz, Leipzig J. A. Earth (1920), Vol. 3, pp. 597-724. The older literature is also summarized in Winkelmann's Handbuch d. Physik, Vol. 4, pp. 344-384, and Baedeker's Elektrische Erscheinungen in Metallischen Leitern, Vieweg, Braunschweig (1911). 8 Lewis, Adams and Lanman, J. Am. Chem. 8oc. 37, 2656 (1915). 386 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS conclusions as to the part which the positive constituent plays in metallic conduction. It appears probable, however, that in suitable metallic systems an appreciable transfer of matter accompanies the passage of the current. The view that the conduction process in metals is an ionic one is the only one in agreement with our present notions regarding the constitu- tion of matter. The absence of material effects accompanying the trans- fer of electricity indicates a common carrier in all metallic substances. The fact that no positively charged carrier of sub-atomic dimensions is known lends probability to the view that metallic conduction is due to the motion of the negative electron, the only known carrier of sub-atomic dimensions. Direct evidence in support of the electron theory of metallic con- duction is very meager. Tolman and Stewart 6 have studied the current flow induced in metallic conductors under acceleration. From their meas- urements, they have calculated the ratio of the effective mass of the carriers to the quantity of electricity flowing. Their results indicate that the current is due to the motion of a negative carrier, the ratio of whose mass to the charge corresponds with that of the negative electron. For copper, aluminum and silver conductors, Tolman and Stewart found for the value of 1/ra, assuming 0 = 16, the values 1660, 1590, and 1540 respectively. These are somewhat lower than corresponds to the mass of a slowly-moving negative electron, but the difference lies within the limits of experimental error. The results of investigations on the prop- erties of solutions of the alkali metals in liquid ammonia, described in the preceding chapter, likewise furnish striking evidence in support of the electron theory of metallic conduction. Other properties of the metals, such as the Hall effect, and particularly the emission of negative electrons by metals at higher temperatures, lend support to this theory. The precise nature of the conduction process of metals, however, still remains very obscure. 3. The Conductance of Elementary Metallic Substances. The order of magnitude of the conductance of metals, in itself, furnishes evidence in support of the electron theory of metallic conduction. In Table CLIII are given values of the atomic conductance and the spe- cific resistance, as well as of the mean temperature coefficient a of the resistance of a number of elementary metals. •Tolman and Stewart, Phys. Rev. 8, 97 (1916) ; i?w?., 9, 164 (1917), THE PROPERTIES OF METALLIC SUBSTANCES 387 TABLE CLIII. ATOMIC CONDUCTANCE, SPECIFIC RESISTANCE AND RESISTANCE TEMPERA- TURE COEFFICIENT OF ELEMENTARY METALS AT 0°. Metal A X 10-6 Silver 6.999 Potassium 6.503 Sodium :.. 5.288 Rubidium 4.845 Copper 4.559 Gold 4.547 Caesium 3.898 Aluminium 3.834 Magnesium 3.215 Chromium 2.989 Calcium 2.457 Indium 1.905 Cadmium 1.875 Rhodium 1.811 Zinc 1.713 Lithium 1.534 Iridium 1.414 Tantalum 1.339 Tin 1.252 Osmium 1.119 Thallium 0.9775 Nickel 0.9613 Lead 0.9222 Palladium 0.9082 Platinum 0.8314 Iron 0.8031 Strontium 0.7194 Cobalt 0.7064 Manganese 0.6561 Antimony 0.4658 Arsenic 0.3735 Gallium 0.2208 Bismuth 0.1972 Mercury 0.1564 CTO X 106 1.468 6.100 4.28 11.60 1.561 ' 2.197 18.12 2.563 4.355 4.40 10.50 8.370 10.023 4.700 5.751 8.550 8.370 14.60 13.048 9.500 17.633 12.323 20.380 10.219 11.193 9.065 24.75 9.720 4.400 39.00 35.10 53.40 108.00 95.80 Oo-100Xl03 4.10 5.5 5.1 4.33 3.98 4.26 3.90 4.74 4.24 4.43 4.17 4.57 3.71 3.47 4.47 4.2 5.17 4.87 4.22 3.77 3.92 6.57 3.66 4.73 3.89 4.46 0.88 As may be seen from the table, the specific resistance of silver is 1.47 X 10'6. Compared with this, the specific resistance of fused salts is of the order of 1.0 and that of electrolytes, at normal concentration, 10. In comparing the conducting power of metals it is more rational to employ the atomic, or perhaps even the equivalent, rather than the spe- cific conductance, On this basis, metallic conductors exhibit many rela.- 388 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS tionships which otherwise are not apparent.7 The atomic conductance of potassium and of silver is of the order of 6 X 106 and that of mercury at ordinary temperatures, which is a relatively poor conductor, 1.5 X 105. Compared with these values, the equivalent conductance of fused salts is in the neighborhood of 50 and that of electrolytes at low concentra- tions 100. In a few instances, the equivalent conductance of electrolytes is considerably higher, as, for example, in aqueous solutions at high tem- peratures, where it approaches a value of 1000, and in solutions of the alkali metals in liquid ammonia at low concentrations. The above values relate to the conductance of metals at ordinary temperatures. If a simi- lar comparison were made at lower temperatures, the relative conduct- ingf power of the metals would be found to be enormously greater. The conductance of metals at very low temperatures will be discussed in the next section. The conductance of elementary metals in the liquid state is, in gen- eral, lower than in the solid state. The process of fusion is accompanied by a discontinuous change in the conductance values. In the following table are given the ratios of the specific conductances \is /^ of metals in the solid and liquid states, together with the ratio of their specific volumes Vi/vs. TABLE CLIV. CHANGE OF THE SPECIFIC CONDUCTANCE OF ELEMENTARY METALS ON MELTING. Specific Conductance Melting at the Metal Point Melting Point Hs/ty vl/vs Lithium. 177.8° 2.6 X 104 2.51 Sodium 97.6 9.5 X 104 1.34 1.024 Potassium 62.5 7.7 X 104 1.39 1.024 Caesium. 26.4 2.54 X 104 1.65 1.027 Zinc... 419. 2.7X104 2.0 >1 Cadmium 321. 2.9 X 104 1.96 1.047 Mercury —38.8 1.10 X 104 4.1 1.036 Thallium.. 301. 1.35 X 104 2.0 Tin 232. 2.1 X 104 2.2 1.028 Lead 327. 1.06 X 104 1.95 1.034 Antimony 629.5 0.88 X 104 0.70 Bismuth 269. 0.78 X 104 0.46 0.967 7 Richarz, Zfschr. }. anorp. Chew. 50, 356 (1908) ; Benedicks, JaJirb. f. Ro4, IS, 351 THE PROPERTIES OF METALLIC SUBSTANCES 389 As may be seen from the table, expansion of the metal on melting is, in general, accompanied by an increase of resistance. The change in the specific conductance is particularly marked in the case of mercury. In the case of antimony and bismuth, the specific conductance increases on fusion. This is particularly marked in the case of bismuth, which expands on fusion. A change in state of an elementary metal is at times accompanied by a discontinuous change in the conductance values and at times only by discontinuity in the temperature coefficient. The transition from gray tin to ordinary tin is doubtless accompanied by a discontinuous change in resistance, although the specific conductance of gray tin appears not to have been determined. In the case of elementary metals of very low conducting power, such as metallic silicon, discontinuous changes in the conductance curve have been observed. In other cases, as, for example, the transition of the magnetic metals at the recalescence point, the resist- ance curve itself is continuous, but the temperature coefficient under- goes a discontinuous change, as we shall see below. 4. The Conductance of Elementary Metals as a Function of Tem- perature. The electrical properties of different solid elementary metals are strikingly similar. With increasing temperature, the resistance of elementary metals increases, the mean coefficient having a value in the neighborhood of 0.004, which does not differ greatly from the coefficient of expansion of gases at low pressures. Certain metals, as, for example, the magnetic metals iron and nickel, have coefficients much higher than this value, particularly at higher temperatures. The resistance of most metals increases approximately as a linear function of the temperature, and over larger temperature ranges the resistance may be expressed very nearly as a function of the temperature by means of a quadratic equation. With decreasing temperature, the resistance of pure metals decreases and, down to liquid air temperatures, it would appear that a value of zero is being approached as a limit at the absolute zero. The experi- ments of Kammerlingh Onnes at liquid helium temperatures, however, have brought to light the remarkable fact that at very low temperatures the resistance of pure metals undergoes a discontinuous change. When a certain temperature is reached, the resistance falls off abruptly to values which are almost negligible, if not actually zero.8 For example, at 4.24° K. the resistance of mercury in terms of its value at 0° (extrapo- • Kammerlingh Onnes, numerous papers in the Proceedings of the KoninklHkP Ak*»/i emie van Wetenschaf ten te Amsterdam. A summary of the work relatfng ; t "the pr of metals at low temperatures will be found in articles by J. <6M- 8- 383 390 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS lated) is 0.163, while at 4.185° the resistance is less than 10~6, and at 2.45° less than 2 X 10~10. Similarly, the resistance of tin vanishes at a temperature of 3.78° K. and that of thallium at 2.3° K. The resistance of lead vanishes at a temperature between 4.3° and 20°, probably in the neighborhood of 6° K. Metals in a condition in which their resistance vanishes are said to be in a supraconducting state. Certain metals, such as platinum and copper, do not exhibit supraconductance. In such metals the conductance falls to a low limiting value, after which it remains independent of temperature. In the following table are given values for the resistance of platinum in arbitrary units, at a series of temperatures. TABLE CLV. RESISTANCE OF PLATINUM AT Low TEMPERATURES. T abs. Resistance 273.1 1.0 20.1 0.0170 14.3 0.0136 4.3 0.0119 2.3 0.0119 1.5 0.0119 It is apparent from this table that at a temperature in the neighborhood of 4.3° absolute the resistance of platinum falls to a value a little greater than 0.01 of its value at 0°. Below this temperature, the resistance remains constant. Similar results have been obtained for other metals such as copper and iron. Apparently, those metals, which exhibit a marked tendency to form solid solutions with other metals, do not exhibit the phenomenon of supraconductance. It has been suggested that the absence of this phenomenon in these metals is due to the influ- ence of minute traces of impurities. The significance of the phenomenon of supraconductance is not fully understood as yet. Various theories have been proposed in explanation of this phenomenon, as, for example, that of J. J. Thomson.9 Bridg- man 10 has recently suggested that a polymorphic change takes place at the point where supraconductance intervenes. According to this view, the normal state of a substance, or of a crystal, at very low temperatures is that of supraconductance. The residual resistance found in the case of such metals as platinum is due to non-homogeneity between the sur- faces of the individual crystals of which the conductor is composed. At •J. J. Thomson, Phil. Mag. SO, 192 (1915). 10 Bridgman, J. Wash. Acad. 11, 455. THE PROPERTIES OF METALLIC SUBSTANCES 391 the present time it is not possible to reach any certain conclusion as to the nature of these phenomena. The mean temperature coefficients a for a number of elementary sub- stances are given in Table CLIII above. In the following table are 1 dfy given values of the temperature coefficient a = — -=-— for a number of tit Ut metals at different temperatures. TABLE CLVI. TEMPERATURE COEFFICIENT ^ -5— FOR METALS AT DIFFERENT Rt tit Temperature Ag 25° 0.0030 100 0.0036 200 0.0039- 300 0.0040 400 0.0042 500 0.0044 600 0.0046 700 0.0047 800 0.0052 900 0.0058- 1000 1075 . TEMPERATURES. Fe Ni Al 0.0052 0.0043 0.0034 0.0068 0.0043 0.0040 0.0090 0.0070 0.0042 0.0111 0.0080 0.0043 0.0133 0.0036 0.0046 0.0147 0.0030 0.0050 0.0170 0.0028 0.0060 0.0224 0.0026 0.0120 0.0120 0.0025 at 625° 0.0046 0.0028 • • 0.0050 0.0037 f . , . 0.0062 . . Mg 0.0050 0.0045 0.0041 0.0043 0.0040 0.0036 0.0100 0.0250 at 625° Cu 0.0036 0.0038 0.0040 0.0041 0.0042 0.0043 0.0044 0.0047 0.0053 0.0057 0.0062 It will be observed, from the table, that the temperature coefficient in- creases with increasing temperature. The magnitude of the coefficients of different metals differs considerably, particularly those of the magnetic metals, iron and nickel. It is interesting to note that, as the transition point of these metals is approached, the temperature coefficient increases very largely. The temperatures at which the transition points are reached are indicated in the table by heavy type. Beyond the transition points, the temperature coefficients fall back to normal values, in the case of both iron and nickel. A somewhat similar phenomenon is ob- served in the neighborhood of the melting point, which is illustrated in the case of aluminium and magnesium, particularly in the case of the latter element. The temperature coefficient increases considerably as the melting point is approached. Beyond the melting point, the coefficients are, in general, smaller than below this temperature. The temperature coefficients of elementary liquid metals vary within 392 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS wide limits. The coefficients are greatest for the alkali metals, in which case they differ very little from those of the solids. In other cases, the temperature coefficients reach extremely small values, as, for example, in that of zinc. As a rule, the temperature coefficients of liquid metals have values in the neighborhood of one fifth that of the solid metals. In the following table are given the mean temperature coefficients of a number of liquid metals referred to their resistance at the lowest tem- perature given. TABLE CLVII. TEMPERATURE COEFFICIENT OF LIQUID METALS. Temperature Metal a Interval Sodium 38.5 X 10"4 M.P. Potassium 41.8 X 10~4 " Lithium 27.3 X 10'4 178-230 Tin 5.9 X 10'4 M.P.-350 Bismuth 4.1 X 10'4 Thallium 3.5 X 10~4 Cadmium 1.3 X 10-4 Lead 5.2 X 10~4 Copper 4.12 X 10'4 1084-1500 Aluminium 5.42 X HH 653-1250 Iron 3.66 X10-4 1055-1650 Nickel 1.67 X 1Q-4 1451-1650 Zinc 0.3 XIO'4 419-500 Tin 4.68 X 10'4 232-1600 Cadmium 2.26 X 10~4 500-650 Antimony 1.37 X 10"4 631-800 The temperature coefficients here given cannot be directly compared with those of the solid metals at ordinary temperatures, since the coeffi- cients are referred to the resistance of these metals at higher tempera- tures. In a number of instances values have been extrapolated to ordi- nary temperatures, in which case the coefficients are invariably smaller than those of solid metals. For example, the values for copper, aluminium and iron are 7.45 X 10~4, 8.40 X 10'4 and 8.15 X 10'4, re- spectively. The temperature coefficient as commonly measured is the resultant effect of temperature change and volume change. The temperature coef- ficient at constant volume differs materially from that at constant pres- sure, depending upon the influence of pressure upon the resistance of the conductor in question. In solid metals, the pressure effect is relatively THE PROPERTIES OF METALLIC SUBSTANCES 393 small, while the resistance-temperature coefficient is large; consequently, the temperature coefficient is not greatly affected by the volume change. In liquid metals, however, where the temperature coefficient is small and the resistance pressure coefficient relatively large, the volume change has a material influence on the observed temperature coefficient. In the case of mercury,11 the resistance temperature coefficient I D ) 1 -JT I — — 6.9 X 10'4 as against the value of + 8.9 X 10~4 for the resistance-temperature coeffi- cient at constant pressure. It is a significant fact that the resistance of a liquid metal at constant volume should decrease with increasing tem- perature. In this connection it may be noted that Somerville 12 -found that zinc wire, wrapped in the form of a spiral around a silica tube, exhibited a marked negative temperature coefficient above the melting point, the resistance varying very nearly as a linear function of the tem- perature. In this case the metal in the fluid state was held together by surface forces. The temperature coefficient of molten zinc in a quartz tube was found to be positive but of a very low value. 5. The Conductance of Metallic Alloys. Metallic alloys may be divided into four classes which exhibit distinct properties.13 These are: First, solid alloys in which pure crystals of the constituent elements are present in intimate contact; second, solid alloys in which mixed crystals of the constituent elements are present; third, solid alloys in which com- pounds of the constituent elements are present; and fourth, liquid alloys. Among the solid alloys, several of these types often appear in a single alloy. This is the case, for example, when mixed crystals are formed over limited concentration intervals. a. Heterogeneous Alloys. Except in so far as the resistance of alloys is influenced by the distribution of the crystals and the presence of resist- ance at the interface between crystal elements, solid alloys of the first class do not differ in their properties from pure metals. The specific resistance of such" alloys is a linear function of the composition and with change of temperature the properties vary as a linear function of the composition, b. Homogeneous Alloys. Homogeneous mixed crystals of pure metallic elements, or of compounds, form an important class of substances which are remarkable for the uniformity of their behavior among them- selves and the divergence of their behavior from that of their constituent elements. The addition of a second metallic component to another metal, "Kraus, Physical Review k, 159 (1914). 12 Somerville, Physical Review 33, 77 (1911). u A summary of the properties of metallic alloys is given by Guertler, Jahrb. /. Rad. 5, IT 394 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS whether" elementary or compound, causes a marked decrease in the con- ductance of the resulting homogeneous alloy. The decrease due to the addition of a given amount of the second constituent is the greater the lower its concentration. If the conductance is represented graphically as a function of the composition of the system, the resulting curve is throughout convex toward the axis of concentration. The minimum point in all cases lies in the neighborhood of a composition of 50-50. In o Au 20 UO 60 SO Composition, volume per cent. 700 Ag FIG. 68. Representing the Conductance of Homogeneous Alloys of Ag and Au as a Function of Composition. Figure 68 is shown the conductance curve at ordinary temperatures for homogeneous mixtures of silver and gold. As may be seen, the conduct- ance of either component is greatly reduced on the addition of the second constituent. The decrease in the conductance due to the addition of a second component depends upon the nature of the substance added and is, in general, the greater the less electropositive the added constituent. Thus, the decrease in the conductance of iron due to the addition of carbon or silicon is much greater than that due to the introduction of THE PROPERTIES OF METALLIC SUBSTANCES 395 tungsten or nickel. On the other hand, certain variations occur in the order of the effects. Thus, due to the addition of aluminium, the con- ductance of iron is lowered very nearly as much as due to that of silicon. The resistance-temperature coefficient of solid alloys of the second class likewise varies continuously as a function of composition. The curve of temperature coefficients is similar to the conductance curve, being convex toward the axis of concentration and having a minimum point in the neighborhood of a composition of 50-50. In Figure 69 is shown the curve of temperature coefficients for alloys of silver and gold. It will 0.004 I 0*01 a H . "i 90 100 A* Composition, volume per cent. FIG. 69. Temperature Coefficient of Silver-Gold Alloys as a Function of Composition. be observed that the temperature coefficient falls from a value of approxi- mately 4 X 10"3 for the pure elements to 7.5 X 10~4 for an alloy contain- ing 50 volume per cent, each, of the constituents. This behavior of homo- geneous metallic alloys is general. In many cases, the effect is very pronounced and the temperature coefficient falls to very low values. With decreasing temperature, particularly at low temperatures, the resistance of homogeneous metallic alloys decreases nearly as a linear function of the temperature. This form of the curve persists even to the lowest temperatures attainable. Apparently, then, the resistance of alloys of this type approaches a finite limiting value at the absolute zero. In the following table are given values of the resistance of manganin wire (84 Cu, 12 Mn, 4 Ni) down to liquid helium temperatures. TABLE CLVIII. RESISTANCE OF MANGANIN WIRE AT Low TEMPERATURES. Temp ..... 16.5 — 193.1 — 201.7 — 253.3 — 258.0 — 269.0 — 271 5 Resist ..... 124.20 119.35 117.90 113.42 112.91 111.92 111.71 396 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS Other alloys of this type exhibit a similar behavior at low temperatures. At high temperatures, the resistance curves of many of the alloys of this type are very -complex, often exhibiting both maxima and minima and the temperature coefficient at times becoming negative.13* The curve for manganin wire, for example, exhibits two maxima at approximately 25° and 475° C. and two minima at 360° and 525° C. respectively. In a few instances, the temperature coefficient is very nearly zero over a large range of temperature, as, for example, in the case of advance wire, for which the temperature coefficient varies very little up to a temperature of 250° C. Taken all together, the resistance curves of solid solutions of metals are very complex at higher temperatures. c. Solid Metallic Compounds. The conductance of a solid compound of two elements is always lower than that of one of the constituents and is often lower than that of both. The specific resistance of a compound relative to that of the constituent elements depends upon the nature of the elements and upon tne nature of the compound formed. In general, the more stable the compound, the higher is its resistance relative to that of the constituent elements. Compounds between strongly electro- positive and strongly electronegative metallic elements, as a rule, exhibit a very high specific resistance. In the following table are given values of the specific conductance of a number of compounds at room tem- peratures. TABLE CLIX. SPECIFIC CONDUCTANCE OF A NUMBER OF METALLIC COMPOUNDS. Metal Mg2Sn Cu2Mg CuMg2 MgZn2 Mg3Bi2 Al3Mn Al3Fe n x lo-4 .. 0.0912 19.4 8.38 6.3 0.76 0.20 0.71 Metal Al3Ni AlMg Al2Mg3 Al2Ag3 AlAg3 Sb2Te2 TeSn H X 10-4 .. 3.47 2.63 4.53 3.85 2.75 0.48 0.97 Metal Bi2Te3 SbAg3 Cu3As MgAg Mg3Ag 1* X 10-* .. 0.045 0.93 1.70 20.52 6.16 It will be observed, from the table, that the compound between mag- nesium and tin has a very low specific conductance. Where two ele- ments form a number of different compounds, that compound, in gen- eral, has the lowest specific conductance which corresponds to the normal electronegative valence of the less metallic element. Thus, the specific conductance of Cu4Sn is much lower than that of Cu3Sn or of CuSn. The low value of the specific conductance is well shown in the case of the alloys of magnesium and tin which form the compound Mg2Sn. The »• Somerville, Phys. Rev. 31, 261 (1910). THE PROPERTIES OF METALLIC SUBSTANCES 397 specific conductance of this compound at 25° is 0.0912, as compared with 8.65 for tin and 22.73 for magnesium. While the conductance of inter-metallic compounds is thus, in gen- eral, very low, the temperature coefficient of these compounds is of the same order of magnitude as that of pure metals. While, therefore, the addition of a second metallic component increases the resistance of the metallic alloy, whether a compound or a solid solution is formed, so that it is at times difficult to distinguish between these two cases by this means, the temperature coefficient of the resulting alloy will, in general, differ widely in the two cases. The high value of the temperature coeffi- cient of metallic compounds and the low value of this coefficient for homogeneous alloys afford a delicate method of detecting the presence of solid solutions in metallic alloys. d. Liquid Alloys. The properties of liquid alloys differ greatly from those of homogeneous solid alloys. On the addition of a second com- ponent, the conductance of a liquid metal may either increase or de- crease. The relative conductance of the two substances does not deter- mine the magnitude and sign of the initial conductance change. If the specific conductance of two metals is nearly the same, the conductance curves often exhibit maxima or minima and sometimes both maxima and minima. In Figure 70 are shown the conductance curves for mixtures of mercury with bismuth, lead, tin and cadmium. Small additions of these elements to mercury cause a relatively large initial rise of the conductance curve. This rise is particularly noteworthy in the case of bismuth, which itself is a relatively poor conductor. The four curves are evidently similar. With bismuth and lead, whose specific conductances are relatively low, both a maximum and a minimum occur in the con- ductance curve. With tin the maximum and minimum have disappeared, but an inflection point is present in the conductance curve. The curve for alloys of cadmium and mercury exhibits a constant curvature. The four elements, the conductance of whose amalgams are shown in the figure, do not form compounds with mercury according to their melting point diagrams. The behavior of amalgams, in which compounds are formed, differs markedly from that of amalgams in which compounds are absent. The addition of small amounts of lithium, calcium and strontium increases the conductance of mercury, while that of potassium, sodium, caesium and barium reduces its conductance.14 With increasing temperature, the relative effect of such addition is increased. According to Hine,15 the 14 H. Fenninger, Dissertation, Freiberg, 1914 ; J. Koenigsberger, loc. cit.t p. 654. »»Hine, J. Am. Chem. Soc. 39, 890 (1917). 398 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS specific conductance of sodium amalgams passes through a minimum at about 2.5 atom per cent of sodium. McCoy and West 15a have determined the conductance of amalgams of substituted ammonium bases. The conductance of these amalgams decreases with increasing concentration, passing through a minimum. In general, liquid alloys whose components do not form compounds exhibit conductance curves without pronounced minima. On the other hand, alloys which form compounds often exhibit pronounced minima. This is, for example, the case with alloys of sodium and potassium. In the following table are given conductance values of mixtures of sodium and potassium, together with their temperature coeffi- cients.18 TABLE CLX. CONDUCTANCE OF LIQUID SODIUM-POTASSIUM ALLOYS AT 200°. Specific Atom Per Cent Conductance Potassium \i X 10~4 a X 103 0 7.37 +3.85 4.2 5.55 3.222 8.0 4.42 2.43 26.5 2.690 1.725 44.5 2.150 1.555 63.0 5.095 1.585 82.0 2.250 1.860 93.0 3.230 2.91 100.0 4.59 4.98 It will be observed that the conductance curve exhibits a minimum in the neighborhood of 50 atomic per cent of sodium and potassium, which corresponds with the composition of the compound NaK. The existence of this compound has been established by means of the melting point diagram. It will be observed, also, that the temperature coefficient of the sodium-potassium alloys exhibits a minimum value at a composition cor- responding with that of the compound. The conductance of alloys of copper and lead exhibits neither a maximum nor a minimum, but the tem- perature coefficient exhibits a minimum at a composition in the neighbor- hood of 40 per cent of lead. The conductance curves of liquid alloys of copper and antimony exhibit singularities corresponding with the com- position of the compounds Cu4Sb and Cu3Sb. The temperature coeffi- cients of both these compounds are negative, while, those of the pure metals are positive. The conductance curve for liquid mixtures of copper »« McCoy and West, J. Phys. Chem. 16, 261 (1912), 16 Koenigsberger, \oc. cit, THE PROPERTIES OF METALLIC SUBSTANCES 399 and tin likewise exhibits singularities, which indicate the formation of compounds. The temperature coefficients of these compounds are negative. It may be concluded that liquid alloys, in which compounds are formed, exhibit properties which differ markedly from those of alloys in which compounds are not formed. When the compounds formed are very stable, the conductance of the resulting alloy is usually less than that of the pure components. The temperature coefficient of fused metal- lic compounds is, as a rule, either very small or negative. 0 Hg ?0 2O JO £0 6O 70 80 90 700 B Weight Per Cent B FIG. 70. Conductance of Liquid Amalgams as a Function of Composition. 6. Variable Conductors. Within this class are included those ele- mentary substances which lie upon the border line between metallic and nonmetallic elements. There are also included a considerable number of metallic compounds in which one of the constituents is strongly electro- negative. The elementary substances comprised within this class often appear both in a metallic and in a nonmetallic state. Carbon is a typi- cal example of this type which, in the form of diamond, is a noncon- ductor, and, in the form of graphite, a relatively good conductor. Many of the metallic compounds, also, may appear both in a conducting and in a nonconducting state, as, for example, various sulphides and oxides 400 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS which are metallic in a crystalline state and which are nonmetallic when precipitated from solution. The specific conductance of the metals of this class is often relatively low. In the following table are given values of the specific conductance of a few of these metals. TABLE CLXI. SPECIFIC CONDUCTANCE OF VARIOUS SUBSTANCES AT 0°. Conductor Specific Conductance Graphite (Siberia) ................... 8.71 X 102 Silicon (+ 3.3% impur.) ........ . ...... 10.0 Titanium ............................ 2.8 X 103 Zirconium ........................... 5 X 103 CuS . ............................... 8.5 X103 Pb02 ............................... 4.3 X 103 CdO ................................ 8.3 X 102 PbS ................................ 4.2 X 102 Fe304 ............................... 1.16 X102 FeS2 (Pyrite) ....................... 0.42 X 102 FeS2 (Marcasite) ... ................. 0.06 The resistance of metals of this class at lower temperatures decreases greatly with increasing temperature, approximately as an exponential function. At higher temperatures, the conductance reaches a minimum value, after which it increases approximately as a linear function of the temperature. A familiar example of this type of substance is carbon. It is uncertain, however, that the observed conductance curves of this type actually relate to pure substances. Kammerlingh Onnes and Hof 17 have shown, for example, that graphite may be purified to a point where its resistance decreases with temperature down to approximately — 173° with a coefficient of 0.0029. At lower temperatures the resistance de- creases somewhat more rapidly. Similar results have been obtained in the case of bismuth. In the earlier experiments of Dewar and Fleming/8 bismuth was found to exhibit a minimum resistance at temperatures varying from room temperatures to — 80° C., depending upon the purity of the sample. Later, however, this element was purified to a point where its resistance decreased throughout with decreasing temperature down to liquid hydrogen temperatures.19 Since many of the substances of this class cannot be prepared readily in a pure state, it follows that the pecu- 17 K. Onnes and Hof, KoninkUjke Akad, van Wetensch. Amsterdam 11, 520 (1914). "Dewar and Fleming, Phil. Mag. W, 303 (1895). 18 J. Clay, Dissertation, Leiden (1908) ; Jahrb. f. Rad. 8, 391 (1911). THE PROPERTIES OF METALLIC SUBSTANCES 401 liar form of the conductance curve may be due primarily to the presence of impurities. Many of these substances exhibit transition points at which the resist- ance changes discontinuously. In some instances these processes are reversible and in others irreversible. Silicon exhibits transition points at approximately 220° and 440°. Titanium exhibits discontinuities in the neighborhood of 300° and 600°, the first of which is slowly reversible and the second irreversible. Among variable conductors are included many compounds on the borderline between metallic and nonmetallic substances. These com- pounds often appear in several modifications whose properties may differ greatly. For example, silver sulphide, which has already been mentioned in a preceding chapter, conducts electrolytically in one form, while in another form it exhibits mixed electrolytic and metallic conduction. Many solid oxides and mixtures of oxides, which at ordinary temper- atures are nonmetallic, appear to conduct the current metallically at high temperatures. The Nernst filament is a familiar example of this type of conductor. While it is possible that a portion of the current in some of these substances is carried electrolytically, the greater portion appears to be carried metallically. As the compounds become more distinctively metallic, which is as a rule the case as the more electronegative element becomes more metallic and the more electropositive element becomes less metallic, the conduct- ance approaches that of typical metallic compounds. In such cases, the temperature coefficient becomes less negative or even positive. In gen- eral, the higher the conductance of a compound, the greater is the value of its positive temperature coefficient. Many of the conductors belonging to this class exhibit singular prop- erties. In many cases, also, systems, which might not be expected to exhibit metallic properties, nevertheless belong to this class of conductors. Such is, for example, the case with cuprous iodide, Cul, which absorbs iodine reversibly. The resulting product conducts the current metal- lically and its conductance is the greater the greater the amount of iodine absorbed. The smaller the resistance of the iodide, the greater is the value of the positive temperature coefficient. As the specific resistance increases, the temperature coefficient becomes negative. The examples of this class of substance are extremely numerous and a great deal of experimental material is available. It is not to be doubted that a study of such systems will throw a great deal of light on the nature of the conduction process and conceivably on the constitution of metallic 402 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS compounds. A more detailed discussion, however, is not possible in this monograph.20 7. The Conductance of Metals as Affected by Other Factors. a. Anisotropic Metallic Conductors. As might be expected, the con- ductance of many crystalline substances depends upon the orientation of the crystal. Thus, the conductance of a crystal of bismuth at right angles to its base at 15° is 1.78 times that parallel to its base.21 It has been shown that the conductance of a bismuth crystal may be represented . by means of an ellipsoid of rotation.22 b. Influence of Mechanical and Thermal Treatment. The conduct- ance of metals is dependent upon their previous mechanical and thermal treatment. Wires which are hard drawn in general exhibit a lower con- ductance than do annealed wires. The thermal treatment of metals has an influence on their conductance, not only in that it tends to relieve mechanical stresses resulting from previous mechanical treatment, but also in that it tends to induce various transformations in the body of the metal, some of which are reversible and others of which are irreversible. c. The Influence of Pressure on Conductance. The resistance of most metallic elements is decreased under the action of uniform pressure. The coefficient -~ -3- for solid metallic elements varies between— 15.1 XlO'7 R dp for nickel and — 152 X 10~7 for lead. For bismuth the value of the coefficient is positive and equal to + 196 X 10~7. The resistance does not vary as a linear function of the pressure, the pressure coefficient de- creasing with increasing pressure. The resistance of manganin wire varies very nearly as a linear function of the pressure. The only pure liquid metal for which data are available is mercury. At 25°, the value of its resistance-pressure coefficient is — 334 X 10~7. It would be inter- esting to know whether other liquid metals exhibit a similarly high value of this coefficient. The influence of pressure on the resistance of variable conductors is often extremely marked.23 d. Photo-electric Properties. A few substances are sensitive to the action of light. Selenium is the most remarkable example of this type of substances. The influence of light and various other factors on the conductance of selenium has occupied the attention of a great many inves- tigators. A detailed discussion cannot be given here.24 8. Relation between Thermal and Electrical Conductance in Metals. 80 A very complete summary is given by Koenigsberger, loc. cit., pp. 661-680. "Lownds, Ann. d. Phys. 9, 681 (1902). 22 van Everdingen, Versl. Akad. van Wetensch. Amsterdam 3, 316 and 407 (1900), 23 For references, see Koenigsberger, loc. cit., pp. 694-7. *« For references, see Koenigsberger, Iqc. cit., pp. 681-694, THE PROPERTIES OF METALLIC SUBSTANCES 403 As was first pointed out by Wiedemann and Franz,25 the thermal con- ductance of metals at ordinary temperatures is very nearly proportional to their electrical conductance. Subsequent investigations 26 have shown that the ratio of thermal to electrical conductance is not a constant, but increases with increasing temperature. Lorenz 2T showed that the ratio of thermal to electrical conductance - for pure metallic substances and H some alloys increases approximately as a linear function of the absolute temperature, the coefficient being very nearly equal to the coefficient of expansion of gases. Since the resistance varies approximately as a linear function of the absolute temperature, it follows that the thermal con- ductance of metals is relatively independent of temperature. At very low temperatures, however, the thermal conductance of metals increases markedly. Nevertheless, as K. Onnes and Hoist,28 have shown, the thermal resistance of metals does not approach a value of zero in regions where metals are in the supraconducting state. For example, at its melting point, the thermal conductance of mercury is 0.075; between 4.5° K and 5.1° K it is 0.27; and between 3.7° K and 3.9° K it is 0.40. At very low temperatures, therefore, the thermal and electrical conduct- ance do not follow a parallel course. The thermal conductance of alloys varies with composition in a man- ner somewhat similar to that of the electrical conductance. The change in thermal conductance, due to a given change in composition, is consid- erably smaller than is the corresponding change in electrical conduct- ance. The thermal conductance curves of alloys which form a complete series of mixed crystals exhibit a minimum similar to that of the elec- trical conductance curves. The relative decrease of the thermal con- ductance, however, is much smaller than that of the electrical conduct- ance. Accordingly, the ratio of the thermal to the electrical conductance for homogeneous alloys is considerably greater than it is for pure metals. Somewhat similar relations are found in the case of metallic compounds. While compounds in general exhibit a lower thermal conductance than do the pure components, the ratio of thermal to electrical conductance is larger for the compounds than it is for pure metals. The thermal conductance of variable conductors is often as great as that of typical metallic elements. Since the electrical conductance of these substances is relatively low, the ratio — for these substances is often "Wiedemann and Franz, Pogg. Ann. 89, 497 (1853) ; ibid., 95, 338 (1895). 26 The literature relating to this subject has been collected in various handbooks; see footnote, p. 385. 27 L. Lorenz, Pogg. Ann. U{1, 429 (1872) ; Wied. Ann. IS, 422 (1881). »K. Onnes and Hoist, Proc. Amsterdam Acvd. 171, 760 (1914). 404 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS very great. Thus the value of - for graphite, silicon and hematite (Fe203) is 2.5 X 1012, 6.8 X 1014 and 7.3 X 1014 respectively. For ordi- nary metals the value is in the neighborhood of 6.7 X 1010 at room tem- peratures.29 In this connection it is interesting to note that the thermal conductance of some nonmetallic crystals is greater than that of many metallic substances. Thus, the thermal conductance of rock salt is 0.0137 and that of quartz -L to its axis is 0.0263, while that of bismuth is 0.0194. While thermal and electrical conductance are intimately related, the fact that some nonmetals are likewise excellent thermal conductors should not be lost sight of. 9. Thermoelectric Phenomena in Metals. We have to consider three related thermoelectric phenomena, namely: 1, the electromotive force arising in a metallic system as a result of a temperature difference be- tween the junctions of two metals; 2, the Peltier effect which is a heat transfer taking place when a current passes through a junction between two different metallic conductors; and, 3, the Thomson effect which is a heat transfer accompanying the passage of the current through a con- ductor in which a temperature gradient exists. From a practical point of view, the first of these effects is the most important and has been investigated most extensively. The thermoelectric force of a thermocouple may be expressed very nearly as a function of the temperature by means of an equation of the form: Usually a quadratic equation suffices. For smaller temperature differ- ences, the sign of the constant a corresponds with the direction of the thermoelectric force. The sign of this electromotive force depends upon the nature of the metals. Let us call the effect positive for the two metals AB, when the current flows from A to B at the cold junction. The metal A will then be said to be positive with respect to B. The values of the coefficients a and |3 for different metals with respect to lead, the cold junction being kept at a temperature of 0° C., are given in Table CLXII. As may be seen from the table, metals which are closely related often have thermoelectric constants which are opposite in sign; thus, lithium and potassium stand in reverse order to lead, which, in the table, is taken as a standard. So, also, the closely related elements, antimony and bismuth, which exhibit a relatively high thermoelectric power, lie near n See Koenigsberger, IQC. eft., p. 720-, THE PROPERTIES OF METALLIC SUBSTANCES 405 TABLE CLXII. VALUES OF THE THERMOELECTRIC COEFFICIENTS a AND (3 WITH RESPECT TO LEAD IN MICROVOLTS PER DEGREE. Metal Si Tea Sb || Fe Li Ag Pb a +443 + 163 + 22.6 + 13.4 + 11.6 + 2.3 0 (3 X 102 . . . . . . . . — 3.0 +3.9 -f- 0.76 Metal Mg Sn Na K Co Ni Bi || a —0.12 —0.17 —4.4 —11.6—20.4 —23.3 —127.4 (3 X 102 . . 4- 0.20 + 0.20 - 2.1 — 2.5 - 7.5 — 0.8 — 70. the opposite ends of the table. Similar inversions are found in the case of other closely related elements, such as iron, cobalt and nickel. In alloys, the thermoelectric force is, in general, a function of the composition. The thermoelectric force of heterogeneous alloys varies approximately as a linear function of the composition, while that of homogeneous alloys, in general, exhibits a marked minimum somewhat similar to that of the conductance curve. The thermoelectric power of a compound, in general, differs from that of its component elements. The formation of compounds by a given pair of elements is indicated by dis- continuities in the curves connecting the thermoelectric force with the mean composition of the alloy. As a rule, the thermoelectric force is high for compounds which are relatively poor conductors. For a more detailed discussion of the thermoelectric properties of metals the reader is referred to the various handbooks in which these data have been collected. 10. Galvanomagnetic and Thermomagnetic Properties. When a cur- rent of electricity flows through a conductor, the distribution of the current in the conductor is altered under the action of an external mag- netic field. The effects observed depend upon the relative direction of the current and of the field. The application of the magnetic field, there- fore, gives rise to potential differences between points in the conductor which normally are at the same potential. With a field acting at right angles to the direction of the current flow, potential differences arise in the conductor transverse to the magnetic field, one at right angles to the direction of the current flow and the other parallel to this direction. With a longitudinal field, that is, a field acting parallel to the direction of the current flow, only a single effect is observable; namely, an electro- motive force parallel to the direction of current flow. Similar effects are observed when a current of heat flows through a conductor in a mag- 406 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS netic field. Conversely, when a current flows through a conductor in a magnetic field, temperature differences, as well as potential differences, arise in the conductor. Altogether, there are twelve effects of this type: four thermomagnetic effects in transverse fields, two thermomagnetic effects in longitudinal fields, four galvanomagnetic effects in transverse fields, and two galvanomagnetic effects in longitudinal fields. Of these various effects, the transverse galvanomagnetic effect in a transverse field has been studied most extensively. This is commonly known as the Hall effect. The relation between the electromotive force and the variables of the system are given by the equation: _ RHi D ' where H is the field intensity, i is the total current flowing, and D is the thickness of the conducting sheet carrying the total current i. R, which is the constant of the Hall effect, is a property of the conductor in ques- tion. This constant varies greatly for different metals and may have either positive or negative values. As a rule, the effect is greatest in substances of relatively low conducting power. It is particularly marked in bismuth. Here, however, as might be expected, the value of the coeffi- cient depends upon the orientation of the crystal. Since the flow of current in a conductor is influenced by an external magnetic field, it fol- lows that the resistance of a conductor will be influenced by an external field. At low temperatures, the influence of a magnetic field on the resist- ance becomes marked, particularly for bismuth. K. Onnes 30 has shown that at very low temperatures, where metals are normally in the supra- conducting state, the curves connecting resistance and field strength are similar to those connecting resistance and temperature. The action of transverse and longitudinal fields differs little. For lead and tin the critical value of the field strength at which the resistance rises abruptly to measurable values lies between 500 and 700 G. It varies slightly with temperature. The various galvanomagnetic and thermomagnetic effects would ap- pear to be of great importance from a theoretical standpoint; for, if a current is carried by charged particles, the observed effects must be due to the reaction of the field on these particles. It might be expected that the reaction of the field on the moving particles in a metallic conductor would be similar to that observed in the case of the cathode rays. Actu- ally, however, the observed effect in the case of most metallic conductors •°Ver8l. Akadf van Wetensch. Amsterdam 23, 493 (1914). See also J. Clay, Joe. cit. THE PROPERTIES OF METALLIC SUBSTANCES 407 is in a direction opposite to that observed in the case of P particles, assum- ing that the conducting particles in metals are negatively charged. Since a great many facts indicate that the current in metallic conductors is not carried by positive particles, it appears that the various galvanomagnetic effects cannot be accounted for by a simple theory of this type. A num- ber of theories, that of J. J. Thomson for example, have been suggested to account for the Hall effect and similar phenomena.81 At the present time, however, a satisfactory theory of these effects does not exist. In- deed, the same may be said of the theory of the conduction process in metals under normal conditions. It may be expected, however, that ultimately the thermomagnetic and galvanomagnetic effects will play an important role in the development of the theory of metallic conduction. A detailed study of the properties of conductors in a magnetic field would lead far beyond the scope of the present monograph. The ob- served facts will be found summarized in the references already given. 11. Optical Properties of Metals. According to the electromagnetic theory, the electrical and optical properties of metallic substances are intimately related. The reflecting power and absorbing power of metals, according to this theory, should be very great. From the known values of the conductance of metallic substances, the optical constants of these substances may be derived for long wave lengths when selective action does not occur. The theory of the optical effects in metals, together with the most important facts, will be found summarized in treatises on electricity and magnetism and on physical optics.32 12. Theories Relating to Metallic Conduction. The theory of metal- lic conduction, like the theory of electrolytic conduction, is still in a very unsatisfactory state. Qualitatively, the theory that the current is carried by negative electrons is in good agreement with the facts, but a satisfac- tory quantitative theory has not, as yet, been established. The difficulties confronting a comprehensive theory of metallic conduction are, indeed, very great, as is apparent when it is considered how many detailed facts must be accounted for. A number of theories which have been proposed are able to account for a limited number of the properties of metals in a fairly satisfactory manner. So, for example, the theories of Drude and of Thomson render an account of the relation between the thermal and the electrical conductance of metals and, to some extent, also, of the thermo- and galvanomagnetic effects and thermoelectric effects in metals. On the whole, however, these theories are far from satisfactory. They " J. J. Thomson, Rapp. Congr. Phys. 3, 143, Paris (1900). " See, for example, VVinkelmaun, Handbuch d. Physik ; Oraetz Handbuch d trizitat u. d. Magnetismus, etc. 408 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS are not able to account for the properties of metallic substances at very low temperatures. Neither are they able to account successfully for the properties of alloys and of liquid metals.33 It is obvious that the electrical properties of metallic substances are extremely sensitive to all agencies. Temperature and density, as well as all external forces, have a marked influence upon the electrical properties of metals, and particularly on the conductance. So, also, the properties of metallic substances are very sensitive to change in the state of the system. The formation of compounds, of mixed crystals, or any poly- morphic change is invariably accompanied by a great change in electrical properties. Ultimately, it would appear that a study of the electrical properties of metals, and particularly of metallic compounds, should yield some clue as to the constitution of these substances. At the present time, however, the constitution of metallic substances, and particularly of metallic compounds, remains an unsolved problem. 18 Very complete references to the theories dealing with metallic conduction are given by Koenigsberger, loc. cit., p. 385, above. SUBJECT INDEX Acetone, conductance of CoCl2 in — at dif- ferent temperatures, 163 ; — conductance of Nal in, 47 ; — values of A0 in, 62 ; — values of mass-action constant in, 62 Acid, acetic, mass-action constant of, 43 ; — amides, nature of, 315 ; — formic, hy- drolytic equilibria in, 230 ; — formic, solution of formates in, 101 ; — sulphuric, intermediate ions in aqueous solutions of, 148 ; — trichlorobutyric, mass-action con- stant of, 44 Acids, conductance of — in alcohol-water mixtures, 181 Activity Coefficient of T1C1 from solubility data, 337 ; — Coefficient, definition of, 331 ; — Coefficient, numerical values for concentrated solutions, 334 ; — Coeffi- cient, numerical values for dilute solu- tions, 333 ; — Coefficient, values obtained by different methods compared, 334 ; — definition of, 331 Alcohol, ethyl, conductance of Nal in, 47 ; — - ethyl, solubility of phenylthiourea in — in presence of electrolytes, 250 Alcohols, influence of water on conduct- ance of acids in, 181 Alloys, compound, conductance of, 396 ; — compound, resistance-temperature coeffi- cient of, 397 ; — heterogeneous, 393 ; — liquid amalgams, conductance of, 397 ; — liquid conductance of, 397 ; — liquid, conductance of mixtures of sodium and potassium, 398; — mixed crystals, 393; — mixed crystals, conductance change with composition, 394 ; — mixed crys- tals, conductance-temperature coefficient, 395 ; — properties of, 393 ; — thermal conductance of, 403 Ammonia, conductance of AgCN in, 53 ; — conductance of Hg(CN)2 in, 53; — con- ductance of higher types of salts in, 105, 108 ; — conductance of KNO3 in, 52 ; — conductance of solutions in — at different temperatures, 145 ; — hydrolytic equilibria in, 230 ; — molecular weight in — solutions, 240 ; — reactions in, see Reactions ; — solutions of metallic com- pounds in, 215 ; — solutions of metals in, 367; — viscosity of, 65 Ammonium Complex, nature of the, 213 Anions, complex, 213 ; — complex, in liquid ammonia, 215 ; — complex, nature of. 214 Antimony, complex anion of, 216 Bases, organic, free radicals of, 213 ; — or- §anic, nature of the positive ions of, 13 ; — organic, positive ions of, 212 Basic amides, nature of, 316 Bromine, conductance of solutions in, 50 Catalytic action of acids, esterification con- stants in methyl alcohol, 289 : — action of alcoholate ion, 291 : — action of elec- trolytes, Arrhenius' theory of, 291 ; — • action of hydrogen ion, velocity constants. 690 ; — action of ions, 287 ; — action of ions, as influenced by their thermody- namic potential. 291 ; — action of ions, inversion coefficients, 288 ; — action of un-ionized molecules. 288 ; — action, re- lative— of ions and un-ionized molecules. 290 409 Clausius, ionization according to, 34 Complexes, formation of — in mixed solvents, 177 Compounds, metallic, nature of, 216 Concentration cells, electromotive force of, 298 ; — cells, energy effects in, 306 Conductance, abnormal — of hydrogen and hydroxyl ions, 205 ; — dependence of — on fluidity at different temperatures, 122 ; — equation, constants of, for different solvents, 75 ; — equation, constants of, for dilute aqueous solutions, 100 ; — equation, constants of, for solvents of low dielectric constant, 77 ; — equation, con- stants of, in ammonia, 73, 77 ; — equa- tion, geometrical interpretation of, 80 ; — equivalent, and transference numbers, 32 ; — equivalent, defined, 27 ; — equivalent, influence of concentration on, 30 ; — equivalent, influence of temperature on — in sulphur dioxide, 155 ; — equivalent, influence of viscosity on limiting value of, 109 ; — equivalent, ionic, 37 ; — equi- valent, limiting value of, 30 ; — equi- valent, limiting value of, in acetone, 62 ; — • equivalent, limiting value of, in alcoholic solutions containing water, 181 ; — equivalent, limiting value of, in differ- ent solvents, 62; — equivalent, limiting value of, for organic electrolytes in am- monia, 60 ; — equivalent, limiting value of, for salts in ammonia. 59 ; — equi- valent, of aqueous salt solutions at high temperatures, 147 ; — equivalent, of higher types of salts at higher tempera- tures in water, 148 ; — equivalent, table of, 28; — function, applicability of — to ammonia solutions, 70 ; — function, form of, 67 ; — function, form of, in dilute aqueous solutions, 98 ; — function, graphical treatment of, 69 ; — function, Kraus and Bray's, 68 ; — function. Storch's, 67 ; — in critical region, 167 ; — in critical region, in methyl alcohol, 169 ; — in mixed solvents, 176, 190 ; — in vapors near critical point, 170 ; — influence of complex formation on — in mixed solvents, 197 ; — influence of con- centration on, 46 ; — influence of density of solvent on, 172 ; — influence of tem- perature on -- at high concentrations, 166 ; — influence of water on — in non- aqueous solvents, 178, 179 ; — influence of water on — in solutions of acids in alco- hols, 180 ; — ionic, abnormal values of, 206 ; — ionic, comparison of, in ammonia and water, 64 ; — ionic, comparison of, in different solvents, 63 ; — ionic, influ- ence of temperature on, 123 ; — ionic, influence of viscosity on, 111 ; — ionic, table of values of, in ammonia, 64 ; — ionic, values of, in formic acid, 207 ; — ionic, values of. in water. 37 ; — of fused salts, 353 ; — of glass, 356 ; — of pure substances, 351 ; — of solid electrolytes, 359 ; — of solutions in non-aqueous sol- vents, 46 ; — -temperature coefficient, influence of concentration on the, 161 ; — -temperature coefficient of solutions In halogen acids at high concentrations, 165 Conduction process, relation between metal- lic and electrolytic, 366 410 SUBJECT INDEX Conductors, electrolytic, 14 ; — metallic, 14 384 ; — metallic, anisotropic, 402 ; — . metallic, influence of treatment on properties of, 402 ; — metallic, influence of pressure on, 402; — metallic, photo- electric properties of, 402 ; — mixed me- tallic and electrolytic, 366 ; — variable, 399 Constant, ionization, influence of water on — of acids in alcohols, 185 Critical point, conductance in neighbor- hood of, 167 Density coefficient of ions, additive nature of 286 • — coefficient of un-ionized mole- cules, 285 ; — of electrolytic solutions, 283 • — of electrolytic solutions, as a function of ionization, 284; — of elec- trolytic solutions, according to Heydweil- ler, 284 ; — of solutions in acetone, 287 ; — of solutions in ethyl alcohol, 287 ; — of solutions in methyl alcohol, 287 Dielectric constant, dependence of ioniza- tion on, 89 ; — constant, influence of, on conductance, 16 ; — constant, influence of, on constants of conductance equation, 90 ; — constant, influence of, on ioniza- tion according to Walden, 92 ; — con- stant, influence of salts on, 92. Diffusion coefficient of electrolytes, 280 ; — coefficient of electrolytes, in presence of other electrolytes, 282 ; — of electrolytes, 280 ; — of electrolytes, in presence of other electrolytes, 281 Dilution law, see Conductance function Electricity and matter, 17 ; — discrete structure of, 20 Electrolytes, conductance of, in pure state, 15 ; — diffusion of, 280 ; — equilibria in mixtures of, 218 ; — ionization of, 34 ; — • molecular weight of, in solution, 37 ; — principles applicable to mixtures of, 220 Electromotive force and conductance meas- urements compared, 300 ; — force of concentration cells, 297, 298 ; — force of concentration cells, numerical values, 300 ; — force of concentration cells, the- ory of, 297 ; — force of concentration cells, with mixed electrolytes, 302 Energy effects in concentration cells with mixed electrolytes, 307 Equilibria, heterogeneous, 232; — homo- geneous ionic, 218 ; — hydrolytic, 225 ; — hydrolytic, equations of, 225 ; — in mix- tures with common ion, 219 Ethyl alcohol, conductance of CoCl2 in — at different temperatures, 162 Ethylamine, conductance of solutions in, 51 ; — conductance of solutions in, at different temperatures, 159 Faraday's Laws, 19 ; — Laws, applicability of, 19; — Laws, applicability of, to metal-ammonia solutions, 20 ; — Laws, exceptions to, 20 Fluidity, see also Viscosity ; — of mixed solvents, 187 Formates, conductance of — compared with acetates in water, 102 ; — solutions of, in formic acid, 101 Freezing point, comparison of — for solu- tions of different salts in water, 232 Fused salts, applicability of Faraday's Law to, 353 ; — salts, conductance and fluid- ity compared, 354 ; — salts, conductance or, 353 ; — salts, conductance of mix- tures of, 355 ; — salts, influence of tem- perature on conductance of, 354 Gases, conduction in, 13 Glass, conductance of, 356 ; — influence of temperature on conductance of, 357 ; — ionization value for, 358 ; — speed of ions in, 359 ; — transference in, 357 Graphite, pure, conductance of, 400 Hall effect, theory of, 407 Heat effects in concentration cells, 306; — of dilution of electrolytes, 305 ; — of neutralization of acids and bases, 304 ; — of neutralization of acids and bases and ionization constant of water, 304 Hexane, conductance in, 13, 351 Hittorf's numbers, see Transference Hydration, from transference measurements, 198 ; — influence of concentration on, 201 ; — influence of — on conductance, 201 ; — influence of temperature on 125 • — • of ions in water, 198, 200 ; — rela- tive— of ions, 201 Hydrogen bromide, conductance of methyl alcohol in, 49 ; — solubility of — in pres- ence of electrolytes, 245 Hydrolysis, see also Equilibria ; — 225 ; — at low concentrations in water, 228 ; — in phenol, 244 ; — influence of, on con- ductance, 228 ; — of salts at high tem- peratures, 150 Insulators, conductance of, 351 Iodine, conductance of, in sulphur dioxide, 322 Ion, chloride, conductance of, in formic acid, 207 ; — complex iodide, 214 ; — complex sulphide, 214 ; — conductance, independence of nature of other ions, 309 ; — conductance, of chloride ion with different cations compared, 309 ; — con- ductance, of potassium ion of different salts compared, 310 ; — hydrogen, as ox- onium complex, 205 ; — hydrogen, con- ductance of, in formic acid, 207 ; — hy- drogen, in liquid ammonia, 206 • — - hydrogen, nature of, 205 ; — hydroxyl, 205 ; — product, constancy of — for strong electrolytes, 262; — pyridonium, conductance of, in pyridine, 208 Ionic speed, influence of temperature on, 124 ; — speed, influence of viscosity on, in differetft solvents, 111 Ionization as a result of compound forma- tion, 322 ; — as measured by conduct- ance, 34 ; — as related to constitution of electrolyte, 320; — constant of am- monia and acetic acid at elevated tem- peratures, 149 ; — constant of water, 225 ; — constant of water and heat of neutralization, 304 ; — constant of water at high temperature, 150 ; — dependence of, on dielectric constant according to Walden, 92 ; — dependence of, on prop- erties of solvent, 88; — dependence of, on solvent, 48 ; — derived from osmotic and conductance measurements com- pared, 233; — factors influencing, 318; — influence of temperature on — in water, 150 ; — of electrolytes, by freezing point method, 38 ; — of salts of organic bases, 321 ; — values, table of. 35 Ionizing power as dependent on dielectric constant, 318 ; — power of solvents in critical region, 319 ; — power of solvent in relation to constitution, 318 Ions, catalytic action of, 287 ; — charge on — as determined by conditions, 322 ; — complex negative, 216 ; — complexity of — as influenced by temperature, 125 ; — dimensions of — as calculated by Born and Lorenz. 202 ; — dimensions of — as de- rived from conductance, 202 ; — hydra- tion of, in water ; see Hydration, 198 ; — interaction of, with polar molecules, 198 ; SUBJECT INDEX 411 — intermediate, 217 ; — intermediate, influence of, on conductance, 104 ; — in- termediate, influence of, on dilution func- tion, 97 ; — intermediate, influence of, on molecular weight, 41 ; — nature of — in electrolytic solutions, 198 Isohydric principle, 219 ; — principle, ap- plied to solubility data, 262 ; — principle, test of, 224 Law of Kohlrausch, 33 ; — of mass action, applicability of, to ammonia solutions, 56 ; — of mass action, applicability of, to aqueous solutions at high temperatures, 153 ; — of mass action, applicability of, to dilute aqueous solutions, 98 ; — of mass action, applicability of, to elec- trolytes, 41 ; — of mass action, appli- cability of, to non-aqueous solutions, 53 ; — of mass action, applicability of, to solutions in formic acid, 101 ; — of mass action, applicability of, to weak elec- trolytes, 43 ; — of mass action, devia- tions from, in ammonia, 58, 86 ; — of mass action, graphical treatment of, 54 ; — of mass action, limited applicability of, 238 ; — of mass action, theories of deviations from, 96 Lead, complex anion of, 216 Lithium hydride, conductance of, 364 ; — hvdride, nature of conduction process in, 365 Mass-action constant, dependence of, on di- electric constant, 90 ; — constant, table of values of — for different solvents, 62 ; — constant, table of values of — for or- ganic electrolytes in ammonia, 60 ; — constant, table of values of — for salts in ammonia, 59 ; — constant, table of val- ues of — in acetone, 62 ; — function, form of, for salts of higher types in am- monia, 108 ; — function, in ammonia and water compared, 55 function, in am- monia solutions, KNO8, 55 ; — function, influence of temperature on, 153, 156 ; — function, for aqueous KC1 solutions, 45 ; — function for HC1 in water, 45 ; — function, variation of, for higher type salts in water, 106, 107; — law of, see Law Metal-ammonia solutions, ammoniation of negative electron in, 374 : — solutions, atomic conductance of concentrated solu- tions, 380 ; — solutions, complexes formed in, 367 ; — solutions, conduct- ance of sodium in, 376 ; — solutions, equi- libria in, 371 ; — solutions, limiting con- ductance of negative electron in, 377 ; — solutions, method of determining rela- tive speed of ions in, 372 ; — solutions, molecular weight determinations, 367 ; — solutions, nature of carriers in, 369 ; — solutions, properties of, 366 ; — solutions, relative speed of ions in, numerical val- ues, 373 ; — solutions, specific conduct- ance of concentrated solutions in, 378 ; — solutions, temperature coefficient of. 382 ; — • solutions, transference effects in, 368 Methyl alcohol, conductance of salts in — near critical point, 169 Methylamine, conductance of KI in. 50 : — conductance of KI in, at different tem- peratures, 164 ; — conductance of solu- tions in — at different temperatures, 159 Metallic alloys, see Alloys ; — conduction, theories of. 407 Metals, see also Alloys ; — see also Con- ductors. Metallic ; — see also Variable Conductors ; — atomic conductance of, 387 ; — change of resistance of, due to change of state, 389 ; — change of spe- cific resistance of — on melting, 388 ; — compound, 384 ; — conduction of solu- tions of — in ammonia, 20 ; — conduc- tion process in, 385 ; — effects in — under acceleration, 386 ; — elementary, resist- ance-temperature coefficient of, 387, 391 ; — elementary, resistance-temperature co- efficient of, at constant volume, 393 ; — elementary, resistance-temperature coeffi- cient of, in liquid state, 392 ; — galvano- magnetic properties of, 405 ; — Hall ef- fect in, 406 ; — influence of impurities on conductance of, 400 ; — influence of temperature on conductance of, 389 ; — influence of temperature on conductance of, at low temperatures, 389 ; — nature of, 384 ; — optical properties of, 407 ; — properties of, 384 ; — relation between thermal and electrical conductance of, 403 ; — specific resistance of elementary, 386 ; — state of, 384 ; — supraconducting state of, 390 ; — thermal conductance of, 403 ; — thermal conductance of, at low temperatures, 403 ; — thermoelectric properties in, 404 ; — thermomagnetic properties in, 405 ; — transference effects in, 385 Mercury methyl, properties of, 213 Mixed solvents, conductance in, 120; — solvents, fluidity of, 187 Mixtures of electrolytes, equilibria in, 218 ; — of electrolytes, freezing points of, 234 Molecular weight, determination of, by vapor pressure method, 238 ; — weight, from osmotic data, 232 ; — weight in non-aqueous solutions, 239 ; — weight in sulphur dioxide, 239 ; — weight of electrolytes by freezing point method, 38 ; — weight of electrolytes in solution, 37 ; — weight of electrolytes in water. 232 ; — weight of electrolytes, limitation of method of determining, by osmotic meth- ods, 40 Optical properties of electrolytes, absorp- tion coefficients in water and methyl alco- hol, 295 ; — properties of electrolytes, absorption curves, 294 ; — properties of electrolytes, extinction coefficients of acetyloxindon salts in alcohol, 297 ; — properties of electrolytes, extinction co- efficients of acetyloxindon salts in water, 296 ; — properties of electrolytes, extinc- tion coefficients of the chromate ion, 293 ; — properties of electrolytic solutions, 292 Potassium iodide, correction of conduct- ance of, for viscosity, 116 Pressure, influence of, on conductance, 129, 134 ; — influence of, on conductance, at different concentrations, 134 ; — influence of, on conductance, due to viscosity change in non-aqueous solution, 142 ; — influence of, on conductance, in non-aque- ous solvents, 139 ; — influence of, on con- ductance, of alcohol solutions, 139 ; — influence of, on conductance, of different electrolytes, 131 ; — influence of, on con- ductance of KC1 in water, 129 ; — in- fluence of. on conductance, of weak elec- trolytes. 136 ; — influence of, on electro- lytic conduction, 126ffi — influence of, on viscosity of solvent, 126 ; — influence of, on viscosity of solutions, 127 Propyl alcohol, influence of water on con- ductance of solutions in, 178 Reactions, electrolytic, 16; — electroly- tic, in ammonia. 314 ; — in ammonia and water, compared, 314 ; — in electrolytic solutions, 312 ; — in solvents of low di- electric constant, 317 412 SUBJECT INDEX Salts, conductance of higher types of, 104 ; — • complex metal-ammonia, 209 ; — com- plex metal-ammonia, conductance of, 211 ; — complex metal-ammonia, ionization of, 211 ; — complex metal-ammonia, Werner's theory of, 210 ; — fused, see Fused salts ; — • of higher types, conductance of — at higher temperatures in water, 148 ; — solid, applicability of Faraday's Law to, 362 ; — solid, change of conductance at transition point, 362 ; — solid, conduct- ance of, 359 ; — solid, conductance of, at different temperatures, 360 ; — solid, conductance of, lithium hydride, see Li- thium hydride, 364 ; — solid, conduct- ance of mixtures of, 363 ; — ternary, conductance of, in ammonia, 105, 108 ; — ternary, variation of conductance func- tion for — in water, 106 Sodium acetate, conductance of, in water, 102 ; — plumbide, electrolysis of, 19 Solubility experiments, assumptions under- lying interpretation of, 264 ; — experi- ments, constant concentration of un- ionized molecules in, 262 ; — Harkins' theory of influence of intermediate ions on, 277 ; — influence of complex ions on, 267 ; — influence of electrolyte on — in ethyl alcohol, 250 ; — of electrolytes in presence of common ion, 254 ; — of elec- trolytes in presence of other electrolytes, 254 ; — of electrolytes in salt mixtures, Bronsted's theory of, 337 ; — of gases, influence of electrolytes on, 239 ; — of higher types of salts, theory of, 275 ; — of lithium carbonate in presence of non- electrolytes, 252 ; — of non-electrolytes in presence of electrolytes, 245 ; — of non-electrolytes, influence of electrolytes on 249 ; — of non-electrolytes, influence of organic salts on, 250 ; — of salts in presence of non-electrolytes, 251, 253 ; — of salts in presence of other salts, lan- thanum iodate, 274 ; — of salts in pres- ence of other salts, lead iodate, 270 ; — of salts in presence of other salts, silver sulphate, 268 ; — of salts in presence of other salts, strontium chloride, 271 ; — of salts in salt mixtures, ther- modynamic 'treatment, 335 ; — of salts of high type in presence of other salts, 268 ; — of strong electrolytes in pres- ence of other electrolytes without com- mon ion, 268 ; — of strong electrolytes in presence of other strong electrolytes, 261 ; — of T1C1 in presence of other elec- trolytes, 261 ; — of weak acids in pres- ence of other acids, 256 Solutions, aqueous, molecular weight in, 232 ; — electrolytic, 15 ; — electrolytic, conductance of, 26 ; — electrolytic, den- sity of, 283 ; — electrolytic, equilibria in, 16 ; — electrolytic, non-aqueous, 46 ; — electrolytic, optical properties of, 292 ; — electrolytic, reactions in, 16, 312 ; — electrolytic, thermal properties of, 303 ; • — electrolytic, various properties of, .280; — • non-aqueous, molecular weight in, 239 Solvents, mixed, conductance in, 176 ; — mixed, ionization in, 177 ; — pure, con- duction process in, 352 Sulphur dioxide, conductance of KI in, 47 ; — • dioxide, conductance of solutions in — at different temperatures, 155 ; — dioxide, molecular weight of solutions in, 239 Tellurium, complex anion of, 215 Temperature, conductance of aqueous solu- tions at elevated, 146 : — influence of, on conductance, 122, 144; — influence of. on conductance of ammonia solutions, 145 : — influence of, on conductance of methylamine solutions, 146; — influence of, on conductance of non-aqueous solu- tions, 154 ; — influence of, on conduct- ance of solutions, 51 ; — influence of, on conductance of solutions in amines, 159 ; — • influence of, on constants of con- ductance equation, 156 ; — influence of, on ionization constants, 149 ; — influence of, on ionization of salts, 150 Theories of electrolytic solutions, miscel- laneous, 347 ; — relating to electrolytic solutions, 323 Theory, ionic, 17 ; — ionic, origin of, 21 ; — of Berzelius, 20 ; — of electrolytic solu- tions, from thermodynamic standpoint, 324 ; — of electrolytic solutions, Ghosh's, 340 ; — of electrolytic solutions, Ghosh's, compared with experiments, 341 ; — of electrolytic solutions, Hertz's, 345 ; — of electrolytic solutions, inconsisten- cies in, 328 ; — of electrolytic solutions, Jahn's, 326 ; — of electrolytic solutions, limitations of — for strong electrolytes, 323 ; — of electrolytic solutions, Malm- strom's and Kjellin's, 339; — of elec- trolytic solutions, Milner's, 343 ; — of electrolytic solutions, present state of, summarized, 349 ; — of Grotthuss, 206 ; — of Werner, 210 Thermal properties of electrolytic solutions, 303 Thermodynamic potential of 'electrolytes and electromotive force, 298 ; — proper- ties of electrolytic solutions, 328 ; — properties of electrolytic solutions, nu- merical values, 333 Transference effects accompanying the cur- rent, 21 ; — numbers, by moving bound- ary method, 23 ; — numbers, change of, at low concentrations, 307 ; — numbers, change of, for strong acids, 307 ; — num- bers, definition of, 21 ; — numbers, in ammonia, 64 ; — numbers, influence of complex ions on, 24 ; — numbers, influ- ence of concentration on, 24 ; — numbers, influence of hydration on, 22, 198 ; — numbers, influence of temperature on, 26 ; — numbers, methods of determining. 22 ; — • numbers, table of, 25 ; — numbers, true, 200 ; — numbers, true, relation of — to ordinary, 199 Van't Hoff's factor, 38; — factor, limiting value of, 41 Variable conductors, change of conductance at transition points, 401 ; — conductors, specific conductance of, 400 ; — conduc- tors, thermal conductance of, 403 Velocity of reactions as influenced by ions, 287 Viscosity change due to salts in different solvents, 112 ; — change, influence of — due to non-electrolytes, on conductance, 119, 121 : — dependence of — on dielec- tric constant, 112 ; — effect, correction of conductance for. 114 ; — effect, nega- tive. 113 ; — influence of concentration on, 112 ; — influence of on conductance, 111 ; — influence of, on conductance in mixed solvents, 176 ; — influence of on conductance in non-aqueous solutions, 118 ; — influence of, on conductance of concentrated solutions. 116; — influence of on conductance of different ions, 114 ; — influence of, on ionic speeds in different solvents. Ill ; — influence of, on A0 values. 109 ; — influence of pressure on — in different solvents, 143 ; — influence of temperature on. 113 ; — of ammonia at boiling point, 65: — of fused salts, 354 ; — of mixed solvents, 177 Water, influence of — on conductance of acids in alcohols. 180, 186 ; — ioniza- tion constant of, 225 NAME INDEX Acree, 291 ; — see Loomis ; — see Robert- son Adams, 233, 234, 343 ; — and Lanman, see Lewis Akerlof, 292 Allmand and Polack, 300, 334 Amagat, 130 Andrews, see Kendall Archibald, 49, 165, 205 ; — and Mclntosh, see Steele Argo, see Gibson Arrhenius, 17, 18, 21, 34, 37, 38, 42, 54, 219, 221. 225, 267, 280, 281, 287, 291 Avogadro, 341 Baedeker, 385 Baldwin, see Cady Bancroft, 68 Bates, 69 ; — and Vinal, 19 Beattie, see Maclnnes Bedford, 233 Bekier, see Bruner Benedicks, 388 Benrath and Wainoff, 364 Berzelius, 20, 21 Biltz, 249, 367 Bingham and McMaster, see Jones Bishop, see Kraus Bisson. see Randall Bjerrum. 331. 337 Blanchard, 119 Born. 202. 203, 204 Bottger, 228 Bousfield and Lowry, 114 Braun, 249 Braune, 185 Bray, 68. 266 ; — see Kraus ; — and Hunt, 222, 267 ; — and MacKay, 214 ; — and Winninghoff, 261, 262, 265 Bridgman, 390 Brighton and Sebastian, see Lewis Bronsted. 331. 333, 337. 338, 339 Bruner and Bekier, 322; — and Galecki, 322 Bruyn, Lobry de, 198 Buchbock, 198 Bunting, see Schlesinger Cad.v, 367, 373 ; — see Franklin, — and Baldwin, 317 ; — and Lichtenwalter, 317 Caldwell. see Hantzsch Callis, 321. 353; -- and Greer, 318 Calvert, see Schlesinger Carlisle, see Nicholson Cavanagh, 343 Centnerszwer. see Walden Chapman and George, 340 Chiu. 215 Chow, 303 Clark. 121 Clausius, 34 Clay, 389. 400, 406 Coehn, 213 Cohen. 126. 127. 131, 134, 138 Coleman, see McBain ; — see Schlesinger Crommelin, 389 Cushman. see Randall Dalton. 326 Danneel. 206 Darby. 49. 79. 357. 358 Davis and Jones, 113 413 Davy, Sir Humphrey, 19 Dawson and Powis, 290 de Bruyn, Lobry, 198 Dennison and Steele, 310, 311 de Szyszkowski, 69 Dewar and Fleming, 400 Drude, 407 ; — and Nernst, 284 Dummer, 204 Dutoit and Rappeport, 47 ; — and Levrier, Eastman, see Noyes Eggert, see Tubandt Einstein, 202, 204 Ellis, 300, 306, 307 ; — see Noyes Essex and Meacham, see Loomis Euler, 248, 249 Eversheim, 319 Falk, see Noyes Fanjung, 136 Faraday, 14, 17, 19, 20, 21, 33, 206, 353, 357, 362, 363 Fenninger, 397 Ferguson, see Tolman Fitzgerald, 50, 51, 109, 112, 119, 158, 163 Fleming, see Dewar Foote and Martin, 353 Forbes, 268 Franklin, 47, 52, 69, 108, 155. 161, 206, 207, 230, 315, 316. 373 ; — and Cady. 64 ; — and Kraus, 52, 53, 55, 105, 145, 206, 240, 316 ; — and Stafford, 206, 316 Franz, see Wiedemann Frazer and Sease, see Lovelace Galecki. see Bruner Gates, 317, 318 Geffcken, 245 George, see Chapman Georgievics. 324, 348 Ghosh, 324, 340, 341, 342, 343 Gibbs. 325. 326 Gibson and Argo, 367 Goldschmidt. 180. 182. 183 ; — and Thue- sen, 181, 183. 184, 289 Goodwin and Mailey, 353, 355 Gordon, 249 Graetz, 407 Green, 121 Greer, see Callis Gross, see Kendall Grotthuss, 206 Guertler, 393 Hall, 386. 406, 407: — and Harkins, 233. 234. 235 Hantzsch. 293, 295, 296; — and Caldwell, 206, 208 Harkins. 41. 269. 275. 277; — see Hall; — and Pearce, 273 Harned, 291, 292, 300, 303, 306, 307, 331, 335 Hartung, 242 Heberlein, see Kiister Helmholtz. 17. 20 Herty, see Werner FTprtz. 345. 346, 347 Heuse. 239 Heydweiller, 283, 284, 285, 286; — see Kohlrausch ; — and Kopfermann, 358 414 NAME INDEX Hine, 397 Hittorf, 21, 22, 23, 24, 34, 206, 345, 348 Hof, see Onnes Holborn, see Kohlrausch Hoist, see Onnes Hugot, "215 Hunt, see Bray Jaeger and Kapma, 355 Jaffa1, 351 Jahn, 326, 327, 328 Johnston, 110, 114, 122 Jones, see Davis ; — and Veazey, 187, 190 ; — Bingham and McMaster, 187, 190, 191, 192, 194 Kalian, 183 Kahlenberg, 317 Kanolt, 225 ; — see Morgan Kato, see Noyes Kendall, 43, 256, 263, 267 ; — and Andrews, 260 ; — and Gross, 321 Kerschbaum, see LeBlanc Keyes and Winninghoff, 74 Kjellin, 339 Koenigsberger, 385, 397, 398, 402, 404. 408 Kohlrausch, 33, 34, 110, 224 ; — and Heyd- weiller, 225, 352; — and Holborn, 27 Kohnstamm, see Van der Waals Kopfermann, see Heydweiller Korber, 129. 131, 134 Kraus, 20, 44. 68. 84, 98, 100, 111, 116, 123, 146, 168, 172, 213. 216. 322, 340, 343. 367, 376, 381, 382, 384. 393 ; — and Bishop, 178 ; — and Bray, 52, 56, 58, 60, 61, 64, 68, 70, 72, 74, 77, 82. 98, 109, 208 ; — and Lucasse, 378, 381 ; — see Franklin Kurtz, 74, 243 Kiister, 214 ; — and Heberlein, 214 Lanman and Adams, see Lewis Lattey, 92 LeBlanc and Kerschbaum, 357 Levrier, see Dutoit Lewis, 23. 308, 331 ; — Adams and Lan- man, 385 ; — Brighton and Sebastian, 300 ; — and Randall, 330, 332, 333, 335, 337, 345 Lichtenwalter, see Cady Linhart, 300 Lodge, 23 Loomis and Acree, 300; — Essex and Meacham, 300 Lorenz, 202, 203, 204, 347, 356, 403 ; — see 'Fubandt Lovelace. Frazer and Sease, 238 Lowenherz, 225 Lownds, 402 Lowry, see Bousfleld Lucasse, 206, 380, 383 ; — see Kraus McBain and Coleman. 242 McCoy and Moore, 213, 384 ; — and West, 398 MacDougall, 68 MacKay, see Bray Maclnnes, 308, 309 ; — see Washburn ; — and Beattie, 300 ; — and Parker, 301 Mclntoah and Archibald, see Steele McLauchlan, 249 McMaster and Bingham, see Jones Magie, 283 Mailey. see Goodwin Malmstrom, 339 Martin, see Foote ; — see Schlesinger Meacham and Essex, see Loomis Melcher, see Noyes Millard, 307 ; — see Washburn Milner, 337, 343, 344, 347 Moers, 364 Moissan, 319 Moo.re, see McCoy Morgan and Kanolt, 198 MulJinix, see Schlesinger Nernst, 89, 225, 238, 245, 280, 299, 302, 326, 328, 339, 401 ; — see Drude Nicholson and Carlisle, 19 Noyes, 146, 148, 149, 150, 152, 267, 304, 308, 340 ; — and Eastman, 41, 148 ; — and Ellis, 300 ; — and Falk, 24, 26, 30, 35, 37, 38, 114, 232, 309, 310, 337 ; — and Kato, 308 ; — and Melcher, 228 ; and Sammet, 308 Ohm, 22, 352 5holm, 121, 204, 280 Onnes, Kammerlingh, 389, 406 ; — and Hof, 400 ; — and Hoist, 403 Ostwald, 287, 288, 348 Ottiker, 208 Palmaer, 213, 384 Parker, see Maclnnes Partington, 340 Patroni, see Poma Pearce, see Harkins Peck, 19, 216 Peltier, 404 Planck, 136, 137, 141, 326 Plotnikow and Rokotjan, 79 Polack, see Allmand Poma, 302 ; — and Patroni, 302 Poole, 352 Powis, see Dawson Ramstedt, 290 Randall, see Lewis ; — and Bisson, 305 ; — and Cushman, 300 Raoult, 38 Rappeport, see Dutoit Reed, see Schlesinger Reychler, 348 Richards and Stull, 19 Richarz, 388 Riesenfeld, 242 Rimbach and Weitzel. 162, 163 Robertson and Acree, 207 Roemer, see Thiel Rohrs. 287 Rokotjan, see Plotnikow Rontg'en, 127 Rothmund. 245, 249, 252 Rupert, 353 Ruthenberg. 287 Ryerson, 121 Sachs, see Warburg Sack, 145 Sammet, see Noyes Sammis, 317 Schlesinger. 101. 102, 103, 230; — and Calvert, 101, 208 ; — and Bunting. 101, 207 ; — and Coleman. 101 : — and Mar- tin. 101, 207 ; — and Mullinix, 101 ; — and Reed, 101 Schmidt, 139, 141, 142 Sease and Frazer. see Lovelace Sebastian and Brighton, see Lewis Serkov, 242 Setschenow, 249 Smith, see Steam ; — Steam and Schnei- der, 305 Smyth, 19, 216. 322 Snethlage, 324 Somerville. 393, 396 Sprung. 112 Stafford, see Franklin Steele. see Dennison : — Mclntosh and Archibald, 206. 347 Steam and Schneider, see Smith ; — and Smith, 305 Steiner, 249 Stewart, see Tolman Stieglitz, 264, 267 NAME INDEX 415 Stokes, 202, 204 Veazey, see Jones Storch, 67, 68, 69, 98, 348 Vinal, see Bates Stull, see Richards Szyszkowski, de, 69 Wainoff, gee Benrath Walden, 92, 93, 95, 110, 241, 320, 322 ; — rr „ 100 191 IQ« IQ? 190 and Centnerszwer, 146, 239 Tammann 129, 131, 136, 137, 138 Warburg and Sachs, 127; — and Teget- layior, zyu meier 359 Tegetmeier see Warburg Washburn. 26. 43, 99, 100, 114, 121. 198, Thiel and Roemer 230 199 228 239 ; — and Maclnnes, 232 ; - Thomson, J. J~ SJO, 406 407 and Millkrd, 198 ; — and Weiland, 98 Thomson, Sir William, 89, 339, 404 Weiland, 44; — see Washburn Goldschmidt ; f 312 ; _ and Herty, Tolman 297 : — and Ferguson, 300 ; — and w^ gee McCoy •&„„*„+ Qfio . QT1/, Wiedemann and Franz, 403 Tuhandt, dbd ; — ana Ji,ggert, dbd ; — ana Lorenz, 19, 355, 356, 360, 362, 364 Winkelmann, 385, 407 Winninghoff, see Bray ; — see Keyes Van dor Waals, 42. 325, 326 WOrmann, 304 van Everdingen, 402 van't Hoff, 38, 239, 337, 343 Zeitfuchs, 215 YC 3261 M543792 16 SUPPLIED BY THE SEVEN BOOKHUNTERS STATION 0. BOX 22, NEW YORK I I, N. Y. Out-of-Print Books