S. Arrhenius and His Theory of Electrolytic Dissociation1

P. A. Kablukov, Moscow.

It has fallen to me as an honorable and sorrowful duty to share with you my recollections of my teacher—the famous Swedish scientist Svante August Arrhenius, who died on October 2, 1927. The name of Svante Arrhenius, together with the names of van ’t Hoff and W. Ostwald, marks the beginning of a new epoch in the history of physical chemistry.

I shall first briefly set forth, as it were, the record of the services of S. Arrhenius, and then dwell on the history of the emergence of the theory of electrolytic dissociation, which made the name of S. Arrhenius famous. At our gathering there is no need to expound this theory, which brought about a revolution in the doctrine of solutions and has entered the textbooks.

Svante August Arrhenius was born in Uppsala on February 19, 1859. He entered the University of Uppsala in 1876. In 1884 he defended his doctoral dissertation, in which we find the germ of the theory of electrolytic dissociation. (We shall speak of this dissertation in greater detail below.) In 1884

receives the position of docent of physics at Uppsala University. In 1886 he is sent abroad by the Swedish Academy of Sciences and during 1886–1889 works with W. Ostwald in Riga, then in Leipzig, with Kohlrausch in Würzburg, with Boltzmann in Graz, and visits van ’t Hoff in Amsterdam. In 1891 he receives the position of lecturer in physics at the university in Stockholm, and in 1895 the chair of physics there; in 1897–1903 he is elected rector; in 1902 he receives the Davy Medal, and in 1903—the Nobel Prize. He was offered the post of professor at the Berlin Academy of Sciences, but he receives the position of director of the Nobel Institute and remains in Stockholm until his death.

Such is the brief curriculum vitae of S. Arrhenius. Let us now turn to the history of the emergence of the theory of electrolytic dissociation.

“My chemistry teacher, Prof. Cleve, during his lectures pointed out,” Arrhenius recalls, “that it is impossible to determine the molecular weight of such substances as, like cane sugar, do not pass into the gaseous state. I understood that here lay a major deficiency, the removal of which could bring great benefit to chemistry. At that time Raoult was carrying out his classical work, which was unknown to me. The determination of the electrical conductivity of salts in solutions containing, along with water, a large quantity of nonconductors seemed to me likely to provide a key to the determination of molecular weight, proceeding from the principle that the resistance of an electrolytic solution is greater the greater the molecular weight of the solvent. Upon a more detailed investigation of electrical conductivity, I turned my attention to the conducting part of the salt molecule.”

Thus S. Arrhenius, having chosen physics as his principal subject in 1881, sets about his doctoral dissertation and begins in 1882–1883 his experimental investigations in the field of the electrical conductivity of aqueous solutions, under the direction of the professor of physics Edlund in Stockholm. The choice of topic was conditioned, on the one hand, by earlier investigations on electrical conductiv-

nesses of solutions, which belong to our well-known scholar R. Lenz (1878) and which yielded interesting and remarkable relations precisely for highly dilute solutions; on the other hand, by Arrhenius’ considerations that the electrical conductivity of dissolved salts, containing alongside them considerable quantities of non-conductors, could give indications of the molecular weight of the latter: for, according to Lenz’s investigations, it turned out that the electrical conductivity of salts decreases in the following order: aqueous solutions \(>\) alcoholic \(>\) ethereal and alcoholic \(>\) kerosene. From these results Arrhenius draws the conclusion that the resistance of the solution increases as the molecular weight of the solvent increases, since the molecular weights of water, alcohol, and ether stand in the ratio \(18:46:74\). During the experimental work, in a detailed study of the electrical conductivity of various solutions of forty-five substances, his interest took an entirely different direction: instead of the determination of molecular weight, his attention was wholly absorbed by that fractional part of the molecules of the dissolved salt which takes part in electrical conductivity. Let us cite several propositions at which Arrhenius arrived. “The electrical conductivity of dissolved salts is equal to the number of electrolytic molecules present in the solution”... “If upon dilution the electrical conductivity does not change proportionally to the quantity of electrolyte, then a chemical change in the solution has been caused by the addition of the solvent”... “The resistance of an electrolytic solution is the greater, the more complex the ions”... Normal salts form complex molecules in water, or: “aqueous solutions of all electrolytes contain the dissolved electrolyte, at least in part, in the form of molecular complexes”... “The limit approached, at extreme dilution, by the complexity of a dissolved normal salt is one and the same for all normal salts”... As for the aqueous solution of ammonia and its electrical conductivity, Arrhenius assumes the formation of the hydrate “\(\mathrm{NH_4OH}\)”. “The electrical conductivity of an ammoniacal solution is based on the presence of a small quantity of \(\mathrm{NH_4OH}\). The same circumstances also occur with other bases,

and likewise with acids: hydrochloric, acetic, sulfuric, nitric, phosphoric, and so on. As a result, the following important proposition is obtained: “An aqueous solution of some hydrate (ammonia, an acid) consists, besides water, of two components—one active, electrolytic, and one inactive, non-electrolytic. These constituent parts of the water—the active hydrate and the inactive hydrate—form a chemical equilibrium in such a way that, upon dilution, the active part increases, while the inactive part decreases.” To determine the active part, he introduces a special coefficient of activity (“coefficient d’activité”). The latter “gives us the ratio of the number of ions actually present in the electrolyte to the number of ions that would be obtained upon complete dissociation of the electrolyte into simple electrolytic molecules.” Then the following expression is obtained: “the better a solution of some acid (and likewise of a base) conducts electricity, the greater its active part.” Finally, he arrives at the important postulate that “for acids and bases, galvanic activity runs parallel to chemical activity,” or “a given acid (or base) is the stronger, the greater its coefficient of activity (its molecular electrical conductivity).” Let us recall that not only salts, acids, and bases—or, in the sense of Hittorf, “salts”—are electrolytes, but that, according to Arrhenius: “water, alcohols, phenols, aldehydes, and many other substances are electrolytes and, consequently, conductors of current.”

In conclusion we shall cite the generalization which Arrhenius gives to the Clausius–Williamson hypothesis for electrolytes and from which the connection between chemical and galvanic activity follows. “All ions are associated with a definite quantity of electricity, the anion with negative, the cation with positive. This quantity must be the same for all ions. If, therefore, the cation of one molecule combines with the anion of another, the cation of this one with the anion of a third, and so on, the process will not cease until the cation of the last molecule combines with the anion of the first molecule... During this process (which proceeds instantaneously),

obviously, a definite quantity of electricity has moved, i.e. that associated with one ion in a closed line. I shall call this phenomenon a circular current. In an electrolyte, consequently, circular currents are constantly taking place.” Since electrical conductivity depends on whether the ions of electrolytes exchange with one another and on how often such exchange occurs, and since a chemical reaction is likewise connected with the rate of exchange of place in the particles, it follows that, for example, the acids with the greatest electrical conductivity will also be the acids that react most rapidly.

This, in general outline, is the content of the dissertation that appeared in 1883 under the title: “Recherches sur la conductibilité galvanique des électrolytes.” Part 1, “Conductibilité galvanique des solutions aqueuses extrêmement diluées.” Part 2, “Théorie chimique des électrolytes.”

Arrhenius calls his theory chemical. “As is seen from this brief survey, this theory is entirely chemical,” says P. I. Walden, “it proceeds: 1) from the idea of the complexity of the molecules of dissolved salts and their disaggregation upon dilution and 2) from the formation of hydrates of weak bases and acids; 3) it introduces the concept of active hydrates (conducting current), without, however, giving an exact definition of how the latter differ from inactive hydrates; and 4) it gives a new formulation to Clausius’s hypothesis, allowing an uninterrupted movement of ions (without the access of an electric current) as a consequence of the ‘circular current’ and an increase in active molecules with dilution of the solution; 5) it establishes proportionality between the rate of chemical reactions and the electrical conductivity of acids and bases.”

What reception did Arrhenius’s results and theory meet with? In the examination of the dissertation by the faculty opponent (Dr. A. G. Ekstrand), it was pointed out that the assumption of the decomposition of current-conducting molecules (salts) into free ions presented extreme difficulties. As a result, Arrhenius initially did not want to print his theory at all, and, having decided toward the end to publish it, deliberately recast the doctrine of free ions. Recalling this

At this point, Arrhenius, 23 years later, notes (1907): “Foreseeing that this objection would arouse the greatest number of chemists against my views, I tried to put forward this dissociation as little as possible. Thus the full development of the theory of dissociation was delayed by three years.”

P. I. Walden relates that in 1884, when a vacancy opened for the position of docent at Uppsala University, it was offered to Arrhenius thanks to W. Ostwald, who, during a summer trip to Uppsala, succeeded in dispelling the fears of the local scholars, who were afraid that by officially accepting such a wild young physicist the university might compromise itself.

The first and almost the only scholar to respond to Arrhenius’s theory was W. Ostwald. The point is that W. Ostwald himself at that time was working in the field of studying the electrical conductivity of solutions: in July 1884 he published a study in which, using 34 acids, he showed a parallelism between their electrical conductivity and the rates of the reactions caused by them. At the same time he indicates that Arrhenius’s conclusion belongs among “the most significant that have appeared in the field of the theory of affinity.”

In the major work Lehrbuch der allgemeinen Chemie, published in 1885–1887 in Riga, W. Ostwald expounds Arrhenius’s theory and makes it widely known. Thus Arrhenius owed the dissemination of his theory in large measure to W. Ostwald. During his trip abroad, Arrhenius in 1886 went first of all to W. Ostwald, who was then a professor at the Riga Polytechnic, and there carried out various physicochemical investigations (see below). The lively exchange of ideas between W. Ostwald and Arrhenius greatly contributed to clarifying various aspects of the emerging theory.

Arrhenius’s relations with van ’t Hoff began in 1885. Arrhenius sent his dissertation to van ’t Hoff; the latter answered him with a long letter (of August 4, 1885), in which he thanked Arrhenius for the dissertation sent to him, and also for the favorable review of van ’t Hoff’s work.

Goff’s Études de dynamique chimique. Then he indicates that he delayed his reply until such time as he would be able to express his opinion on Arrhenius’s theory and, in general, on the fundamental electrochemical quantities in chemical equilibrium, further mentioning his works on this question, sent for publication in the proceedings of the Swedish Academy of Sciences. Noting further that the relations indicated by Arrhenius between reaction rates and electrical conductivity are of great interest, Van’t Hoff adds: “Only the guiding ideas of my theory in the known relations differ from yours.” “I cannot suppose, as you do, that electrical conductivity alone determines the state of equilibrium attained. This is the chief objection that arose in me while studying your work. Electrolytic resistance appears to me to be a quantity in chemistry analogous to friction in mechanics, in the motion of liquids, i.e. it does not determine the final state of equilibrium, although it does affect the time required for it to be reached. This objection compelled me to seek which of the electrical quantities determines equilibrium, and it seems to me that this role belongs to the electromotive force that can produce the given transformation.

“The following considerations led me to this conclusion:

“1. The electromotive force that a reaction can call forth, if it takes place in a galvanic cell, serves as a measure of the work that the affinity performs.

“2. The sign of the work that a chemical reaction can perform determines the direction in which the latter proceeds of itself (in the absence of external resistance).

“3. Equilibrium in a system in which two opposite reactions take place can be established only when the electromotive force of the reactions is equal to zero.

“4. The law of equilibrium at constant temperature.”

Here Van’t Hoff develops the ideas that led him to the derivation of the well-known isotherm equation on the basis of the laws of thermodynamics.

In the conclusion of the letter Van’t Hoff writes: “De ce point de vue il me parait donc que votre opinion et la mienne peuvent aller ensemble.” This letter marked the beginning of collaboration between Van’t Hoff and Arrhenius.

In Van’t Hoff’s letter there is mention of the following works, sent to the Swedish Academy to Prof. Petterson: 1) Lois de l’équilibre chimique, dans l’état dilué, gazeux ou dissous, 2) Une propriété générale de la matière diluée, and 3) Conditions électriques de l’équilibre chimique.

In these works Van’t Hoff studies the fundamental propositions of his theory of solutions, i.e., he shows how, on the basis of the laws of thermodynamics, one can establish a mathematical dependence between the osmotic pressure of a solution and the lowering of the vapor pressure, the freezing temperature, and the elevation of the boiling temperature of solutions; he derives the well-known formula: \(t = 0.01976 \frac{T^2}{w}\) (where — the molecular lowering of the freezing point of the solution, \(T\) is the absolute freezing temperature of the pure solvent, and \(w\) is its latent heat of fusion).

According to Van’t Hoff’s law, the fundamental laws of the gaseous state (Boyle, Gay-Lussac, and Avogadro) are also applicable to the dissolved substance, and the equation: \(P \cdot v = RT\) proves to be common to gaseous and dissolved bodies (at extreme dilutions). But, as experiments have shown, for solutions of a whole class of bodies: acids, salts, and bases (i.e., electrolytes), the osmotic pressure (and consequently the lowering of vapor pressure, freezing temperature, etc.) more or less exceeds that calculated by the above formula. Van’t Hoff introduced the coefficient \(i\) (equal to the ratio between the found and the theoretical osmotic pressure) into the above formula, and then the gas equation becomes: \(P \cdot v = iRT\).

To the question of what is the cause of these deviations, we find the answer in a letter from Arrhenius (of March 30, 1887) to Van’t Hoff, sent from Würzburg, where he was working with Kohlrausch. At the beginning of the letter Arrhenius explains the reason why only after a year and a half he re-

answers the letter quoted above: he first wanted to acquaint himself with the manuscripts of van ’t Hoff that had been sent to Prof. Peterson, but it turned out that the latter had already been forwarded to the Academy, and Arrhenius had to wait until they appeared in print. Upon reading them, however, much became clear to Arrhenius in the question of the structure of solutions.

“Die Abhandlung,—he writes,—hat mir nämlich in unerhörtem Grade Klarheit geschafft über die Konstitution der Lösungen.

“If, for example, sodium chloride (NaCl) behaved normally, i.e. consisted of simple molecules, then for it \(i\) would have to be equal to unity. But since \(i\) is considerably greater than unity, in order to explain this we shall find a way out by assuming that NaCl is partly dissociated, just as it is accepted that at high temperature the iodine molecule \(\mathrm{I}_2\) breaks up into atoms.”

Arrhenius then develops the fundamental propositions of his theory in considerable detail. Informing van ’t Hoff of the plan of his studies during his foreign assignment, he asks whether it would be convenient for van ’t Hoff if Arrhenius came to Amsterdam at the beginning of 1898?

Van ’t Hoff, immediately upon receiving this letter, answered (April 7, 1887) Arrhenius’s letter, and a lively correspondence began between them. Without dwelling on it, we shall give only the dates of the following letters: Arrhenius’s letter of April 13, 1887, from Graz (where he was working with Boltzmann), and four days later another letter (April 17, 1887), van ’t Hoff’s reply of April 24, 1887, then Arrhenius’s letter of July 12, 1887. In these interesting letters many aspects of the theory of solutions were clarified before they appeared in print.

The year 1887 may be noted as the year in which the beginning was laid for a new epoch in the theory of physical chemistry: Volume I of the Zeitschrift für physikalische Chemie, Stöchiometrie und Verwandtschaftslehre appeared, published by Prof. W. Ostwald of Leipzig University and Prof. van ’t Hoff of Amsterdam University, with the participation of many outstanding scholars. Among Russians, D. I. Mendeleev and N. A. Menshutkin were drawn into participation.

In the third issue of the first volume we find the article by Arrhenius: “Einfluss der Neutralsalze auf die Reaktionsgeschwindigkeit der Verseifung von Aethylacetat,” containing the results of research carried out in V. Ostwald’s Riga laboratory. In the sixth issue there is Arrhenius’s study of the internal friction of dilute solutions (“Ueber die innere Reibung verdünnter wässeriger Lösungen”), begun in the same laboratory of V. Ostwald and completed in Würzburg with Kohlrausch (the article is dated Graz, 20 April 1887).

In the ninth issue there is the classic article by Van’t Hoff: “Die Rolle des osmotischen Druckes in der Analogie zwischen Lösungen und Gasen”; and in the last issue (11 and 12) Sv. Arrhenius: “Ueber die Dissociation der in Wasser gelösten Stoffe”—a translation of the article published in the Proceedings of the Stockholm Academy on 8 July and 9 November 1887.

In his classic article Arrhenius proceeds from the following propositions:

1) Van’t Hoff’s law is valid not only for nonconductors, but also for electrolytes, which had previously been regarded as an exception.

2) Every electrolyte (in aqueous solution) consists partly of active molecules (in the electrolytic and chemical sense), partly of inactive molecules; and the latter, as dilution proceeds, are transformed into active ones, thus yielding in infinitely dilute solutions only active molecules.

On the basis of these propositions, he calculates for 90 substances (nonelectrolytes and electrolytes) the coefficient \(i\). Using Raoult’s cryoscopic data for \(i\), one obtains \(i = \dfrac{t}{1.85}\), if \(t\) denotes the lowering of the freezing temperature found for 1 mole in 1 l of water; and from electrical conductivity one obtains \(i = 1 + (n - 1)a\), where \(a\) is the coefficient of activity (degree of dissociation), and \(n\) is the number of ions into which one molecule of salt dissociates. On comparing both series of values for \(i\), it is evident that, for all 90 substances, they are close to one another; for a given salt, always

to the larger \(i\) (cryosc.) there corresponds a larger value of \(i\) (electrol.), to the smaller \(i\) (cryosc.)—a smaller \(i\) (electrol.); in general \(i\) (cryosc.) \(= i\) (electrol.).

Thus abundant experimental material, by two different routes, led to the confirmation of both of the propositions stated above. If they are correct, then the following conclusion follows from this:

“If a salt (in aqueous solution) is completely dissociated into ions, then most of the properties of this salt must be represented as the sum of the properties of the ions, since the ions are independent of one another; each ion, consequently, possesses a characteristic property... The properties of dilute (aqueous) solutions are additive.” Arrhenius confirms this on the following phenomena: 1) on Hess’s law of the thermoneutrality of dilute solutions of different salts; 2) on the heat of neutralization, equal for all strong bases and strong acids; 3) on the specific volumes and specific gravity of dilute solutions (Valson); 4) on molecular refraction (Gladstone); 5) on electrical conductivity (the law of the independent velocities of transport of ions of F. Kohlrausch); 6) on the lowering of the freezing temperature (according to Raoult, this is an additive property).

The appearance of the Zeitschrift für physikalische Chemie, as well as W. Ostwald’s move in 1887 from Riga to Leipzig, promoted the development and popularization of the theory of solutions of van ’t Hoff and Arrhenius. Just as at the beginning of the nineteenth century chemists from all ends of Europe flocked to the laboratory of Liebig in the small German town of Giessen, so in the last quarter of the nineteenth century scholars from all parts of the world gathered in the Leipzig laboratory of W. Ostwald in order to study the new science: physical chemistry.

Arrhenius came here as well, and in 1888–1889 assisted W. Ostwald as his personal assistant. The work of the Leipzig laboratory was directed toward developing questions connected with the new theory of the decomposition of salts into ions. On 17 May 1888 van ’t Hoff wrote a letter addressed: Herrn S. Arrhenius. Hauptagentur für Ionenspaltung. Brüderstrasse, 34, Leipzig (the address of W. Ostwald’s laboratory).

In this same friendly letter he inquires about the health of Arrhenius and W. Ostwald, writes about their works, which had given him much pleasure, and, speaking of Tollens’s work on determining the freezing temperature of solutions, adds: “For Europe an ice age is coming” (“Es kommt faktisch eine Eisperiode über Europa”).

The theories of van ’t Hoff and Arrhenius at first, as was to be expected, did not meet with general recognition: the idea of the decomposition of such stable compounds as acids, salts, and alkalis contradicted established views. I shall never forget the heated disputes that took place over the theory of electrolytic dissociation in our chemical section of the Society of Devotees of Natural Science, Anthropology, and Ethnography, and also during the congresses of Russian naturalists and physicians. Such prominent representatives of Russian science as Academician N. N. Beketov, my teacher V. V. Markovnikov, and Professor of Kazan University F. M. Flavitskii took part in these debates; all of them attacked those beginning scientists who ventured to come forward in advocacy of the theory of solutions. D. I. Mendeleev came out with a sharp criticism of both theories (van ’t Hoff’s and Arrhenius’s). In France they were met with contemptuous silence.

English chemists and physicists—headed by Pickering, Armstrong, and other defenders of the hydrate theory—organized a special meeting of the British Association in Leeds in 1890, to which van ’t Hoff, Arrhenius, and Ostwald were invited.

Ostwald describes this public dispute, so rare in the history of science, in the following way: “During the first days our opponents alone spoke, so that to a certain extent one might think that we had already suffered defeat. But when, after prolonged and lively personal disputes, the representatives of the new ideas finally obtained the floor and spoke at the public sessions, the picture changed at once, so that we could part from our hosts in a friendly manner and not without the consciousness of triumphant victory.”

And soon the theory of Arrhenius began to win ever greater attention and to penetrate the most diverse fields; and at the present time we know that it is difficult to point to a field of natural science which, to a greater or lesser degree, has not felt the influence of the theory of electrolytic dissociation.

In keeping with this, the fame and renown of Arrhenius grew, and honors and scholarly distinctions, one may say, were showered upon him.

In 1902 he received the Davy Medal; in 1903, the Nobel Prize; in 1904 he received an invitation to America to deliver a course of lectures at the University of California at Berkeley. This course, under the title “Theories of Chemistry,” appeared first in an English edition, and then in German translation (1906) and in Russian (1907).

In 1911 Arrhenius again traveled to America to deliver lectures (Silliman Lectures) at Yale University. These lectures were published under the title: “Theories of Solutions” (“Theory of Solutions”). The American Chemical Society awarded him the Willard Gibbs Medal.

In that same year he delivered a series of lectures at the Sorbonne. In 1914 he received the Faraday Medal, and in 1920 the Franklin Medal. It is difficult to enumerate the learned societies, academies, and universities of which he was an honorary member: the universities of Cambridge, Oxford, Paris, Groningen, and others elected him doctor honoris causa.

In 1909, on the 25th anniversary of the theory of electrolytic dissociation, Moscow University, the Moscow Society of Naturalists, and the Society of Amateurs of Natural Science, Anthropology, and Ethnography elected him an honorary member.

In the summer of 1909, admirers and students of Arrhenius gathered in Stockholm to celebrate the 25th anniversary of the appearance of his doctoral dissertation. A special jubilee volume (the 70th) was published: “Zeitschrift für physikalische Chemie: Jubelband II. Svante Arrhenius. Zur Feier des 25-jährigen Bestandes seiner Theorie der elektrolytischen Dissociation gewidmet von seinen Freunden und Schülern.”

The popularity of Arrhenius was greatly promoted not only by his outstanding scientific activity, but also by his

personal qualities. I am happy that I had the opportunity to become closely acquainted with him and to be his pupil.

In 1889 I was sent abroad for scholarly purposes and in May entered the Leipzig laboratory of W. Ostwald, where I carried out my first investigation of the electrical conductivity of nonaqueous solutions, which laid the foundation for my doctoral dissertation: “Modern Theories of Solutions (van ’t Hoff and Arrhenius) in Connection with the Doctrine of Chemical Equilibrium,” 1891. I learned how to measure electrical conductivity from Arrhenius, and I am proud that from that time on friendly relations were established between us. It was impossible, knowing Arrhenius, not to respect and love him. Subsequently I had occasion more than once to meet him at international congresses and meetings.

In December 1907 Arrhenius came to Petersburg for the First Mendeleev Congress, at which he was elected deputy chairman. From there he intended to come to see me in Moscow, but when on the appointed day I was preparing to set out to meet him, a telegram arrived at the station reporting his illness.

The last time I saw him was in June 1914, at the celebration of the 400th anniversary of the University of Groningen.

When in September 1927 I learned that I was to travel to Paris for the celebration of the centenary of the birth of M. Berthelot, I gladly thought of a possible meeting with Arrhenius, but… with pain in my heart I had to read of his death, which occurred on October 2, 1927.

He is no more. He has left us, but his creations live on, and his name, alongside the names of van ’t Hoff and Ostwald, marks a new epoch in the development of physical chemistry. Those who had the good fortune to know Arrhenius will preserve the memory of him not only as an outstanding scholar, but also as a man who attracted others by his personal qualities and inspired the respect and affection of all who had occasion to meet him.

1. Address delivered on February 16, 1928, at the joint meeting of the learned societies of Moscow devoted to honoring the memory of Svante Arrhenius. In preparing this address, the sources used, in addition to the works of Arrhenius, were the following: P. I. Walden, The Twenty-Fifth Anniversary of the Theory of Electrolytic Dissociation and Non-Aqueous Solutions. Moscow, 1910. Ernst Cohen, J. H. van’t Hoff. Sein Leben und Wirken. M. A. Bloch, The Life and Work of van ’t Hoff. Petrograd, 1923. ↩