Early Chemical Thermodynamics: Its Duality Embodied in Van’t Hoff and Gibbs.

Published in:

Van’t Hoff and the Emergence of Chemical Thermodynamics,

Willem J. Hornix and S.H.W.M. Mannaerts, Eds.,

Delft University Press, 2001, p. 212-242

ISBN 90-407-2259-5

1. Introduction

Van’t Hoff said once: “Emerging out of the waves which separated from time immemorial the both continents of physics and chemistry, a new world is gradually arsing. Initially groups of isles, then foothills developing on the both sides, eventually here and there a connecting piece of ground stretches where it sometimes to turn out to be a swamp. This is physical chemistry, earlier a colony but now a large free country”1.

The same is true for chemical thermodynamics which formed the theoretical base of physical chemistry in those times. The birth-marks originating from the parent sciences were always stamped on physical chemistry, but in the case of chemical thermodynamics they are especially distinct because of individual peculiarities and attitudes of two men, J. H. van’t Hoff and J. W. Gibbs, who became main creators of this borderland discipline.

The emergence of chemical thermodynamics was determined by demands of scientific development: in physics the newborn science of thermodynamics reached some maturity and had to seek for further applications of its general principles; in chemistry a doctrine was wanted which would unite the two contradictory approaches to affinity, the theory of mass action and thermochemistry 2.

Branches of the new discipline were sprouting even before van’t Hoff and Gibbs entered the field. At first two unconnected groups of publications appeared. One concerned equilibria between a solution and a pure substance - vapour of the solvent (water), or the solid phase of this solvent (ice), or the pure solute (a salt or a gas) 3-5. The other consisted in applications of the Clapeyron-Clausius equation to the dissociation of solids 6-9. Neither of these trends had to consider changes of composition as a variable in equations. Thus, the problem, to that time not yet formulated, was to take into account the role of each substance in a chemical transformation. In other words, a new kind of variable was to be introduced into thermodynamics.

The subjects considered up to 1873 were the more simple cases where this problem remained aside. The first general approach was from Horstmann who introduced as the condition of equilibrium that the entropy (S) of the system under consideration has a maximum (dS = 0) and derived the law of mass action from this principle10. Unfortunately this important contribution obtained no recognition: it was incomprehensible for the chemists at that time. Nevertheless Horstmann proceeded to elaborate his theory experimentally and later his publications became an impetus for van’t Hoff.

At a far better timeappeared memoir by H. Helmholtz on thermodynamics of chemical processes 11, which very soon became famous. Of course, the big name of the author favoured its influence 12. The main point was that a new notion of ‘free energy’ (F) was introduced, which is the part of the total energy (U) of a system that can be freely converted to work. The minimum of free energy gives the condition of equilibrium for isothermal systems. The discovery implied in particular that the thermochemical measure of affinity had to give way to the thermodynamic one. Helmholtz never had developed this conclusion further, however. This task fell on van’t Hoff.

2. Van’t Hoff’s thermodynamics

One might say that van’t Hoff’s thermodynamics emered as a by-product of his efforts to solve chemical problems when he started with a general study of chemical reactions; he was interested in the chemical process on the whole: the equilibrium state was a particular case for him, connecting a reaction with the reliable basis of thermodynamics. As he stated later: “Reaction rate at first as the main purpose. Chemical equilibrium, however, immediately next to it. For the equilibrium, on the one hand, is based on equality of the two opposite reactions, on the other hand it offers a firm support by its connection with thermodynamics. ... I had to go further, for the question of equilibrium bordered directly on the problem of affinity and so I came to the very simple phenomenon of affinity manifesting itself as attraction of water” 13.

From the beginning of this work van’t Hoff was aware of some advances made by thermodynamics in chemistry. For him it was enough to comprehend that thermodynamic approach can be carried much further than had previously been realised and that thermodynamics could be a solid foundation for some chemical studies. “One should go back to Clausius if it were not just for chemistry having hardly thought of there”, he remarked later 14. No doubt, he was right, because all what Clausius ever had said on the topic was but a few lines 15. (Nevertheless it would be interesting to know, if Clausius’s suggestions had influenced van’t Hoff’s research: too often he claimed the same efforts of finding similarity between physical and chemical processes to use this analogy).

So van’t Hoff went his own way. If one takes into consideration that not only in politics but also in science it is necessary to use ‘the art of possible’, and that thermodynamics was in those times the only reliable theoretical basis for quantitative approaches to chemical processes then it would account for van’t Hoff’s move “from ‘chemical dynamics’ to chemical thermodynamics” 16.

Van’t Hoff did not pretended to develop thermodynamics, he spoke always about its application to chemistry. Just as mathematics is for the physicist a method of investigation, not a science with its own subjects, the same goes for thermodynamics for the chemist. This is how van’t Hoff treated it. He used thermodynamics only as a method for solving chemical problems. As his biographers wrote, van’t Hoff “selectively accepted some separate advances of thermodynamics” 17. A telling detail is that even as late as 1895 van’t Hoff was seeking “a good book on thermodynamics” 18. Thus it may be repeated after Laidler: “His approach to thermodynamics was that of a practical chemist interested in understanding chemical reactions, and he was less concerned with scientific rigour than in arriving at simple relationships applicable to laboratory work” 19.

In view of this, no wonder that van’t Hoff had never presented his contribution to chemical thermodynamics as a ‘system’. Nevertheless the word is to the point. His system, as it is generally known, was not very harmonious, it was not even published in an orderly manner, having been built within about three years, from ‘Études’ (1884) to the paper on role of osmotic pressure in the analogy between solutions and gases (1887). However that may be, it was in the work of van’t Hoff, that all the already existing germs – that were dissipated among the immense number of conventional descriptive chemical publications, and in all the preceding achievements in thermodynamics which were of importance for a chemist, came to be united within a consistenly introduced concept of (chemical) equilibrium considered from the standpoint of thermodynamics.

Van’t Hoff’s contributions to the chemical thermodynamics have been considered in literature time and again 20, so it will do to present a short summary. His main results founding the new chemical discipline are, as follows:

(1) The modern measure of affinity was introduced, namely the maximum work, mechanical or electrical, that a chemical transformation would be capable of performing 21.

(2) The method of reversible cycles has been extended to chemical systems by means of an imaginary device with semipermeable membranes, known as the ‘equilibrium box’ 22. The device allowed reversible changing the concentrations of gas mixtures or of solutions, so that chemical reactions could be performed, at least in principle, in a reversible (more exact, ‘quasistatic’) way. It was thus shown that the laws of thermodynamics could be applied to any chemical transformation and it became possible to take into account the role of every individual substance of the system.

(3) The law of mass action has been generalised with the help of ‘equilibrium constant’ (K), developed as a thermodynamically determined quantity: K is connected with the work of affinity (A) by the relation

RTlnK = A  (1)                                                                                        

and with the heat of transformation (Q) by the relation

dlnK/dT = Q/RT2  (2)                                                                                        

The latter relation, a generalisation of the Clapeyron-Clausius equation, was soon designated as the equation of reaction isochore 23.

(4) A series of relations for heterogeneous equilibria with solutions were derived thermodynamically.

These included empirical formulas of cryoscopy, tensimetry and ebullioscopy as well as the equation

 dlnc/dT = Q/RT2  (3)                                                                                          

This is the temperature dependence of solubility (c) in diluted solutions (this was found as a special case of the reaction isochore where Q stands for the heat of solution). heterogeneous equilibria with solutions were involved in the same thermodynamic system.

(5) Thus the relation for the ideal gas equation of state,

PV = RT, (4)                                                                                           

was expanded to the (dilute) solutions (of nonelectrolytes) with osmotic pressure instead of gas pressure.

Although the latter proposition does not belong to thermodynamics proper, it was this discovery, that allowed to connect all the thermodynamic derivations with real chemical experience and to give them an understandable and applicable form.

The most impressive feature of van’t Hoff’s work was that it involved equilibria in solutions. Moreover, it was his ‘osmotic theory of solutions’ that became soon a central theme in this new field. In other words, the great impetus given to chemistry by van’t Hoff’s work was caused not by the application of thermodynamics, but first of all by his extension of ‘Avogadro’s law’ (in form of equation of state of the ideal gas) on the immense realm of solutions. This discovery gave rise to the first quantitative theory of solutions (not to mention its significance for formulation of the Arrhenius’s theory of ‘electrolytic dissociation’) and offered ways to study chemical equilibrium in solutions. It is this ‘osmotic theory’, not thermodynamics that impressed the majority of contemporary chemists. (A rather typical detail: Professor J. Brühl, one of the founders of physical organic chemistry, devoted not a single word to applications of thermodynamics in his article on election van’t Hoff as a member of Academy of Sciences to Berlin 24).

Harry Jones, a physical chemist originating from the German school, (a pupil and passionate van’t Hoff’s admirer) even wrote: “If the author were asked to select the most important generalisation which ever been reached in chemistry, tending to convert chemistry from empiricism into science, he would unhesitatingly name the application of the gas laws to solution” 25.

Later, the place occupied by osmotic pressure in the physical chemistry of 1890s-1910s seemed disproportionately big. This has been caused by the van’t Hoff’s method. If it were not for van’t Hoff’s thermodynamics, osmotic pressure would have remained of little importance in the theories of solutions and in electrochemistry.

Coupled with the theory of solutions, and propelled by a short period of Sturm- und Drang of the new ‘physical’ theory of solutions, the van’t Hoff’s system became an important part of physical chemistry.

Some opposition against ‘electrolytic dissociation’ and ‘osmotic theory of solutions’ 26, especially in England and Russia, did not prevent the rush development of van’t Hoff’s chemical thermodynamics. Its acceptance by contemporary chemists was confirmed and consolidated since 1893 by W. Nernst’s well known “Theoretical chemistry from the standpoint of Avogadro’s rule and thermodynamics”. “Nernst’s standard work, ‘Theoretical Chemistry’, offers, not only to the student but also to the scholar, an abundance of stimulating ideas; it is theoretically elementary, bur clever, vivid and full of intimations of manifold interpretations” 27.

Thus chemical thermodynamics in Europe grew from its embrionic state into a scientific discipline with its own method and subjects of investigation. (In contrast to the term ‘Physical Chemistry’ which existed long before physical chemistry was institutionalised, the term ‘chemical thermodynamics’ appeared much later, probably for the first time in the German translation of a paper by Lewis in 1908 28).

The new chemical discipline had very much to do. On the one hand, a wide field for experimental investigations opened for its adepts, in particular due to the possibility to treat equilibria in solutions from the standpoint of the law of mass action. F. Haber wrote later on “the extraordinary stimulus given by van’t Hoff to the study of the influence of concentration in systems which obeyed the gas law” 29.

On the other hand, many theoretical problems remained unsolved. The analytical methods known from Kirchhoff, Horstmann, Guldberg and Helmholtz were neither full developed nor perfected; and in particular no relation was established between the conditions of equilibrium discovered by Horstmann and by Helmholtz. Moreover, approaches to a theoretical treatment of complicated heterogeneous equilibria had not been created. Contributions of each individual substance in an equilibrium state were not easy available in the van’t Hoff’s method (not to mention the limitations imposed by the ideal gas equation of state).

It is now well known that all these problems had been resolved, or at least correctly formulated, by J. W. Gibbs who published his main results in 1876-1878. Their importance was slowly recognised by the majority of the workers in the field: only since the end of 1880s. Thus it is worthwhile to turn here to Gibbs’s work.

3 . The system of Gibbs 30

Gibbs set himself the task to develop a „general theory of thermodynamic equilibrium“ 31, in particular, „to arrive as directly as possible at the most characteristic and essential laws of chemical equilibrium“ 32.

For extension of thermodynamics into chemistry, some additional information was needed about new subjects for thermodynamic investigation. This information may be called a ‘pre-thermodynamic model’ of the subject. Gibbs proceeded from the experimental fact that the ‘equilibrium of heterogeneous substances’ existed (the first to use the expression ‘heterogeneous substances’ was probably Thomas Young 33) and generalised this information by means of notions ‘phase’ and ‘component’, and further, in the course of his investigation, also: ‘critical phase’, ‘interphase boundary’, ‘semipermeable membrane’, and ‘charged component’. All these are very general concepts necessary to structure chemical systems. They are taken from the experience and form the material for thermodynamics proper. Such an ‘explicit’ preparation for the application of thermodynamics to chemical subjects assumed a very general and therefore abstract theory. (For van’t Hoff and his followers the logical structure of thermodynamics was of no importance and such a preparation would be needless).

Now Gibbs could fulfil his mission. His starting point was ‘the principle of equilibrium’, the term coined later 34 to discern the two propositions, on the existence of entropy and on its increase in natural processes, included in what is named ‘the Second Law’. In mathematical form that means

                                                                    (dS)U ≤ 0,                           (5)                                                         

or, as Gibbs shows,

                                                                    (dU)S ≥ 0                           (6)                                                               

To apply this principle Gibbs builds a formalism with functions

                                             U;    H = U + PV;      F = U – TS;     G = U – TS + PV = H – TS,

which possess two properties: they are ‘characteristic functions’ 35 and, at the determined conditions of isolation of the system, they simultaneously offer the maximal work which could be performed by the system. Thus they are ‘force functions’  (the modern term ‘thermodynamic potential’ was introduced 1884 by P. Duhem 36), in other words these functions offer conditions of equilibrium, e. g.

                                                                      (dF)T ≥ 0                         (7)                                                                      

This formula, coinciding with that given by Helmholtz , as well as the similar formula (6) may “both regarded as extensions of the criterion employed in ordinary statics to the more general case of a thermodynamic system” 37. Gibbs shows, moreover, that the formula (7) results also from the general principle (5) 38, thus establishing the connection between criteria of Horstmann and of Helmholtz.

In short, Gibbs created the general method consisting in use of thermodynamics potentials both as characteristic functions and as functions directly giving conditions of equilibrium. This is the first of his main achievements.

Secondly, he expanded his method to chemical systems having introduced ‘chemical potentials’ to take into account the role of individual substances in the equilibrium. (The conventional name ‘chemical potential’ is probably due to W. Ostwald; it was copied into English-language literature by W. D. Bancroft 39. Gibbs used the word ‘potential’). Namely, Gibbs generalised the Clausius’s equation

                                                    dU = TdS – PdV                                            (8)                                                  

to systems composed of many components, quantities (m) of these components being independently variable:

                                     dU = TdS – PdV + μ1dm1 + μ2dm2... + μndmn         (9)                                               

The “differential coefficients” μ1, μ2,...μn are ‘potentials’ of the components 1, 2, ..., n 40. These ‘potentials’ are the central notion of Gibbs’s chemical thermodynamics; they have the same significance for chemical equilibrium, as temperature for thermal and pressure for mechanical equilibrium. As Gibbs said, these functions “play the principal part in determining the behavior of matter in respect to chemical equilibrium” 41.

The most voluminous part of Gibbs’s work is the theoretical investigation, on the said foundation, of main cases of equilibrium in chemistry, i.e. of chemical and phase equilibria, stable and unstable states, and equilibria involving capillary and electric forces.

The acceptation of Gibbs’s thermodynamics did not go so quickly and smoothly as in case of van’t Hoff. Until Wheeler’s book on Gibbs was published (1951) a legend circulated that Europe was simply unaware of Gibbs’s work. This is certainly not the case. There were fairly many references to the work of Gibbs in the European literature in the first decade after its publication, but with the exceptions those of Maxwell 42 almost all of them are evidence of the gap between the level of Gibbs’s writing and the abilities of the readers. The Gibbs’s work was of immediate importance for general thermodynamics, both for the development of its methods and as its enormous expansion on subjects different from the motive power of heat. Chemical thermodynamics emerging in Europe was to be influenced by this work only later, after a prolonged ‘incubation’ – and for two reasons. Firstly, chemists felt no need yet to go beyond their usual subjects of research before these were not exhausted, and secondly they had no satisfactory knowledge to comprehend even the problems considered by Gibbs.

The ‘incubation’ in perception of Gibbs’s work has ended since the middle of 1880s, after the contributions of Massieu, Maxwell, Horstmann and especially Helmholtz became partly mastered. In the real history of chemical thermodynamics Helmholtz should be considered, in a sense, rather as Gibbs’s predecessor. This is, of course, wrong from standpoint of mere chronology, but in fact the Gibbs’s thermodynamics began to work in Europe only when Helmhotz’s memoir had prepared ground for its perception. His formalism, very similar to that of Gibbs, was simpler for comprehension and made understanding Gibbs’s work possible, even if in part.

(As to Helmholtz himself, he stated in 1889 that the Second Law offered “the most astonishing and unexpected connections between the farthest branches of physics...e.g. in the development of modern chemical mechanics, the principles of which, as far they are firm and reliable, essentially rest on that law” 43).

It does not mean that Gibbs’s work could be assimilated within a few years. As Nernst wrote on Gibbs, “Unfortunately the calculations of this author are much too general to be directly and simply transferred to special experimentally investigated cases” 44.

Although it would be unfair to say Gibbs made no contacts with chemical experience 45, these contacts were not easy to see. He referred to some twenty experimental works including those on solutions, dissociation and thermochemistry in ‘Equilibrium of heterogeneous substances’, but his concise remarks were hardly intelligible to chemists. There were also problems that Gibbs did not tackle at all. He never mentioned the problem of affinity and its measure - the notion was obviously alien to mathematical physics. The only place that might be interpreted as a hint to this topic is perhaps his discussion of electromotive force, where “the necessity of regarding other considerations in determining the electromotive force of a galvanic or electrolytic cell than the variation of its energy alone” is shown 46. So, the task was not simple.

Nevertheless the ice had begun to break. After the middle of 1880s elaboration of Gibbs’s ideas got under way in Europe. First of all the Dutch school headed by J. D. van der Waals 47 should be named and then the ‘uneasy genius’ P. Duhem 48 in France. The Gibbsian thermodynamics was backed by the system developed by M. Planck 49; the difference between them consisted “only” in the lack of chemical potentials in Planck’s works, although he invented (much less convenient) substitute for them. He contributed to recepting thermodynamic theories by chemists, anyway, especially because his work lent strong support to the hypothesis of electrolytic dissociation 50.

4. The twofold discipline

The story returns to the late 1880s-early 1890s. A peculiar state of affairs formed in the chemical thermodynamics at that time: the van’t Hoff’s system was now settled and the said ‘incubation’ for Gibbs’s system came to its end, so that the both systems began their further development. Thus two separate directions in chemical thermodynamics came into existence.

Demarcations between the two trends were manifold.

Above all, they were different by birth. The first was born, as already noted, almost exclusively on chemical ground as the result of attempts to solve problems of chemical transformation by applying thermodynamics as a method. The second direction emerged as a natural extension of thermodynamics itself. As could be seen, the Gibbs’s approach was different from that of van’t Hoff. Gibbs’s purpose was to facilitate “the comprehension of the laws which govern any material system”, “to develop the principle [of equilibrium] as a foundation for the general theory of thermodynamic equilibrium” 51. Hence, his subject was thermodynamics, not chemistry. Investigating the subject he showed, using Planck’s words, that the Second Law allowed, like the First Law, “a grandiose generalisation which extends to all the known physical and chemical phenomena” 52.

Keeping in mind the different origins, one might more or less conventionally call these lines ‘chemical’ and ‘physical’ directions; earlier they were designated as ‘pregibbsian’ and ‘gibbsian’ chemical thermodynamics 53. (The both pairs of designations are used in the subsequent discussion.)

Objectively, all the differences between the two directions were caused by the difference between the two thermodynamic methods applied.

From the standpoint of completeness in using thermodynamic principles, methods of van’t Hoff and Gibbs only differ in the topic concerning conditions of stability and related problems: the method of cycles uses the constancy of entropy in a reversible cycle and/or in a state of equilibrium (dS = 0), whereas the Gibbs method takes also into account that the entropy in a state of equilibrium has its maximum; hence his method uses the both conditions, dS = 0 and d2S < 0. In other words the both methods are theoretically equipollent till one has to treat problems of stability. Beyond these problems, in the broad field of equilibrium studies, the existing differences are not of principal (in the above sense), but of formal nature.

Van’t Hoff’s method is mathematically simple, difficulties by its application were shifted into inventing a suitable cycle. Objections were once and again raised against this method on the ground there were no perfect semipermeable membranes in nature, so that cycle processes proposed by van’t Hoff could not be realised. In fact such objections are not valid; van’t Hoff’s operation is no less realisable than any other imaginary reversible (‘quasistatic’) process 54.

The real weak point here was not the problem, whether the cycle is feasible, but how to get a correct construction of a suitable cycle. It was here, that scientists sometimes went astray, - but certainly not van’t Hoff himself. „Van’t Hoff can be outright designated as the master of cyclic processes, no scientist before him and none after him was ingenious as he was in inventing of proper cyclic processes adapted to each special case and no one in doing so evolved such an abundance of original ideas as he did” 55.

Van’t Hoff’s opinion was therefore definite: “I shall make a suggestion as to the choice of the most suitable form of this [Carnot-Clausius] principle. It may be applied by carrying out so-called reversible cycles of operations or by the introduction of abstract physical conceptions and mathematical functions, such as entropy, as is done by physicists like Gibbs, Planck and Duhem. I am convinced, that, for the chemist, the first form, in which reversible cycles are employed, is the most advantageous“ 56.

On the other hand, the straightforward and exact analytical method developed by Gibbs is free from inventing ad hoc adopted special cycles and was more attractive for those who possessed sufficient mathematical means. Gibbs wrote on his method modestly as on “a process which seems more simple, and which lends itself more readily to the solution of problems, than usual method, in which the several parts of a cyclic operation are explicitly and separately considered. Although my results were in a large measure such as had previously been demonstrated by other methods, yet, as I readily obtained those which were to me before unknown, I was confirmed in my belief in the suitableness of the method adopted” 57.

It should be added that the same division also remained for geometric methods. Van’t Hoff adhered to ‘natural’ coordinates as composition and temperature. Here he attained perfection when investigating experimentally complicated salt systems. (His approach consisted in determining non-variant equilibria between three solid phases, solution and vapour at each particular temperature, so that a general ‘map’ for the whole system could be drawn). The only exception where van’t Hoff deviated from this ‘natural’ line was his consideration the temperature dependence for the free energy of a reaction by low temperatures 58.

In contrast to that conventional approach Gibbs designed a principally new geometric method consisting of applying thermodynamic functions as coordinates of state diagram, so that each time a characteristic function against its arguments is plotted. This method has great potentialities especially for study of phase equilibria.

The differences considered, resulted in a division of research fields: adherents of van’t Hoff’s and Nernst’s thermodynamics treated first of all chemical reactions in gases and diluted solutions as well as accessible phase equilibria between an ideal phase (gas or solution) and a pure substance. Gibbs’s followers especially studied more general cases of heterogeneous equilibria.

Typical achievements of ‘chemical direction’ can be exemplified by several works. Equilibria in and with electrolytic solutions were treated by Arrhenius 59, Ostwald 60 and Nernst 61. Such a choice has been greatly determined by the impetus given by the theory of electrolytic dissociation. Nernst was an especially prolific and successful researcher. “His theoretical equipment was somewhat elementary, but he mastered it with a rare ingenuity” 62. Nernst’s ‘osmotic theory’ of electrode potentials 63 opened a new period for thermodynamics in electrochemistry. As is well known, he achieved one of the most significant results both in chemical and in general thermodynamics, the heat theorem or the ‘third law of thermodynamics’ (from 1906 onwards) 64.

Among other significant events, it is worth to recall the birth of thermodynamics of ‘ideal solutions’ (i.e. solutions with weak chemical interaction between the solvent and the solute). These solutions obey Raoult’s law on lowering the vapour pressure of the solvent at all concentrations. (As a matter of fact thermodynamics could not forecast the existence of such solutions. Once they were discovered experimentally, however, the building of a ‘thermodynamics of ideal solutions’ became possible). For solubility in such solutions a simple equation holds connecting it with the melting heat and melting point of the solute 65.

Another interesting contribution to be mentioned concerns equilibrium liquid-vapour in binary mixtures (M. Margules). It laid foundations for quantitative theory of distillation of binary fluid solutions 66. Such investigations of theoretical importance were not very numerous. For the most part, this direction of chemical thermodynamics was essentially experimental; it treated mainly chemical equilibria in gases and solutions as well as simple heterogeneous equilibria with gas or vapour phase where the ideal equation of state could be applied.

In the ‘gibbsian’ direction, there was here more place for theorizing. The main subject, as mentioned, was phase equilibrium. To exemplify some most interesting achievements, the van der Waals’s equations of coexisting phases for binary and ternary systems (1897) might be mentioned 67 as well as the classic Roozeboom’s work in which the phase diagrams of condensed binary systems were derived from the plots of thermodynamic potentials 68.

There was a distinction between ‘chemical’ and ‘physical’ directions concerning inclinations to treat their subjects respectively mainly experimentally or theoretically. That depended both on the level of the thermodynamics mastered and on the attitudes and opportunities of doing to experiments. That does not mean, of course, that the first direction was exclusively experimental, and the second one exclusively theoretical. Nevertheless, Germany became a metropol for ‘chemical’ experimental thermodynamics. In France, by contrast, theoretical thermodynamics predominated with regard to chemical systems in particular. (There were special circumstances in that country: because of the obstinate Berthelot’s position 69 all the thermodynamics was controlled by physicists and engineers with few opportunities for chemical studies). A happy balance could probably onlybe found in the Netherlands, especially presented by the work of laboratories under van der Waals, Roozeboom, and Schreinemakers 70.

Thus the demarcation between the two trends even had some geographic boundaries, Germany being main country of van’t Hoff’s thermodynamics and the Netherlands of that of Gibbs. (An anonymous reviewer from ‘Nature’ wrote that “we may fairly call the science of heterogeneous equilibria a Dutch science” 71; a similar opinion expressed Gustav Tammann 72).

Another difference between the directions becames clear from the above cited suggestion of van’t Hoff stating that chemists could better do with cycles whereas mathematical functions should be let for physicists. This professional separation was not absolute, too. Physicist Nernst belonged to the ‘chemical’ direction, whereas several chemists, the most known being Bakhuis Rooseboom, followed ‘physical’, or‘gibbsian’ direction. Nevertheless this demarcation, reminding us once more of the origins of the both directions, was quite real because chemists mainly avoided “the precise, but rather abstruse equations of entropy and thermodynamic potential” 73, whereas physicists considered method of cycles as awkward and artificial. In view of the fact that mathematical education for chemists was then as now below the requirements of development of science, such professional separation was inevitable.

The ‘gibbsian’ direction would have advanced into a broader circle of chemists perhaps more effectively, if good ‘translators’ had appeared. It did not happen. As M. Planck once remarked, “Often it is not easy for a theoretical physicist to accomodate himself to the train of thought and style of chemists” 74.

It is well known that Gibbs’s thermodynamics found two very active proponents in the persons of P. Duhem and J. J. van Laar 75. Both acted on what they conceived to be the most important for development of the field, but their efforts had only a limited effect: neither of them was able to display results in a form accessible to chemists.

The book on ‘Thermodynamics in Chemistry’ published by van Laar had but few readers: “The author overestimates from the very beginning both the mathematical knowledge of a majority of chemists and their experience in seeing a definite physical sense in algebraic formulas” 76. Also, original results of van Laar in the thermodynamics of solutions remained unclaimed, and after about fifteen years an American chemist wrote on them: “If it occurs to any one to wonder why the theory has not come into general use in the chemical world, he has only to glance through some of van Laar’s papers, especially his earlier ones, and the reason will be more or less obvious” 77.

Duhem’s work evoked much the same response: “thermodynamics in which there were plenty of integrals, but no atoms” 78. This is a typical judgement on Duhem’s fundamental Traité élémentaire de mécanique chimique fondée sur la thermodynamique; and it is worth notice that it issued by a chemist who followed Gibbs: “We admit that this work probably contains grave and original ideas, but they are diluted with such enormous multitude of commonplaces and insignificant propositions presented in form of theorems, lemmas, laws, etc., that extracting them from under overloading trumpery becomes almost excessive toil for a foreign investigator. Let us wait, maybe the author will give us a Traité plus élémentaire, than this one” 79As if in reply to this opinion Duhem has published an elementary book 80, without mathematics, which was very useful for popularization of chemical thermodynamics – but scarcely for its mastering - both in France and abroad.

Such details show that in addition to objective factors, subjective ones were of importance, that is, possibilities and attitudes of personalities involved.

Here it may be interesting to mention some personal attitudes inherent to both main creators of chemical thermodynamics that also contributed to its duality. In short, their approaches corresponded to their professions.

As discussed earlier, van’t Hoff‘s attitude to chemical thermodynamics (or more exact, to the application of thermodynamics to chemistry) was much that of a user. No doubt, he respected physics, he said on “the new building in the world of chemistry half of which rests on physical ground” 81, he valued opinion of physicists as regards his osmotic theory (here we should recollect Kamerlingh Onnes’s opinion that “van’t Hoff owes more than is generally known to the scientific influence of van der Waals” 82).

At the same time his attitude both to physics and to mathematics was perhaps somewhat reserved, if not ambivalent. Certainly he declared his purpose, “connecting chemistry and mathematics” 83 and for a chemist of 1880s-1890s he did know much mathematics. He recognised that mathematics could be useful, moreover, that it was sometimes a necessary tool. That tool stayed for him only an auxiliary one, however.

His mathematical apparatus was of a very simple kind, anyway 84, and with his mode of thinking too much mathematics was for him unacceptable: “if possible, please restraint in using notorious physical ink-well” – such was his reaction to the Duhem’s formula for osmotic pressure. Such formulas were transformed for him into “dead letters” 85.

This makes understandable that probably the only fully loyal van’t Hoff’s response to the abstruse theory could be found in his letter to P. Duhem of 1887: “If I am not mistaken in this opinion, the thermodynamic potential presents in its applications a route much simpler to arrive at relations presented by osmotic pressure than the one which had to be followed so far, and will not fail to signal new relations” 86.

His reserved attitude to abstract theories revealed itself in particular in his words on Gibbs: “It is simply to regret that with regard to the exceedingly rich contents of the treatise the author has almost nowhere verified the usefulness of his results through connecting them with the observation” 87.

Van’t Hoff was not alone at this point. One example from Horstmann can be offered: „Willard Gibbs published an extensive book, where the whole field was thoroughly investigated and treated with great mathematical skill. This interesting book made me especially clear, however, where were real limits for these investigations. All that was theory only, but almost absolutely were lacking facts which always give and must give the judgement in the natural sciences. There was no experimental experience to test and to corroborate the theory giving it a convincing force” 88.

For Gibbs, thermodynamics had been his immediate subject. Correspondingly, mathematics was for him the language adequate to the problems to be treated. He confessed to the end of his life “that in all his years of teaching he had had only six students sufficiently prepared in mathematics to follow him“ 89So it was typical of him that with reluctance he met suggestions to popularise his results, although he admitted, not without regret, that his beloved creation, chemical potential, stayed less-known: “I cannot say that the term has been adopted by physicists. It has, however, received the unqualified commendation of Professor Maxwell (...); and I do not see we can do very well without the idea in certain kinds of investigations” 90.

Gibbs said once, he could reach some results because he had been “able to dodge mathematical difficulties” 91. Van’t Hoff could say the same, the difference being in the level of the mathematics employed and, correspondingly, in the “order of magnitude” of difficulties.

The opposition van’t Hoff versus Gibbs appears in retrospect to relate more to a choice of formalism rather than to logic. Such an opinion is expressed especially in a modern biography of van’t Hoff 92. It should be recognised, however, that the very choice of formalism reflects the two different attitudes to thermodynamics in chemistry.

It is to add here that van’t Hoff’s approach was substantionally inductive, partly intuitive, which is perhaps best of all displayed by his general program: “Chemistry searches for connection with physics, it is particularly endeavoured to put phenomena of chemical transformations down to phenomena of physical transformations, especially, to find a contact with mutual transformations of different states, solid into liquid, liquid into vapour, etc., in order that, after the connection is reached, the simple physical principles which rule over these phenomena could be fruitfully transferred to the much more complicated chemical relations” 93(The most famous example of this approach was the analogy between gaseous and osmotic pressure).

On the other hand, Gibbs’s methodology was, by contrast, an act of deduction, if possible, from the first principles. His ‘Equilibrium of heterogeneous substances’ (as well as ‘Statistical Mechanics’) is a great deduction.

One more detail: both were convinced atomists. As van’t Hoff told in his inauguration address in Berlin, his stereochemistry stemmed from the idea of building a mechanics of atoms. He later saw that his dream was unattainable and recognised thermodynamics as the only reliable basis for quantitatative theories in chemistry. It was in this sense, that his known letter to Arrhenius (1893) 94 was written. Gibbs, however, had enough potentialities to endeavour to construct his ‘statistical mechanics’ “developed with especial reference to the rational foundation of thermodynamics” 95.

It was because the both systems of chemical thermodynamics were created by very pronounced scientific individualities, and each of them having adequately responsed to the summons of the time – but each in his own science! – that the duality surfaced much more distinct than elsewhere in physical chemistry. Personal differences between the ‘romantic’ van’t Hoff and ‘classic’ Gibbs 96 added to differences between physics and chemistry and enhanced that duality.

It would be interesting to trace the quantitative representation of the both trends in the literature for the period where the said duality established and developed, between 1870-1920. Statistical data are only available for Russia till 1917 97, a country that was not a leader in physical chemistry. Its literature then reflected an approximately picture of European chemical thermodynamics. The evidence shows a continuous growth of the share of ‘gibbsian’ thermodynamics in the period 1886-1915 from 7 to 30%.

As a matter of fact the trends were not absolutely separated from each other. The abovementioned Margules’s theoretical work on the vapour-liquid-equilibrium was, for example, a sign that the boundary separating the two main trends was not always distinct: there was a rather diffuse transition region. It was filled in particular with experimental researches based on the phase rule and partly bridging the gap.

To summarize briefly, whatever complicated the whole picture of early chemical thermodynamics may be, the two main trends associated correspondingly with van’t Hoff and Gibbs can be clearly distinguished. Both branches were viable enough and had their own methods, own subjects, own people and partly even own geographic boundaries.

5. Overcoming the duality

Both lines of developments in chemical thermodynamics coexisted till the late 1930s. It is worth investigating why the better system did not win earlier and the coexistence lasted over a period of about 50 years.

First of all the ‘pregibbsian’ thermodynamics had a good storage of vitality and efficiency. Lewis asserted the following about it in 1907: “It must be admitted that it is the second method to which we owe nearly all of the advances that have been made during the last thirty years through the application of thermodynamics to chemical problems, and which is now chiefly used by investigators and in the text-books of physical chemistry” 98.

This is certainly an exaggeration, but it reflects the prevailed attitude of those times. One year before van Laar expressed his hope: “My audience will probably live till the time when thermodynamic potential will be considered as an absolutely simple quantity...The truth is coming, and nothing will detain it” 99. At the time this sounded as a voice crying in the wilderness. The amalgamation was developing more slowly than van Laar dreamed. (It is true, he lived long enough to see his vision almost realised).

As already mentioned, one of the main causes of such a long delay was the poor physical and especially mathematical education of chemists. At the end of 19th century the view prevailed that mathematics is not needed for chemists. Only few chemists, like Horstmann and younger van’t Hoff and Ostwald understood and showed the necessity of a physical and mathematical training for the chemist who wishes go beyond the purely empirical side of his science. The Netherlands were probably the only country where the state of affairs was satisfactory. “Dutch chemists, - van Laar once stated, -... should be glad that they had a teacher as exacting as van der Waals, and as Lorentz in Leiden. This solid background meant that they could not be taken unawares, with an inadequate knowledge of physics and mathematics, by the continuously developing stream of science, which, in our day, has been particularly swift in theoretical and mathematical chemistry” 100.

The general situation changed slowly during the course of three decades. “Until well after World War I even those educated in science at universities were often surprisingly deficient in their knowledge of mathematics. On the continent of Europe the situation was not too bad, but it was less satisfactory in Britain and worse in the United States. At Harvard, for example, it was possible until about 1930 to obtain a Ph.D. degree in physical chemistry without any knowledge of the calculus” 101.

The mathematisation of physical chemistry was still a long way off in the early 1920s. One could read in 1923: “It may be possible to acquire a very serviceable knowledge of thermodynamics without any understanding of the calculus, and indeed many important discoveries in thermodynamics have been made by non-analytical methods; but, for any presentation of the subject which is both concise and comprehensive, calculus is indispensable” 102In the same year a new textbook on physical chemistry published in Germany was prefaced with a rather long mathematical introduction 103.

The events were leading chemists, however, towards a better command of mathematics. The main proponent of Gibbs’s chemical thermodynamics in the United States, W. L. Miller wrote in 1925: “Eventually this will be changed by pressure from without, by demand for men capable of applying thermodynamic methods to the solution of technical problems. But why wait for pressure? If the trouble lies in inadequate mathematical preparation of the students, as has often been suggested, the remedy lies in our own hands” 104.

The most general cause of seemingly late amalgamation of the both trends was that new problems were but slowly maturing and their treatment was or seemed to be possible without modernisation of the formal apparatus of chemical thermodynamics. It was the necessity to treat increasingly complicated subjects, which ultimately caused the merger of the both main directions with leadership of ‘gibbsian’ thermodynamics.

This requires some elucidations.

As stated above, some ‘pre-thermodynamic’ models were to be adopted for expansion of thermodynamics on chemistry. Such models are a necessary condition to allow thermodynamics to work in chemistry. This is, however, only part of the problem, since, even after the assumption of these ‘pre-thermodynamic’ models, a thermodynamic equation connects unknown quantities. “If we do not know either side of the equation from other sources then the equation tells us nothing” 105.

This is the second aspect of the problem – the “fertilisation of thermodynamics”, in the apt expression belonging to the Russian physical chemist A. Rakovsky 106, or the introducing some additional information, which might be called ‘post-thermodynamic’ models.

What is meant here by the use of the word ‘model’? The data needed to make a thermodynamic equation convey information can be embodied either in experimental results for the system under consideration, or in some model which is a representation of the system. We may distinguish three kinds of model – physical, mathematical and structural. A physical model is a known system similar to that under consideration. A mathematical model, which can be analytic or geometric, is a formula such as an equation of state that is inserted into the bare thermodynamic equations or a geometric form that represents the system. A structural model is a set of propositions concerning the entities from which the system is constructed. The three classes of model are clearly linked, but the structural one comes first if one is to choose adequate physical or mathematical models.

To begin with mathematical models, the following Gibbs’s exposition on chemical potentials might be appropriate: “...it is the office of theoretical investigation to give the form in which the results of experiment may be expressed. In the present case we are led to certain functions which play the principal part in determining the behaviour of matter in respect to chemical equilibrium. The forms of these functions, however, remain to be determined by experiment, and here we meet the greatest difficulties, and find an inexhaustible field of labour. In most cases, probably, we must content ourselves at first with finding out what we can about these functions without expecting to arrive immediately at complete expressions of them. Only in the simplest case, that of gases, have I been able to write the equation expressing such a function for a body of variable composition, and here the equation only holds with a degree of approximation to the approach of the gas to the state which we call perfect” 107.

The problem had not been evident until the end of 19th century. Probably only three men, Gibbs, Guldberg and van der Waals, realised clearly in those times that all the branches of thermodynamics, general, technical and chemical were essentially the thermodynamics of ideal systems. All the advances in connecting thermodynamics with real facts and experimental data were based on the equation   PV/T = const, first for gases and later, beginning from van’t Hoff, for solutions. Van’t Hoff saw the limitations of this equation, but he had nothing better.

The equation of state for ideal gases was the first of ‘post-thermodynamic’ models in chemical thermodynamics. The second one only appeared 1889: that was the van der Waals equation of state for binary mixtures 108At that point the history of chemical thermodynamics ceased to be the history of thermodynamics of ideal systems and became the history of overcoming the ‘ideal approach’; it became the history of changing the single model for a multitude of models destined to represent a multitude of real systems.

This task first occurred beyond the reach of the ‘chemical’ direction. This is especially clear from the attempts to treat systems which did not obey the simple ideal equation. The fact that as early as 1890 a sober theory of binary mixtures had been published did not stop numerous attempts to modify van’t Hoff’s relation for osmotic pressure in imitation of van der Waals equation of state for real gases. These efforts constitute a regrettable episode in the history of thermodynamics of solutions.

At that time Ph. Kohnstamm wrote: “Physical chemistry in its present state reminds us strongly with regard to its quantitative part, of a people who do not yet know of the compass. The coastal-trade is carried on with great vigour, the same limited region is traversed again and again; but they do not dare to venture on the main sea far from the coast, and with reason, for great is the danger of ruin in towering waves of random hypotheses. This can only be remedied by a trustworthy compass. Physical chemistry may obtain it if it will abandon the method of osmotic pressure and adopt that of the thermodynamic potential in connection with a well-grounded equation of state” 109.

It would be wrong to say that no sound attempts from the side of ‘osmotic school’ were taken to get away from ideal approximation. In particular those of Washburn are worth mentioning. His fairly ingenious constructions, as “the perfect thermodynamic engine” 110 were too complicated, however, to find advocates.

The way of combining thermodynamics with corresponding equation of state found but few followers, too. They had to contend with two obstacles. The first was the notorious inaccuracy of the equation of state, which could be compensated only by direct experiments, and the second, the extreme complexity of the calculations. As one of the best experts in the field remarked, “the length of the equations can be measured in metres” 111.

The demand for a simpler approach to the description of non-ideal systems was satisfied by efforts on the part of the ‘chemical’ direction: the ‘method of activities’ is meant, introduced by G. N. Lewis 112The purpose of the author was to retain the form of usual thermodynamic equations for ideal systems “in such a way as to render them exact” 113. The approach had been much criticised as purely formal. It became useful, however, giving a convenient form for description of experimental data, in particular by researches of electrolytic solutions. Further progress was due to A. Noyes who introduced the notion of ‘activity coefficient’, that is “the ratio of activity to concentration” 114. Then J. N Brønsted used widely both activities and activity coefficients. He was the first to connect the activity (a) of a component with its chemical potential 115:

                                                                  μ = RTlna + const              (10)                                                                           

This principal step in the development of the method was consolidated especially by P. Debye in his theory of strong electrolytes 116. (Lewis himself had never did this step, although he was in fact moving towards Gibbs’s thermodynamics having introduced partial molar free energies). All that remained was to construct a systematic presentation of the thermodynamics of non-ideal systems on the basis of the method of chemical potentials, including activities. This work was done especially by E. A. Guggenheim 117.

Another line in the evolution of chemical thermodynamics important for overcoming its duality is connected with elaboration of ‘structural models’ in thermodynamics.

For the nineteenth century physics was typical “to separate sharply the purely thermodynamic laws from those special modifications which belong rather to the theory of the properties of matter” 118, that is from molecular-kinetic theories. The purity of these lines could be easy kept at the times where structural variety of subjects treated stayed fairly poor. This is also true of chemical thermodynamics which considered simple topics at first.

Nevertheless, the more the variety of topics increased, the more, hence, the variety of structures to be included into consideration became and the more persistent and advisable became the assimilation of molecular-kinetic theories by thermodynamics.

In fact, “statistical mechanics owes its origin to investigations in thermodynamics” 119. One may think such an assimilation would be not difficult for chemical thermodynamics. This was not the case. Actually, it was chemical thermodynamics that served as a stronghold of anti-atomistics in 1890s and 1900s, most known representants being W. Ostwald and P. Duhem. Partly because of influence from the side of ‘energetics’, partly because of inability of chemists to master molecular-kinetic theories, chemical thermodynamics stayed a purely phenomenological discipline at the time.

Of decisive importance in changing this state of affairs was the establishing and working out the Nernst’s ‘heat theorem’ 120. Elaboration of the heat theorem marked the beginning of active permeation of molecular-kinetic concepts into chemical thermodynamics. The first events were related to quantum theories of specific heat of a crystal and to experimental researches of specific heats at low temperatures. Next specific heats of gases have been theoretically investigated. A general result was that new connections between chemical thermodynamics and statistical physics were established. Problems of chemical thermodynamics drew the attention of several theoretical physicists. An important success was the theory of strong electrolytes which also became, as mentioned, a link between the 'method of activities' and method of chemical potentials.

In the 19th century the classical chemical thermodynamics had been created as a result of application of the thermodynamic laws to simple ‘pre-thermodynamic’ information on macroscopic structure of chemical subjects, so that these simple models and thermodynamics became an integral whole. After about 1910 processes of fusing chemical thermodynamics and detailed microscopic models started to develop: statistical chemical thermodynamics came into existence.

The field is far from being accomplished. Although the general way of obtaining analytic forms for thermodynamic functions from structural models is given by statistical mechanics, this route is almost always impassable for most real systems, so that at some point in the derivation from first principles one must introduce assumptions on the values of parameters or the forms of functions in the general equations of statistical mechanics. That is why many of versions existed and exist even for the same systems, e. g. in thermodynamics of solutions. Be that as it may, a general result was building more powerful formalisms in chemical thermodynamics using the full range of thermodynamic functions and special methods.

Both lines considered, the development of ‘method of activities’ and the development of the heat theorem had similar paradoxical features. The first had adhered to van’t Hoff’s thermodynamics and led it to formalism of chemical potentials. The second was born within classical ‘pregibbsian’ thermodynamics, but prepared its transformation into statistical chemical thermodynamics and contributed greatly to mathematization of the field, so that, again ‘chemical’ and ‘physical’ direction were bridged.

It can be seen that putting bridges across the gap between the two directions was occurring at first spontaneously and unintentionally, as a natural process of scientific evolution. In 1929 the first significant work appeared, where the task has been deliberately set to overcome the duality of chemical thermodynamics. The main author, W. Schottky 121 accentuated: “the discord of the different thermodynamic schools. With a thermodynamics of cycles, of chemical reactions, quantities of work and heat effects, which is so well applicable to gas reactions and to some transformations of solutions and solids, is confronted the thermodynamics of characteristic functions and chemical potentials as well as, lately, of ‘activities’ which originates fundamentally from Gibbs’s reasoning. ...the development simply has not led yet to a selection and synthesis of what exists” 122This interesting work offered much to create such a synthesis attempting “to follow a middle course between Gibbs’-Planck’s and van’t Hoff’s-Nernst’s manners of representation” 123.

Following this the purposeful building a more harmonious apparatus of chemical thermodynamics began where could find place achievements both of Gibbs’s and of van’t Hoff’s thermodynamics. It would be incorrect to think van’t Hoff’s chemical thermodynamics had been absorbed by Gibbs’s system without leaving a trace. It is true, the method of cycles disappeared fast completely (it survived in particular form in the known Born-Haber cycle). Likewise, even ‘chemical’ direction has progressed from the original ‘osmotic’ foundation. The matured chemical thermodynamics has, however, adopted both equilibrium constants and integral characteristics of transformations, such as reactions heats, reactions free energies, etc. This way of consideration came from the van’t Hoff’s system. Besides the heat theorem, a new formulation of chemical thermodynamics, which uses a pair of variables, ‘affinity’ and ‘extent of reaction’ had been elaborated by T. De Donder 124 and his followers. This version prepared development of irreversible thermodynamics by Belgian school as a general phenomenological theory of chemical processes. (One should remember that connections between thermodynamics and chemical kinetics, embodied in this branch of science have their origin in van’t Hoffs “Études”).

Modern chemical thermodynamics became a complicated net of subdisciplines, according to the variety of its subjects and models used. Nevetheless, as at the times of van’t Hoff and Gibbs, it feeds off physics and chemistry, but now from biological, geological and technical sciences too. Its continuous and manifold connection with experimental researches in chemistry and related sciences probably constitute the main that chemical thermodynamics has inherited from van’t Hoff .


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Biographical information is given only for persons to which no article in the Dictionary of Scientific Biography is devoted. References to Poggendorffs Biographisch-literarisches Handwörterbuch are given simply as Poggendorff .

1 J. H. van’t Hoff: Ein Blick in das neue chemisch-physikalische Forschungsgebiet. Deutsche Revue,1895, Jg. 20, Bd. 4, S. 113.

2 See A. Kipnis, “Essay on the history of the emergence of chemical thermodynamics”, Trudi Instituta istorii estestvoznaniya i techniki (Proceedings of the Institute for history of science and technology, Moscow), 1961, 35: 39-107; V. V. Raman, “The permeation of thermodynamics into nineteenth century chemistry”, Indian Journal of history of science, 1975, 10: 16-37; A. Kipnis, “Die Herausbildung der chemischen Thermodynamik”, Rostocker Wissenschaftshistorische Manuskripte, 1984, 10: 45-61 (Unfortunately, horrible distortions were introduced there by the translation from the Russian manuscript, and the German text had not been shown the author before print; the flow-chart in which the genealogy of chemical thermodynamics is visualised is right, anyway).

3 G. Kirhhoff, “Über einen Satz der mechanischen Wärmetheorie und einige Anwendungen desselben”, Poggendorffs Annalen der Physik und Chemie, 1858: 103, 177-206; Ostwalds Klassiker, Nr. 101, 1898.

4 J. Loschmidt, “Der zweite Satz der mechanischen Wärmetheorie”, Berichte der Wiener Akademie der Wissenschaften, Mathematisch- Naturwissenschaftliche Classe, 1869, 59, II Abt.: 395-418.

5 C. M. Guldberg, “Sur la loi des points de congélation de solutions salines”, Compt. rend., 1870, 23: 537-540. This article is a part of the extended work published in Norwegian and translated in German too late; see: Oswalds Klassiker Nr. 139 (1903), 27-70; see also A. Kipnis, “Cato Maximilian Guldberg and his contribution to the development of physical chemistry”, Otcherki po istorii chimii (Essays on History of Chemistry), (Moscow, Academy of Sciences, 1963), p. 329-369, on p. 352-357.

6 A. Horstmann, “Dampfspannung und Verdämfungswärme des Salmiaks”, Berichte der deutschen chemischen Gesellschaft, 1869, 2: 137-140; “Zur Theorie der Dissociation”, Ber., 1871, 4: 635-639.

7 Peslin, “Sur les lois des tensions de dissociation des composés chimiques”, Annales de chimie et de physique, 1871, 24: 208-214. Information on H. Peslin is extremely scanty; neither his birth and death dates nor his full name are not found yet. It is known only that his first publication, a thesis on celestial mechanics appeared in 1843; his further writings the latest of them was published in 1884 concerned mainly physical astronomy.

8 J. Moutier, “Sur la dissociation au point de vue de la thermodynamique”, Comptes rendus, 1871, 72: 759-762.

Jules Moutier (1829-1897), physicist, graduated from l’École polytechnique to Paris, worked as an inspector of the telegraphic services and as a teacher for physics and chemistry; 1881 he became a ‘repetiteur’ at l’École Polytechnique. He worked in particular on thermodynamics; some of his numerous publications are devoted to chemical topics. (Poggendorff, III: 941-942, IV: 1037; S. L. Jaki, Uneasy Genius:The Life and Work of Pierre Duhem (Nijhoff, The Hague, 1984), p. 32, 262.)

9 C. M. Guldberg “Bidrag til Theorien for Dissociationen”, Forhandlinger i Videnskabsselskabet i Christiania,1872, 14: 136-143; Ostwalds Klassiker, Nr. 139 (1903): 71-79.

10 A. Horstmann, “Theorie der Dissociation”, Annalen der Chemie und Pharmacie, 1873, 170: 192-210. For details see A. Kipnis, August Friedrich Horstmann und die physikalische Chemie (ERS Verlag, Berlin, 1997), p.86-94.

11 H. Helmholtz, “Die Thermodynamik chemischer Vorgänge”, Sitzungsberichte der königlichen preussischen Akademie der Wissenschaften, 1882: 22-39; Ostwalds Klassiker, Nr. 124.

12 See: Helge Kragh, “Between Physics and Chemistry: Helmholtz’s Route to a Theory of Chemical Thermodynamics”, in: Hermann von Helmholtz and the Foundations of Nineteenth-Century Science, Edited by David Cahan (Univ. of California Press, Berkeley, 1993), p. 403-431.

13 J. H. van’t Hoff, “Wie die Theorie der Lösungen entstand”, Berichte der deutschen chemischen Gesellschaft, 1894, 27: 6-19, on p. 7.

14 J. H. van’t Hoff, in: J. J. van Laar, Thermodynamik in der Chemie (Amsterdam, van Looy, H. Gerlings, Leipzig, H. Engelmann, 1893), Vorwort.

15 As early as 1862 Clausius wrote: „I believe, indeed, that we must extend the application of this theorem [the Second Law], supposing it to be correct, still further, and especially to chemical combinations and decompositions. The separation of chemically combined substances is likewise an increase of disgregation, and the chemical combination of previously isolated substances is a diminution of their disgregation; and consequently these processes may be brought under considerations of the same class as the formation or precipitation of vapour“. R. Clausius, „On the application of the theorem of the equivalence of transformations to the internal work of a mass of matter“, Philosophical Magazine, 1862: 24, 81-97, 201-213, on p. 205-206. Italics in original. On the notion of ‘disgregation’, a function introduced by Clausius to “express the degree in which the molecules of a body are dispersed” (Ibid., on p. 85) see: M. J. Klein, “Gibbs on Clausius”, Historical Studies in the Physical Sciences, 1969: 1, 127-148, on p. 135-140.

16 R. B. Dobrotin, Yu. I. Solov’ev, Van’t Hoff, (Moscow, Nauka Press, 1977), p. 115.

17 Ibid., p. 118.

18 W. P. Jorissen, “Mijn herinnerungen aan Jacobus Henricus van’t Hoff en de studie der chemici aan de Universiteit van Amsterdam onder zijn leiding”, Chemisch weekblad, 1952, 48: 647-658, on p. 652

19 K. J. Laidler, The World of Physical Chemistry, (Oxford University Press, 1993), p. 118.

20 J. A. A. Ketelaar, “J. H. van’t Hoff en de physische chemie”, Chemisch Weekblad, 1952, 48: 622-629, on p. 626-628; Dobrotin, Solov’ev, Van’t Hoff, p. 115-140; H. A. M. Snelders, “J. H. van’t Hoff’s research school in Amsterdam (1877-1895)”, Janus, 1984, 71: 1-30; J. W. Servos, Physical Chemistry from Ostwald to Pauling (New Jersey, Prinstone University Press, 1990), p. 26-33; Laidler, The World of Physical Chemistry, p. 114-123.

21 Van’t Hoff contented that this work coincided with the free energy of the process only after twenty years. J. H. van’t Hoff, “Einfluß der Änderung der spezifischen Wärme auf die Umwandlungsarbeit”, Festschrift Ludwig Boltzmann gewidmet zum sechzigsten Geburtstage, (Leipzig, 1904), p. 233-241.

22 The designation ‘equilibrium box’ is due to F. Haber, Thermodynamics of technical gas reactions, (Longman, New York, 1908), p. 55; it had been then adopted by van’t Hoff, Die chemischen Grundbegriffe nach Menge, Mass und Zeit, (Braunschweig, Vieweg, 1912), p. 54.

23 W. Nernst, Theoretische Chemie vom Standpunkt der Avogadro’schen Regel und der Thermodynamik (Stuttgart, Verlag von Ferdinand Enke, 1893), p. 509

24 J. W. Brühl, “Der neue Akademiker”, Die Zukunft, 1896, 16: 151-159, 213-222. On Julius Wilhelm Brühl (1850-1911) see Neue Deutsche Biographie, 2: 663 and references therein.

25 Harry Jones, The Nature of solutions, (New York, 1917), p. 79. A biography of Harry Clary Jones (1865-1916), by E. E. Reid, is placed in the same book on p. VII-XIII. See also J. W. Servos, Physical Chemistry, p. 75-78.

26 See R. G. A. Dolby, “Debates over the Theory of Solution: A Study of Dissent in Physical Chemistry in the English-Speaking World in the Late Nineteenth and Early Twentieth Centuries”, Historical Studies in the Physical Sciences, 1976, 7: 297-404.

27 A. Einstein, “The work and personality of Walther Nernst”, The Scientific Monthly, 1942, 54: 195-196, on p. 196.

28 G. N. Lewis, “Umriss eines neuen Systems der chemischen Thermodynamik”, Zeitschrift für physikalische Chemie, 1908, 61: 129-165.

29 Haber, Thermodynamics..., p. 41.

30 Gibbs’s thermodynamics has been much considered, interpreted and commented. For bibliography see L. P. Wheeler, Josiah Willard Gibbs: The History of a Great Mind, (Yale University Press, New Haven, 1951); U.I. Frankfurt, A. M. Frenk, Josiah Willard Gibbs (Moscow, Nauka Press, 1964). See also: A. Kipnis, „J. W. Gibbs and chemical thermodynamics“, in: K. Martinas, L. Ropolyi, P. Szegedi, eds., Thermodynamics: History and Philosophy. Facts, Trends, Debates (World Scientific, Singapore, 1991), p. 492-507.

31 J. W. Gibbs, „On the equilibrium of heterogeneous substances. Abstract by the author“ [1879], The Collected Works (Longman, 1928, reprinted by Yale University Press, New Haven, 1948), vol. I, p. 354-371, on p. 354

32 J. W. Gibbs, „On the equilibrium of heterogeneous substances“ [1876-1878], The Collected Works, vol. I, p. 55-353, on p. 62.

33 Th. Young, “Cohesion” [1816], Miscellaneous Works (London, 1855), vol. I, p. 454-484 (see Section II: “Relation of Heterogeneous Substances”).

34 J. D. van der Waals, Ph. Kohnstamm, Lehrbuch der Thermodynamik in ihrer Anwendung auf das Gleichgewicht von Systemen mit gasförmig-flüssigen Phasen. Nach Vorlesungen von J. D. van der Waals bearbeitet von Ph. Kohnstamm. 1. Teil (Leipzig-Amsterdam, Maas & Van Suchtenen 1908), p. 114.

35 F. Massieu, “Sur les fonctions caractéristiques des divers fluides”, Comptes rendus hebdomadaires des Séances de l’Academie de Science, 1869, 69: 858-862, 1057-1061. Massieu, François Jacques Dominique (1832-1896), engineer and geologist, was professor of mineralogy and geology in Rennes. (Poggendorff, III: 881; Index Biographique Française 1998, 5: 2276). See also: Bertrand, “Rapport sur un Mémoire de M. Massieu, intitulé: Mémoire sur les fonctions caractéristiques des divers fluides et sur la théorie des vapeurs”, Comptes rendus; 1870, 71: 257-260. This memoir of  Massieu had been published by the Paris Academy in Mémoires des savants étrangeres, 1876, 12: No.2, 1-91; here, as Bertran recommended, functions -F = TS – U and -H = TS – (U + PV) were used instead of originally introduced characteristic functions ψ = S – U/T and ψ´ = S - (U + PV)/T.

36 P. Duhem, “Sur le potentiel thermodynamique et la théorie de la pile voltaique”, Comptes rendus, 1884, 99: 1113-1115; Le potentiel thermodynamique et ses applications à la mécanique chimique et à l’étude des phénomènes électriques (Paris, A. Hermann, 1886).

37 Gibbs, The Collected Works, vol. I, p.355.

38 Ibid., p. 90-91.

39 W. Ostwald, “Über chemische Energie”, Verhandlungen der Gesellschaft deutscher Naturforscher und Ärzte,1893, 65: 2. Teil, I. Hälfte, 49-55, on p. 50; (reprinted in Abhandlungen und Vorträge allgemeinen Inhalts (1887-1903) (Leipzig, Verlag Veith, 1904), p. 207-219, on p.210); W. D. Bancroft, The Phase Rule, (Ithaca – New York), 1897, p. 2.

40 Gibbs, The Collected Works, vol. I, p. 63.

41 J. W. Gibbs, “To the American Academy of Arts and Sciences”, Proceedings of the American Academy of Arts and Sciences, 1881, 16: 420-421, on p. 421; reprinted in: Wheeler, Josiah Willard Gibbs, p. 88-89, on p. 89.

42 See E. W. Garber, “James Clerk Maxwell and Thermodynamics”, American Journal of Physics, 1969, 37: 146-155 and references therein.

43 H. v. Helmholtz, “Zur Erinnerung an Rudolf Clausius”, Verhandlungen der Physikalischen Gesellschaft zu Berlin, 1889, 8: 1-6, on p. 3.

44 Nernst, Theoretische Chemie, p. 480; the same in the 2nd edition (1898), p. 562.

45 It seems as a Clio’s smile that Gibbs took lessons on theoretical chemistry, namely on thermochemistry, by Horstmann in Heidelberg: University Archive Heidelberg, Akademische Quästur A. Horstmanns (Rep. 27, Nr. 621, Bl. 3); Kipnis, August Friedrich Horstmann, p. 82.

46 Gibbs, The Collected Works, vol. I, p. 348.

47 A. Ya. Kipnis, B. E. Yavelov and J. S. Rowlinson, Van der Waals and Molecular Science (Oxford Univ. Press, 1996), Ch. 8.

48 Jaki, Uneasy genius [Note 8], p.66, 263.

49 Max Planck, “Über das Princip der Vermehrung der Entropie”, Wiedemanns Annalen der Physik und Chemie, 1887, 30: 562-582, 31: 189-203, 32: 462-503.

50 Ibid., 32, p. 499-502.

51 Gibbs, The Collected Works, vol. 1, p. 55, 354.

52 Planck, Wiedemanns Annalen, 1887, 30, p. 562.

53 A. Kipnis, “On the history of Gibbs’s thermodynamics”, Voprosi istorii estestvoznaniya i techniki (Problems of the History of Science and Technology, Moscow), 1959, 8: 127-132; Trudi, 1961, p.90.

54 For literatur and discussion see Dolby, Historical Studies in Physical Sciences, 1976, p. 377-380 and J. D. van der Waals, Ph. Kohnstamm, Lehrbuch der Thermostatik, Teil I: Allgemeine Thermostatik (Leipzig, Verlag von Johann Ambrosius Barth, 1927), p. 26-27, 168, 203.

55 Richard Lorenz. Das Gesetz der chemischen Massenwirkung. Seine thermodynamische Begründung und Erweiterung (Leipzig: Voss, 1927), p. 14.

56 Jacobus H. van’t Hoff. Physical Chemistry in the Service of the Sciences. (The Decennial Publications of the University of Chicago, 2nd Ser. Vol. 18, Chicago, 1903), p. 21.

57 Gibbs, Proc. Amer. Academy of Arts and Sciences, 1881, p. 420-421 (or Wheeler, Josiah Willard Gibbs, p. 89).

58 van’t Hoff, Boltzmann Festschrift, p. 237.

59 Sv. Arrhenius, “Über die Gleichgewichtsverhältnisse zwischen Elektrolyten”, Zeitschrift für physikalische Chemie, 1890, 5: 1-22; 1892, 9: 339-342.

60 W. Ostwald, “Über die Dissociationstheorie der Electrolyte”, Ibid., 1888, 2: 270-283.

61 W. Nernst, “Über gegenseitige Beeinflüssung der Löslichkeit von Salzen”, Ibid., 1889, 4: 372-383; Verteilung eines Stoffes zwischen zwei Lösungsmitteln und zwischen Lösungsmittel und Dampfraum”, Ibid., 1891, 8: 110-139.

62 Einstein, The Scientific Monthly, 1942, p. 195.

63 W. Nernst, “Die elektromotorische Wirksamkeit der Ionen”, Z. physik. Chem., 1889, 41: 129-181

64 For references and discussion see Erwin Hiebert, “Walter Nernst”, Dictionary of the Scientific Biography, Vol. XV, p.432-453; Arnold Münster, Statistical Thermodynamics (Berlin-Heidelberg, Springer-Verlag, 1974), vol. II, p. 70-81.

65 I. Schroeder, [On relation between melting points of solids and their solubility in organic liquids], Gorni Journal, 1890, IV: 272-327; “Abhängigkeit der Löslichkeit eines festen Körpers von seiner Schmelztemperatur”, Z. physik. Chem.1893, 9: 449-465; H. Le Chatelier, “Sur la loi générale de solubilité des corps normaux”, Comptes rendus, 1894, 118: 638-641.

Ivan Fjodorovich Schroeder (1858-1918) graduated from the Mine Institute of St. Petersburg in 1884. He worked there until his death, since 1899 as the full professor of chemistry; in 1912-1917 he was the director of the Institute. The cited work was his thesis; later he devoted himself to applied sciences. (A. Kipnis, Razvitie chimicheskoi termodinamiki v Rossii (The development of the chemical thermodynamics in Russia) (Moscow, Nauka Press, 1964), p. 337; Poggendorff, IV: 1354; VI: 2371)

66 M. Margules, “Über die Zusammensetzung der gesättigten Dämpfe von Mischungen”, Sitzungsberichte der Akademie der Wissenschaften Wien, Math. Cl., 1895, 104, Abt.IIa: 1243-1278.

67 Vor bibliography see Kipnis, Yavelov, Rowlinson, Van der Waals, p. 257, 262

68 H. W. Bakhuis Roozeboom, “Erstarrungspunkte der Mischkristalle zweier Stoffe”, Z. physik. Chem., 1899, 30: 385-412, 413-429.

69 Here is van’t Hoff’s judgement (1899): “Berthelot has stubborn resisted against the best what is attained in chemical theories, atomistics, Avogadro’s law, theory of chemical structure, stereochemistry, the inferences of thermodynamics, ... whereby, with his incontestable authority, the young french school is influenced highly unfavorably.” In: Chemiker über Chemiker. Wahlvorschläge zur Aufnahme von Chemikern in die Berliner Akademie (Berlin, Akademie-Verlag, 1985), p. 150-151.

70 Franciscus Antonius Hubertus Schreinemakers (1864-1945) studied at the University of Leiden, 1898 dr chemistry honoris causa, 1901-1934 professor of chemistry in Leiden. One of the most outstanding researchers in the thermodynamics of phase equilibria. (Poggendorff, IV: 1353; V: 1131; VI: 2368; VIIb: 4732; H. A. M. Snelders, Biografisch Woordenboek van Nederland (2 Deel, Elsevier, Amsterdam, 1985), 505-506 and references therein).

71 Anonym, “L’Espace dans la Chimie”, Nature, 1921:108, 171-172, on p. 171.

72 Gustav Tammann, Lehrbuch der heterogenen Gleichgewichte, (Braunschweig, F. Vieweg & Sohn, 1924), Vorwort.

73 G. N. Lewis, “Outlines of a new system of thermodynamic chemistry”, Proceedings of the American Academy of Arts and sciences, 1907: 43, 257-293, on p. 260.

74 Planck, Wiedemanns Annalen, 1887, 30, p. 582

75 Johannes Jacobus van Laar (1860-1938), 1879 graduated from the Royal Marine Institute, 1881-1884 studied in Amsterdam physics by van der Waals and chemistry by van’t Hoff, earned for life as a schoolteacher; 1898-1907 worked in physical chemistry at the University of Amsterdam partly as privat-docent in ‘mathematical chemistry’ later as assistant to Roozeboom. Since 1912 lived in Switzerland. (E. P. van Emmerik, J. J. van Laar (1860-1938). A mathematical chemist. (Doctoral thesis, Delft, 1991); H. A. M. Snelders, “The Dutch physical chemist J. J. van Laar (1860-1938) versus J. H. van’t Hoff’s osmotic school”, Centaurus, 1986, 29: 53-71; Biographisch Woordenboek van Nederland (Deel 2, Elsevier, Amsterdam, 1985), 333-334 and references therein.

76 H. Jahn, [Book review], “Die Thermodynamik in der Chemie. Von J. J. van Laar...”, Zeitschrift für den physikalischen und chemischen Unterricht, 1893, 7: 104.

77 E. W. Washburn, “The fundamental law for a general theory of solutions”, Journal of the American Chemical Society, 1910, 32: 653-670, on p. 659.

78 H. Poincaré, “Les conceptions nouvelles de la matière”, Le matérialisme actuel (Paris, 1913), p. 49-67, on p. 54.

79 A. N. Shchukarev, Uchenie ob energii v ego prilozheniyakh k zadacham chimii (The doctrine of energy in its applications to problems of chemistry) (Moscow, 1900), p. 77.

Alexander Nikolaevich Shchukarev (1864-1936) graduated from the Moscow University in 1889, was simultaneously a school teacher and an assistant in Louginin’s ‘Thermal Laboratory’ to Moscow, 1906-1910 he was ‘privat-docent’ there; he studied calorimetrically critical phenomena in one- and two-component fluids using Gibbs’s theory. In 1911 he became a professor at the Technological Institute in Kharkov. Published several interesting textbooks on thermochemistry and on physical and general chemistry. (Kipnis, Razvitie chimicheskoi termodinamiki v Rossii, p. 337; Poggendorff, IV:1357; V: 1225; VI: 2374; VIIb: 4756-4757).

80 P. Duhem, Thermodynamique et chimie. Leçons éléméntaires à l’usage des chimistes (Paris, A. Hermann, 1902; 2me ed., 1910); Thermodynamics and Chemistry. A Non-mathematical Treatise for Chemists and Students of Chemistry (New York – London, Wiley, 1903).

81 van’t Hoff, Vorwort [Note 14].

82 Kipnis, Yavelov, Rowlinson, Van der Waals, p. 114.

83 Van’t Hoff, “Antrittsrede”, Sitzungsberichte der K. Preussischen Akademie der Wissenschaften zu Berlin,1896: 745-747, on p. 747.

84 See: J. Walker, “Van’t Hoff memorial lecture”, Journal of the Chemical Society, 1913, 103: 1127-1143, on p. 1141; Snelders, Centaurus, 1986, p. 61.

85 Ernst Cohen, Jacobus Henricus van’t Hoff. Sein Leben und Wirken (Leipzig, Akademische Verlagsgesellschaft, 1912), p. 299.

86 Quoted after Jaki, Uneasy Genius, p. 68.

87 J. H. van’t Hoff. Wahlvorschlag für J. W. Gibbs zur Aufnahme in die Berliner Akademie der Wissenschaften [1900]. In: Physiker über Physiker, Wahlvorschläge zur Aufnahme von Physikern in die Berliner Akademie... bearbeitet von Chr. Kirsten und H.-G. Körber. (Akademie-Verlag, Berlin, 1975), p. 147-148.

88 August Horstmann, Lebenserinnerungen eines Kurzsichtigen, (Heidelberg, 1925, a typescript in possession of family Horstmann), p. 72.

89 C. Truesdell, „What did Gibbs and Caratheodory leave us about thermodynamics?“, In: New Perspectives in thermodynamics, (Ed. by J. Serrin, N. Y., Springer, 1986), 101-124, on p. 107.

90 J. W. Gibbs, Letter on electrochemical thermodynamics to O. J. Lodge [1887], The Collected Works, vol. I, p. 406-408, on p. 407-408.

91 Wheeler, Josiah Willard Gibbs, p. 53.

92 Dobrotin, Solov’ev, Van’t Hoff, p. 126-129.

93 J. H. van’t Hoff, Zinn, Gips und Stahl vom physikalisch-chemischen Standpunkt (München-Berlin, Verlag Oldenburg, 1901), p. 3-4.

94 Cohen, J. H. van’t Hoff, p. 306.

95 Gibbs, The Collected Works, Vol. II, Part 1. See also: Gibbs, “On the fundamental formula of statistical mechanics” [1884], Ibid., Part 2, p.16.

96 W. Ostwald, Grosse Männer (Leipzig, Akademische Verlagsgesellschaft, 1909), p. 7, 371-388.

97 Kipnis, Razvitie chimicheskoi termodinamiki v Rossii, p. 311-317.

98 Lewis, Proc. of the Amer. Academy of Arts and Sciences, 1907, p. 259.

99 J. J. van Laar, Sechs Vorträge über das thermodynamische Potential und seine Anwendungen auf die chemische und physikalische Gleichgewichtsprobleme (Braunschweig, Vieweg, 1906), p. 35.

100 J. J. van Laar, J. D. van der Waals (Leipzig, J. A. Barth, 1900), p. 38-39.

101 Laidler, The World of Physical Chemistry, p. 11. See also Servos, Physical Chemistry from Ostwald to Pauling, p. 181.

102 G. N. Lewis, M. Randall, Thermodynamics and the free energy of chemical substances, (New York, McGraw-Hill Book Company, 1923), p. X.

103 F. W. Küster, A. Thiel, Lehrbuch der allgemeinen physikalischen und theoretischen Chemie, (Heidelberg, Carl Winter, 1923), Bd. II.

104 W. Lash Miller, “The method of Willard Gibbs in chemical thermodynamics”, Chemical Reviews, 1925, 1: 293-344, on p. 296.

105 J. D. van der Waals, Ph. Kohnstamm, Lehrbuch der Thermodynamik, Teil I, p. 24.

106 A. Rakovsky, Foreword to the Russian edition of van der Waals-Konstamm’s Lehrbuch der Thermostatik (Moscow, 1936).

Adam Vladislavovich Rakovsky (1879-1941), son of a school teacher, 1903 graduated from the University of Moscow, since 1915 lectured there in particular chemical thermodynamics, since 1922 professor in the same place. He had published interesting manuals on physical chemistry and chemical thermodynamics. (Poggendorff, VI: 2110, VIIb: 4215-4216; Kipnis, Razvitie chimicheskoi termodinamiki v Rossii, p. 331).

107 Gibbs, Proc.of the Amer. Academy of Arts and Sciences, 1881, p. 421.

108 J. D. van der Waals, “Moleculartheorie eines Körpers, der aus zwei verschiedenen Stoffen besteht”, Z. physik. Chem., 1890, 5: 133-176. See also Kipnis, Yavelov, Rowlinson, Van der Waals, p. 110-113, 266-267.

109 Ph. Kohnstamm, “Osmotic pressure or thermodynamic potential”, Proceedings of the Section of Science, K. Akademie van Wetenschappen te Amsterdam, 1905, 7: 741-751, on p. 751.

Philipp Abraham Kohnstamm (1875-1951), the nearest pupil of J. D. van der Waals, graduated from the University of Amsterdam in 1900, till 1908 was his assistant, and after van der Waals’s retirement lectured thermodynamics as extraordinary professor. After 1928 he devoted himself purely to social problems. (G. J. van de Poll, In: Biografisch Woordenboek van Nederland, Vol. I (‘s-Gravenhage, Nijhoff, 1979), p. 306-310; Kipnis, Yavelov, Rowlinson, Van der Waals, p. 123-124, 146 and the references therein).

110 E. W. Washburn, “A simple system of thermodynamic chemistry based upon a modification of the method of Carnot”, Journal of the American Chemical Society, 1910, 32: 467-502, on p. 469; also “The fundamental law for a theory of solutions”, Ibid., p.653-670.

111 D. S. Ciklis, Phasentrennung in Gasgemischen. Phasengleichgewichte in binären und ternären Systemen im Gebiet überkritischer Parameter. (Leipzig, VEB Deutscher Verlag für Grundstoffindustrie, 1972), p. 121.

Daniil Semenovich Ciklis (1911-1978), Russian physical chemist, coauthor of the discovery of phase separation in gas mixtures (that is of limited mutual solubility of gases above their critical point).Born in Moscow, 1936 graduated the Moscow Institute for Chemical Technology. Since 1941 he was research wprker of Physical Chemistry Laboratory at State Institute for Nitrogen Industry, since 1955 professor there. His main work was devoted to experimental investigation of the effects of very high pressures on gases and gas mixtures.

112 See Servos, Physical Chemistry from Ostwald to Pauling, p. 139-149.

113 Lewis, Proc. Amer. Acad. of Arts and Sciences, 1907, p. 260.

114 A. A. Noyes and W. C. Bray, “The effect of salts on the solubility of other salts. I”, Journal of the American Chemical Society, 1911, 33: 1643-1649, on p. 1646.

115 J. N Brønsted, “Studies on solubility. I. The solubility of salts in salt solutions”, Journal of the American Chemical Society, 1920, 42, 761-786, on p. 763.

116 P. Debye, “Osmotische Zustandsgleichung und Aktivität verdünnter starker Elektrolyte”, Physikalische Zeitschrift, 1924: 25, 97-107; English translation in The Collected Papers of Peter J. W. Debye (Interscience Publishers, New York, 1954), p. 326-346.

117 E. A. Guggenheim, Modern Thermodynamics by the methods of Willard Gibbs, (London, Methuen, 1933).

Edward Armand Guggenheim (1901-1970) graduated 1927 from the University of Cambridge and became one of the leading experts in chemical thermodynamics. (Poggendorff, VI: 974, VIIb: 1770-1772).

118 Gibbs, The Collected Works, vol.II, Part 1, p. xii.

119 Ibid., p. viii.

120 A. Kipnis, “The heat law in the history of chemical thermodynamics”, Voprosi istorii estestvoznaniya i techniki, 1976, 4(53): 42-47.

121 Walter Schottky (1886-1976), physicist, a pupil of M. Planck, 1912 graduated from the University of Berlin and worked mainly in electronics for Siemens & Halske. Contributed much to the development of electronic tubes and to the theory of solids.

122 W.Schottky, H. Ulich, C. Wagner, Thermodynamik. Die Lehre von den Kreisprozessen, den physikalischen und chemischen Veränderungen und Gleichgewichten (Berlin, Verlag von Julius Springer, 1929), p. VII.

123 Ibid., p. 151.

124 Théophile De Donder (1872-1957), 1911-1942 professor of mathematical physics at the University of Brussels.