Maurice W. Lindauer
Valdosta State College Valdosto, Georgia
The Evolution of the Concept of Chemical Equilibrium from 1775 to 1923
The explanation of the wide diversity of chemical change has long challenged man's ingenuity as it continues to do to this day. A large part of the history of chemistry is the result of man's attempts to meet this particular challenge, and much of our present knowledge of chemistry grew out of such investigations. Although chemical equilibrium is no longer looked upon as a revelation of the forces which control chemical change, much of its development arose out of just such an expectation. It is the purpose of this paper to trace some of the major attitudes and ideas which led to the present concept of chemical equilibrium.
tion of B from substance AB required several times the stoichiometric amount of substance C; but considering the basic requirement of displacement, Bergman still maintained that the affinity of substance h for substance C was greater than that for substance B. Bergman's concept of elective affinity was widely accepted, and it did much to systematize the knodrdge of chemical reactions of that day. I t is interesting to note that the displacement reaction still finds use in modern inorganic chemistry, although not as a method of first choice, in classifying the stability order of coordination complexes (4).
Chemical Afflnity and Early Methods of Its Evaluation
C. F. Wenzel and the Influence of Quantity
The idea of affinity, as an expression of the tendency of substances to enter into chemical combination, was introduced sometime during the 13th century by Albertus Magnus, who reflected the earlier view of Hippocrates that chemical action is the result of a similarity or kinship between the reacting substances (1, 2). Walden (8) reported that the alchemist Geber, also about the 13th century, arranged a number of metals in several primitive activity series according to their behaviors toward sulfur, mercury, and oxygen; later, Paracelsus, Stahl, and others employed similar series. In 1718, E. F. Geoffroy enunciated his "Tables des differents rapports" (affinity table) in which substances were arranged in vertical columns in order of decreasing affinity, going down the column, with respect to the substance at the head of the column. A considerable amount of affinity data was compiled during the 18th century, and this activity was climaxed with the concept of elective affinity as enunciated by T. Bergman in 1775, in a treatise entitled "De Attractionibus Electivis." Bergman concluded that chemical combinations were the result of the elective affinities which depended solely upon the nature of the reacting substances. Bergman further unified this concept by specifying that affinities were to be determined on the basis of displacement reactions. That is, if the addition of a substance, C, to another substance, AB, produced the substance AC and eliminated substance B, then it can be concluded that substance C has a greater affinity for substance A than does substance B. Bergman also noted that in some displacement reactions, the eliminaThe author is indebted to the National Science Foundation for the opportunity to attend the Academic Year Institute at Harvard Univemity, where this work was undertaken; and he especially wishes to acknowledge the advice and encouragement offered by Dr. Leonard K. Nash of the Harvard Chemistry Department.
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In 1777, two years after Bergman's publication, C. F. Wenzel published a paper entitled "Lehre von der chemischen Affinitat der Korper" in which he attempted to estimate chemical affinities by noting the rate a t which different metals were dissolved by various acids. In his experiment,^, Wenzel observed that the rate at which metals were dissolved was influenced by the quantity of acid as well as by the nature of the acid. However, Wenzel's observations did not attract the attention of his contemporaries, and his work was forgotten. Wenzel's work illustrates several of the principles which J. B. Conant, in his book "On Understanding Science," calls the "tactics and strategy of science." Two principles which are among the requirements for the acceptance of an idea or concept are (1) the proposal must fit the times, and (2) the proposal must be better than its predecessor. Thus, in spite of the limitations of the elective affinity concept, it is still more general, and hence more acceptable, than the fact that the quantity of acid influencesthe rate a t which metals are dissolved. This illustrates the second of Conant's principles in that callmg attention to the shortcomings of a concept is not sufficient, in itself, to displace an established mental construct or concept. Furthermore, Wenzel's observations preceded the similar one of Wilhelmy, made in a much more sophisticated era, by some 70 years, and even Wilhelmy's observation was not fully appreciated until later. In view of the supporting concepts (which were developed long after Wenzel) that were necessary for the acceptance and understanding of the influence of the quantity of reactants on the outcome of chemical reactions, t,here is little reason to credit Wenzel with a significant foresight in the mat,ter of chemical equilibrium. Instead, it is to his credit that he published an objective report of his observatious in spite of the contradiction with the then popularly accept,ed idea ofelective affinity.
C. 1. Berthollet and the Influence of Quantity
In June of 1799 during Napoleon's Egyptian campaign, Claude Louis Berthollet, one of Napoleon's most trusted advisors, read a paper before the National Institute of Egypt in which he called attention to the fact that chemical combinations are also influenced by other principles in addition to that of chemical affinity. Among the many principles which he noted, Berthollet is remembered mostly for his emphasis on the influence of the quantity of reactants upon the course of chemical combinations. J. W. Mellor (5) strongly suggested that Berthollet's ideas on the effect of quantity stem from Berthollet's proposcd explanation of the large trona (sodium carbonate) deposits found on the shores of the Natron Lakes in Egypt. Mellor explained that Berthollet recognized in this natural phenomenon the reaction CaCO,
+ 2NaCl-
CaCL
+ NaCOa,
as being the reverse of that predicted by the elective affinities, and that Berthollet concluded that this reversal was the result of the large quantity of calcium carbonate present on the shores of these lakes which reacted with the sodium chloride brought in from the rivers. Upon examining Berthollet's later writings, it does not seem reasonable that the trona episode was entirely responsible for his ideas on the effect of quantity. Berthollet stated, in a footnote on the opening page of his short treatise entitled "Recherches sur les lois de I'affinite" ("Researches"), which was published in 1801 upon his return to Paris, that "The reading of this Treatise was commenced in the Institution of Cairo. June. 7th vear" (6). but he does not give any direct indication "of the'diigin of his ideas. In this
-
t,rona de~ositsin connection with the influence of efflorescence on the outcome of chemical reactions. In this discussion, which he also repeated in a somewhat modified form in a lengthy two-volume exposition of his ideas (published in 1803 under the title, "Essai de statique chemique"), Berthollet mentioned three and possibly four requirement,^ for the formation of natural trona deposit,^; these are "lst, a sand containing a great quantity of carbonate of lime; Znd, humidity; 3rd, muriate of soda. I have aiso remarked that reeds cont,ribute much to its (i.e., trona) formation" (7) Berthollet went on to say that a small amount of trona is formed in solution as a result of the action of the large quantity of calcium carbonate and the sodium chloride, but he emphasized that the large trona deposits are the result of the trona being removed from further action (e.g., the decomposition into calcium carbonate) by the process of efflorsscence. If the trona episode was singularly responsible for his ideas, as Mellor implied, then it seems that he would have devoted much more attention to the subject than he did. I t is interesting to note that in his "Researches" but not in his later "Essay," Berthollet described an unsuccessful att,empt to demonstrate the formation of sodium carbonate under laboratory conditions. Berthollet rat,ionalized the failure of the trial on the basis of insufficient time; the deposition of trona, he explained, required a long period of time. He therefore
dismissed the exneriment-but not his conclusions. Thus, it appears'that Berthollet did not attach the significance to the trona episode which Mellor implied, and it seems reasonable that his ideas on the influence of quantity on chemical reactions were at least in the embryonic stages of development before he ever went to Egypt. His presence in Xapoleon's retinue indicates the extent of his prominence eveu a t a time preceding the events for which he is best known. Early in his "Researches" (Art. I, No. 3), Berthollet criticized Bergman's failure to consider the influence of the quantity of substance required to accomplish displacement. I t appears that Berthollet was fairly well acquainted with Bergman's theory before he went to Egypt, and his ideas may well have originated from an earlier dissatisfaction with Bergman's ideas. The fact that his writings call attention to many principles which influence chemical combinations indicates his general dissat,isfaction with the single principle of elective affinity as Bergman proposed and lends support to the contention expresspd above. Whereas Bergman's theory was a collection of independent affinities, Berthollet attempted in his "Researches" (Art. I, No. 1)to unify the understanding of chemical phenomena by the cousideration of all of the forces which effect such phenomena. In order to emphasize the existence of such forces, he called attention to experimental results which were contrary to the predictions of the elective affinities. I n an attempt to explain these contradictions, Berthollet performed a number of experiments whose results he interpreted as being due to the effect of the quantities of substances. In Art. I, KO.5, Berthollet statpd: I t is my purpose to prove in the following sheets, that elective
subiect of the'combination.'betwe& the two bodies whose actions are opposed; and that the proportions of this partition are determined, not solely by the difference of energy in the affinities,but also by the difference of the quantities of the bodies; so that a n excess of quantity of the body whose affinity is the weaker, compensatesfor the weakness of affinity.
In Article I1 of this same treatise, hc cites a number of experiments which, according to him, prove the above assertion. These experiments are summarized in Table 1. The second and fourth experiments are obvious misinterpretations in the light of present chemical knowledge, but this is characteristic of early work in all fields; as a whole, Berthollet's experiments were quite reasonable. Berthollet did not indicate the Table 1.
A Summary of Article II of Berthollet's "Researches" Ezpen'ments which pmoe that i n Elective Afinities, the Bodies whose Powers ale opposed, diuide between them the Body which is the subject of the Combination.
Expt. 1. 1 part 1pat 1 part 4. 1 part 5. 1 part 6. 1 part 7. 1part 2. 3.
Reactants and their ~rouorticr.;
. .
BaSO,, 1 part KOH &SO4, 1 part CaO CaC& 2 parts KOH CaC201, 2 parts HNOa CadPO,)., 2 parts KOH KOH, 1 part CaC03 NaOH, 1 part K$04
Products K2S04 CaSO, and K5S04 KG04 Ca(N0.h &PO4 IGCOs Na?SO, and K d 0 4
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quantities of the products obtained in these experiments, except for the first experiment in which he stated that the amount of barium sulfate decomposed was small. This omission of the quantity of product seems odd in view of Berthollet's emphasis on this principle, but then the concept of elective affinity adequately explained that aspect (i.e., the reverse of Berthollet's reactions) so that further explanation was deemed unnecessary. Berthollet must be given credit for having devised a clever experimental scheme. I t must be remembered that he regarded salts as combinations of the entire acid and the entire base, and not as combinations of parts of the acid and base as we now regard them to be. In the fourth experiment, he demonstrated the partition of a base between two acids by the isolation of calcium nitrate from the mixture which still contained some of the original calcium oxalate; therefore, he concluded that both the nitric acid and the oxalic acid had divided the base between them. One is tempted to wonder what Berthollet might have concluded had he used an excess of nitric acid in this experiment. In other experiments, he demonstrated the partition of two bases between a single acid. In his attempt to establish the universal validity of his idea, Berthollet was careful to demonstrate that the idea applied to a number of different situations. Toward the end of Article I1 of his "Researches," Berthollet gave an explanation (No. 10) of chemical reactions that bears a remarkable resemblance to thz present concept of the dynamic nature of chemical equilibrium: It follows as ts aenssquence of the preceding ohserva,tions, t h a t the action of a substance which tends t o decompose a combination, diminishes in proportion as its saturation advances; for this substance may, in such case, be composed of two parts, one of which is saturated, and the other free. The former msy he considered as inert, and as unconnected with the latter, the quantity of which diminishes according as the saturation advances; whilst, on the contrary, the action of t h a t which has been eliminated, increases in proportion t o the augmentation of its quantity, until equilibrium of the contending forces ends the operation, and limits the effect.
As Berthollet's statement indicates, the term equilibrium was used to denote a balance of chemical forces, exactly as the term is used in mechanics. Having demonstrated such remarkable foresight, we may wonder why the ideas of chemical equilibrium were mired for over 50 years before another significant advance appeared. I n his emphasis on the effect of quantity of substance, Berthollet concluded that it was possible to obtain combinations of different compositions simply by varying the proportions of reactants. For example, in Volume 2 of his "Essay," he regarded mercury(1) and mercury(I1) compounds as the extremes of oxidation and that all intermediate compositions were also possible. It was over this "law of variable composition" that Berthollet became involved in the famous controversy with Proust, in which Proust and the law of definite proportions emerged victorious. Several years later, Dalton published his famous atomic theory which rcadily explained the law of definite proportions and the law of multiple proportions, but not the law of variable composition. With this, Berthollet's law of variable composition fell into disrepute, and as a 386
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result, chemists no longer seemed to give any serious consideration to Berthollet's ideas. Several writers have expressed regret over the rejection of Berthollet's valid ideas on mass action along with his erroneous idea of variable composition (8,Q). While it is true that Berthollet's ideas were generally ignored by his contemporaries, the idea of the effect of quantity on chemical reactions was kept alive well into the middle of the 19th century through the efforts of a number of prominent chemists. The first of these to perpetuate this idea was Gay-Lussac, who had formerly worked under Berthollet and who is mentioned in both the "Researches" and the "Essay." Gay-Lussac's articles (10) continued to remind chemists of this effect as late as 1839. I n the early 1830Js, Berzelius (11) also commented favorably on Berthollet's ideas of mass action. In the 1840's, H. Rose (1B) demonstrated the same effect of quantity that Berthollet mentioned 40 years earlier. Rose demonstrated that alkaline earth sulfides were decomposed by water into hydrogen sulfide and calcium hydroxide in contradiction to the predictions of their elective affinities. At this point, it is worth while to compare briefly the contributions of Wenzel and Berthollet. Whereas Wenzel simply called attention to a phenomenon which was inconsistent with elective affinities, Berthollet attempted to rationalize such phenomena in terms of a more inclusive theory. I t must be remembered that Berthollet was not trying to completely discredit and supplant Bergman's theory; he simply insisted that chemical combinations were affected by other principles in addition to that of elective affinity. The chemical literature of the first half of the 19th century contains many papers dealing with Berthollet's idea of mass action, and the interested reader is directed to an excellent study of this subject by Holmes (IS). The Influence of Quantity in the Period 1850-1864
The first widely accepted demonstration of the effect of mass action was reported in 1850 by Ludwig Wilhelmy, who showed that the rate of inversion of cane sugar in the presence of a large and essentially constant amount of water is proportional to the amount of sugar. This work is generally regarded as one of the earliest instances of a quantitative study of chemical kinetics and a serious consideration of the effect of mass action on chemical reactions. In 1855, Gladstone (14) studied the now-classic reaction of iron(II1) ion and thiocyanate ion, and he noted that changes in the amount of the colored substance resulted from changes made in the amounts of the reactants. In 1862, attention was again dranm to the effect of mass action by M. Berthelot and Pean de St. Giles, who studied the esterification of acetic acid by ethanol. I n these studies, they showed that the rate of formation of the ester is proportional to the amount of the reacting substances, and that the same equilibrium point is reached by the hydrolysis of ethyl acetate, the reverse of the esterification reaction. The experiments performed in this period constitute an important milestone in the development of the concept of chemical equilibrium, because from this point on, mass action was recognized and accepted as an important factor in the outcome of chemical reactions. It is interesting to note that the experiments
of Wilhelmy, Gladstone, and Berthelot and St. Giles can still he found in many of the current chemistry laboratory manuals of general and physical chemistry. Guldberg and Waage's Law of Mass Action
it was well known that velocity is related to force, there do not seem to have been any significant attempts before 1865 to relate velocity of chemical reactions with the affinities of the reactants (18). The law of mass action, as expressed in equation (4), aroused considerable interest in the evaluation of the affinity coefficients. After all, this expression offered for the first time some promise of the quantitative evaluation of affinity, a goal which had defied measurement for many years. In fact, much of the scientific activity of the 19th century can be characterized by the determination of coefficients of all sorts, such as coefficients of linear expansion, of cubical expansion, of resistivity, of electrical and thermal conductivities, and many others. Most of these coefficientsproved to be of greater value to technology than to science. Underlying the determination of these coefficients was the hope that, somehow, a grand synthesis of some sort could be derived which would explain these phenomena. Likewise, the determination of affinity coefficientsheld forth the promise of explaining the mysterious phenomenon of chemical affinity.
In 1864, C. M. Guldberg and P. Waage of the University of Christiania published a general law of mass action in their native Norwegian, and later, in 1867, they republished this article in French (16). In this paper, Guldberg and Waage introduced a new term called "active mass," which is essentially the same as the present term, concentration. Berthollet introduced the term mass into chemistry, and he defined mass as the product of the weight of substance required to produce a certain degree of saturation (16). In terms of acid-base reactions, Berthollet's mass was simply proportional to the present equivalent weight. Berthollet also spoke of a "sphere of action" in connection with chemical combinations, which referred to a proximity requirement of the reactants. Both the sphere of act,ion and mass were important in the work of Guldberg and Waage who effectively combined these two ideas in their law of mass action. Guldberg and M. Berthelot and J. Thomsen and Their Ideas Waage reasoned that the effect of quantity was due to the amount of reactant within a sphere of action The chemical forces implied by the law of mass action, in which the combination could take place. Not and hence the related affinity coefficients, were not knowing exactly how to estimate this sphere of action, directly measurable, and therefore a considerable effort Guldberg and Waage decided to use the space in which was devoted to a search for an indirect method of the masses of reactants was contained. Hence, the evaluating these coefficients. W. Ostwald, in his term active mass merely refers to the mass per unit Masters dissertation (19) in 1877, pointed out that the volume. ratio of the affinity coefficients, (approximately the Guldberg and Waage applied their ideas to incomequilibrium constant) could be computed readily from plvtr or m d y rrvrriith~rwvti(~ns,for which they stared the active masses present under equilibrium conditions. rhar t hc cht,rniv:~lforrc,s wliirh givr risc to r,~ml~in~lti~m, However, a t that time, such a ratio was of only secoudare proportional to the active mass product of the ary importance; the values of the coefficients themreactants, and the state of equilibrium results from an selves were of primary interest. In this connection, it equality of t,he chemical forces exerted by the opposing is necessary to mention the ideas of M. Berthelot in reactions, i.e., the forward and reverse reactions. For Paris and J. Thomsen in Copenhagen, who regarded the example, in the general reaction, heat evolved by chemical reactions as a measure of the chemical affinities. In order to appreciate the contributions of Berthelot the chemical force in the forward direction is and Thomsen, it is worth while to consider the general methods by which forces can be measured. One k(A)(W (2) method of measuring force is the relatively direct static and the chemical force in the reverse direction is method, and another method is the more indirect dynamic method. I n the static method, the force to be k'(C)(D) (3) measured is connected to a known and variable force, and t,he condition of equilibrium is such as a spring, and the system is allowed to come to equilibrium. I n the equilibrium condition, the two k ( A ) ( B ) = k'(C)(D) forces are equal in magnitude, and the amount of the where ( A ) , ( B ) , (C), and (D) represent the respective unknown force is determined directly by observing the active masses of the substances A, B, C, and D. The amount of known force required to effect an equilibconstants k and k' were called coefficients of affinity, rium. Weighing objects with a simple spring scale following a usage established by R. W. Bunsen (17)in is an example of the static method. Chemical re1853. I t should be noted that these equations repactions, however, are not amenable to this type of resent chemical force, and not reaction velocity which measurement. I n the dynamic method, a force is was hter represented by these same equations. allowed to do work, and the amount of work done is The influence of Newtonian mechanics appears measured, and the force can then be computed from throughout this early work on chemical equilibrium, the amount of work done. Around the middle of the and the idea that chemical combinations are the result 19th century two important relationships were esof mutual attractive forces acting between the reactants tablished which enabled workers to measure the is implicit in the term affinity. Berthollet regarded amount of work done by a chemical reaction; these t,hese forces as being similar to gravitational force. were Hess's law of constant heat summation, and The primary interest was in chemical affinity, the Joule's mechanical equivalent of heat. It occurred to driving force responsible for chemical reactions. While both Berthelot and Thomsen that the heat evolved by Volume 39, Number 8, August 1962
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a chemical reaction was due to the operation of the chemical forces, and therefore, this heat of reaction should be a measure of the chemical affinity. Thomsen pointed out that Hess's law followed as a consequence of the law of conservation of energy, and that the heat of reaction is the result of the difference of energy content of a chemical system before and after a chemical reaction. As such, the heat of rehetion reflects the chemical affinity involved in the reaction. Berthelot expressed a similar view, which he called the "principle of maximum work," in which heat was liberated only from reactions which occurred spontaneously. The erroneous ideas of Thomsen and Berthelot seem understandable and pardonable when it is considered that the second law of thermodynamics, the basis of our present understanding of chemical equilibrium, was being formalized by Clausius at this time (ca. 1867). Relative to the earlier discussion of Berthollet's contributions, it is interesting to note that during the 1860's there was a revival of interest in his writings. Lothar Meyer's widely used textbook, "Modern Theorics of Chemistry," includes a six-page discussion of Berthollet in the introduction, and many references are made to him in connection with the effect of mass action. Julius Thomsen was also very much aware of Berthollet.'~work as is indicated by a paper which he published in Poggendorffs Annalen in 1869 entitled "On Berthollet's 'Theory of Affinity'." There is also a certain similarity in the work of Thomsen and Berthollet in that both workers devoted a lot of attention to reactions of acids and bases. Thomsen did a great deal of experimental work on the thermic effects, as he called them, of neutralization reactions and mixtures of salt solutions, but his interests were focused more on chemical affinity than on chemical equilibrium. Both Thomsen and Berthelot are now regarded as the founders of thermochemistry, but they should also be remembered as important contributors in the development of the concept of chemical equilibrium. J. 0. van't Hoff and Chemical Equilibrium
Among the many important contributions to chemistry made by van't Hoff, his ideas concerning chemical affinity and chemical equilibrium are perhaps the most significant, but strangely enough, these contributions are among the lesser known works of this great chemist. The mention of his name immediately brings to mind his great contribntions to structural chemistry and osmotic pressure, but usually not chemical equilibrium. I n fact, our present concept of chemical equilibrium differs little from the form in which it is presented in van't Hoff's "Studies in Chemical Dynamics," which was published in 1884. His contributions in this area range from the double-arrow innovation, still universally used to indicate the dynamic nature of chemical equilibrium, to the well-known van't Hoff equation which described the variation in the equilibrium constant as a function of the temperature. Although Guldberg and Waage are generally credited as the first to have developed the law of mass action, van't Hoff also developed this same law independently and from a different basis. Van't Hoff derived the law of mass action on the basis of reaction velocities, 388
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the velocities of the forward and the reverse reactions being equal a t equilibrium. This is exactly the explanation of the dynamic nature of chemical equilibrium and the derivation of the law of mass action that is found in practically every introductory college chemistry textbook. Guldberg and Waage also used the reaction velocity concept, but their original concept of chemical equilibrium involved the idea of a balance of opposing forces ($0). Through the consolidation of chemical kinetics and thermodynamics, van't Hoff provided the law of mass action with a more logical basis than it previously had. The first two sections (120 pages) of van't Hoff's "Studies in Chemical Dynamics" are devoted to a thorough discussion of chemical kinetics in a treatment that differs little from that in many present day physical chemistry textbooks. The third, fourth, and fifth sections of this book deal with "The Influence of Temperature on Chemical Change," "Chemical Equilibrium," and "Affinity." We must recognize that van't Hoff was equipped with the very powerful tool of thermodynamics, which was unavailable to many of the earlier workers. I n this treatise, van't Hoff asserted that the maximum work done by a chemical process could be regarded as a measure of the chemical affinity. At long last, the illusive affinity had been objectively defined! Van't Hoff defiued chemical affinity as the maximum amount of work, A, that could be obtained from a chemical process minus the amount of work required to maintain the system at constant volume. The symbol A has long been used to represent the Helmholtz work function, but Sackur ($1) wrote that this symbol represented affinity. I t is often believed t,hat this symbol was introduced as an abbreviation of the German word for work, arbeil. I t seems that during the latter part of the 19th century this symbol was used somewhat loosely to represent either work or its chemical equivalent, affinity. Van't Hoff certainly used the ~ymbolA , but he called it ". . . the work which can be done by the force of affinity which brings about a chemical reaction. . ." ($2). Van't Hoff also recognized that the second law of thermodynamics imposed certain restrictions upon the nature of the process by which the maximum amount of work can be obtained, namely, that the process must be carried out reversibly and isothermally; van't Hoff was careful to consider both of these restrictions, particularly the influence of temperature. He pointed out that the law of mass action is valid only for coustant temperature conditions, and that the influence of temperature on the equilibrium constant can be determined from considerations involving the second law of thermodynamics. By considering equilibria in terms of a reversible cycle of operations, van't Hoff derived the equation,
where q is "the quantity of heat which is absorbed when a unit quantity of the first system (i.e., the reactants) is converted into the second (i.e., products) without any external work being performed" ($3). I n his "Studies," van't Hoff applied the law of mass action and the "van't Hoff equation," equation (5),
to a variety of situations such as heterogeneous and homogeneous equilibrium of several kinds and also reactions for which q = 0, and others for which q 2 0. Later in this same work, he enunciated his "principle of mobile equilibrium" in the following statement: "Every equilibrium between two different conditions of matter (systems) is displaced by lowering the temperature, a t constant volume, towards that system the formation of which evolves heat" ($4). He also showed that this principle applied to all possible cases of both chemical and physical equilihria. By making the appropriate substitutions for the case of physical equilibria (i.e., changes of state) the van't Hoff equation becomes identical with the special form of the Clausius-Clapeyron equation. Van't Hoff also showed that the conclusions of both Berthollet and Arrhenius were only special cases of his more general formulation. However, van't Hoff's greatest triumph was in the derivation of the well-known reaction isotherm, which states that for the general reaction,
the maximum work is
where CA,CB,CC,and CDrepresent concentrations, or partial pressures of the substances A, B, C, and D respectively. Thus in the case where all of the substances are present a t unit concentration, the equilibrium constant, K, is a direct measure of the maximum work, A, and the related affinity. By partial differentiation of the reaction isotherm equation, followed by appropriate substitution, van't Hoff obtained the familiar Helmholtz equation,
The reaction isotherm and affinity were the subjects of the great interest in the study of equilihria of every imaginable sort during the late 19th century; and it should also he mentioned that van't Hoff, along with Helmholtz, did much to stimulate the great interest on the potential measurement method of determining maximum work. Chemistry is indebted to van't Hoff for his consolidation of chemical kinetics, thermodynamics, and physical measurements in the elucidation of chemical phenomena; and therefore he must he regarded as one of the greatest founders of physical chemistry. J. Willard Gibbs and Chemical Equilibrium
I t is well known that Gibbs, in the 1870's, conceived an even more general approach to chemical equilibrium than van't Hoff's; but his work was obscured, for the most part, by the abstract form in which it was presented. It was several years after van't Hoff had published his "Studies," that a few workers, notably Roozeboom, recognized the significance of the work of Gibbs and showed that the earlier conclusions of van't Hoff and others could he derived on the basis of the thermodynamic potentials of Gibbs. By and large, chemical equilibrium is still presented along the lines
of van't Hoff's arguments; and it is only recently that thermodynamic potentials have appeared in undergraduate physical chemistry textbooks. G. N. Lewis and Chemical Equilibrium
I n 1923, G. N. Lewis and M. Randall published their now classic "Thermodynamics" which was largely responsible for the widespread applicationof thermodynamics to the study of chemical reactions and chemical equilibrium in this country. The "maximum work" of van't Hoff later gave way to the term "free energy" which was coined by Helmholtz. Because of the chemist's greater interest in constant pressure than in constant volume (in earlier years), the so-called Gibbs free energy was introduced. At the suggestion of G. N. Lewis this free energy was defined as "the work available for use"; t,herefore when a system at constant temperature passes spontaneously from one state to another, the maximum useful work which becomes available represents the decrease in the free energy of the system. This decrease can be taken as a measure of the affinity of the chemical process (25). Lewis actually makes very little reference to the term affinity; in many respects, the term free energy has replaced chemical affinity as the driving force of chemical reactions. In 1907, Lewis introduced the concepts of activity and fugacity to replace the less adequate one of concentration, in the rigorous definition of chemical equilibrium ($6). Lewis defined the condition of equilibrium as the state of a system in which the fugacity, and hence the related activity, of a given substance is the same in each phase or part of the system. The concepts of activity and fugacity were devised to take into account the fact that mass action generally does not vary linearly with concentration as lvas assumed by earlier workers. The concept of activity is responsible for the attempts of a number of workers, such as Debye, Hiickel, Onsager, Harned, and others, to devise better theories of solutions; and in this respect activity played a role analogous to that of Berthollet's mass. Thus, this brief historical account illustrates another of Conant's principles, namely, that an important function of a concept is to suggest and stimulate further investigations. Conclusion
In the historical development of the concept of chemical equilibrium there are a number of events which stand out as significant contributions to our present understanding of the concept. These are (1) the recognition and acceptance of the influence of the amount of reactant on chemical reactions, (2) the quantitative formulation of this effect in the law of mass action, (3) rationalization of the effect of mass by chemical kinetics and thermodynamics, (4) refinement of the law of mass action with the introduction of activities, and ( 5 ) the wide application of chemical thermodynamics to equilibrium situations. There is a tendency among many students of chemistry to regard the ideas and activities of the 19th century workers as being entirely obsolete and therefore Volume 39, Number 8, August 1962
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worthless as far as understanding of modern chemistry is concerned. Such an attitude indicates a gross misunderstanding of the objective of a historical study; the purpose of a historical study is to improve our understanding of the present. For example, if we consult almost any college general chemistry textbook, we find that both Bergman's theory and Berthollet's idea of mass action are, in essence, present in the discussion of the factors which affect the extent of equilibrium-type chemical reactions. To say, as do modern textbooks, that the extent of reaction depends on the nature of the reacting substances is simply restating Bergman's statements about elective affinities. To say that the extent of chemical reaction depends on the concentration of the reacting substances is simply a refinement of Berthollet's statements on mass action. I n a sense the late Wendell M. Lather's book, "Oxidation Potentials," is the 20th century equivalent of Bergman's 18th century classic on elective affinities. The term affinity is still encountered occasionally, and its usage today seems to be more prevalent among British chemists. However, this is not t,o say that the concept of chemical affinity has fallen int,o disuse. Instead, the concept of affinity still survives in more sophisticated forms and under a variet,y of names. For example, t,he terms nucleophilic, electrophilic, dienophilic, and electron affinity are all widely used to designate specific types of combinations. The concept of chemical equilibrium developed as a byproduct of studies directed toward the understanding of chemical affinity, and today this concept serves many important utilitarian roles in both chemical science and technology. Certainly chemistry would not he the science it is today without the concept of chemical equilibrium; on the other hand, its progenitor, chemical affinity, continues to challenge the minds of chemists and physicists to new heights of understanding of t,he age-old phenomena of chemical combinations.
Literature Cited (1) PARTINGTON, J. R., "A Short History of Chemistry," Harper andBrothers, New York, 1960, p. 322. A,, "A Hundred Years oi Chemistry," The Mac(2) FINDLAY, millan Ca., New York, 1937, p. 110. (3) WALDEN, P. (translated by R. Oesper), J. CAEM.EDUC.,31,
-77. (19.64) - - -,. \
(4) GOATEE,G. E., "Organometallic Compounds," 2nd ed., Methuen and Co., Ltd., London, 1960, p. 346. J. W., r'Chemical Statics and Dynamics," Long(5) MELLOR, . mans, Green, & Co., NewYork, 1 9 0 4 , ~177. (6) BERTAOLLET, C. L. (translated by M. Farrell), "Researches into the Laws of Chemical .&nity," Philip H. Nicklin and Co., Baltimore, 1809, p. 1. (7) BERTAOLLET, C. L. (translated by B. Lambert), "Essay an Chemicd Statics," J. Mawman, London, 1804. J. W., op. eil., p. 178. (8) MELLOR, (9) MEYER,L. (translated by P. P. Bedson and W. C. Williams), "Modern Theories of Chemistry," 5th ed., Longmans, Green. & Co.. New York. 1888. D. 452. ~
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(11) PARTINGTON, J. R., Op. d., p. 323. J. W., op. tit.,p. 180. (12) MELLOR, F. L., Chymia,vol. 8 (in press). (13) HOLMES, J. W., op. cit., p. 182. (14) MELLOR, J. W... OD. 115) MELLOR. . eit.., n. - 183. (16) B E R T H o L ~ T , C. L., "Resertrches into the Laws of Chemical Affinity," Philip H. Nicklin and Co., Baltimore, 1809, p. 5. (17) MEYER,L., op. tit., p. 458. (18) GUGGENAEIM. E. A,. J. CHEM.EDUC.. ~ ,33.54411956) . , . (19) METER,L., op.eit., p. 423. (20) MOORE,F. G., "A History of Chemistry," 3rd ed., McGrawHillBook Co., New York, 1939, p. 372. 0. (translated by G. E. Gibson), "Thermochem(21) SACKUR, istrv and Thermodvnsmics." The Macmillan Co.. Loidon, 1917, p. 317. " (22) YAN'T HOW, J. H. (translated by T. Evan), "Studies in Chemical Dynamics," Chemical Publishing Co., Easton, Pa., 1896, p. 251. (23) VAN'T HOFF,J.H., op. Cit.,p. 148. (24) ~ A N ' THOFF,J.H., op. cit., p. 123. (25) LEWIS, G. N. AND RANDALL,M., "Thermodynamics," McGraw-Hill Book Co., New York, 1923, p. 584. (26) L ~ w r sG. , N., Proe. Amer. A d . A d s . Sci., 43,260,261, 284 (1907).
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Evaluation of Programed Instruction Programed instruction during the recitation period of the General Chemistry course was found to be beneficial to the average and below average student in an experiment which was conducted this year a-t Fairleigh Dickinson University. The 46 students in the experimental group were matched with students in the eame lecture group of the General Chemistry class according to such criteria as I. Q . and schievements in the previous year in English, mathematics, and physics. The experimental group reviewed the m a t e d that had been covered in the lectures with the help of a program; tho control group reviewed the same material in question and answer periode conducted by an instructor both orally and through blackboard written work. All students t,ook the same quizzes and the same final examination. The above average students in both groups performed on comparable levels. Among the average and below average students there were twice as many C grades and half as many D grades in the experimental group as in the control group. Only one student in the programmed group failed the oourse, compared to five in the control group. Details of the experiment and a more complete analysis of the results will be supplied interested readers upon request. LUCIANA SACERDOTE FAIRLEIGE DICEINSON UNIYERSITY TEANECK, NEWJERSEY
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Journal of Chemical Education
