Edward E. Daub General Enaineerino - and History of Science Department University of Wisconsin Madison. 53706
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Gibbs Phase Rule: A Centenary Retrospect
The Semlcentenary: A Dutch Event The vear of the Bicentennial haovens also to mark the centen& of Gihbs' phase rule, and ii Should not slip by with as little notice as America aooarentlv vaid Iiftv vears aeo. John Johnston of the United states ~ t &~i o r ~ o ¬ed m remorsefully to a Yale audience in 1928 (1) It is somewhat of an anomaly that the fdtieth anniversary of the publication, in the Tmransactionsof the Connecticut Academy, of the first part of Gibbs' great work on the equilibrium of heterogeneous substancesshould have been signalized in Holland hy the publication of a Gibbs number of their chemicaljournal, the Chemkch Weekblad; whereas few, if any, in America took thought of the matter s t all. I t is further anomalous that the contributors to this nwnber should include besides the Hollanders, a Frenchman, a Canadian, a Norwegian, two Englishmen, but no American. Truly a prophet is not without honor save in his own country.
t Figure 1. Rwlebwm's puule.
The only recognition accorded Gihbs in Ameriean scientific journals in 1926 seems to have been a brief article which appeared in Science, "The Semi-centenary of Willard Gibbs' Phase Law (18761926)." Even here the writer was the famous Dutch ohvsical . . chemist Ernest Cohen. then visitine a t the University of Michigan, alerting Ameiicans u, the''special numher of the Chemisch Wcekblad It was. Cohen said. devoted to "what science owes to Josiah ~ i l l a r d~ i b b .s . . doubtless the meatest -eenius oroduced hv the United States of America" But Americans had not been as remiss in .. eivine..homaee to Gihbs' achievements as the silence in 1926 might suggest. Numerous dienitaries had oraised Gihhs at the dedication of the new ~ t e r h C g h e m i c a i ~ a b o r a t oar t~Yale University in 1924 (3), and W. Lash Miller prepared an extensive essay, "The Method of Willard Gihhs in Chemical Thermodynamics" (4) expressly for that dedication. And on the occasion of the centenary celebration of the founding of the Franklin Institute in 1925, F. G. Donnan gave tribute in his address, "The Influence of J. Willard Gibbs on the Science of Physical Chemistry" (5).Thus, Gibhs' achievements had been prominently s&g a t both American celebrations. The absence of festivities in 1926 may signify a restful lull rather than a forgetful silence. Moreover, the Dutch had not been wholly altruistic in dedicating a number of the Chemisch Weekblad to the semicentenary of the phase rule. W. P. Jorissen introduced the tooic with a ouote from a recent hook review in Nature: "So great and cunspicuous is the work of the five Dutch physical chemists IRoozehoom. van'c Hoff. Schreinemakers. Cohen. and ~ m i r cthat j we may fairly call the science of heterdgeneoG eauilihria a Dllt&, science" (6). ti^^ alsothe 25th . . anniversary of Schreinemaker's appointment a professor a t the University of Leyden, the number included articles on his significant work and the earlier groundbreaking labors of Bakhuis Roozeboom. The Dutch were eminently fair, however, for they gave greatest prominence to Gihhs and his watershed work in the thermodynamics of heterogeneous ~~d they were right to claim due credit for the tremendously rapid growth of this science a t the close of the nineteenth century hecause i t was BakhuisRoozehoom whocatalyzed thatgrowth when, with the help of van der Wads, he discovered the genius of Gibbs' phase rule and publicized his discovery in 1887 (7).'
(5).
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TheDutch ,he Phase Rule, ,884-88 Bakhuis Roozehoom begar? his research on complex phase equilibria in 1884 (9).He chose systems which consisted of two sut~xancesand which formed three phases-a solid, a liquid, and a vapor phase. His experiments led him to the disco\,ery of a new phase chanee never before observed. Althoueh Roozehoom &as able tohetect this unique change, he could not identifv what had ha~oened.Rwzebwm aooroached van der \Vaals kho derived 1,;; him a set of thcrm&namic equations based on Gibtx' vhase rule. The wuations not onlv exolained the phenomena'hut also the presence o i a new compound whose existence could hardly have been foreseen without the aid of theory. Roozehoom met the puzzling behavior in his study of the HBr-Hz0 system, represented in Figure 1.He hegan with the system at point A where the three coexisting phases were the solid hydrate HBr.2Hz0, a solution of HBr in water with a concentration less than the HBr composition of the hydrate, and a vapor phase of HBr and water. The HBr concentration in thesolution gradually increased with the rising pressure and temperature of the system until point F was reached where the composition of the solution became identical with the com~ositionof the hvdrate. T ~itself S presen&d a new experimental situation hecause, in his orevious work with svstems of hvdrates (SO.,-HqO. . " " . CIZ-HZO,BIZ-HzO), the hydrates had aiways decomposed before reaching their melting points. So Roozebnom now had his first opportunity to observe what would happen to a hydrate in a three phase syswm at pressures twyond the pressure at its meltlng pwnt. Roo7ehoom increased the pressure and found that the equilibrium temperature reversed its previous trend. It now hegan to decrease. The solution concentration, in contrast, continued to increase, becoming greater than the HBr composition of the hydrate. Thus, Roozeboom easily Prior to this time, the only scientist to pay heed to Gihhs' thermodynamics was James Clerk Maxwell. He revised his "Theory of Heat" in 1875 in order to include a section on Gibhs' representation of
properties in terms of an entropy.energy.volume
surface.H~ the idea of a chemicalpotential independently of Gibbs, calling it the "reaction." See Elizabeth Garher's "James Clerk Maxwell and Thermdynamics" (8). Maxwell made no mention, however, of the phase rule. Volume 53. Number 12, December 1976 / 747
handled the first noveltv to arise in the HBr-Hz0 svstem by using his traditional experimental techniques. when the svstem reached point B. however, insurmountable difficulties arose whirh req&d the wisdom of thermodynamic theory. At point B Roozel)oom found that his vapnr pressure curve for the hydrate branched into two directions. If he lowered the temperature, the solid and liquid phases congealed into one solid phase so that the system apparently had become a two phaie solid-vapor system. If he raised the prewue, the system continued to maintain three phases; but i t began to trace out a vapor pressure curve akin in form to the curve AF traced out a t the start. Roozeboom imagined that for some reason he was getting a second vaoor nressure curve for the hvdrate HBr.2H90. He was not able to test this supposition because, a t the ternperature of -15.5'C and the pressure of 2.5 atm for point B, he could not examine the hydrate without its decomposing. Only later, after gaining a thermodynamic understanding of how the vapor pressure of a hydrate changes in a three phase system. did Roozeboom devise a special apparatus in order to analyze the hydrate and todeteimine theconcentration and the amount of theaccom~ansinesolution(11)).BYthen theory had predicted that!t w k l d h e a new hydrate. At first, however, Roozeboom never imagined that possibility. Roozehoom turned to van der Waals for help with this problem, and van der Wads applied Gibhs' phase rule to the system. Gihhs had shown that, for a system of n 1phases and n components, there would be hut one degree of freedom. The system would therefore behave like a two phase system of a single component and an equation comparable to the Clausius-Clapeyron equation would apply (11). Van der Waals derived the appropriate form of the equation for the case at issue. and thus solved Roozehoom's ouzzle. Van der ~ a a l spoint ' of departure was the general thermodvnamic eauation which Gihhs had shown an~licableto 1 phases formed from n components all sistems of
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+
n+
T d p l d t = Qldu where Q is the heat necessary to effect a given phase transition a t constant t and p. To simplify the analysis, van der Wads assumed that the vapor phase contained but a single component. Thus, the water vapor was neglected in the case of a hvdrate. His analysis continued as follows. Let the hydrate have a comwsition of c mol of eas perm01 of water and thesolution a concentration of x molof gas per mol of water. If c is greater than x, then the hydrate, upon decomposing, would produce (1 x ) mol of solution and (c - x ) mol of gas. If x is greater than e, then the hydrate would form (1 x ) mol of solution with an absorption of (x - c ) mol of gas. The amounts of heat involved in this decomposition would be the heat of fusion for the hydrate Qf,and the heat necessary to expel 1 mol of gas from solution where the solution concentration changes from c to x molof gas per molof water, Q,,. By neglecting the volumes of the condensed phases of hydrate and solution and by assuming the ideal gas law for the gas phase, van der Waals obtained the following expression (12).
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2 The curved lines represent vapor pressure curves for various solutions, their concentration increasing continuously from ab to cd. Intersection with the hydrate vapor pressure curve represents the temperature and pressure at which the solution is in equilibrium with the hydrate. Roazehoom also included in his analvsis for the . an eauation . variatitm ofmncvnrratim in thcsoluti,rn (dr dl,,. Since hisarpumenc is c l e w without Illis romplirar~on, I haw omitted it from m) presentation. 4 Ostwald's contribution to the semi-centenary issue of Chem. Weekbl. ( 6 )wss the excerpt on Gihbs from his Lebenslinien. Chem. ~~~
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Weekbl., 23,409 (1926). 748 / Journal of Chemical Education
Figure 2. Van der Waab' solution.
Roozehoom sketched out the implications of this equation as shown in Fieure 2.2 The corres~ondencebetween the theoretical curve ;"Figure 2 and the plot of the ohserved data for the HBr.2H.Ll - svstem . in Firure 1 is immediatelv anoarent. In Figure 2, c is greater than; from A to F and dbldi is correspondingly positive. At point F, x becomes equal to c and dpldt becomes infinite. From point F to point T,x is greater than c so that (e - x ) is neeative and duldt as well. At point T,however, the negative heat of absorption of gas Q,,(;- x ) exactly cancels the heat of fusion Qf, and dpldt reduces to zero. Roozeboom labeled these two portions of the curve I and
11. In curve 111 beyond point T,dpldt would again become positive. This also occurred a t point B of Figure 1 in the HBI-H~Osystem. I t was ohvious,however, that ihe new curve which originated at point B in the HBr-Hz0 system did not correspond to curve 111, the continuation of the original hydrate vapor pressure curve. Its shape corresponded instead with curve 1, the vapor pressure curve for a hydrate whose composition c is greater than the concentration x of the solution with which it is in equilibrium (13).3Thus, thermodynamic theory predicted that a new hydrate of HBr and water had emerged a t point B whose composition was greater than the concentration of the solution. Rnozebnom found that it was HBr.HqO. a hvdrate whose existence could not have been foreseen"e&ep
