472 PROCEEDINGS OF THE AMERICAN ACADEMY. 



than does the consideration of volume or entropy, which have the dimen- 

 sions of caj^acities merely. 



There are of course many possible ways of attacking the subject math- 

 ematically. Perhaps the simplest is given below. 



In his recent comprehensive and exceedingly interesting paper on 

 equilibrium and free energy,* Gilbert N. Lewis has shown that the 

 following equation is a very general one, applying to both homogeneous 

 and heterogeneous systems, but rigorously accurate only when the sys- 

 tem is composed of ideal gases, ideal solutions, and "■ condensed phases " 

 of constant volume. This is of course the equation of van't Hoff. 



»5 "i ■>}' "'i . . ^ "2 /•' "'2 rT 



Vi y J 1 . . . ^ Co ■= C 2 - •  • _ (J .^ . 



dT dT ' RT^ 



In this expression v means molecular volume ; T, absolute temperature ; 



c, concentration f = - J ; w, the number of reacting molecules of any 



given molecular species ; U, the diminution in the internal energy of the 

 process, or the heat of reaction at constant volume ; and R, the gas con- 

 stant (1.98 calorie-units, or better 8.31 c. g. s.). The products of a 

 reaction are indicated by a subscript 2, the factors by 1. The chief dis- 

 advantage of the equation for practical purposes is the fact that the 

 numerator of the second member does not always represent the actual 

 heat of the reaction, since it does not take account of the work which the 

 reaction may involve on account of changing volume. 



Let us now introduce pressure instead of concentration into this 



expression, c = 777^, hence the expression becomes 

 R I 



d (R Tf^- + "'' • • •>j9i"'/i"''  . . _ U 



* These Proceedings, 35, 1 (1899) ; Z. phys. Chem. 32, 364 (1900). 



I am much indebted to Dr. Lewis for valuable mathematical criticism of the 

 present paper. To Dr. Edgar Buckingham also I owe thanks for his interest, 

 and for valuable suggestions as to matters of detail. Since reading the manuscript 

 the latter has derived the " reaction-isobar " according to the method of Duhem ; 

 but in the present exposition I have retained the original derivation, because it is 

 much simpler than Ids more rigorously exact method, as well as because most 

 readers of physical chemistry are accustomed to the method and nomenclature of 

 Nernst. 



