LEWIS. — FREE ENERGY AND EQUILIBRIUM. 29 



RT dWi 



P = 1 + -r- • (42) 



v — b dv 



Except that v represents the heat of dilution instead of the heat of 



r dv 



free expansion, equation (42) is identical with the equation obtained for 

 gases. The comparison of this formula with experiment is not possible 

 with the experimental data at present available, since, as far as I know, 

 the heat of dilution has been determined only in the case of electrolytes, 

 and in these cases a complication is introduced, due to the heat of disso- 

 ciation. An abstract * has just come to hand of a recent work by 

 Kistiakovski,t in which he shows that the lowering of the freezing point, 

 which is proportional to the osmotic pressure, is, in a concentrated solu- 

 tion, equal to the lowering calculated for an ideal solution plus a term 

 that is proportional to the heat of dilution. This is the result that would 

 be given by equation (42). Kistiakovski shows that there is perfect 

 agreement between the lowering of the freezing point calculated in this 

 way and that found by experiment. It seems questionable, however, 

 whether his application of the formula to electrolytes, neglecting the heat 

 of dissociation, is justifiable. Unfortunately I have not access to his 

 original paper. 



The osmotic work obtainable from the change of a gram-molecule of a 

 solute from a solution of one concentration to one of another concentra- 

 tion may be found by direct application of equation (6), or by integration 

 of p dv, where p may be expressed in terms of v by means of equation 

 (42). Then 



A = R Tin ^—, + U. (43) 



For all except very concentrated solutions b may be neglected, and 



A = R Tin ^ + U. (43a) 



Cady % has recently shown that in a galvanic cell in which the total 

 result of the current is the passage of a certain amount of a metal from 

 an amalgam of one concentration to one of another, 



RT. v 2 



■k = In — h q , 



n e Vi 



* Chem. Centr. Blat., 1899, I. 89. 



t Jour. Russ. Phys. Chem. Ges., XXX. 576. 



t Jour, of Phys. Chem., II. 551, 1898. 



