286 PROCEEDINGS OF THE AMERICAN ACADEMY. 



Since at constant temperature K is independent of the conditions 

 under which a reaction occurs, it is obvious that the change with the 

 temperature of the equilibrium ratio of the reaction in any system 

 whatever is given in equation XXIV. The important quantity U, the 

 heat of reaction in the dilute gaseous phase, is equal to the heat of re- 

 action in any other condition less the algebraic sum, for all the sub- 

 stances taking part in the reaction, of the quantities which we have 

 denoted by the symbol Y. 



The importance of this quantity U has been recognized by Berthelot, 

 who wrote in 1875,^^ " J'ai dt^fini sp^cialement la chaleur de comblnai- 

 son atomique, laquelle exprime le travail rdel des forces chimique, et 

 doit etre rapportde k la reaction des gaz parjaits, operee a volume 

 constant." 



The following interesting example will serve to illustrate the simul- 

 taneous application of equation XXIII or XXIV with the preceding equa- 

 tions. Let us prove the theorem first demonstrated by Stortenbeker,^^ 

 namely, that the freezing point of a substance like CaCl2 • 6H2O which 

 partly dissociates in the liquid phase, is not changed by the ad- 

 dition to the liquid of a small quantity of either of the products of 

 dissociation (CaCL or H2O). When the solid, CaCU-GHaO, melts, 

 there are in the liquid Nx mols of CaC]2 • 6H2O, to N^ mols of CaCls 

 and N^ mols of H2O, where N^ = 6i\^2- Let us find the effect produced 

 by adding dN^ mols of H2O at constant temperature and pressure. 

 According to equation XVIII, 



( N,d In ^1 + Nod In h + N^d In ^A 



\ SN3 Jp,T~ 



From this equation, since iVg = 6 N^, it is obvious that, 



i\"if/ln ii + N. (din .^o -f 6 c?ln $^) = 0. 



Now since the CaCl2 • 6H0O, CaCL, and HoO are in equilibrium, 

 equation XXIII states that, 



Taking the logarithm of both members and differentiating we have, 



c? In ^2 + Qdln^s = dhi^i. 



" Ann. Chim. Phys., 4, 1 (1875). 

 " Zeit. phys. Chem., 10, 183 (1802). 



