286 PBOCEEDDraB OF THE AMERICAN ACADEMV. 



Since at constant temperature K is independent of the conditions 

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

 temperature of the equilibrium ratio of the reaction in any sy. -tern 

 whatever is given in equation XXIV. The important quantity 11, the 

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

 ion in any other condition less the algebraic Bum, 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, 15 " J'ai detini Bpecialement /</ chaleur de combinai- 

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

 doit cire rapporte'e a la reaction des >j<iz par/aits, operas « oil, 

 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 Stortenbekcr, 10 

 namely, that the freezing point of a substance like CaCl..»- GlL ( > 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 product- of 

 dissociation (CaCl 2 or H 2 0). When the solid, Ca<"_ f,lU), melts, 

 there are in the liquid jYi inols of CaCl 2 -6H 2 0, to X 2 mols of CaCla 

 and X s mols of II 2 0, where X 3 = GX... Let us find the effect produ 

 by adding dN z mols of HjO at constant temperature and pressure. 

 According to equation XVIII, 



/ X,g In fi + NJd In A, + K£ In \ 



\ M\ Jr,T~ ' 



From this equation, since X 3 = G X., it is obvious that, 



V./ln;! -f ff l (<Hn& + 6<fln&) = 0. 



Now since the CaCl 2 -GlU), CaCla, and H a are in equilibrium, 

 ei | nation XXIII states that, 





= K 



Taking the logarithm of both members and differentiating we have, 



,/\ni, + 6rfln& = rfln&. 



18 Ann. Chim. 1'liys., 4, 1 (1875). 

 16 Zeit phys. Chem., 10, Is:; ,i- _ 



