288 Mr. S. R. Milner on the Variation of the 



where p is the osmotic pressure of the undissociated molecules, 

 and R the ordinary gas-constant. Transforming G into c, by 

 means of (2) and (4), we have 



2VKJ, S (e+VKcf 



i *Vc 3 +^K (/c>^K)(^"+^K)J 



(5) 



where Cj and c 2 are the initial and final concentrations of the 

 undissociated part of the electrolyte. If we put K = 0. this 

 of course coincides with the ordinary formula for the work of 

 expansion of a non-dissociable salt, 



w = RT log Cj/cg. 



The work done during expansion by the two ions of the 

 electrolyte is 



p'dV = 2B.T\ c'±dG, 



p f being the osmotic pressure of either of the ions. Trans- 

 forming this as before into terms of c f only, we find 



, oprr1z f^ V(K-t-2</) ^ 



Jc 2 >( C + Kc ) 



which gives on integration 



^=2RT(log- / .^^ + ?7TE -^ TZ ), . (6) 



Ci' and c 2 ' being the concentrations of the ions before and after 

 expansion. In (6) if we put K = go , or the salt is completely 

 dissociated, the work reduces to 



w'=2RTlogc//V, 



the ordinary form for a simple mixture of ions. 



Before expressions (5) and (6) can be used, they must be 



changed into terms of the independent variables l\ and C 2 , 



the total concentrations, since c and c' are functions of K. 



This may be simply done by (2) and (4), substituting from 



which we obtain 



