OSMOTIC AND MEMBRANE EQUILIBRIA 193 



the value of fo being that at an external pressure p', and [vq] 

 being the value of the partial molar volume of the pure solvent 

 at the given temperature and at a pressure equal to the mean of 

 those (p' and p") at either side of the membrane. 



9: Iricompressible Solutions. If it is allowable to neglect the 

 compressibility kq of the solvent, one need not distinguish 

 between [vo] and vq*, and the formulae for P may be written 



At 1 



P = — log — 45) 



Vo* No 



for ideal solutions, and 



At 1 , , 



P = — log 77-7 46 



Vo* Nofo 



for non-ideal solutions, the value of /o being that corresponding 

 to an external pressure p' somewhat exceeding the osmotic 

 pressure P. From (45) we see that when compressibility is 

 neglected the osmotic pressure of an ideal solution is independent 

 of the external pressure on the pure solvent with which it is in 

 osmotic equilibrium. 



10. Relation between Activity Coefficients. The variations of 

 the activity coefficients of the different species with variations 

 of composition at a given temperature and pressure are not 

 completely independent. For according to [98] (Gibbs, I, 88) 

 we have at given temperature and pressure 



or, dividing by (mi + m2 . . . + m„), 



NidfX, + N2dtJi2 ... + NndlXn = 0. (48) 



If we substitute from (34) or (35) into (48), we obtain 



N4 log N,f, + N^d log N^U . . . + Nnd log .¥„/„ = 0. (49) 



