OSMOTIC AND MEMBRANE EQUILIBRIA 205 



and is the ratio of the partial molar volume of the electrolyte 

 to that of the solvent, both at the given temperature and at a 

 pressure equal to the mean of those at either side of the mem- 

 brane. At extreme dilutions the mol fraction No of the solvent 

 differs very shghtly from unity, and (93) approximates to (91). 

 31. Membrane Equilibrium of Non-ideal Ionic Solutions. 

 The corresponding formulae for non-ideal solutions are obtained 

 similarly by substituting from (77) in the general condition of 

 membrane equilibrium, 



[Mi]' = [m.]". (95) 



For two ionic species i and h of the same valency, we obtain 

 in analogy with (88) 



At log ^1^-^ ^1^^ = (p' - v") ( k] - M), (96) 



Nn"h"Ni'fi' 



where [yj, [vh] are the values of the partial molar volumes at 

 infinite dilution at the given temperature and at a pressure 

 equal to the mean of those (p' and y") at either side of the mem- 

 brane. It is to be observed that the combinations of activity 

 coefficients occurring in (96) are the ratios of the activity 

 coefficients for two ions of the same valency and are therefore 

 physically definite. If the right hand side of (96) is neghgibly 

 small compared to At, then (96) approximates to the simple 

 relation 



N-' f' N-" f" 



Nh'Sh' Nk"U" 



For the membrane equilibrium of an electrolyte consisting of 

 g+ cations of valency z+ and g_ anions of valency z-, the exact 

 formula obtained from (77) and (95) is, in analogy with (90), 



= (p'-p")(9+M + 9-[y-]), (98) 



which involves only the mean activity coefficients /^ of the 

 electrolyte in the two phases. If the right hand side of (98) 



