OSMOTIC AND MEMBRANE EQUILIBRIA 191 



be of the same form as for ideal solutions. In accordance with 

 (29) we may therefore write 



MA = MA*(0 + PVh*(l - hxhP) + At log NhSh, (35) 



where Hh*it) is independent of the pressure as well as the com- 

 position; Vh* is the value of the partial molar volume of the 

 species Sh at the given temperature, at zero pressure and at 

 infinite dilution; kh is independent of the pressure and the com- 

 position; while Vk*(l — Khp) is the value of the partial molar 

 volume of the species Sh at the given temperature, the given 

 pressure and at infinite dilution. The activity coefficient fk at 

 given temperature and pressure tends to unity at infinite 

 dilution. 



If we differentiate (35) with respect to p and use (22) we 

 obtain 



Vfc = — = Vh* (1 - KhP) + At (36) 



or 



d log fh _ Vh - Vh* {I - Khp) 



dp ~ At 



(37) 



From this we see that the activity coefficient fh will or will not 

 vary with the pressure at given temperature and composition, 

 according as the partial molar volume Vh in the solution is un- 

 equal or equal to its value Vh*{l — Khp) at infinite dilution at 

 the same temperature and pressure. 



If we now substitute from (35) into the general condition of 

 membrane equilibrium (4) [77] we obtain 



p'vh*{l - hxkP') -\- AtlogNh'U 



= p"vh*(l - hKhp") + At log Nh'Jh" (38) 



or 



ip' - P") Vh* (l - K. ^) = At log ^^'. (39) 



