OSMOTIC AND MEMBRANE EQUILIBRIA 189 



This definition of ideality is exactly equivalent to the condition 

 that for a given temperature and external pressure on a solution 

 the partial vapor pressure of each component shall be directly 

 proportional to its mol fraction. 



Since A, t and Nh are all independent of p, it follows from 

 (22) that 



P = ... (27) 



dp 



As, by definition, fXfP at given temperature and pressure is inde- 

 pendent of the composition, it follows that the same is true 

 of Vh. This means that the transference of any part of an ideal 

 solution to another ideal solution in the same solvent takes 

 place, at constant temperature and pressure, without volume 

 contraction or expansion. 

 For the dependence of Vk on the pressure p we may write 



Vh = Vh*(l - khp), (28) 



where Vh* is the value of Vh at vanishing pressure, and where 

 it will always be allowable to assume that kh is independent of 

 the pressure p. The compressibility coefficient kk may depend 

 on the temperature but this need not concern us. 



Owing to the relations (27) and (28) we may replace (26) by 



M/. = y^h*{t) + pv,*{l - hxhP) + At log Nk, (29) 



where Hh*(t) is independent of the pressure as well as of the 

 composition. 



If we now substitute from (29) into the general condition of 

 membrane equilibrium (4) [77], we obtain 



w 



p' vh*{1 - hhP' ) + At log N,/ 



= p"vh*{l - hhP") + At log Nh", (30) 



or 



Nh" 



(p' - P") Vh* (l - KH ^^-^) = At log 



Nh'' 



(31) 



