196 GUGGENHEIM art. e 



Thus at given temperature and composition the osmotic co- 

 efficient, hke the activity coefficient of the solvent, will or will 

 not vary with the pressure according as the partial molar 

 volume of the solvent Vq in the solution is unequal or equal to its 

 value yo*(l — kqp) in the pure solvent at the same temperature 

 and pressure. 



12. Osmotic Equilibrium in Terms of Osmotic Coefficient. 

 Substituting from (57) into (4) [77] we obtain as the general 

 condition of membrane equilibrium for the solvent between 

 two non-ideal solutions 



ip' - V") vo* (l - Ko ^^^') = At ig" log No" - g' log N^'), 



(60) 



or introducing [vo] 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. 



At 

 V' -V" = ^^^ ig" log No" - g' log No'), (61) 



the values of g' and g" being those at pressures p' and p" 

 respectively. 



K we assume the membrane to be permeable to the solvent 

 species only, and take the phase denoted by the double accent 

 to be pure solvent, we have 



log N" = 0, (62) 



and so obtain for the osmotic pressure P 



At 1 



^ = "'-''" = ''Si 'OS iv'' («3) 



the value of g' being that at an external pressure p'. 



If it is allowable to neglect the compressibility of the solvent 

 one need not distinguish between [vo] and vo*, in which case 

 instead of (63) one may write 



At 1 

 P = 0'-,iogj,. (64) 



