OSMOTIC AND MEMBRANE EQUILIBRIA 195 



Using the sufl&x s to denote solute species and substituting (52) 

 into (51) we obtain 



Nodil - g-log No) = - Nod log/o 



= ^Nsd\ogU (54) 



s 



If No is almost unity and all the A^,'s are very small compared 

 with unity, we have approximately 



- log No= - log (i-1^n)\ = Yj Ns, (55) 



and (54) becomes approximately 



d(r^'^ n)\ + Yj Nsdlogf, = 0. (56) 



From this approximate relation we can conclude that 1 — g^ is 

 likely to be of the same order of magnitude as log /,, or as 1 — /,. 

 Thus in very dilute solutions not deviating greatly from ideality 

 the osmotic coefficient g will have a more convenient numerical 

 value than the activity coefficient /o of the solvent species. 



Substituting (53) into (35) we obtain for the chemical po- 

 tential of the solvent in a non-ideal solution 



MO 



= Mo*(0 + PVo*(l - h xop) + gAt log No. (57) 



The osmotic coefficient g, like the activity coefficient /o of the 

 solvent species, will at given temperature and pressure tend to 

 unity at infinite dilution when the solutions become ideal. 



Differentiating (57) with respect to p and using (22) we ob- 

 tain for the dependence of the osmotic coefficient on the 

 pressure 



vo = vo* (1 - Kop) + At log No- J- (58) 



op 



or 



di _ yp - ro* (1 - KqP) 



dp ^ At log No * ^^ 



