of Chemical Potential to the T heory of Solutions. 39 



I£ the pure solvent under a pressure p is in osmotic equi- 

 librium with the solution under a pressure p, we have 



^o(i>(b 0)=/o(*U S 2, .. , Sn 9 p, 0), 



where yjr is the chemical potential of the pure solvent *. I£ 

 we write 



p—p = Cl(s i , s 2 , ... , s n ,p , 6), 

 we have 



i/r (p , 0) -f (s u S 2 , . . . , S n , p + n,6). 



The effect of variation of the pure solvent pressure on the 

 osmotic pressure is given by the equation 



where v (p , 6) is the specific volume of the pure solvent. 

 If we write 



A (si, »», ..... , s„, #, 0) = ^ {x, 6) —f (s if s 2 , ...s n , x, 6), 

 we have 



AqOi, « 8> ... , 5„,p , 0) = {2(5!, S 2 , . . . 9 S n , p , d)F (s l9 S 2 ,.. ., S n , p<y+p, 6). 



. . . (18) 



If the pure solvent is in equilibrium with the solvent 

 vapour under a pressure IT we have 



to(n o ,0) = F o (l7 o ,0). 



If the solution is in equilibrium with the solvent vapour 

 under a pressure II we have 



/ o (*i,%...,s»>n/0)=F o (n,0). 



Hence we have 



/»n 



A (.<i, s 2 , ... , s m JJ w 6)— t V(.r, d)dx 



- (n - ri)p ( 5l , ,„..., Sm n ->n 0j 0). (19) 



If the pure solvent is in equilibrium with the solid solvent 

 at a temperature T , we have 



^oCP> T o)=</>o(p, T ). 

 * The symbol / (0, 0, . . . , ? p Q1 Q) is rather unwieldy. 



