Dr. F. Tinker on Osmotic Pressure. 443 



Starting from inside the membrane, and travelling out- 

 wards into pure solvent and solution respectively through 

 the surface film between the membrane and the liquid in 

 each case, let us now apply the Dieterici equation in its 

 simplest form. 



For the pressure ir l{a) inside the pure solvent we have 



?! 



„ ., ^/(P) °^ * ne solvent inside the solution 



we 



have 



"Mr^PiV™' 



where B x and B^ have a similar meaning to A 2 and A/, 

 referring, however, to evaporation into the membrane. 

 Hence, since p^ {F) -=: p 1( . a) (see above), we get 



/ B/-B, SB Q^ 



1 ( p ) _ e ET _ e RT _ e UT* 



whence 



7r i'(P) = 7r i(a)^ T = 7r i a) ( 1 +^) (approx.). . [17] 



From this equation [17] it appears that, if the solution is 

 an ideal one with zero heat of dilution, at osmotic equilibrium 

 the pressure tti^ of the solvent inside the solution is equal 

 to the pressure 7r 1(a) of the solvent inside the pure solvent. 

 When therefore the solution has no heat of dilution, we can 

 lay down the fundamental generalization that at osmotic 

 equilibrium the pressure of the solvent is uniform in similar 

 phases throughout the wliole osmetic system. The pressure of 

 the solvent throughout the vapour phase is uniform ; it is 

 also uniform throughout the membrane ; whilst the pressure 

 of the solvent inside the solution is equal to that inside the 

 pure solvent. The generalization breaks down, however, in 

 the case of non-ideal solutions. Although it is still true 

 that the pressure within the membrane and in the vapour 

 phase proper is uniform, the pressure inside the solution is 

 not equal to that inside the pure solvent. It is greater or 

 less than the latter according as the heat of dilution of 

 the solution is positive or .negative (cf. equation [17]). 



* Supra, p. 436. At osmotic equilibrium the relationship $B = Q 

 is absolutely accurate, for the change in internal energy is zero when 

 there is no expansion. 



