﻿•48t> Mr. S. A. Shorter : Application of the Theory 



Generalised Vapour-Pressure and the Vapour-Pressure 

 Iheory of Osmotic Pressure. 



Under ordinary circumstances the solution and solvent 

 vapour when in equilibrium are under the same pressure, so 

 that the vapour-pressure is a function of the concentration 

 and temperature. We have seen, however, that the two 

 phases may co-exist under different pressures. We may 

 therefore generalise the idea of vapour- pressure, and sup- 

 pose a solution of given concentration at a given temperature 

 to have different vapour-pressures corresponding to different 

 pressures in the solution. The generalised vapour-pressure 

 P of a solution is determined as a function of the con- 

 centration, temperature, and pressure in the solution, by the 

 equation 



f (s,p, 6) =F o (P,0) (3) 



If we differentiate this equation with respect to the solution 

 pressure, we obtain the equation 



-dp V(P,0) w 



showing the effect of pressure on the generalised vapour- 

 pressure. 



Suppose that we have a solution of concentration s x under 

 a pressure^ in osmotic equilibrium with a solution of con- 

 centration s 2 under a pressure p 2 . The generalised vapour- 

 pressures P 1 and P 2 of the two solutions are determined by 

 the equations 



A(s 1 , Pli e)=F () (p 1 ,e), 

 M**>p*> 0)=F o (P 2 , 0). 



Since the solutions are in osmotic equilibrium we must have 



Hence we have 



F,(P„tf) = F (P 1 ,tf); 



and therefore, since F always increases with the pressure, 



Pi=p 3 . 



Hence two solutions in osmotic equilibrium have the same 

 generalised vapour-pressure. The converse of this is obvi- 

 ously true. Two solutions of different concentrations under 

 pressures such that their generalised vapour-pressures are 

 equal w 7 ill be in osmotic equilibrium under these pressures. 

 We may therefore regard the osmotic difference of 



