﻿of Chemical Potential to the Theory of Solutions. 487 



pressure as the increase of pressure which must be ap- 

 plied to the stronger solution to make its generalised 

 vapour-pressure equal to that of the weaker solution. It 

 seems to me, however, that there is nothing fundamental 

 in this idea. It seems quite a mistake to define the osmotic 

 pressure of a solution a^ the increase of pressure which must 

 be applied to the solution to make its vapour-pressure equal 

 to that of the pure solvent. Thus Callendar's * vapour-pres- 

 sure theory of osmotic pressure " according to which the 

 osmotic pressure is simply the pressure required to produce 

 equilibrium of vapour-pressure between the solvent and 

 solution" is merely a particular statement of the general 

 thermodynamical truism that the conditions of co-existence 

 of two parts of a system are independent of the precise 

 nature of the mechanism of the co-existence, and depend 

 only on the " constraints " of the mechanism. Callendar's 

 " vapour-sieve J) has the same constraint as the semi-perme- 

 able membrane — it does not allow the solute to pass from 

 one part of the system to the other. Hence the conditions 

 of equilibrium are the same in the two cases. Whatever 

 may be the nature of the osmotic mechanism, and whatever 

 may be the relation between the magnitude of the osmotic 

 pressure and the composition of the solution, the statement 

 quoted above is true ; so it can in no sense be regarded as a 

 theory of osmotic pressure. 



The Thermo dynamical iheory of the Equilibrium between 

 the Solution and Solid Solvent. 



If the pure liquid solvent is in equilibrium with the solid 

 solvent, the temperature T is determined as a function of 

 the pressure only, by the equation 



/„(0, p, T )=<j>o(p, T„) (5) 



If the solution is in equilibrium with the solid solvent, the 

 temperature T is determined as a function of the concentra- 

 tion and pressure by the equation 



'Ms,p,T) = i tl ( P ,T) (6) 



Freezing-point determination forms a third method of 

 investigating the thermodynamical properties of solutions. 

 In order to compare the results of such determinations with 

 measurements of the osmotic pressure and vapour-pressure, 

 it is necessary to obtain an expression for the lowering of 

 the chemical potential of the solvent caused Iry the addition 

 of the solute, similar to those which have been obtained in 



* Loc. cit. 



