﻿of Chemical Potential to the Theory of Solutions. 485 



Dashes will be used to indicate differentiation with respect 

 to the temperature, thus : 



l '(s, p, 8) - |^ 0, P , 0), 4> "(P, &) ^Up, o). 



The Effect of Pressure on Vapour-Pressure . 



If the solution and solvent vapour are in equilibrium, the 

 surface of separation having a curvature such that the pres- 

 sure of the solution exceeds that of the vapour by an amount 

 ?> c , the vapour-pressure II C is determined by the equation 



/„(», n.+j% ^)=F (n c , &). 



When ihe surface of separation is plane the vapour-pressure 

 II is determined by the equation 



f o (s,n,6)=v o (ii,0). 



Hence we have 



Uc 



(n c +2?c-n)P o 0y, n 4m+Po o)= f vfa o)d*. . . (i) 



J n 



This equation agrees with that obtained in a different 

 manner by Callendar * for the effect of capillary pressure, 

 and with that obtained by Porter f for the effect of the 

 pressure of an insoluble gas. 



In the case of the pure solvent, the ordinary vapour- 

 pressure n and the vapour-pressure n 0c corresponding to 

 a capillary excess pressure p c , are related by the following- 

 equation, which may be derived from equation (1) by 

 putting 5 = 0, 



(n£+ J? » c -n u )r(o,n ->n oc +/>c,^)=i v(*, *)<**. (2) 



If we neglect the compressibility of the liquid and suppose 

 that the solvent vapour behaves as an ideal gas, we obtain 

 the well-known expression t for the effect of capillary curva- 

 ture on the vapour-pressure of a liquid. 



* Hoy. Soc. Proc. A. vol. Ixxx. p. 466 (1907). 



t Roy. Soc. Proc. A. vol. lxxix. p. 519 (1007). 



| J. J. Thomson, 'Conduction of Electricity through Gases,' p. 180. 



