﻿of Chemical Potential to the Theory of Solutions. 491 

 values of the pressure, 



\(s,p 2 , 0)- A -(*,/>i, $ = (p2—Pi)*>oO, Pi-*P2, #)• (14) 



The mean value of S is easily calculated. In general, 

 however, the effect of pressure variations is so small that the 

 value of 8 corresponding to atmospheric pressure may be 

 used in this formula. 



The value, at a pressure p and temperature t, of the solvent 

 potential lowering is given, therefore, in terms of the osmotic 

 pressure at the same temperature, corresponding to a pure 

 solvent pressure p Q , by the equation 



A (*, p, = &(s,p , t) P 0,^0-^0 + 12, 



+ (p-Po)$o{s,Po-*'P,t), . . (15) 



and in terms of the vapour-pressure at the same temperature, 

 by the equation 



\(s, P , t) = ( °vo, o <fo-(n - u)p ( JJ , n-*n , t) 



Jn 



+ 0-n )ao(*,n -*^o- • ( 16 ) 



Equation (8) gives the value of the solvent potential 

 lowering at the freezing-point of the solution. Calculating 

 the value at the temperature t by means of equation (12) we 

 obtain the formula 



A (s,p, t) = L t / - - T ) - — j k [s,p, 0„) - ~ J °y d (p, r)dr 



Jt t !Jt 



-( °Vfep,T)rfT-^f^^- T) ^T. . (17) 



J* Jt t 



Equations (15) and (17) give an exact relation between 

 the osmotic pressure and the freezing-point, and equations 

 (16) and (17) an exact relation between the vapour-pressure 

 and the freezing-point. By combining equations (15) and 

 (lb*) we obtain the equation connecting vapour-pressure and 

 osmo.tic pressure deduced in a slightly different manner in 

 Part I. * 



In the next section we will simplify these relations by 

 making various approximations and compare the results thus 

 obtained with expressions deduced by other investigator-. 



