﻿of Chemical Potential to the Theory of Solutions. 493 



If in the above equation we make = t, and neglect the 

 compressibility and powers of: T — T and t — T higher than 

 the second, we obtain Ewan's expression * connecting the 

 osmotic pressure and the freezing-point. 



In the absence of any information regarding the precise 

 form of the isothermal of the solvent vapour, the definite 

 integral in equation (16) must be evaluated on the assumption 

 that the solvent vapour behaves as an ideal gas, i. e., we must 

 assume that 



'>foO^ = Ro*log^°, . . . . (21) 



J' 



II 



where R is the "gas constant 5 ' of the solvent vapour. If 

 we make this assumption we must, of course, neglect the 

 term (n — II)P . The magnitude of the third term on the 

 right-hand side of equation (16) will depend upon several 

 factors. Speaking generally, we may say that its retention 

 in the equation is justifiable only in the case of strong solu- 

 tions at low temperatures (when 8 is a fairly large fraction 

 of the specific volume of the pure solvent, and II — II only a 

 small fraction of p — II ). Making these approximations and 

 putting p = <57, we ohtain the following expression connecting 

 the vapour-pressure and the freezing-point : — 



IVlogg * («r-bo)$o(*,^0 = Lo^-A) 



, k't(t-T)r6 -d^i,t-T\* n 



+ 



f-=9 -...}. . . . «» 



x—^—j—'-s- 



If we make t = T , and neglect the terms containing £ 

 and Z / , we obtain Dieterici's f equation connecting the 

 freezing-point of the solution with the vapour-pressure at 

 the pure solvent freezing-point. 



If we substitute in equation (8) the approximate value of 

 the potential lowering calculated as in equation (21) we 

 obtain Calendar's J expression for the ratio of the vapour- 

 pressures of the pure solvent and solution at the freezing- 

 point of the latter. 



The simplest method of comparing a large number of 

 experimental data relating to a particular solution is to 

 calculate the value of the solvent potential lowering at some 



* Zeit.fiir Phys. Chem. xxxi. p, 22 (1809). 



f Wied. Ann. lii. p. LHW (1804). J Loc. cit. 



