﻿of Chemical Potential to the Theory of Solutions. 489 



Substituting this value in equation (7), and performing 

 the integration with respect to 0, we obtain the following 

 expression for the lowering of the solvent potential at the 

 freezing-point of the solution ; — 



w „ L„'T -T) C T ° • |T f Tg Y^T) , 8 . 



The osmotic and vapour-pressure measurements with which 

 the freezing-point determinations have to be compared may 

 have been made at any temperature. It is necessary, there- 

 fore, to. obtain a formula connecting the potential lowering at 

 two different temperatures. Such a formula is also useful 

 for tbe comparison of osmotic and vapour-pressure measure- 

 ments made at different temperatures. We will therefore 

 consider this question in a general manner (apart from its 

 present application) in the next section. 



The Variation of the Solvent Potential Lowering 

 with 1 \ my era t are , 



Duhem's expression * for the heat of dilution in terms of 

 the solvent potential lowering may be written in the form 



Hence if 6 X and 2 ar © any two temperatures we have 



By combining this equation with equation (8) we could 

 obtain an expression connecting the potential lowering at 

 any temperature with the freezing-point. The equation 

 involves;, however, a knowledge of the beat of dilution as a 

 function of the temperature. Now in general the heat of 

 dilution will be known at one temperature only. AVe will 

 therefore deduce a formula involving a knowledge of the 

 heat of dilution for a single value of the temperature, making- 

 use of the well-known expression connecting the temperature 

 derivative of the heat of dilution with specific heat data : 



. W(;p, 0) = -»(/>. Q-vtop, ") +<i+«)^7(m>, <?)• (in 



* Loc. cit. vol. iii. p, 139. 



