374 KEYES 



ART. J 



Again for constant pressure there is obtained from the general 

 equation 



^dt\ t a * 



(97) 



(; 



dr/p Xi 



From the previous inference it is clear that a is a positive 

 quantity, hence dr and dt change in the same sense or for 

 increased concentration there is a proportionate rise in tem- 

 perature. Inserting the value of a found in the preceding 

 paragraph we find on integrating : 



i - fo = -7- -' 98 



which is the usual equation for the elevation of the boiling point. 

 A similar equation of corresponding form gives the depression 

 of the freezing point for dilute solutions. 



If Xi is assumed given by [Xo + ci\r we obtain 



i — t{s , t n-2, , ^ 



Xo— — + clog- = R— (99) 



to' to IT'S 



Expanding log t/to in a series of powers of — - — leads, as a first 



fo 



approximation, to equation (98); retaining however the second 

 term leads to the equation 



Rtot 712 r. c^o~l 

 Xo Us L Xo J 



From the foregoing discussion the nature of the deficiencies in 

 the formulae arising from the approximations used will be clear. 

 A more complete theory may be constructed in various ways, 

 but up to the present time no very systematic coordination of 

 the theoretical development and exact experimentation has 

 been undertaken. Recently a method has been discussed 



* Note that Xi is the heat required to remove unit mass of solvent 

 vapor from the salt solution. We may assume that Xi is equal to the heat 

 of evaporation of the pure solvent, or better, that it is a function of 

 temperature of the form [Xi = Xo + cit]r where ci is a constant. 



