LE\nS. — A NEW SYSTEM OF THERMODYNAMIC CHEMISTRY'. 281 



But the activity of the solvent in the liiiuid phase is changed both by 

 the change in temperature and by the presence of dj\\ mols of solute. 

 That is, 



dT J 'V ^-^^1 J 

 Whence by means of equations XII and XIX 



Equating the second members of this equation and the one above, 

 Y'2 - Pv', ^^ ^ %- Pi, _jj,_ dJS\ 



HI" pr iVo' 



or — iVs 



dT RT'' 



2 7 AT 



dN^ Y'2 - Pi)', - Y2 -1- Pc.2 



But it is obvious on inspection that the denominator of the second 

 member is merely the heat of fusion of one mol of solid, which we may 

 call Q. If the solution is very dilute we may also simplify by writing 

 N2 = 1. Hence, 



dT _ RT' 



d^\~ Q 



This is the familiar equation of van't Hoflf for the lowering of the 

 fi'eezing point by a dissolved substance. 



As a second example we may study the following system, A mix- 

 ture of X2 and X3 in the molecular proportion of 1V2 to JVs are in equi- 

 librium with a second phase consisting of pure X,. Let us determine 

 the change in activity of X3 when a small quantity d]S\ of a substance 

 Xi is dissolved in the mixture. At constant temperature and pressure 

 the activity ^''2 of the pure phase of X, is a constant, and therefore 

 the activity, $2, of Xj in the mixture is also constant. Equation XX 

 therefore becomes, 



iWlnc^3 = -^^i. XXI 



This interesting equation has, I believe, not hitherto been obtained, 

 even in an approximate form. Its meaning may be illustrated by the 

 following example : If a saturated solution of salt in 1000 grams of 

 water is in contact with solid salt, and 1 gram of sugar is added, then 



