LEWIS. — A NEW SYSTEM OF THERMODYNAMIC CHEMISTRY. 281 



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

 the change in temperature and by the presence of dN\ rnols of solute. 

 That is, 



"Whence by means of equations XII and XIX 



d In f 2 = </7 ^-. 



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



1 2 -* < 2 7 yi I 2 -* *2 7 yr " - * 1 



or — iv 2 



rfiVi Y' 2 - 2V 2 - Y, + /^ 



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 

 iV*2 = 1. Hence, 



dT _ RT 2 



dNx == Q 



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

 freezing point by a dissolved substance. 



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

 ture of X 2 and X 3 in. the molecular proportion of iV 2 to N 3 are in equi- 

 librium with a second phase consisting of pure X 2 . Let us determine 

 the change in activity of X 3 when a small quantity dX t of a substance 

 X : is dissolved in the mixture. At constant temperature and pressure 

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

 the activity, £ 2 , of X 2 in the mixture is also constant. Equation XX 

 therefore becomes, 



N z d\n^ = -dN 1 . 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 



