LEWIS. — A NEW SYSTEM OF THERMODYNAMIC CHEMISTRY. 267 



change when X dissolves.) The first of these terms we will call Z7 ( y n , ; 

 the second, according to the principle of van't Hoff, is equal to RT ; and 

 the third is equal to — Pv, where v is the molecular volume of pure X. 

 We may write equation VI, therefore, in the form 



/31nII\ Uw+ET-Pv s . 



V cT )p RT* V 



Now the activity, £, of X in the pure state is always equal to that in 

 the saturated solution. The latter is related to II, according to equation 

 III, by the formula, 



P 

 Substituting this value of II in equation VII gives, 



1_ ^Uw + BT-Pv 



I rn 



/dlnA (ZJnn\ I 

 V dT Jp" V cT )p + 1 



RT 1 



Substituting for the second term the value given by equation IV, and 

 simplifying, we have, 



/gin A 

 \d'T ) 



p ~ RT* 



j^vii) is the increase in internal energy -when a mol of X dissolves in 

 the ideal solvent and U aV \ is the increase when it passes from that 

 solution into the state of infinitely attenuated vapor. The sum of 

 these two is the increase in internal energy when a mol of X is evapo- 

 rated and the vapor expanded indefinitely, or in other words it is the 

 increase in internal energy when a mol of X evaporates into a vacuum. 

 This important quantity, which we may call for the sake of brevity the 

 ideal heat of evaporation, will be designated by the symbol Y. Sub- 

 stituting it in the last equation gives, 



m,= 



1=^?. VIII 



RT 2 



This is the general equation for the effect of temperature on the 

 activity of any pure solid, liquid, or gas. Except in very rare cases 

 the second member is positive and £ increases with T. 



