LEWIS. — A NEW SYSTEM OF THERMODYNAMIC CHEMISTRY. 283 



The numerator of the first term, which we may call Q, is obviously the 

 heat absorbed when a mol of the mixture passes from the first phase to 

 the second, and (y — v') is the decrease in volume accompanying the 

 same change. Thus, 



% dT + ^^ dP - dA\ + dN', = 0. XXIP 



This extremely general equation shows how the variations in temper- 

 ature, pressure, and quantity of solute must be regulated in order to 

 maintain equilibrium in such a system. Several special cases are 

 worthy of notice. If pressure and temperature are the only variables, 

 in other words if dNi and dN'i are zero, then the equation becomes, 



dP Q 



dT {v'-v)T 



This equation is identical with the familiar Clapeyron-Clausius equa- 

 tion. It shows, for example, that the vapor pressure from a constant . 

 boiling mixture varies with the temperature in the same way that the 

 vapor pressure of a pure substance does. 



If in equation XXII, dP and dN'i are zero, there remains an equation 

 for the change in temperature which compensates for the addition of a 

 solute soluble in one phase only, namely, 



dT=^dX,. 



Thus, for example, the boiling point of a constant boiling mixture is 

 changed by the addition of a non-volatile solute according to the same 

 law as that which applies in the case of a simple solvent. ^^ Q is of 

 course the heat of vaporization of one mol of the mixture. 



In the same way, by making c?!" equal to zero in equation XXII, a 

 formula may be derived for the lowering of the vapor pressure of a con- 

 stant boiling mixture when a solute is added at constant temperature. 



1* Tliis equation I have already proved in a less rigorous way (.Journ. Amer. 

 Chem. Soc, 28, 7G6, 1906). It has considerable practical importance, as it in- 

 creases the number of solvents iu which molecular weights may be determined 

 by the boiling point method. 



