LEWIS. — A NEW SYSTEM OF THERMODYNAMIC CHEMISTRY. 283 

 (Y — Pv) — (Y' — Pc) (v — r> ) 



{ - — ^-jTf* — ^ dT + ^p dp - dx 1 + aw x = 0. 



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 (v — v') is the decrease in volume accompanying the 

 same change. Thus, 



KT dT+ '^T dP ~ JXl + dN>1 = °' XX11 * 



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 dXy and dN\ are zero, then the equation becomes, 



dP Q 



dT (v 1 - <■) r 



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, 



JIT" 

 dT=-^ T dX l . 



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. 14 Q is of 

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



In the same way, by making dT 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. 



14 This 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 in which molecular weights may be determined 

 by the boiling point method. 



