158 PROCEEDINGS OP THE AMERICAN ACADEMY, 



because the change in the attractive pressure is always compensated by 

 an equal change in the thermal pressure, and these two changes produce 

 equal and opposite effects upon the vapor pressure. This conclusion will 

 simplify the discussion of the second influence of the solute, the effect of 

 thermal pressure ; for since the attraction or repulsion of solute for solvent 

 is without effect, we may consider with perfect generality the case in which 

 this attraction or repulsion is zero. In such a case, if P and a represent 

 the thermal and attractive pressures of the pure solvent, when the solute 

 is added in general a change in volume occurs in which /3 and a change 

 to (3 -\- d /3 and a -\- da. The total attractive pressure of the solution 

 is a -{- da; but the total thermal pressure of the solution includes the 

 partial thermal pressure of the solute, which may be designated by d /3'. 

 The equation of the solution is, then, 



P =z (fS ^ d(3 + d/S') - (a+ da). (13) 



Combining this with the equation of the pure solvent, 



we obtain 



d(3- da = - dft'. (14) 



Now the vapor pressure depends on the attractive pressure and the ther- 

 mal pressure of the solvent alone, in accordance with equation (7), 



which may be written, 



dl\ _ rf (/3 - a) 



V 



Substituting equation (14) and writing from equation (10), 



we obtain, 



(d7i) R T 



dP^ V dn 



Pi m R T m 



V 



d Pi being negative for a decrease in Pi. This is a statement of the law 

 of Raoult, which is thus shown to be a direct consequence of the princi- 

 ple of thermal pressure expressed in equation (10). Perhaps a more 

 intimate understanding of the way in which the thermal pressure of the 

 solute affects the vapor pressure of the solvent may be obtained from 

 another point of view which affords a simple but somewhat less rigorous 

 demonstration. 



