L58 PROCEEDINGS OF THE AMERICAN ACADEMY. 



b, cause the change in the attractive pressure is always compensated by 

 :in 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 Bince the attraction or repulsion of solute for solvent 

 is \\ ithout effect, we may consider with perfect generality the case in which 

 tlii-. attraction or repulsion is zero. In such a case if (1 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 aud a change 

 to /i + d/3 and a + da. The total attractive pressure of the solution 

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

 partial thermal pressure <>f the solute, which may be designated by « 

 The equation of the solution is, then. 



P =-- (P + df3 + d&) - (a + da). (13) 



Combining this with the equation of the pure solvent, 



P = P-a, 



we obtain 



dp-da = -dp. (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, 



d_P x _d(p-u) 



P l mRT ' 



V 

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



we obtain, 



(rfw) R T 



d P, V dn j 



/', m R T ' m 



V 



<l I\ being negative for a decrease in P,. This is a statement of the law 

 of Raoult, which is thus shown to 1"' 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 Bolveni may be obtained from 

 another point of vi< w which affords a simple but somewhat less rigorous 

 demonstration. 



