LEWIS. — THERMAL PRESSURE. 159 



In any pure solvent, according to equation (5), the tendency to escape 

 into some other phase is dependent, not upon the actual values of the 

 thermal and attractive pressures, but only upon their difference, which is 

 the external pressure. At constant external pressure, therefore, the 

 escaping tendency of the solvent is constant under all circumstances as 

 long as the external pressure represents the difference between the ther- 

 mal pressure of the solvent and the attractive pressure. If in a solution 

 tlie thermal pressure of the solvent were equal to the total thermal 

 pressure, the difference between this and the attractive pressure would 

 be equal to the external pressure, and the escaping tendency would be 

 the same as that of the pure solvent under the same external pressure. 

 In reality the total thermal pressure is the sum of the partial thermal 

 pressures of the solvent and solute ; therefore, other things being equal, 

 the escaping tendency should be to that of the pure solvent as the partial 

 thermal pressure of the solvent is to the total thermal pressure. That is, 



where ^ is the partial thermal pressure of the solvent, /3' that of the 

 solute; but from equation (10), 



therefore. 



From this equation, 



^, nRT ^ mRT 



\po m 



xpi — i/^o n 



\pi m -\- n 



which is equation (12a). 



From tliis it appears that the lowering of vapor pressure, the lowering 

 of solubility, and the lowering of the freezing point are all due to the 

 fact that the sohite shares with the solvent the support of the external 

 and attractive pressure. Other things being equal, the greater the ther- 

 mal pressure of the solute the less that of the solvent, and thus an 

 increase in the amount of the solute diminishes the escaping tendency of 

 the solvent, whether towards the gaseous phase, the solid phase, or 

 anotlier liquid. 



An analogy may illustrate this explanation of Raoult's law, and at the 

 same time introduce the consideration of osmotic pressure. If we con- 

 sider m gram molecules of a gas A under a constant external pressure. 



