138 



BUTLER 



ART. D 



they refer. The change of logfpi/pi"), or logori, with tempera- 

 ture can be obtained by dividing equation (166) by t and 

 differentiating. Thus we find that 



d log (p^/p^') ^ M^ ( dMt) _ rfOiiVOl 

 dt A \ dt dt j 



Mi(«> 



(^> 



(182) 



where Mi(xi — xi'*) is the heat absorbed when the molecular 

 weight of the pure solvent is added to a large quantity of the 

 solution at the temperature t. If xi is known as a function of 

 the temperature, this equation may be integrated over a con- 



TABLE III 



Freezing Point Depressions and Vapor Pressure Lowerings of 

 Aqueous Mannite Solutions 



siderable range of temperature, and the values of log(pi/pi") or 

 logai at a given temperature can be evaluated from measure- 

 ments at another temperature. In the data for mannite solu- 

 tions it appears that log{pi/pi^) diminishes slightly as the 

 temperature rises. In these solutions xi — Xi" is therefore a 

 small positive quantity. 



23. Osmotic Pressure of Solutions. We will consider the 

 osmotic equilibrium of a solution of a solute *S2 in a solvent Si 

 separated from the pure solvent by a membrane which is per- 

 meable to Si only. Let the values of the potential of Si at a 

 temperature t and pressure Po be /ii" in the solvent and /xi in the 

 solution. For osmotic equilibrium, by (90), it is necessary that 

 the potential of Si shall be the same on both sides of the mem- 



