﻿Molecular Theory of Solution. 901 



this equation. More recently Kleeman * deduced expressions 

 for osmotic pressure in terms of molecular motion, attraction 

 and volume, remarking tliat " it is evident . . . that osmotic 

 pressure must arise through these properties of matter and 

 the equations are therefore fundamental in character. They 

 are, however, of little use in practice . . . since we have no 

 means yet of determining experimentally how the quan- 

 tities . . . vary." 



Treatment of the problem was omitted from the preliminary 

 paper in the hope of finding a more definite correlation. This 

 was not far to seek. On account of the meagre, and sometimes 

 doubtful, data available for osmotic pressure, cryoscopic deter- 

 minations were considered. From the present point of view 

 the depression of the freezing-point of a solution may be 

 regarded as the sum of two effects : a normal depression cor- 

 responding to van't Hoft's formula 



p __ 0-02P 

 Li 



due to the presence of a solute with the same molecular field 

 as the solvent, together with an effect produced by the altered 

 internal pressure of the solution. The molecular depressions 

 of organic substances, having molecular fields not greatly 

 different from that of the solvent, will not deviate much 

 from the normal. But aqueous solutions of many salts show 

 a marked increase in surface tension that indicates consi- 

 derable alteration in internal pressure. The freezing-point 

 depressions of such solutions should differ appreciably from 

 the normal. Since both surface tension and intrinsic pressure 

 are due to molecular attraction, we may take the one as pro- 

 portional to the other. And since the freezing-point of water 

 is depressed by increase of pressure, it follows that the 

 freezing-points of aqueous solutions of salts should be greater 

 than the normal by an amount which is proportional to 

 the increase of surface tension. It must not be forgotten, 

 however, that substances exhibiting greater molecular attrac- 

 tion than water may tend to aggregate in solution. This 

 must happen at the higher concentrations. In this case the 

 normal depression would be reduced correspondingly to the 

 smaller number of solute particles. Moreover, the field of 

 force surrounding the aggregated particles would differ 

 from that round a simple particle and should be less on 

 account of greater concentration of the lines of force within 



* Loc. cit. 



