28 PROCEEDINGS OF THE AMERICAN ACADEMY, 



In taking up the subject of solutions it will be necessary to consider 

 their probable nature. Although there is some evidence that the phe- 

 nomenon of solution is accompanied by a molecular change, the prepon- 

 derance of evidence seems to be in favor of the theory that the molecule 

 of a substance in solution is free, and not combined in any chemical vpay 

 with the molecules of the solvent. If this is the case, certain properties 

 of the solute should remain unchanged reirardless of the nature of the 

 solvent. In the following work we will assume that, for a dissolved 

 substance, the quantity f) as defined above and the quantity c„ will be the 

 same in any solvent. If this supposition, which seems eminently proba- 

 ble, proves to be not entirely correct, then the equations developed below 

 will only be approximations to the truth. It is to be hoped that in any 

 case their application will conversely give us information concerning the 

 nature of solution. 



Osmotic Pressure. — The simplest phenomenon of a homogeneous so- 

 lution is that of osmotic pressure, which may be determined in the fol- 

 lowing way. The change of free energy on addition of an infinitesimal 

 amount of solvent to a solution containing one gram-molecule of solute is 

 equal to the sum of the changes of free energy in the two constituents of 



the system. From equation (5), if —-^ — 0, and -~ becomes the 



volume correction, which, as is shown by Nernst,* is for each constituent, 

 in the case of osmotic pressure, only the correction for the space occupied 

 by the molecules of the constituent in question, 



— dvx — dWii -\ r 



t\ — 6>i Co — O2 



where the subscript 1 refers to the solute, subscript 2 to the solvent. 



dv-^ , the change in molecular volume of the solute, is also the change in 



volume of the system, and d A = p dvi, where p is the osmotic pressure. 



Therefore 



RT dm. , nRT do^ .^^. 



7'i — Oi dvi fo — 0.2 dvi 



dW. 



where --, — represents the heat produced by the addition of d v^ of the 



solvent. Except in cases of solution of such great concentration that the 

 molecular volume of the solute and that of the solvent are not greatly 



different, -^ is entirely negligible, and the equation for osmotic pres- 

 sure becomes » 



* Theor. Chem., p. 209. (References to tliis book are to the first edition.) 



dA = -^^^ dv, - dUr + r- dv^ - dW^^ , 



