264 PROCEEDINGS OF THE AMERICAN ACADEMY. 



may be found (or imagined) in which that species dissolves to form a 

 perfect solution, at all concentrations up to that of the saturated 

 solution. 



(2) We may further assume that the ideal solvent chosen is one 

 which suffers neither increase nor decrease of volume when the sub- 

 stance in question is dissolved at constant temperature and pressure. 

 In other words, the volume of the ideal solution is the same as that of 

 the ideal solvent it contains.* 



(3) In dealing with mixtures, use will be made of any kind of 

 semipermeable membrane, real or imaginable, that may prove serviceable. 



Probably in no case can the ideal solvent or the perfect semiperme- 

 able membrane be actually found. They will be employed as conven- 

 ient fictions for the purpose of obtaining results which could be obtained 

 without their aid, but by less simple methods. 



Equations of a Solution in the Ideal Solvent. 



Let us consider the vapor of a substance X, together with a solution 

 of X in an ideal solvent. From the laws stated in the preceding sec- 

 tion it may readily be shown that as the quantity of X is diminished, 

 and the solution and the vapor become less concentrated, the ratio 

 between the concentrations of X in the two phases approaches a con- 

 stant value.^ In other words, if c represents the concentration of X in 

 the solution, c' in the vapor, then at infinite dilution, 



c' = pc, 



where p is a constant, when the temperature and pressure are constant, 

 and may be called the distribution coefiicient between solution and 

 vapor at infinite dilution. This equation is merely the exact statement 

 of Henry's law. 



Since the two phases are kept in equilibrium, the activity of X must 

 always be the same in one phase as in the other, that is, 



i = i'. 



* This assumption is of minor consequence, and is introduced merely to sim- 

 plify some of the mathematical work. It can be omitted without materially 

 changing tlie following work. 



" Since our purpose is to develop a set of exact equations, but not to place too 

 much emphasis upon the formal rigor with which those equations are obtained, 

 it will not be necessary to repeat the proof of propositions which have already 

 been proved elsewhere and which can obviously be obtained by familiar methods. 



