8 ART. 10. — K. IKEDA : STUDIES ON THE 



It is enough to use those in the gaseous state. But the molecular 

 weight of a gaseous substance is determined theoretically by the amount 

 of work obtainable by its difl'nsion or expansion. As substances can 

 be made to pass continuously from the gaseous to the liquid state, 

 and as the work obtainable by the interdiffusion of the components 

 is identical in both, the molecular weights of the components in the 

 liquid state must be considered to remain the same as in the gaseous 

 state. In fact all the components which mix with one another with 

 very small changes of volume and energy are without exception unas- 

 sociated liquids. 



From the amount of work obtainable by reversible mixing we can 

 readily calculate the strength of the osmotic pressure exerted on a 

 semipermeable septum if we assume the liquids to be incompressible. 

 When the mixing is accomplished by means of an osmotic apparatus 

 having as many semipermeable pistons as there are components, then 

 the work must be 



"i^ii'i + ^'^:i^^ + = ~ihIlT In C\ — u. ItT In Co— 



where t:^, t:.,, are the osmotic pressures exerted by the solution 



on the pistons allowing the passage of (£j, ©2, respectively. As 



n^jUo, can be varied independently of one another, it follows 



7c,v^ = -ItT In C, 



-JRThi Ci 



or Tt^ = 



which of course gives van t'Hoff's relation for the cases in wliich C\ 



approaches unity. 



The physical properties of the ideal solutions are mostly of 

 an additive nature. That the heat capacity and the compressi- 

 bility must belong to this category follows from conditions (1) 

 and (2). Refraction of light calculated according to the formula 

 of Gladstone and Dale or that of Lorenz and Lorentz agrees 

 in some cases almost exactly with the supposition. Other op)tical 



