The Osmotic Pressure of Solutions. 139 



volume occupied in the solution by the solvent. V is the 



volume of n gr. mols. solvent + 1 gr. mol. dissolved body. 



We have, accordingly, 



V - nv = b, 



where b is the volume in the solution of the dissolved 

 substance (for 1 gram molecule). 

 We get, therefore, (V - b) = nv 



We have also ^ = — , 

 K V 



putting these values into equation (10), it becomes 



aw 



By comparing this equation (which is obtained on the 

 assumption that an equation of the same form as that of 

 Van der Waals holds good for solutions) with (9), it is 

 evident that if the equation connecting osmotic pressure, 

 volume, and temperature of a solution is really of the same 

 form as Van der Waals' equation, we must have 



hi=±l. 



The sign will depend on the sign of k. 



The equation for the osmotic pressure of a solution 

 may, then, be written 



P(V-6)=±ET + J»M„^ .... (11) 



The meaning of RT having the - sign is, that when the 

 solution is diluted in a reversible way, the maximum of 

 external (osmotic) work being done, there is still heat 

 evolved by the system. This is a case which, so far as I 

 know, never occurs with gases. 



The experimental material necessary to test the truth 



of the expression k = - is unfortunately not in existence. 



The only substance for which I have been able to find 

 sufficient determinations of the freezing point and of the 



