132 Dr. Thomas Ewan on 



solvent it contains to a given quantity of dissolved substance. 



M 



We may therefore consider K— - as the increase of volume 



which an infinitely large quantity of the solution would 



experience if M grams ( = 1 gr. molecule) of the solvent 



M 

 were added to it. Call K — - = v and write the equation : 



Vv = KTlogP° (1) 



This equation is true for solutions of any concentration, and 

 is only subject to the restriction that the vapour of the 

 solvent over the solution may be considered as a perfect 

 gas. 



The connection between the osmotic pressure and the 

 freezing point of a solution may be obtained as follows. 

 According to KirchhofPs-J- well-known equation connecting 

 the heat of dilution of a solution with its vapour pressure 

 we have : 



dw JM dT *p 

 where J is the mechanical equivalent of heat, and -=- — the 

 heat of dilution — is taken positive when heat is evolved on 

 dilution. — is very nearly independent of temperature. 

 As a first approximation its variability may be neglected, 

 and the equation integrated gives 



^r^m: 2 < 2 > 



The constant k is of considerable importance, it is inde- 

 pendent of temperature, but varies with the concentration 

 of the solution. Its value may be obtained as follows : — 

 The heat required to melt igr. molecule of the solid solvent 

 at any temperature T (call it w T ) is given by the expression 



J dl p 

 t Ann. Phys. Chem. 103, p. 177. 1858. 



