238 MAGIE— THERMAL RELATIONS OF SOLUTIONS. [April 20, 



with the molecules of the solute are released and their heat capacity 

 is diminished. At the same time molecules of water are associated 

 with the new ions, and their heat capacity is also diminished. 

 The act of dissociation thus diminishes the heat capacity, and 

 therefore the number of degrees of freedom of the solution in 

 proportion to the change of the dissociation factor, and the energy 

 associated with those degrees of freedom, which is proportional 

 at these temperatures to the absolute temperature, is liberated 

 in the solution as heat. The negative term e being nearly equal 

 at each concentration to the corresponding positive term, also 

 varies to a first approximation with the dissociation. When calcu- 

 lated for the dissociation of a complete gram-molecule it is of the 

 same order of magnitude as the heat of combination of the elements 

 constituting the solute. It presumably contains the heat of disso- 

 ciation along with the internal work done during the dilution. 



The condition that dH/dv^a is independent of the temperature 

 enables us to find a formula for the relation between the osmotic 

 pressure and the temperature expressed in terms of the thermal con- 

 stants. A thermodynamic argument shows that the osmotic pres- 

 sure p satisfies the differential equation 



d^P _ a 



and if a is assumed independent of 6 we integrate this equation and 

 obtain 



p^= — ad{\oge—i) -^he + e. 



The quantities b and e are functions of the volume but are inde- 

 pendent of the temperature. 



Now by another thermodynamic argument we can deduce the 

 heat of dilution from this value of the osmotic pressure. We obtain 



l,= — ae-{-e 



as before, in which the function e is that which appears in the ex- 

 pression for the osmotic pressure. This formula can be tested by 

 comparison with the results of experiment. From observations of 

 the depression of the freezing point we can calculate the osmotic 

 pressure for a fixed concentration at 0° C. and using this in con- 



