191-'.] MAGIE— THERMAL RELATIONS OF SOLUTIONS. 237 



capacity of the solution and of an arbitrary amount of additional 

 solvent, from which the solvent is taken with which the solution is 

 diluted, and v, the volume of the solution, we find 



dl dH 



dd dv 



a. 



We may set dH/dv=^a, a quantity independent of the temperature, 

 because, first, Teudt has proven it to be so independent, within 

 reasonable ranges of temperature, by direct observations, and, sec- 

 ondly, because the formula 



obtained from the differential equation on that supposition agrees 

 with observations within the temperature ranges in which it has been 

 tested. Treating a therefore as independent of the temperature we 

 get 



l = — ae'\-e, 



in which the heat of dilution is expressed as the sum of two terms, 

 one of which is proportional to the absolute temperature, the other 

 independent of temperature. Such a relation could not be expected 

 to hold for all temperatures, but within the narrow ranges open to 

 experiment it seems to be valid. Of the two terms the first one is 

 positive in all actual cases, for it is a general rule that the heat 

 capacity of an electrolyte diminishes as the dilution increases. It 

 corresponds to an evolution of heat. The second term is nearly of 

 the same magnitude as the first, and is negative, corresponding to 

 an absorption of heat. 



From the experimental relation already described, connecting the 

 heat capacity of the solution with the dissociation, it follows that the 

 quantity a is equal to a negative constant multiplied by the rate at 

 which the dissociation increases as the volume of solution is in- 

 creased. The evolution of heat therefore which is expressed by the 

 term — aB is proportional to the increase in the dissociation and to 

 the absolute temperature. This can be explained by the theory of 

 the constitution of a solution which has already been described. As 

 dissociation proceeds molecules of water which have been in union 



PROC. AMER. PHIL. SOC, LI. 205 M, PRINTED JULY 24, I9I2. 



