186 
MATHEMATICS: F. L. HITCHCOCK 
Proc. N. a. S. 
A THERMODYNAMIC STUDY OF ELECTROLYTIC SOLUTIONS 
By Frank L. Hitchcock 
Department of Mathematics, Massachusetts Institute of Technology 
Communicated by Edwin B. Wilson, January 30, 1920 
1. Scope of the investigation. — It is well known that aqueous solutions 
of strong electrolytes do not conform to the requirements of the usual 
mass law. Measurements of freezing-point and of electric conductivity 
unite in showing a marked rise of the "ionization-constant" with increase 
of concentration. The accumulation during recent years of a consider- 
able body of accurate data renders a theoretical examination of these 
relationships highly desirable. 
The theory of chemical potentials, due to Willard Gibbs, offers a ready 
tool for examining what the rigorous consequences of the dissociation 
hypothesis must be. From this theory may be deduced, for example: 
1°. An expression for the heat of dilution as a function of temperature 
and of concentration. 
2°. A rigorous equation for determining the freezing-point in terms of 
the concentration — nothing being assumed as to the "ideal" character of 
the solution. 
3°. A generalization of the usual mass law. 
These three equations will contain certain constants, dependent on the 
thermic properties of the solution. Some of these constants can be calcu- 
lated from specific heats, or from latent heats of melting or of evaporation. 
Others, in the present state of our knowledge, must be determined em- 
pirically. The constants in the three equations, in so far as they are 
generalizations of the usual equations, are the same. Hence any results 
obtained under one head can be checked by the others. 
2. Heat developed by chemical or physical changes at constant tempera- 
ture and pressure. — It is well known that when a system at constant tem- 
perature and pressure undergoes any change, the heat Q emitted during 
the change is connected with the total free energy (p of the system by the 
differential equation 
This equation is quite general. It is not necessary that the change in 
question be reversible. If the system consists of several phases it is not 
necessary that the pressure be the same for all, provided it is constant for 
each.^ 
3. The general condition of equilibrium. — It is also well known that for 
a system of several phases whose composition is determined by masses 
mo , Wi, W2, . . .m^i the existence of a state of equilibrium implies the equa- 
tion 
(1) 
