42 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



hypothesis of Arrhenius; namely, that an electrolyte in solution is ion- 

 ized, and its ionization is a function of the concentration, decreasing with 

 increasing concentration. There exists, therefore, in solutions of electro- 

 lytes an equilibrium between the ions and the un-ionized molecules, and 

 this equilibrium must be subject to the usual laws governing equilibria. 

 It is obvious that, according to the law of mass action, the ionization 

 should increase with decreasing concentrations, since there is an increase 

 in the number of molecular species as a result of the reaction. If we 

 assume a simple system, as for example a binary salt MX which forms 

 the ions M + and X~, according to the equation: 



MX = M + + X-, 

 then, according to the law of mass action, we should have a relation: 



(5) 



, 



C MX 



where C^ represents the concentration of the molecular species X. If 



the solution is sufficiently dilute, so that the laws of dilute solutions may 

 be applied, then K will be a function of the temperature only. On the 

 other hand, it is obvious that a concentration must ultimately be reached 

 where the laws of dilute solutions fail, in which case K becomes a func- 

 tion of the concentration as well as of the temperature. 30 



If y is the degree of ionization of the salt and if C is its total concen- 

 tration, then the concentrations of the two ions will be equal to Cy and 

 the concentration of the un-ionized fraction will be equal to C(l y). If 

 these values are substituted in Equation (5), they lead to the equation: 



(6) 



The value of y mav be calculated either from conductance or from 

 osmotic measurements. If the values of y according to the two methods 

 agree, then obviously the two methods must lead to identical results, so 

 far as the mass-action law is concerned. Since the degree of ionization 

 is given by Equation 2, we may substitute this value of y in Equation 6 

 which yields the equation: 



m CA2 _ 



A (A _A)- X - 



This equation, involving the two constants K and A , therefore expresses 

 the relation between the concentration and the conductance of a solution 



80 Van der Waals-Kohnstamm, "Lehrbuch der Thermodynamik," part 2, pp. 604, 

 et seq. 



