THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 327 



the energy containing cross terms due to forces acting between the dif- 

 ferent molecular species present in the mixture. This assumption, which 

 is necessary for a solution of the problem by this method, is obviously 

 an arbitrary one. Proceeding in this way Jahn obtains, for a system of 

 electrolytes in equilibrium, the equation: 



(C-) 2 

 (103) log -J- = (a + fa)C + log tfo, 





where a and (3 are constants. The constancy of the functions ct and (3 

 however, depends upon the original assumption made with regard to the 

 manner in which the energy of the system is dependent upon its composi- 

 tion, and, if a different assumption had been made, it would have led to a 

 corresponding variation in the resulting equation. Methods of this kind 

 are correct enough thermodynamically, but, in order that they may lead 

 to results which may be tested experimentally, an assumption must be 

 made, and this assumption is, in general, arbitrary in its nature. In this 

 sense, therefore, the results of these methods are to be looked upon as 

 being purely empirical in character, unless evidence of an a priori nature 

 can be adduced in favor of the assumptions made. In all cases, the cor- 

 rectness of the assumptions may be tested by comparing the resulting 

 equations with the experimental values. Taking the equation of Jahn, 

 it is easy to make a comparison with experiment. 



This equation obviously involves four constants ; namely, a, (3 and K , 

 together with A , the limiting value of the equivalent conductance. The 

 equation is a fairly complex one and it is not easy to extrapolate for the 

 value of A on the basis of this equation, but it may safely be assumed 

 that, in the case of potassium chloride, the conductance of whose solutions 

 has been measured to 2 X 10' 5 normal, the true value of AO does not 

 differ materially from that ordinarily assumed. At higher concentra- 

 tions, at any rate, a slight error in the value of A will cause a relatively 

 small change in the distribution of the points. Assuming the value of 

 A , and calculating the values of the function K' at three concentrations, 

 it is possible to evaluate the constants a, p and K . The values of a and 

 P being known, the equation may be tested by plotting values of log K 

 against those of (a + py) C. This plot should yield a linear relation, 

 but, in fact, leads to results inconsistent with the experimental values. 

 The value of K' has a maximum in the neighborhood of 0.05 normal, 

 after which it decreases rapidly. The equation as calculated for potas- 

 sium chloride at 18 is as follows: 



log K' = 2.5935 + (592.8 498.7y)C. 



