THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 345 



of particles actually engaged in the transport of the current, but of the 

 mean conducting power of the ions. It does not necessarily follow, how- 

 ever, according to this view, that all the ions in solution are at all times 

 acting as carriers of the current. 



Lewis and Randall 28 have recently pointed out that the ionization of 

 an electrolyte cannot be defined without some degree of arbitrariness. 

 This difficulty is not one confined to electrolytic solutions. In all sys- 

 tems, in which reaction takes place among a number of constituents 

 throughout the mass of the mixture, the definition of the concentration 

 of the various constituents concerned becomes uncertain. So long as the 

 system is dilute, the concept of concentration is definite; but, when the 

 concentrations reach such values that the forces acting between the con- 

 stituents become appreciable, the concept embodied in the term molecule 

 becomes indistinct. This difficulty arises of necessity whenever we pass 

 from the purely thermodynamic to the kinetic method of treating systems 

 of real substances. That these various difficulties should arise in solu- 

 tions of electrolytes is not surprising, since these are the only concentrated 

 systems regarding which we have data sufficiently accurate to enable us 

 to observe the deviations from ideal systems with any considerable degree 

 of certainty. That un-ionized molecules exist in aqueous solutions of 

 ternary salts in water appears to be conclusively demonstrated by the 

 fact that transference measurements have shown that complex cations 

 exist. Thus, the transference number of the cadmium ion, in cadmium 

 iodide, according to Hittorff, is greater than unity at high concentrations, 

 and the manner in which the transference number of cadmium chloride 

 varies with the concentration indicates that its behavior is not essentially 

 different from that of cadmium iodide. It must be assumed, therefore, 

 that, in solutions of cadmium salts, ions of the type CdX> exist. If this 

 is true of one electrolyte, the same may well be true of others. 



Finally, it is not sufficient that a theory of electrolytic solutions shall 

 account merely for a diminution in the conducting power of electrolytes 

 with increasing concentration, for, in solutions in non-aqueous solvents, 

 the conductance increases with increasing concentration at higher con- 

 centrations; and, if the dielectric constant is sufficiently low, the con- 

 ductance increases with increasing concentration even at relatively low 

 concentrations. 



d. Hertz's Theory of Electrolytic Conduction. P. Hertz 29 has at- 

 tempted to solve the problem of electrolytic conduction by taking into 

 account the interionic forces. He has derived the following equation 



*Loc. cit. 



Hertz, Ann. d, Phya. 37, 1 (1911). 



