FORM OF THE CONDUCTANCE FUNCTION 97 



change in the speed of the carriers. It should be stated, however, in 

 this connection, that no theory has thus far been proposed which ade- 

 quately accounts for the change in the carrying capacity of the ions as 

 a function of the concentration, particularly in solvents of low dielectric 

 constant. Any such theory must not only account for an initial diminu- 

 tion in the speed of the ions, but it must also account, in many cases, 

 for a subsequent increase in the speed with increasing concentration. 

 In fact, such a theory must account for the various forms of the con- 

 ductance curves in different solvents and for the change in the form of 

 the curves as the condition of the solvent is altered. Incidentally, it is 

 to be noted that the order of the changes in the speed of the ions on 

 this assumption is very great. It is true that, in aqueous solutions, the 

 speed does not vary greatly from the most dilute solutions up to normal 

 concentration, but in solutions in solvents of low dielectric constant it is 

 not only necessary to account for a decrease in speed but in many cases 

 for an increase in speed which, over a limited range of concentration, is, 

 at times, as great as a thousandfold. It seems very difficult to account 

 for a change of speed of this magnitude on the basis of our present 

 knowledge of the properties of the carriers in different media. In this 

 connection it should be borne in mind that, superimposed on these 

 hypothetical changes in the speed of the ions, there is a change due to 

 the viscosity of the solution which effect appears in every respect to 

 be normal in character. Furthermore, solutions of weak electrolytes, 

 both in water and non-aqueous solvents, conform to the mass-action law 

 up to fairly high concentrations. If the speed of the ions changes with 

 the concentration, then such a simple relation is not to be expected. 



A third hypothesis has been proposed, namely: that the ionization 

 reaction differs from that which is commonly assumed. Certain writers 

 have made the assumption that, in non-aqueous solutions, the electrolyte 

 is associated, the association changing with concentration, and that only 

 the associated molecules are capable of ionization. They assume, for 

 example, in the simplest case, that the following reactions take place: 



= (MX) 2 



As the concentration increases, the amount of the polymer increases and 

 this increase might be sufficient to provide for an actual increase in the 

 number of ions present. If this hypothesis is correct, the current in such 

 solutions is carried chiefly by complex ions and consequently transfer- 

 ence numbers in such solutions should be abnormal. Reliable trans- 

 ference numbers in solvents of low dielectric constant are not available, 



