FORM OF THE CONDUCTANCE FUNCTION 95 



the medium, the greater the discrepancy between the observed and cal- 

 culated values, although there are some marked exceptions. Further- 

 more, the order of the deviations varies as the ionization of the electro- 

 lyte varies. This is particularly noticeable in the case of ammonia and 

 isobutyl alcohol, where the observed and calculated values very nearly 

 agree at 95% ionization, but diverge largely at an ionization of 70%. 

 On the other hand, in other cases, the deviation changes sign. For 

 example, at 70% ionization the observed value for ethyl alcohol is 125.9 

 and the calculated value 39.2, whereas at 95% ionization the observed 

 value is smaller, being 3590, and the calculated value 5880. 



That Walden's relation cannot hold generally may most readily be 

 shown by graphical means. If we take logarithms of both sides of 

 Equation 39, we have: 



log V 2 log V x = 31og^. 



8 2 



If the values of y f r an electrolyte in different solvents are plotted 

 against values of log V, then obviously for any given value of y the 



abscissas on the curves will differ by 3 log . In other words, the curve 



2 



for an electrolyte in any one solvent may be derived from that in any 

 other solvent by merely displacing the curve along the axis of log V by 



p 



an amount equal to 3 log . An inspection of Figure 3, where values 



E 2 



of y f r different solvents are plotted as functions of log V, shows at 

 once that this condition is not fulfilled, for, if the curve for water were 

 displaced parallel to itself, it would not coincide with the curves for 

 solutions of typical electrolytes in other solvents, such as ethyl alcohol, 

 ammonia and ethylene chloride. Indeed, in order to test the applicability 

 of Walden's relation it is not even necessary to know the value of A , 



since it follows readily from Equation 39 and from the equation y = r- 



A 



that if the conductances themselves are plotted as functions of log V, it 

 must be possible to derive the curve for an electrolyte in any one solvent 

 from that in any other solvent by displacing the curve parallel to itself 

 in some direction, this direction being determined by the values of A 

 and of the dielectric constant 8. Those familiar with the properties of 

 electrolytic solutions will at once recognize that this condition is not 

 fulfilled. 



Actually, it is not to be expected that any simple relation will exist 

 between the ionization y and the dielectric constant of the solvent, for, 



