FORM OF THE CONDUCTANCE FUNCTION 93 



of the dilution have the same value. More recently, a number of writers 

 have proposed theories of electrolytic solutions which lead to Walden's 

 relation as a consequence. Walden has made an extensive study of 

 available data 20 from which he draws the conclusion that his relation 

 holds practically without exception. The theories in question will be 

 discussed in another chapter. We shall here consider Walden's relation 

 from an experimental point of view only. 

 In mathematical terms, we have: 



if 



(37) YI = Y 2 = Ya =, etc. 

 then 



(38) e^* = e 2 F 2 * = E 3 F 3 * = , etc. 



where E is the dielectric constant of the medium and V is the dilution 

 of the solution of a given electrolyte, whose ionization fulfills the con- 

 dition 37. Walden has tested the relation by comparing the values of 

 eF* for solutions of typical electrolytes in different solvents and believes 

 to have shown that this quantity is a constant within the limits of experi- 

 mental error and minor variations due, perhaps, to differences in the 

 condition of the electrolyte in different media. 



It is clear, from Equation 38, that a small variation in the value of 

 the product F* will have as a result a large variation in the resulting 

 conductance curve, since the dilution enters as the cube root. Actually 

 the variations of the constants are quite large. For example, at an 

 ionization of 82%, the product eF* in water has a value of 156, in 

 ammonia 286, in isobutylalcohol 333, and in ethylene chloride 315. The 

 constancy of the values which Walden has found is in part due to the 

 use of unreliable conductance data and in part to the use of A values 

 which are unquestionably in error. 



It is obvious, according to Equation 38, that, if the ionization curve 

 is fixed for a typical electrolyte in one solvent, it is fixed for typical 

 electrolytes in all other solvents. For we have, considering solutions of 

 a given electrolyte in two different solvents, 



(39) or ^ 



If F! is the dilution in the first medium, at which the ionization of the 

 electrolyte is y, then F 2 , as determined by Equation 39, is the dilution in 



Walden, Ztschr. f. phys. Chem. 9$, 263 (1920). 



