the Conductivity of Solutions of Double Salts. 511 



especially from Bender's observations that the differences 

 between observed and volume mean conductivities, even for 

 equal volume mixtures of equi-molecular solutions, increase 

 with the concentration ; and no observations are available to 

 determine within what limit of concentration the differences 

 become negligible. 



For the second assumption we have of course no experi- 

 mental ground whatever. 



With regard to the third it should be noted that both 

 Bender's and Chroustchoff and PackbofPs observations show 

 that the differences between observed and volume mean con- 

 ductivity are in some cases positive and in others negative. 

 Unless therefore the effect produced on the conductivity 

 by the formation of double molecules has always the same 

 sign as the effect produced by mere mixing, the resultant 

 differences, in cases in which double salt exists in solution, 

 might be smaller than the differences exhibited in other 

 cases. 



It would seem therefore that except in cases in which a 

 large amount of double salt is present as such in solution, the 

 volume mean criterion cannot lead to conclusions of any high 

 degree of probability. 



There is one source, however, from which assistance may 

 be obtained in researches of this kind and which has not yet 

 been used, viz., the dissociation theory of electrolytic con- 

 duction. Whether that theory be ultimately well founded 

 or not, it has at any rate shown itself to be capable of 

 coordinating the phenomena of electrolytic conduction to 

 a remarkable extent ; and what it has to say with respect 

 to the point under consideration should therefore be at- 

 tended to. 



And first with regard to the agreement between the actual 

 and the volume mean conductivity of a complex solution : — 

 If we mix volumes v 1} v 2 of solutions of electrolytes 1 and 2, 

 which have a common ion, and whose concentrations, ioniza- 

 tion coefficients, and molecular conductivities at infinite 

 dilution, are n ls n 2 ; a 1? « 3 ; and \l ^ l9 yu.^2, respectively, the 

 concentrations being so low that no appreciable change of 

 volume occurs on mixing, and there being no formation of 

 double salt, and if, after mixing, the ionization coefficients 

 become a/, a 2 f respectively, the excess of the actual con 

 ductivity over the volume mean conductivity will be 



{(*/ — *lWtfi/*oo 1+ W— «2)^2Wx>2}/(>l + t>2)- 



This will not vanish unless (1) the solutions are infinitely 



2N2 



