[macgregorJ conductivity OF ELECTROLYTES 67 



From (1) and (3) we obtain : 



. A _ ^- + /^^' 



Hence A^ /^^ + ^^ 



Vi 



Vl + V2' 



and A = A=. 



If we combine (2) and (4), we obtain the same result. Hence the sole 

 condition of equilibrium is that the numbers of dissociated <^-ramme-equi- 

 valents of the two electrolytes, per unit volume of the regions occupied 

 by them, or the concentrations of the ions of the two electrolj^tes, shall be 

 equal. 



Arrhenius has shown' (and the above is but a slightly modified form 

 of his reasoning') that two simple solutions of electrolytes, having a com- 

 mon ion, which undergo no change of volume on being mixed, will alsa 

 undergo no change iii their state of dissociation, provided the concen- 

 trations of ions of the simple solutions were eqiial. 



The equations necessary for the determination of the ionisation co- 

 efficients, o-j and a.,, may now be obtained, as follows : — From the defin- 

 ition of a coefficient of ionisation we have : 



A _ ^i-^^i _ ^1 _ ^1 

 t\ ~ i\ ~ t\/N, - v; 



if the dilution of an electrolyte in the solution, /.e., the volume per 

 gramme-equivalent, of the region occupied by it, be indicated by V. 

 Similarly, 



Hence we liave 



(r/) from the condition of equilibrium, 



«Tj a. 2^ 



A second equation is obtained from the eqviulity of the volume of th& 

 solution to the sum of the volumes of the regions occupied by the elec- 

 trolytes it contains. Hence, since i\ = ]S\ Vj and v.^ = iV^ V.^, we have 

 (b) from the volume relation. 



Other two equations are furnished b}^ our knowledge that, at a definite 

 temperature, the ionisation coefficients depend upon dilution alone, and 



1 Ztschr. f. physikal. Cheniie, vol. ii., p. 284 (1888). 



