66 ROYAL SOCIETY OF CANADA 



cules undergo dissociation is equal to the frequency with which free 

 ions re-comhino. The amount of an electrolyte which is dissociated when 

 the equilibrium condition has been attained is, therefore, to be determined 

 by the application, of the law of chemical equilibrium, which expresses 

 the equality of the two frequencies just mentioned. 



As any electrolyte which is in dissociational equilibrium is to be 

 rcû^arded as being in this state not onlj' throughout the whole volume of 

 the solution, but also throughout any linite part of it, the law of equili- 

 brium may be applied to any such part. 



As each electi'olyte in a complex solution, with its undissociated and 

 dissociated parts, though disseminated throughout the whole volume, may 

 be regarded as occupying a deiinite portion of the volume, which we may 

 speak of as its region, the law of equilibrium may be applied either to 

 one such region or to the regions of two or more electrolytes which have 

 ions in common. 



We shall consider, tii-st, solutions containing electrolytes which have 

 all a common ion, and, next, the more complex cases of solutions contain- 

 ing two or more electrolytes having no common ion. 



Case I. — .Solutions containing Two Electrolytes avith a Common 



Ion. 



In such a case the two electrolytes added to the solvent, in preparing 

 the solution, are the only electrolytes present. The nunabers of gramme-, 

 equivalents (A^, and iV^) ^^ ^^Y giv'en volume of the solution are thus 

 known. Call the electrolytes 1 and 2, respectively. Let i„ b.^ be the 

 numbers of undissociated, and yS„ /J^ the numbers of dissociated gi-amme- 

 cquivalents of 1 and 2 in the given volume v of the solution, and let 

 Vy, i'2, be the volumes of the regions occupied b}^ them, respectively. 



Applying the law of equilibi'ium to electrolytes 1 and 2 throughout 

 their own regions, respectively, we obtain : 



V, V, V, 



(1) . . . . 



(2) . . . . .,A = ^ . Ê 



V, v., V, 



where c^ and ^^ arc constants. Applying the law throughout the whole 

 VMJuine. Ave have : 



(3) .... . 



' f, -f fo i'l -f- V.2 ' Vi + Vo 



CO . . . . c. 



b, ^, + A (-l: 



I' J + I' 2 '"l + '\' ■ '-"l + Oo 



