72 ROYAL SOCIETY OF CANADA 



and these three, Avhen combined, reduce to 



It is, therefore, also a necessary condition of equilibrium that the pro- 

 ducts of the numbers of the dissociated gramme-equivalents of the two 

 pairs of electrolytes having no common ion, shall be equal. 

 This condition may be otherwise expressed. For, by (7), 



Hence, 



(9) . . . . rii-2 = v,v, ; 



i.e., for equilibrium, the products of the volumes of the regions occupied 

 by the two pairs of electrolytes having no common ion, must be equal. 

 In the case of a solution containing two electrolytes with no common 

 ion thei'e are, therefore, four necessary conditions of equilibrium, ex- 

 pressed in equations (7) and (!:i). 



Arrhenius^ has shown that if a solution containing two electrolytes 

 with no common ion have been prepared as a mixture of four simple 

 solutions of these electrolytes and of the products of their double decom- 

 position, if the simple solutions before mixture had equal concenti'ations 

 of ions, had such volumes that the products of the volumes of the solu- 

 tions containing electrolytes with no common ion were equal, and were 

 so dilute that no change of volume occurs on mixing, and if no change 

 occur in the state of dissociation on mixing, the mixture will satisfy the 

 conditions of the equilibrium. 



For the determination of the coefficients of ionisation and the num- 

 bers of gramme-equivalents of the four electrolytes in any volume v of 

 the solution, we have, therefore, the following equations: 

 (rt) from the conditions of equilibrium. 



3 equations ; 



N^V^ • . . . 1 equation ; 



(6) from the volume relalion. 



Nx \\ + No V2 + N, V, + N, V, = . . . . I equation ; 

 (r) from the relation of ionisation to dilution, 



'Y = f\ i^i)- I 4 equations. 



etc.. ) 



Although in this case we do nrrt, know the values of ^Vj. N2, iVj, j^\, wo 

 <lo know the numbers of gramme-e([uivalcnts of 1 and 2 added to volume 



'^ 



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



