the Conductivity of Mixtures of Electrolytes. 279 



such restriction by employing a more general form of Arrhe- 

 nius's deduction. Two electrolytes having a common ion and 

 in a state of equilibrium in the same solution, may be regarded 

 as occupying definite portions of the volume of the solution. 

 If we apply the equilibrium conditions to the parts of the 

 solution occupied by the respective electrolytes as well as to 

 the whole solution, we obtain equations which, mutatis mu- 

 tandis, are identical with those obtained by Arrhenius for 

 isohydric solutions and their mixture, and which give a 

 similar result, viz., that for equilibrium the concentrations of 

 the ions of the respective electrolytes per unit volume of the 

 portion of the complex solution or mixture occupied by them 

 must be the same. 



With the aid of this result, we can find the ionisation- 

 coefficients of the constituents of a mixture. For if, in 

 addition to the symbols used above, v x and v 2 be taken to 

 represent the volumes of the portions of the mixture occupied 

 by the respective electrolytes, it gives us the equation 



c tinjih' __ a 2 n 2 v 2 ' 

 v x v 2 



We have also 



vi + «m=P(vi+v*) ; (2) 



and as the coefficients of ionisation are functions of the dilu- 

 tion only, at constant temperature, we have 



«*(*> ••■•■•■ w 



-MM <*' 



Of the quantities involved in these equations, n u n 2 , »/, vj 

 are known, and p may be determined by density measure- 

 ments before and after mixture. The form of the functions 

 in (3) and (4) maybe determined if measurements of the 

 conductivities of sufficiently extended series of simple solu- 

 tions of the constituent electrolytes are made. We have thus 

 four equations with but four unknown quantities. 



If we employ the symbol V to represent the dilution (v/nv 7 ), 

 we may write the above equations as follows : — 



rrv ■ ■ ■ ■ • • < l > 



