[macgregor] conductivity OF ELECTROLYTES 69 



Case II. — Solutions containing any number of Electrolytes 

 HAVING A Common Ion. 



In this case also the electrolytes added to the solvent in the j^repar- 

 ation of the solution are the only ones present in it, and the N's are 

 thus known. We may indicate the electrolytes in the solution by the 

 numerals 1, 2. ... . p. 



Applying the law of equilibrium to the dilterent electrolytes through- 

 out the regions occupied by themselves only, and using the same symbols 

 as above, we obtain a set of equations similar to (1) and (2) of Case I. 

 Applying the law to the various electi'olytes throughout the regions occu- 

 pied by themselves and one other electrolyte, we obtain a set of equations 

 similar to (3) and (4) of Case I. Combining these equations, as in that 

 case, we find that they reduce to 



Vl VO l\ • • • . y^- 



If we now ap])ly the law to each electrolyte throughout the region occu- 

 pied by it and two other electrolytes, we obtain a series of equations, 

 such as 



,^ ^^1 ^ /^i + fti + A A 



^^ i\+ v-i + t-, Vi -f r. + ^3 ■ i\ + To + ^s' 



These equations, however, are not indejjendent of those already obtained. 

 For from (1) and (5) we have 



Hence 



A 



r, + Vo + ^^3 Vj + Vo + Vs ■ t'l + V2 + V. 



Similarly the equations obtained by ajîplying the law to the various elec- 

 trolytes throughout the regions occupied by themselves and other three, 

 four, etc., electrolytes, may be deduced from such equations as those 

 given above. Hence the sole condition of equilibrium is expressed in 

 equations (5). 



For the determination of the coefficients of ionisation we have thus : 

 (rt) from the conditions of equilibrium, 



— ^ = -j^ = ■ . . = :^ V — 1 equations. 



( l>) from the volume relation, 



iVi Fi + j\^2 "^2 + . . . -{- NpVp = V . . , . 1 equation, 



