SOLUTIONS. MACGREGOR. 73 



for electrolyte 2. Thus any one of the quantities a lt a 2 , and 

 the common regional ionic concentration, which is of course 

 equal to the total ionic concentration of the whole solution, 

 being given, the others may be found, if we have sufficient data 

 as to the conductivity of the simple solutions. 



Even if the ratio only of the ionization coefficients is given, 

 the state of ionization is in many cases completely determined. 

 For as 



fi ^_ 

 V ~ V ' 



1 > 2 



we have * = l - t 



a 2 V 2 



and the dilution-ionic-concentration curves are frequently of 

 such forms that a given value of Vj/V^ corresponds to a definite 

 value of \ T ! and V 2 , which may be found by inspection of the 

 curves. 



Some datum in addition to the state of ionization is there- 

 fore requisite, if the concentration of the solution is to be fully 

 determined. It may be the concentration with respect to one 

 of the electrolytes, or the ratio of the concentrations with 

 respect to the two, or the total concentration, or any such func- 

 tion (the conductivity for example) of the concentrations with 

 respect to the two. If the state of ionization is not fully given, 

 an additional datum is obviously required. 



(1.) Given the required state of ionization and the concen- 

 tration with respect to one electrolyte : to find the concentration 

 with respect to the other. A and B (Fig. 3) being the dilution- 

 ionic-concentration curves, OY is given; and N t being also 

 given, we have only to find N 2 /N t in order to determine N 2 . 

 From Y draw YT parallel to the dilution-axis, cutting A and 

 B in X and U respectively. Draw the line R S parallel to the 

 axis of ionic concentrations and distant from it by l/(2 N t ). Let 

 R S cut Y T in W. Cut off W T equal to X \V. Then T Y/UY 

 will be the value of N^N^ (The curve E in Fig. 3 is of course 

 not required.) 



(2.) Given the required state of ionization and the ratio of 



