72 IONIZATION OF COMPLEX 



dilutions, of which the intercept T X, between the curves A and 

 E, is bisected by R S, W being the point of bi-section. Let T Y 

 cut B in U. X and U are the points required. For they have 

 the same abscissa Y, and their ordinates, X Y and U Y, are 

 such that 



XY +-^ 2 UY= 2WY = 



N! ]N 1 



Then o t = OY. XY, and a 2 = OY. U Y. 



The second and third of these methods involve less arith- 

 metical work, and are less liable to error, than the first, and the 

 second does not require the procedure by inspection which is 

 required by the third. The second is therefore the most satis- 

 factory. But the limited area of co-ordinate paper frequently 

 gives the third a practical advantage. 



Only such portions of the curves A, B, C,D, E, need be drawn 

 of course as may be seen by inspection to be required for the 

 purpose in hand. 



Determination of Ihe concentration, when the required 

 ionization is given. 



The determination of the concentration which must be given 

 a complex solution in order that it may have any required state 

 of ionization, is of importance as facilitating the conducting 

 of research based on the dissociation theory of electrolysis. 



It is not sufficient for the determination of the concentra- 

 tion which the solution must have with respect to the two 

 electrolytes, that the required ionization coefficients a l and a a 

 should be given, because they are not independent. For a given 

 value of a l the regional ionic concentration of electrolyte 1 has 

 a determinate value, which may be found by plotting a curve 

 for simple solutions of 1, with ionization coefficients as ordinates 

 and ionic concentrations as abscissae. The regional ionic con- 

 centration of electrolyte 2, must by equation v l) be the same as 

 that of electrolyte 1 ; and since it is thus determined, the ioniza- 

 tion coefficient, a 2 , can have but one value which may be found 

 by the aid of an ionization-coefficient-ionic-concentration curve 



