LAWS OF ELECTROLYTIC DISSOCIATION 47 



as being produced by mixing the two acids, whose dissociation con- 

 stants are ki and k2 and whose concentrations are Ai and A2 respec- 

 tively, with a base whose total concentration is L, where L < (Ai 

 + A2) . Of this amount of base a part Li is bound by the first acid 

 and a part L2 by the second, in such a manner that 



Li + L2 = L (lb) 



In accord with the mass law: 



[H+] = k, ^^^ (Ic) 



[H-] = k. ^^^ (Id) 



L2 



It is now necessary to recollect that equations (1) as well as 

 (la) are only approximations and may be only applied when the 

 second fractional factor on the right side has a value lying between 

 0.01 and 100. In further calculations the conditions under which 

 they are applicable will always be borne in mind. If now in (Ic) 

 we take Li = L — L2 and eliminate L2 by means of (Id) a quad- 

 ratic equation for [H+] is obtained which is capable of solution only 

 in a physical sense: 



, = ki(Ai - L) + k2(A - L) 

 2L 



frMAi^ 



^,, L) + k2(A2 - L) 



2L 



2 kl • k2 



+ —I— (Ai + A2 - L) (le) 



The problem under consideration has the following useful prac- 

 tical application. In the determination of [H+] by indicator methods 

 we add to the given solution some indicator, which is an acid, 

 and we tacitly assume that this addition of acid does not alter the 

 [H+] of our solution. The solution in question is as a rule of the 

 nature of a single acid buffer, such as, for example, a mixture of 

 NaHCOs + H2CO3. Let us carry out the calculation for a most 

 extreme case. Let the solution in question be extremely poor in 

 buffer value, such as ordinary water + conductivity water. Such a 

 solution may be obtained by mixing 0.00300 A'' calcium bicarbonate 

 (NaHCOs will do as well) and 0.00030 A^ H2CO3. In this case L 



