46 HYDROGEN ION CONCENTRATION 



The deviation from this approximate equation is more marked in 

 the case of a solution of a mixture of primary and secondary sodium 

 phosphates. If these salts be assumed to be totally dissociated, 

 then for a mixture of their solutions it would be expected that 



rTX4-i 1 [primary phosphate] 

 [H+] = k 



[secondary phosphate] 



But it is to be remembered that the secondary phosphate is the 

 Na-salt of the weak acid — "primary phosphate." If the above 

 expression were entirely correct, then the absolute concentration of 

 the phosphates would be immaterial. This is true to a certain 

 extent, but not in so strictly proportional a manner as in the case 

 of the acetate mixtures, for the degree of dissociation of dibasic 

 phosphate depends to a much greater extent upon the dilution. 

 Electrometric determinations of the [H+] of a mixture of equal 

 parts of M/15 K2HPO4 + M/15 NaH2P04 yielded the figures in 

 table 10.31 



14. The two-acids problem 



It is frequently desired to calculate the [H+] obtaining in a mix- 

 ture of two weak acids and of its alkali salts. This particular con- 

 dition was designated as the two-acids 'problem. ^^ A general solu- 

 tion of this problem is quite difficult and is barely to be found. But 

 since this problem has a practical bearing, as will be seen later, it 

 will be here detailed for certain simple conditions which should 

 suffice for the handling of any practical question which may arise. 



For this purpose the derivation given in the preceding section 

 will be modified, and we shall return once again to the mixture of a 

 weak acid and its alkali salt. Such a mixture may also be obtained 

 by mixing a weak acid of concentration A with a strong base of 

 concentration L, where L < A. In such mixture then the concen- 

 tration of the salt = L and that of the free acid in excess = A — L. 

 Then the equation (1) on page 44 may be transformed into 



[H+] = k ^^^ (la) 



Similarly a mixture of two acids and their salts may be thought of 

 31 L. Michaelis and A. Kriiger, Biochem. Zeitschr. 119, 307 (1921). 



