56 HYDROGEN ION CONCENTRATION 



The two dissociation constants are: 



[A-] [H+] 



[Ai [H+] 

 ko = 



[A-] 



From the above equations it follows: 



ai [A-] ^ ^ [A-] 



1 [A] IA-] 

 a, [A=] ^ [A=] ^ 



1 [A-] [A=] 



- = 1 + - — - + - — - 

 p ^ [A] ^ [A] 



and through elimination of [A], [A-] and [A=] we finally obtain :^^ 



1 



ai = 



a2 = 



^ kx ^ [H+] 



[H+] [H 



1 + -7-^ + 



ki • kj 



ki ki 



1 + 7^ + 



[H+] [H+] 



The curves shown in figures 5, 6 and 7 are graphic representations 

 of these functions having definite values for the two parameters, 

 ki and k2 and with the pH as the abscissa. The dissociation-residue 

 or p-curve is almost exactly identical with that of a monobasic acid, 

 and its deviations from the latter are so slight that they are not 

 noticeable. The primary dissociation curve, ai, shows the most 

 marked changes. It belongs to the same type as the p-curve of an 

 amphoteric electrolyte, which is to be discussed later, inasmuch as 

 it shows a maximum. Just as in the case of the ampholyte p-curve 

 the kind of the maximum formation of the curve depends upon the 



33 L. Michaelis, in: C. Oppenheimer, Handb. d. Biochem. Erganzungs- 

 band, p. 57 (1913). 



