52 



HYDROGEN ION CONCENTRATION 



The dissociation-residue p is expressed according to the defini- 

 tion as 



and hence 



[HS] 



p = 



[HS] + [S- 

 [H+] 



= 1 - a 

 1 



k + [H+] k 



1 4- 



[H+] 



_ 10-PH 



'' ~ k + 10-pH 



6 



10 11 



(3) 



(3b) 



Fig. 4. Dissociation-resfdwe curve of an acid under same conditions as in 

 figure 3. It also represents the dissociation curve of a base whose dissociation 

 constant is k = 1 X 10"''. 



The graphic construction is best derived from the relationship 

 a = 1 — p, and it is at once perceived from figure 4 that the curve 

 is a mirror image of the a-curve, and that its parameter is exactly 

 the same. 



The mathematical analysis of these functions is as follows: 



Differentiating the function 



k + [H+] 



(1) 



with respect to log [H+] we obtain 

 da d 



d In [H+] 

 d log [H+] d [H+] '^ d In [H+] " d log [H+] 



a d [Hi 



