62 HYDROGEN ION CONCENTRATION 



and 



[A] - [A+] - [A-] = [U] = [A] -K^- kb ^^ 



[H+] [0H-] 



From which follows 



[A] 



[U] = 



ka kh 



1 + 7TT7^ + 



[H+] [0H-] 

 and hence the sought value of p may be stated as 



[U] 1 





[A] 1 , ka , kb 



[H+] [OHi 

 substituting for [0H~] its value as j— ^ we obtain: 



" = — r^-T ® 



1 + J^ + ^ [H+] 

 ^ [H+] ^ k^ ^ ' 



In comparing the expression with that for ai in a dibasic acid 

 as given on page 56, we find them identical, if we only substitute 



in the latter ka for k2 and : — for ki. As in a previous instance (see 



Ivb 



page 54) the specific replaceability of an acid constant by 7— is 



ka 



equally valid. Also in respect to the formation of the maximum 



the p-curve corresponds to the ai-curve. All analytic loci of the 



ai curve hold good in this curve, if we substitute kb for k2 and — 



ka 



for ki. In the ai-curve the width of the maximum depended upon 

 the ki:k2 ratio, therefore in this case it is determined by the product 

 ka X kb. Figure 8 shows the course of various p-curves in which 

 the product ka X kb has different values, ka is assumed to be equal 

 to kb in these curves. When ka X kb is very small, about 10"^", 

 then the maximum elevation of the curve spreads over a very wide 

 stretch. When this product is larger, about 10"^^, then this eleva- 

 tion becomes smaller, the maximum point may be readily seen, 

 and its ordinate value is around 1. With a still greater increase 



