LAWS OF ELECTROLYTIC DISSOCL\TION 65 



It is easier to calculate it as the minimum of the inverse, 1/p, func- 

 tion as follows: 



1 ka kh , , 



p IH+J k„ 



and its derivative in respect to [H+] is: 



p ka kb 



. d [H+] [H+]2 k 



w 



by setting this derivative = we obtain the minimum of 1/p or the 

 maximum of p, which is 



= V^ 



[H+] for p-max. = \r^ k^ (1) 



The isoelectric point I is, therefore, that [H+] which is determined 

 by the equation 



= #^ 



ka 



r k^ (2) 



Kb 



It is characterized by the following properties: 



1. At its isoelectric point the sum of the anions and cations of an 



ampholyte in a given concentration is at a minimum. 



2. The concentration of the anions of an ampholyte at its iso- 



electric point is equal to that of the cations. 

 These conditions may be proved as follows (according to (1) 

 and (2), page 61): 



i 



'^ ' = IhT """^ '^ ' = 15ST 



By substituting for [H+] its value at the isoelectric point, 



-^ kw, and for [0H~] the corresponding value 

 kb 



k 



w 



^H-1 Ik . "Ik 



"■a 



kb 



• k. 



= V^: 



k 



W7 



