76 HYDROGEN ION CONCENTRATION 



root for X is obtained. On the other hand, when Q = 0, we obtain 

 X = Vkw, which means that a solution of an ampholyte in ivhick 

 ka = kb, has a neutral reaction in all concentrations. 

 Now let us write (VIII) in the form 



Q = R 



or, 



S 



it 



Since R is always positive, then x- > k^, when S is positive; 

 and x^ < kw when S is negative. But S is positive or negative 

 when ka > kb or ka < kb respectively. In other words: lohen 

 ka > kb the solution of the ampholyte is always acid, and when ka 

 < kb it is always alkaline. 



Equation (VII) solved for A becomes 



(..-.,)(.. + . i^ + ... I) 



A = -^ '-^ ■ ^^^ ^ (IX) 



Now, when ka > kb, and, therefore, according to the above 

 reasoning, also x- > kw, then both factors of the numerator are 

 positive, consequently the denominator must also be positive, i.e., 

 we must have 



X < 





which denotes that x is smaller than the [H+] at the isoelectric 

 point, or, that the [H+] of the solution must lie between the neutral 

 reaction and that of the isoelectric point. Indeed, with decreasing 

 concentrations of the electrolyte x approaches the neutral reaction, 

 while it approaches the isoelectric point with increasing concentra- 

 tions. 

 By writing equation (IX) in the form 



(.- 



V kw \ / A \ / , , ^w , kwka 



X + V kw ) I x2 + X \- 



■ _ _v -^ / \ ^_j^ kb kb 



'^w'^a . 



— X^ 



kb 



