306 PROPERTIES OF AMINO-ACIDS AND PEPTIDES 



ka (HAOH) = (H+) (AOH-) 

 h (HAiOH) = (0H-) (HAi+) 

 ka _ (H+) (AOH-) (HAiOH) 

 kb ~ (OH) (HAi+) (HAOH) 

 _ (H+)'' (AOH-) (HAiOH) 

 K (HAi+) (HAOH) 



(H+) = Jh u (HA.+) (HAOH) (2) 



J h "" (HAiOH) (AOH-) 

 (a) (b) {c) 



Equation (2) differs from equation (1) in containing the additional 

 terms {h) and (c) . For the two equations to give the same isoelectric 

 point in any given case either of the following relations must hold 

 (these are fundamentally the same with the terms arranged differ- 

 ently) . 



(HA+) (HAiOH) 



(AOH-) (HAOH) 



(HA,+) (AOH-) 



(HAiOH) + (HAi+) (HAOH) + (AOH") 



(3) 



(4) 



From equation (4) it is evident that the degrees of ionization of the 

 two molecular species are the same. This states nothing in regard to 

 the concentrations of the ions or of the molecular species from which 

 they are derived. Also, from equation (3), the ratio of the ampholyte 

 ion concentrations is equal to the ratio of the corresponding unionized 

 molecular species concentrations. That is to say, a greater ionic con- 

 centration of the ampholyte as acid species is accompanied by a greater 

 relative concentration of the corresponding unionized molecular spe- 

 cies. Obviously, also, equations (1) and (2) are identical if (HAi+) = 

 (AOH-) and (HAiOH) = (HAOH), the assumptions under which 

 equation (1) was deduced. 



Equations (1) and (2) do not give the same isoelectric point, if 

 the reciprocal of (c) is larger than (&), or the ionization as acid is 

 greater than as base. The product of {h) and (c) will then be less 

 than unity and the value obtained by means of equation (2) will be 

 less than that given by equation (1). The reverse relation holds 

 similarl3^ 



