702 PHYSICAL CHEMISTRY OF THE PROTEINS. I 



if the protein be considered as a monovalent acid, giving rise to but one 

 hydrogen ion, and a monovalent base, giving rise to but one hydroxyl 

 ion. That the multivalent protein can under certain restricted cir- 

 cumstances be considered as uni-univalent we shall presently show. 

 The mass law equation defining the dissociation of the protein 

 as an acid may be written 



(H^) (POH-) ^ 



(HPOH) ^^ ^^' 



and as a base 



(HP+) (0H-) ^ (HP+) Kw _ ,., 



(HPOH) (H+) (HPOH) ^ ^ 



Equations (3) and (4) on multiplication yield an expression for the 

 dissociation of the pure ampholyte, or rather for the square of the 

 dissociation 



(HP+) (POH-) ^ Ka • Kb ,-. 



(HPOH) (HPOH) Kw ^ 



The method of deriving this equation involves the elimination of 

 the hydrogen ion concentration from both equations (3) and (4). 

 As a result the pure ampholyte can exist at only one hydrogen ion 

 concentration; namely, that at which the ampholyte dissociates to 

 form as many anions as cations. This point has been identified as 

 the point at which the migration of protein in an electric field changes 

 in direction; that is, as the so called isoelectric point. It has been 

 defined by Michaelis as the point at which 



(HP+) = (POH-) (6) 



and is determined by substituting in equation (6) the value of (POH") 

 in equation (3) and of (HP+) in equation (4). We then obtain 



Ka (HPOH) (H+)2 



Kb (HPOH) Kw 



(7) 



and if we assume that the undissociated protein molecule is the same 

 on both sides of the isoelectric point (30) we obtain 



Ka^(H^ (8) 



Kb Kw ^ 



* (H+) (0H-) = Kw 



