58 DONALD D. VAN SLYKE 



2. A given buffer is most efficient in maintaining constancy of pll 

 (that is, in minimizing the proportion by which H + is changed by a given 



HA 



addition of acid or alkali) when the ratio approximates 1, and 



HB 



H + equals K, the dissociation constant of the free acid forming one of the 

 buffer pair. 



The theoretical demonstration of these two laws is the following: 



1. Relationship between pH and the ratio HA (or free buffer acid). 



BA buffer salt 



This relationship is derived as follows: 



Since the reaction of electrolytic dissociation of an acid into H + and 

 anion is HA = H + -{- A', it follows from the law of mass action that, at 

 equilibrium, 



1) K XHA = H + + A', 



K being the dissociation constant of the acid. Hence 



2) H+ == K X HA 

 "A 7 " 



But when the buffer mixture is the salt of a very weak acid plus some 

 free acid, only an infinitesimal part of the anion, A', originates from 

 dissociation of the free acid (H 2 CO 3 in the concentration present in 

 the blood, for example, is dissociated into H + and HCO 3 ' only to the 

 extent of about 1/10,000). Essentially all of the anion originates from 

 dissociation of the salt, BA, into B* and A'. Most salts in 0.1 to 0.01 

 molecular concentration undergo such dissociation to the extent of 60 to 90 

 per cent of the amount present. If the degree of dissociation be repre- 

 sented by A, the concentration of an ions is A' = ABA, and Equation 2 

 may be written 



- HA 



Since A varies to a relatively slight extent over ranges of concentration 

 within such limits as are found in blood constituents, one may state as a 



-rr 



close approximation that -r- = K a and 

 * A 



In terms of pH, since pH = log II +, Equation 4 is 



HA 



5) pH = log K! log^-r, or 



6) pH == 



BA' 

 BA 



