650 



14. EFFECTS OF pH ON ENZYME INHIBITION 



EXPRESSIONS FOR THE pH-FUNCTIONS OF WEAK ACIDS 



AND BASES 



Some convenience and economy of presentation will be gained by express- 

 ing the pH dependence of the concentration of any species of a weak acid 

 or base in terms of a function. The concentration of the species will then be 

 related through this function to the total concentration of the substance. 

 The simplest case is when a single proton is involved in the dissociation: 



H + B 



HB 



K„ 



(14-1) 



where HB is the acid and B is the conjugate base. 



The charges that may exist on these species are intentionally omitted 

 in order to make the treatment more general. Thus the above equation could 

 represent either: 



H+ + B ^ HB+ 

 or: 



H+ + B~ ^ HB 



It is easy to show that the functions to be used will be the same in these 

 cases or in any others, the only requirement being that HB will have one 

 positive charge more than B. 



If the total concentration of the substance (acid + conjugate base) is 

 represented by (B,), the following expressions may be derived: 



(B,) 



-1 



(B) 



1 + 



(H) 



(HB) 



These may be rewritten simply as: 



(B,) =/,'(B) =A,'(HB) 



(14-2) 



(14-3) 



where f^' and f /^^ are functions relating the concentrations of B and HB 

 to the pH. 



When the dissociation of two protons is involved: 



H + B — HB 7C" 



H + HB ;:± H3 K,' 



the following expressions may be written: 



(B,) = 



K„" K„'K„" 



(B) 



(14-4) 

 (14-5) 



(14-6) 



