26 II. METHODS OF INVESTIGATION 



groups: determination of dissociation constants of acidic and basic 

 groups and measurement of oxidation reduction potentials. Although 

 from a thermodynamic point of view these are closely related, it will 

 be convenient to discuss them separately. The former needs little 

 comment since it is familiar to most students; the latter will be 

 treated more extensively. 



7.1. Determination of Dissociation Constants 



7.1.1. Elementary Theory. To establish the nomenclature and 

 symbols to be used, the simple approximate theory of acidic and 

 basic dissociation is given. In practice, the use of more exact equa- 

 tions will frequently be necessary. For these, cf. 4^4.9 and 608. 



For an acid : 



[H+] + [A-] - [HA] 

 [H+] [A-] _ 



nnAT"^" 



If a is the fraction of acid dissociated: 



1 - a 



[H+] = K, 



a 

 Taking the logarithm of the reciprocal of each side: 



log^r— —r = log— - + log 



[H+] "K„ °l-a 



a 



p}I = pK, + \og- (1) 



1 — a 



When a = 0.5 {i.e., acid is half dissociated): 



7>H = pKa 

 Similarly for a base, if j3 is the fraction dissociated: 



p(OH) =pK, + log^-^ (2) 



It is now usual to express basic dissociation constants in terms of pH 

 instead of p(OH). We can therefore write: 



pU = U - pK, - log ^-^ (3) 



and when the base is half dissociated, pH = 14 — pK^. Then for both 

 acid and base, at half dissociation ;;H = pK, where for an acid pK. = pKa 

 and for a base pK = 14 — pKfj. 



