8 OXIDATIOX-REDUCTIOX POTENTIAL 



EFFECT OF pH 



Up to this point we have considered systems of constant pH, but when the 

 hydrogen ion concentration is allowed to vary a further complication arises, and it 

 is necessary to take into account ionisation phenomena. In those reversible 

 oxidation-reduction systems, which are characterised by electron transference, either 

 the reduced or oxidised form, or both, are ionised. The hydrogen ion concentration 

 affects oxidation-reduction systems by altering ionic equilibria. 



Let us consider the simple case in which the oxidised form is un-ionised but the 

 reduced form is an anion with one negative charge. The oxidation-reduction reaction 

 may be represented as : — 



(12) R© ^ Ox. + e 



The general electrode equation (10) may be applied to this equilibrium : — 



(13) L, - L, + ^ In j^ 



The reduced form is ionised in accordance with the formula : — 



(14) HR ^ H® + R© 

 to which the usual mass action equation may be applied : — 



[H©] [RQ] 

 [HR] 



The total concentration of reduced form ([Red.]) will be equal to the sum of the 

 concentrations of the ionised ([R©]) and un-ionised ([HR]) portions, i.e. — 



(16) [Red.] = [R0] + [HR] 

 Combining equations (15) and (16) we obtain : — 



(17) [R©] = [Red.] ^^'' 



(15) '^^ri^' = K 



[H®] + k, 

 and substituting this value in the electrode equation (13) we find 



(18) K-K + ^Um-¥^n '' 



F '" [Red.] F [H®] + k^ 



which is the general electrode equation holding at all values of pH. It will be seen 

 that the electrode potential depends on the hydrogen ion concentration and the 

 dissociation constant of the reduced form. If both the reduced form and oxidised 

 form are ionised, and form polyvalent ions, the expression becomes very complicated.* 

 It is impossible therefore to formulate a general rule as to the effect of pH on electrode 

 potential, the effect of alteration of hydrogen ion concentration being different in 

 different ranges of pH {cf. Clark and Cohen, 1923, 1). With systems that have not 

 been exhaustively studied it is necessary therefore to quote results in terms of 

 E^ and pH. 



The fact that the effect of pH on E^ is complex does not imply that the effect 

 is necessarily great. To take a hypothetical example, consider a biological system 

 in which the E^ : pH curve has "0-03 slope " (a very usual value) in the range 



* Ionic concentrations are referred to throughout although, more accurately, ionic activities should 

 be considered in accordance with modern views. This has been done in order to assist lucidity by the 

 avoidance of more complicated symbols and expressions which confuse the issue without any propor- 

 tionate advantage accruing save that of emphasising the complex relationship between Et and pH. 



