12 OXIDATION-REDUCTION POTENTIALS 



with systems of unknown properties, to avoid the use of the term rH on account of 

 its spurious effect of apparent simplicity. 



With reversible oxidation-reduction systems of the simple type : — 



oxidation 



(35) Eed ©^==^ Ox. + e 



the E^ varies by 0-06 volt per unit pH, that is the Ej, — pH curve is said to have 

 0-06 slope (at 30°C.). In such a system as 



(36) Ked.e© ^ Ox. + 2e 



the variation per unit pH can be 0-03, 0-06 or 0-09 volt. These facts apply only 

 to ideal systems when hydration may be neglected. The variation of E^ with pH 

 occurs only in those ranges of pH in which the dissociation constants are effective, 

 and the systematic study of all the possible cases is outside the scope of this intro- 

 ductory treatment. A very complete study is reported by Clark and Cohen (1923). 



It is shown above that in the simplest case at 30°C. (equation 31) : — 



Eh = 0-03 (rH - 2pH) 



where rH is log ^ (P being the partial pressure of hydrogen in equilibrium with the 



system). With the hydrogen electrode P = 1 atm. so that rH = at any pH. 

 The E^ : pH curve is the lowest one in fig. 1, and shows the electrode potential of 

 an oxidation-reduction system in equilibrium with 1 atmosphere partial pressure 

 of hydrogen. When the partial pressure of hydrogen is 10 ~^" atmosphere, this 

 rH is 10, and the E^ : pH curve runs parallel with that of the hydrogen electrode, 

 and similarly when P = lO"^'' atmospheres, rH = 20. Also included in the figure 

 are the experimentally obtained curves of the methylene blue system at 50 per cent, 

 reduction {i.e., the EJ, : pH curve) and of the indigo-carmine system at 50 per cent, 

 reduction. 



Theoretically, curves can be drawn showing the ^^ : pH relationships at various 

 levels of oxygen partial pressure, or rO ; but as the true oxygen electrode is not 

 capable of experimental realisation (Richards, 1928), and the oxygen tensions en- 

 countered in biological systems, as judged from the potentials, are frequently of the 

 order of 10-**^ atmospheres or less, little advantage accrues from such considerations. 

 Goard and Rideal (1924) and Hoar (1933) are of interest in this connection. 



CONSIDERATIONS OF CHEMICAL AFFINITY 



Considerations of chemical affinity lead to the same general electrode equation 

 as that derived previously (Michaelis, 1933). This treatment is of interest as it 

 presents a slightly different aspect of oxidation-reduction processes although leading 

 to the same general conclusion. 



To return to the ferrous-ferric ion equilibrium : — 



Oxidation 



Fe®® — ==^ Ye®®® + e 

 reduction 



