220 REDUCTION OF CARBON DIOXIDE CHAP. 9 



By this combination of elementary processes, it is possible to achieve the hydro- 



genation of an oxidant even if the reductant is unable to donate hydrogen atoms, for 

 example: 



(9.4a) A + i S > i S«+ + A— 



(9.4b) A~ + 2 H+ > H2A 



(9.4c) 2 H2O > 2 H+ + 2 OH- 



(9.4d) i S«+ + 2 OH- > i H2SO4 + f H2O 



(9.4) A + i S + I H2O > H2A + I H2SO4 



Similarly, the oxidation of sulfite to sulfate can be brought about by the loss of two 

 electrons and addition of two hydroxyl ions. 



The transfer of hydroxyl radicals can be brought about by a transfer of electrons 

 and recombination with hydroxyl ions. The exchange of hydrogen atoms for hydroxyl 

 radicals (once postulated by Franck as the primary process in photosynthesis, cf. page 

 151) is equivalent to the simultaneous transfer of two electrons, combined with the 

 adjustment of acid-base equiUbria: 



(9.5a) AH + BOH > AH++ + BOH~ 



(9.5b) AH++ + OH- > AOH + H+ 



(9.5c) BOH— + H+ > BH + OH" 



(9.5) AH + BOH > BH + AOH 



The free energies of reduction, Usted in table 9.IV, are based on the conception 

 that reduction is a transfer of hydrogen atoms; in cases in which this transfer is coupled 

 with a change in acid di.ssociation (e. g. 14c, 15c, and 16e), the free energy change includes 

 a term corresponding to this dissociation, calculated for standard activity of the hydrogen 

 ions (z. e., for pH = 0). The oxidation-reduction potentials, on the other hand, are 

 based on the conception of reduction being primarily a transfer of electrons. If this 

 transfer is associated with the addition or loss of hydrogen ions (hydrogenation being 

 interpreted as a transfer of an equal number of electrons and H"*" ions), the normal 

 potentials are dependent on pH. Thus, the potential of a hydrogen electrode (H2/2 H+) 

 increases, at 25° C, by 0.60 volt for each pH unit, and is, in neutral solution (pH 7), 

 0.42 volt higher than at pH 0. The potentials of systems whose reduction consists in 

 the addition of hydrogen atoms (without binding or loss of H"*" ions) change with pH 

 in the same way as the potential of the hydrogen electrode. In table 9. IV, the Eo 

 values have been calculated from the free energies of hydrogenation by means of equation 

 (9.2), and the Eo' values of systems which do not change their acid dissociation upon 

 hydrogenation, by the addition of 0.42 volt to Eo. 



For systems whose hydrogenation involves a change in ionization, the oxidation- 

 reduction potentials increase more (or less) rapidly than the potential of the hydrogen 

 electrode. For example, the potential of system No. 16c increases at the rate of 0.03 

 volt per pH unit only (because one hydrogen ion is liberated upon reduction); while 

 the potentials of the systems carboxyl anion-carbonyl (14c and 15c, Table 9.IV) must 

 increase at the rate of 0.09 volt per pH unit, because one hydrogen ion is bound simul- 

 taneously with the addition of two hydrogen atoms. 



Since most tissues are approximately neutral, the best measure of 

 the oxidizing or reducing power of different agents in vivo is given by 

 their potentials at pH 7. Thus, we gain an adequate conception of the 

 thermodynamical difficulty of the reduction of carbon dioxide or of the 



