232 REDUCTION OF CARBON DIOXIDE CHAP. 9 



and is related to the single-step oxidation potentials Ei (semiquinone-hydroquinone) 

 and Ez (quinone-semiquinone) by the equation: 



(9.9) log Kd = 16.67 (El - E^) {t = 25° C.) 



If El = E2, Kd = 1; that is, when one-third of the compound is in the reduced state, 

 one-third is in the intermediate state and one-third in the oxidized state. If Ei < E^ 

 (i. e., the quinone is a stronger oxidizing agent than the semiquinone), Ki < 1, and 

 the equilibrium proportion of the semiquinone is more than one-third. If Ei > Et, 

 Kd > 1, and the maximum proportion of the semiquinone is less than one-third. 



The presence of a semiquinone can be observed by Michaelis' methods, if it forms 

 at least 10% of the total dyestuff. In this case, the dismutation constant, Kd must be 

 ^ 20 and the free energy of dismutation must be < '^ 1.8 kcal at room temperature. 

 In other words, whenever the presence of semiquinones is recognizable at equilibrium, 

 the difference between the free energies of the first and second reduction step is less than 

 2 kcal, instead of about 50 kcal as deduced above from the standard bond strengths. 



An explanation of the stability of semiquinones on the basis of the 



resonance theory has been attempted by Pauling and Wheland (1933) 



and Wheland (1940). who suggested that radicals are stabilized by a 



resonance made possible by the unsaturated valency. In the triphenyl 



methyl radical, for example, the structure usually assumed, PhsC is 



i 

 supplemented by a number of other "resonating" structures, including 



the o-quinonoid forms, Ph2C^<^ \—^ and the p-quinonoid forms, 



As mentioned before, the pairs, carbonate-formate, acetaldehyde- 

 acetic acid, etc. — do not form electrode-active oxidation-reduction 

 systems, probably because their "semiquinones" are not stabilized by 

 resonance; the association with oxidation-reduction enzymes may stabilize 

 these semiquinones and thus reduce the activation energy of the corre- 

 sponding reactions. 



To enable an oxidation-reduction to proceed smoothly at room 

 temperature, it is sufficient for the energy of the semiquinone to be not 

 larger than 10 kcal; this is compatible with a dismutation constant as 

 high as 10^. Thus, a practically negligible equilibrium concentration of 

 the semiquinone may be sufficient to bring about the desired catalytic 

 effect. 



The inclusion of free radicals enlarges the list of reversible oxidation- 

 reduction systems, in both directions, beyond the interval from — 0.4 

 to + 0.4 volt (at pH 7), which is covered by valence-saturated organic 

 compounds. Among "monovalent" organic systems, whose potentials 

 have been measured, we find, for example, the porphyrexide, with a 

 potential of — 0.73 volt at pH 7 (here, the oxidant is a free radical) and 



