THERMODYNAMICS OF FREE RADICALS 231 



liberate 29 kcal, corresponding to an Eo value of about + 1.3 volt, and 

 an Eo' value as high as + 1.7 volt. 



In the two-step hydrogenation of C=C to — CH — CH — , or of 



I ! 



— C=0 to — CHOH, the first step — the formation of a free radical — 

 should consume 16 and 25 kcal, respectively, while the second step should 

 liberate 46 kcal (the sums of the two steps being — 30 and — 17 kcal, 

 respectively; cf. page 217). These estimates, derived from standard 

 bond strengths, may be approximately correct for simple radicals whose 

 energies are not strongly affected by resonance; but may be far off the 

 mark for radicals of a more complex structure. 



The general tendency in reaction kinetics is to resolve chemical 

 reactions into steps involving the transfer of only one simple particle 

 (electron, proton, or hydrogen atom). Michaelis suggested that hydro- 

 genations and dehydrogenations of organic compounds take place in 

 single steps, with one hydrogen atom (or one electron) transferred at a 

 time. This mechanism would be impossible (except at high tempera- 

 tures) if free radicals had the high energies calculated from standard 

 bond strengths. Probably, prohibitively high energies of radicals derived 

 from simple organic molecules (e. g., 0=C — OH or HO — CHOH) are 



i i 



the reason why the corresponding saturated molecules (e. g., CO2 or 

 H2CO2) cannot be reduced or oxidized reversibly at an electrode with an 

 appropriately adjusted potential. 



Reversible oxidation-reduction systems, on the other hand, have been 

 found to form comparatively stable free radicals, whose occurrence can 

 be proved by kinetic observations (two color changes, and transitory 

 paramagnetism during oxidation), as well as by equilibrium measure- 

 ments (analysis of the potentiometric titration curves). 



The formation of free radicals in oxidation-reduction processes was discovered in 

 1931 by Friedheim and Michaelis, and by Elema, working with the same bacterial 

 dyestuflf, pyocyanine. Further investigations, mainly by Michaelis and coworkers (for 

 reviews see Michaelis 1935, 1938, 1940; Michaelis and Schubert 1938) led to the reahza- 

 tion that most, perhaps all, organic systems, both synthetic and natural, capable of 

 (kinetically) reversible oxidation-reduction, form comparatively stable intermediate 

 radicals, called semiquinones. 



The equiUbrium concentration of a semiquinone depends on its constant of dismu- 

 tation Kdi 



(9.8) 2 HR (semiquinone) > R (quinone) + H2R (hydroquinone) 



(9 9) K, = t^^J ^H.R] 



If the free energy of dismutation is AFa, the constant of dismutation is: 

 (9.10) log Kd = - AFd/2.3 RT 



