Downloaded by UNIV OF NEBRASKA-LINCOLN on September 14, 2015 | http://pubs.acs.org Publication Date: June 1, 1984 | doi: 10.1021/ja00324a028
J . Am. Chem. SOC.1984, 106, 3577-3584 hexamethylbenzene-d18 were the same to within the experimental uncertainties. Electron Spin Resonance Studies of Arene Cation Radicals as Intermediates. The direct observation of arene cation radicals as intermediates in the oxidative substitutions with iron(II1) was carried out as follows. Separate trifluoroacetic acid solutions of 6.3 mM hexamethylbenzeneand Fe(phen)3(PF6)3(prepared from 11 mg of complex and 2.0 mL of solvent by heating over a steam bath until complete dissolution) were added to an ESR tube with a side arm affixed. The tube was sealed in vacuo, and the contents were mixed by rapid shaking immediately prior to insertion in the ESR cavity (Varian E-112). The concentration of HMB’. was followed periodically by monitoring the intensity of the M,= 0 line. The dashed line in Figure 1 indicates that 15-20 s were required to obtain the first data point. Since the disappearance of the cation radical was temperature dependent, the ESR spectrum shown in the inset was obtained from a similar reaction which was cooled to -30 OC prior to mixing. Evaluation of the Free Energy Terms. The free energy change AG,,‘ was determined from the standard oxidation potentials in Table I according to eq 20. The work term wp was considered to be only of electrostatic origin, Le., wp = 2 e2/Dd*as given in ref 45. The activation free energy AG*was evaluated from the rate constant k’ listed in Table I11 and eq 21, where w, z 0 and the collision frequency was taken to be 10” M-l s-l. The value of k* was deduced from k, by taking into account the diffusional contributions according to eq 17.36 For rapid oxidative substitutions, the effect of diffusion on k , is small, but increases in importance for the slowest rates, as shown in Table VII. The intrinsic barriers were computed from the values of AG,,’ and AG’ for each system, with the aid of the free energy relationship in eq 22-24. For each methylarene, the three values of AGO’ (obtained with the three iron(II1) oxidants) were averaged for construction of Figure 6. Derivation of the Kinetic Rate Expressions. The kinetics were based on the stoichiometry in eq 6 and the mechanism presented in Scheme I1 for the general case in which back electron transfer (k1) competes with the followup step ( k 3 ) . All derivatives assumed a zero order dependence on arene (Ar) in excess, and a negligible consumption of the pyridine base. The rate of iron(II1) disappearance (taking into account the steady state concentration of ArCH2.) is
-d[Fe(III)] / 2 dt = k,[Fe(III)] [Ar] - k-, [Fe(II)] [Art.]
3577 (30)
Since at steady state, [Ar’.] = kl[Fe(III)][Ar]/(k_l[Fe(II)]+ k3[py]), eq 30 reduces to -d[Fe(III)]/dt = 2kI[Fe(III)1[ArlKl - k-l[Fe(II)l/k-l[Fe(II)l + k,[pyl)l (31) For [Fe(II)] = [Fe(III)lo- [Fe(III)] and x = [Fe(III)]/[Fe(III)]o,eq 31 is simplified to (-dx/x)(l - x + k 2 [ ~ ~ l / ( k - l [ F e ( I I I ) 1=~ ) ) (2kl[Ar1k3[pyl/ ( k - l [ W W l ~ ) )dl (32) Integration of eq 32 between the limits o f t = 0 (x = 1) and t(x) yields (1 + p)ln x + p ( 1 - x) = -2k,[Ar]t (33) where P = k - l [ F e ( I I I ) l ~ / ( k ~ [ ~ ~ l ) . Two limiting situations derive from eq 33, that is, p = 0 and p >> 1, which describe rate-limiting electron transfer (eq 14) and pre-equilibrium electron transfer (eq 12), respectively. The same results are obtained in the latter case, if [Ar’.] is assumed to attain equilibrium rapidly, Le., k l / k - l = [Ar’.][Fe(II)]/([Fe(III)] [Ar]). Note that the previously measured rate constants’2edid not take into account the reversibility in the electron transfer. Correction of this factor, however, does not fundamentally affect the conclusions presented therein.
Acknowledgment. W e thank the National Science Foundation for financial support of this research and for a fellowship to C.A. under the auspices of the United States-France (NSF-CNRS) cooperative program, Dr. W . Lau for help with the ESR experiments, and J. Goncalves for the computer interface of the spectral data. Registry No. ( ~ h e n ) ~ F e14708-99-7; ~+, (5-Cl(phen))3FeZ+,15053-59-5; (5-N02(phen))3FeZ+, 15245-50-8; (phen),Fe3+.(PF6)
