Variation of the heterogeneous electron-transfer rate constant with solution viscosity: reduction of aqueous solutions of [(EDTA)chromium(III)]- at a mercury electrode

The one-electron reduction of Cr"'(EDTA)at a mercury electrode was studied by an AC impedance technique in aqueous solutions of different viscosities (varied by addition of sucrose). The standard rate constant of the heterogeneous electron transfer, k",,, (corrected for diffuse double layer effects with experimentally measured parameters), showed a significant variation with solution viscosity. This viscosity dependence of k",, in the kinetically limited region was interpreted in terms of the dynamic properties of the solvent. A reasonable correlation between k",, and the solvent polarity term (nD-2 e; ' ) could be obtained only when the preexponential factor was allowed to vary inversely with solution viscosity. A variation of the rate constant for heterogeneous electron transfer (et) reactions ( k S ) with solution viscosity was reported by our laboratory for Fe(CN)63-/4in water and ferrocene0/+ in dimethyl sulfoxide, at a Pt electrode.' Although this dependence is not predicted by the classical description of et reaction at rates far from diffusion c ~ n t r o l , * ~ ~ more recent theoretical treatments (1) Zhang, X.; Leddy, J.; Bard, A. J. J . Am. Chem. SOC. 1985, 107,3719. (2) (a) Marcus, R. A. Annu. Rev. Phys. Chem. 1964, 15, 155. (b) Marcus, (3) Hush, N. S. Faraday Trans. 1961,57, 557. R. A. J . Chem. Phys. 1965, 43, 679. suggest this correlation by emphasizing the role of solvent dynamics in the et p r o ~ e s s e s . ~ , ~ , ~ ~ , ~ Generally, explicit studies of (4) (a) Calef, D. F.; Wolynes, P. G. J . Phys. Chem. 1983,87, 3387. (b) Calef, D. F.; Wolynes, P. G. J . Chem. Phys. 1983, 78, 470. (c) Fraunfelder, H.; Wolynes, P. Science 1985, 229, 337. (d) Zusman, L. D. J . Chem. Phys. 1980,49,295. (e ) Van der Zawn, G . ; Hynes, J. T. J . Chem. Phys. 1982,76 (6), 2993. (f) Van der a w n , G.; Hynes, J. T. J . Phys. Chem. 1985,89,4181. ( 5 ) (a) Newton, M. D.; Sutin, N. Annu. Rev. Phys. Chem. 1984, 35, 437. (b) Marcus, R. A.; Sumi, H. J . Chem. Phys. 1986, 84, 4894. (c) Marcus, R. A.; Sumi, H. J . Electroanal. Chem. 1986, 204, 59. (d) Marcus, R. A.; Sumi, H. J. Chem. Phys. 1986,84 (8), 4272. 0002-7863/87/1509-1916$01.50/0