Volumes of Activation for Electron Transfer in Low-Spin/Low-Spin Cationic Couples in Aqueous Solution

Abstract

Volumes of reaction ΔVAg/AgCl (vs Ag/AgCl/4.0 mol L-1 KCl) and of activation ΔVel⧧ for the electrode reactions of the aqueous Co(azacapten)3+/2+, Ru(en)33+/2+, and Co(tacn)23+/2+ couples have been measured by high-pressure cyclic and AC voltammetry. For the low-spin/low-spin Co(azacapten)3+/2+ couple, ΔVel⧧ = −3.3 ± 0.4 cm3 mol-1, whereas high-pressure NMR measurements gave a volume of activation ΔVex⧧ for the self-exchange reaction of −6.5 ± 0.5 cm3 mol-1, in accordance with the “fifty-percent rule” (J. Am. Chem. Soc. 1997, 119, 7137) and with the prediction of an adaptation of the Marcus theory of intermolecular electron-transfer kinetics (Can. J. Chem. 1996, 74, 631). For the Ru(en)33+/2+ self-exchange reaction, ΔVex⧧ was estimated indirectly as −15.1 ± 1.7 cm3 mol-1 from the Co(phen)33+/Ru(en)32+ cross reaction (ΔV12⧧ = −12.9 ± 0.5 cm3 mol-1), for which the rate constant k12 was consistent with the Marcus cross relation. For the Fe(H2O)63+/Ru(en)32+ cross reaction (ΔV12⧧ = −18.3 ± 1.2 cm3 mol-1), k12 was slower than predicted from the Marcus cross relation, and consequently the estimated ΔVex⧧ for Ru(en)33+/2+ (−18.9 ± 2 cm3 mol-1) may be less reliable. For the Ru(en)33+/2+ electrode reaction, ΔVel⧧ = −7.5 ± 0.4 cm3 mol-1, again in accordance with the fifty-percent rule and, conversely, authenticating the estimated ΔVex⧧. The ΔVex⧧ estimates for Ru(en)33+/2+, however, are some 10 cm3 mol-1 more negative than can be accommodated by the adapted Marcus theory. For the low-spin/high-spin couple Co(tacn)23+/2+, ΔVel⧧ (−5.9 ± 0.9 cm3 mol-1) is intermediate between values expected for CoIII/II clathrochelates and low-spin/high-spin tris(bidentate) chelates, although ΔVAg/AgCl places this couple within the latter group.