Self-exchange electron-transfer reaction relationship

The relationship between the rate constants kei for an electrode reaction and fee for the corresponding self-exchange electron transfer reaction is not obvious because kgi can be strongly influenced by the nature and history of the electrode surface and by solvent dynamic effects if present. Electrode properties, however, are not expected to be sensitive to pressures in the 0-200 MPa range. Moreover, the signature of solvent dynamical effects is a dependence of reaction rate on solvent viscosity, but the viscosity of water is effectively independent of such pressures at near-ambient temperatures. Consequently, for typical aqueous electrode reactions, Ai/, = O.SAV, regardless of any involvement of solvent dynamics, and so AVg can be predicted from transition state theory (TST) according to Eqs (5.5)-... 

Another useful linear relationship is based on electrochemical data and is obtained by recourse to the fact that AG° = —nFE°. For a series of outer-sphere electron transfer reactions that meet the criteria discussed in context with Equation 1.14, a plot of In k versus E° will have a slope of 0.5(nF/RT), and a plot of log k versus E° will have a slope of 0.5(nF)/2.303RTor 8.5 V-1 for n = 1 at 25°C.5 All the above methods can be used to obtain a common (approximate) value of X for a series of similar reactions. For single reactions of interest, however, X values can often be measured directly by electron self-exchange. 

The kinetics of several electron transfer reactions of the molybdenum cuboidal system [Mo4S4(edta)2]" ( = 2, 3, 4) with cross-reactants such as [Co(edta)]-, [Fe(edta)]-, [Co(dipic)2] , [Fe(H20)e], and [Pta ] -, have been investigated. The electron self-exchange rate constants determined for the [Mo4S4(edta)2] and [Mo4S4(edta)2] couples, by an application of the Marcus relationship, are 1.5 x 10 and 7.7 x 10 M s , respectively. The rate constants for the outer-sphere oxidation of two dimeric complexes, [MoW 0)2(p-edta-AT,lV )]2- and [W2(0)2(p-0)(p-S)(p-edta-Ar,iV )] -, by [IrCl ] in addic aqueous solution have been measured. While the oxidation of the former complex shows a simple second-order rate law, the kinetics of the oxidation of the latter complex exhibited a rate retardation in the presence of the [IrCl6] complex. 

Thus the Marcus theory gives rise to a free energy relationship of a type similar to those commonly used in physical organic chemistry. It can be transformed into other relationships (see below) which can easily be subjected to experimental tests. Foremost among these are the remarkably simple relationships that were developed (Marcus, 1963) for what have been denoted cross reactions. All non-bonded electron-transfer processes between two different species can actually be formulated as cross reactions of two self-exchange reactions. Thus the cross reaction of (59) and (60) is (61), and, neglecting a small electrostatic effect, the relationship between kn, k22 and kl2... 

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