Self-exchange electron-transfer reaction rate constants

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)-... 

The rate constants from electron transfer reactions in which reactant and products are chemically indistinguishable, self-exchange electron transfer reactions. 

The self-exchange electron-transfer (SEET) process, in which a radical is trapped by the parent molecule, has been studied using the intersecting-state model (ISM).91 Absolute rate constants of SEET for a number organic molecules from ISM show a significant improvement over classical Marcus theory92-94 in the ability to predict experimental SEET values. A combination of Marcus theory and the Rips and Jortner approach was applied to the estimation of the amount of charge transferred in the intramolecular ET reactions of isodisubstituted aromatic compounds.95... 

The rate constants (kex) of the electron exchange reactions between ZnTPP+ and ZnTPP [Eq. (1)] were determined using Eq. (2), where AHms( and AH°msi are the maximum slope linewidths of the ESR spectra in the presence and absence of ZnTPP+, respectively, and P, is a statistical factor [14]. From the linear plots of (AHmsi - Afi°msl) and [ZnTPP] at various temperatures are obtained the self-exchange electron-transfer rate constant (k ). The Arrhenius plots are shown in Fig. 13.3 together with the observed activation enthalpies (AHols ), where the effect of diffusion (kdiff) is taken into account. The AHol/ values are all positive and decrease in order toluene > MeCN > CH2C12 [16],... 

Here, i is the faradaic current, n is the number of electrons transferred per molecule, F is the Faraday constant, A is the electrode surface area, k is the rate constant, and Cr is the bulk concentration of the reactant in units of mol cm-3. In general, the rate constant depends on the applied potential, and an important parameter is ke, the standard rate constant (more typically designated as k°), which is the forward rate constant when the applied potential equals the formal potential. Since there is zero driving force at the formal potential, the standard rate constant is analogous to the self-exchange rate constant of a homogeneous electron-transfer reaction. 

A values have been obtained for oxidation of benzenediols by [Fe(bipy)(CN)4], including the effect of pH, i.e., of protonation of the iron(III) complex, and the kinetics of [Fe(phen)(CN)4] oxidation of catechol and of 4-butylcatechol reported. Redox potentials of [Fe(bipy)2(CFQ7] and of [Fe(bipy)(CN)4] are available. The self-exchange rate constant for [Fe(phen)2(CN)2] has been estimated from kinetic data for electron transfer reactions involving, inter alios, catechol and hydroquinone as 2.8 2.5 x 10 dm moF s (in dimethyl sulfoxide). 

The efficiency of electron-transfer reduction of Cgo can be expressed by the selfexchange rates between Coo and the radical anion (Ceo ), which is the most fundamental property of electron-transfer reactions in solution. In fact, an electrochemical study on Ceo has indicated that the electron transfer of Ceo is fast, as one would expect for a large spherical reactant. This conclusion is based on the electroreduction kinetics of Ceo in a benzonitrile solution of tetrabutylammonium perchlorate at ultramicroelectrodes by applying the ac admittance technique [29]. The reported standard rate constant for the electroreduction of Ceo (0.3 cm s ) is comparable with that known for the ferricenium ion (0.2 cm s l) [22], whereas the self-exchange rate constant of ferrocene in acetonitrile is reported as 5.3 x 10 s , far smaller than the diffusion limit [30, 31]. 

Given the importance and great variety of electron-transfer reactions of polypyridine complexes, systematic kinetic studies are surprisingly scarce and only few kinetic data are available. Some representative rate constant values for homogeneous self-exchange redox reactions were reported ... 

Rate constants for outer-sphere electron transfer reactions that involve net changes in Gibbs free energy can be calculated using the Marcus cross-relation (Equations 1.24—1.26). It is referred to as a cross-relation because it is derived from expressions for two different self-exchange reactions. 

Nuclear tunneling is potentially a significant consideration in outer-sphere radical electron transfer reactions. The case of reduction of NO2 to NO2 is notable in that nuclear tunneling is predicted to increase the self-exchange rate constant by a factor of 79 relative to the classical value.75 Kinetic isotope effect measurements could provide experimental evidence for nuclear tunneling. 180/160 KIE measurements have indeed provided evidence for nuclear tunneling in reactions involving the O2/O2 redox couple.76... 

This relation has been used to predict and interpret both self-exchange and crossreaction rates (or even "12), depending on which of the quantities have been measured experimentally. Alternatively, one could study a series of closely related electron-transfer reactions (to maintain a nearly constant X12) as a function of AG 2 a plot of In ki2 vs. In A 12 is predicted to be linear, with slope 0.5 and intercept 0.5 In ( 11 22)- The Marcus prediction (for the normal free-energy region) amounts to a linear free-energy relation (LFER) for outer-sphere electron transfer. 

It has been shown that, by adding the macrocycUc ligand 18-crown-6 or cr5q>t-[222] to complex the K" " ions (see Figure 10.8), the K -catalysed pathway is replaced by a cation-independent mechanism. The rate constant that is often quoted for the [Fe(CN)g] /[Fe(CN)5] self-exchange reaction is of the order of lO dm moP s , whereas the value of k determined for the cation-independent pathway is 2.4 X lO dm moP s , i.e. sslOO times smaller. This significant result indicates that caution is needed in the interpretation of rate constant data for electron-transfer reactions between complex anions. 

Much of our earlier work on pressure effects on the kinetics of electron transfer reactions focused upon the rate constants kex and corresponding volume of activation for self-exchange reactions... 

The Marcus analysis of the rate constants for electron transfer reactions of the [Ni((-)-(R)-Me[9]aneN3)2] couple with nickel and cobalt complexes yields a self-exchange rate constant of 1.2 x 10" The oxidations of... 

One aspect of the problems encountered in the description of outer-sphere electron transfer reactions within the Marcus formalism is that the self-exchange rate of Eu(III)/Eu(II) has not been measured. Therefore, estimates have been calculated for this rate from measurements of the rates of reactions of systems that are well characterized, i.e. the equihbrium constant is known. In addition, there is substantiating evidence that the reaction is outer-sphere, and the value for self-exchange... 

The "cross-relation which relates the rate constant fcj, for an electron transfer reaction between two different redox species -I- fi to the rate constant k. for the self-exchange reaction (isotropic excKange) A -t- A, and to that of B, 22. the equilibrium constant... 

Marcus theory has been used to interpret the reactions of cytochromes c and blue copper proteins. For thirteen protein-protein electron-transfer reactions, the data can be fitted with the self-exchange rate constants of 2.8 x 10 s ... 

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