Rate constant of self-exchange

The reorganization energy of a self-exchange reaction is denoted A(0) (from the fact that AG° = 0) and is an important quantity in the Marcus theory, where it can be shown that the activation free energy of a self-exchange reaction, AG(0), is equal to X.(0)/4. It is also possible to measure rate constants of self-exchange processes experimentally and thus get access to (0) via this relationship. 

Lind J, Shen X, Merenyi G, Jonsson B (1989) Determination of the rate constant of self-exchange of theCVCV- couple in water by 180/160 isotope marking. J Am Chem Soc 111 7654-7655 Liu Y, Pimentel AS, Antoku Y, Barker JR (2002) Temperature-dependent rate and equilibrium constants for Br (aq) + Br(aq) <=> Br2- (aq). J Phys Chem A 106 11075-11082 Marcus RA (1993) Elektronentransferreaktionen in der Chemie - Theorie und Experiment (Nobel Vortrag). Angew Chem 105 1161-1172... 

The Marcus cross relation can in general be applied to correlate the rate constants of self-exchange reactions, Ku and K12, with the rate constant, K12, and equilibrium constant, JC12, of a cross reaction between two redox systems. For the self-exchange reactions... 

Relationships having the same form as eq 14 can also be written for the enthalpic and entropic contributions to the intrinsic free energy barriers (10). Provided that the reactions are adiabatic and the conventional collision model applies, eq 14 can be written in the familiar form relating the rate constants of electrochemical exchange and homogeneous self-exchange reactions (13) ... 

A literature value for E° for the SCH2COO / SCH2COO redox couple (0.74 V) was then used in conjunction with the cross relationship of Marcus theory to derive a self-exchange rate constant of 1.5 x 105 M-1 s-1 for the SCH2COO / SCH2COO redox couple. 

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. 

The variations of the symmetry factor, a, with the driving force are much more difficult to detect in log k vs. driving force plots derived from homogeneous experiments than in electrochemical experiments. The reason is less precision on the rate and driving force data, mostly because the self-exchange rate constant of the donor couple may vary from one donor to the other. It nevertheless proved possible with the reaction shown in Scheme 3.3.11... 

The kinetics of the reduction of perruthenate(VII) by [FefCbOe]" and [W(CN)g]" and the oxidation of ruthenate(VI) by [Mo(CN)g] and [Ru(Cb06] have been studied in aqueous alkaline solutions. The cross-reaction data have been treated according to the Marcus relations and yield a self-exchange rate constant of 10 s at 25.0 °C and 1.0 M ionic strength for the... 

Q = quinones) have been measured by pulse radiolysis methods. From the results a self-exchange rate constant of 1.1 x 10 s and a reduction potential of -1-0.048 V vs. NHE for Os /Os have been... 

For the relation between the rate constant for homogeneous self-exchange ET process (kex) and the standard rate constant of the corresponding electrode reaction (kg), see 4) in Chapter 9. 

In Table 1 are summarized representative examples of self-exchange rate constant data for a variety of different types of redox couples based on metal complexes, organometallic compounds, organics and clusters. Where available the results of temperature dependence studies are also cited. For convenience, data obtained from temperature dependence studies are presented as enthalpies and entropies of activation as calculated from the reaction rate theory expression in equation (14). 

An important feature to emerge from the comparisons in Table 2 is that variations in the electronic coupling term play a relatively small role in dictating the magnitudes of self-exchange rate constants for outer-sphere reactions, at least for transition metal complexes. Even for reactions... 

From the experimental point of view, significant variations in kobs can be induced by changes in solvent and/or molecular size. For example, there are relatively small contributions to A for the self-exchange reactions for the Ru(NH3)63+/2+and Ru(bipy)33+/2+couples in Table 1 and the effects of the differences in molecular radii on KA and Ao are sufficient to account for the difference in self-exchange rate constants of 106. 

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