Electron-transfer reactions rate constants, driving force

Rate Constants and Reactivity. Electron-transfer reactions of plastocyanin (and other metalloproteins) are so efficient that only a narrow range of redox partners (having small driving force) can be employed. Rates are invariably in the stopped-flow range, Table I. Unless otherwise stated parsley plastocyanin... 

A significant technical development is the pulsed-accelerated-flow (PAF) method, which is similar to the stopped-flow method but allows much more rapid reactions to be observed (1). Margerum s group has been the principal exponent of the method, and they have recently refined the technique to enable temperature-dependent studies. They have reported on the use of the method to obtain activation parameters for the outer-sphere electron transfer reaction between [Ti Clf ] and [W(CN)8]4. This reaction has a rate constant of 1x108M 1s 1 at 25°C, which is too fast for conventional stopped-flow methods. Since the reaction has a large driving force it is also unsuitable for observation by rapid relaxation methods. 

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. 

These driving forces are exergonic and considerably more favorable than those involved in the electron-transfer reactions of the simple, monosub-stituted carbonylmanganese cations Mn(CO)5L+ and anions Mn(CO)4P-(where L and P are both monodentate phosphines and phosphites). Nonetheless, the rate constants for cis- and ra -Mn(CO)2( DPPE )2+ with Mn(CO)2(DPPE)2 are considerably slower than those qualitatively observed between Mn(CO)5L+ and Mn(CO)4P- (67). Such large rate differences that belie thermodynamics can be attributed to steric hindrance in the tetrasubstituted carbonylmanganese cations and the anion which are absent in the simpler ions. Such structural effects, even in these apparently outer-sphere electron transfers, merit a further quantitative evaluation as in the application of Marcus theory (83). 

For solution redox couples uncomplicated by irreversible coupled chemical steps (e.g. protonation, ligand dissociation), a standard (or formal) potential, E°, can be evaluated at which the electrochemical tree-energy driving force for the overall electron-transfer reaction, AG c, is zero. At this potential, the electrochemical rate constants for the forward (cathodic) and backward (anodic) reactions kc and ka (cms-1), respectively, are equal to the so-called "standard rate constant, ks. The relationship between the cathodic rate constant and the electrode potential can be expressed as... 

Some of the new theoretical relations, the cross-relation between the rates of a cross-reaction of two difierent redox species with those of the two relevant selfexchange reactions, were later adapted to non-electron transfer reactions involving simultaneous bond rupture and formation of a new bond (atom, ion, or group transfer reactions). The theory had to be modified, but relations such as the crossrelation or the effect of driving force (—AG°) on the reaction rate constant were again obtained in the theory, in a somewhat modified form. For example, apart from some proton or hydride transfers under special circumstances, there is no predicted inverted effect. Experimental confirmation of the cross-relation followed, and an inverted effect has only been reported for an H+ transfer in some nonpolar solvents. The various results provide an interesting example of how ideas obtained for a simple, but analyzable, process can prompt related, yet different, ideas for a formalism for more complicated processes. 

The rate constants for the investigated arenes vary between 7.8 x 10 and 4.5 X 10 ° M s [62]. The driving forces (-AG°et) calculated on the basis of the difference in the respective arene and fullerene ionization potentials (—AG°et = A/P = /Parene /Pfuiierene) have a pronounced parabolic dependency on the measured rate constants for the electron-transfer reactions, as shown in Figure 2. 

As the driving force for the reaction increases the rate constant increases, reaches a maximum, and then decreases again. When the rate of reaction is a maximum, there is no barrier to electron transfer and the process is activationless. This condition is reached for a rate constant of 1 x 10 s. For higher driving forces, the electron transfer reaction occurs in the Marcus inverted region. Other examples of this behavior have been described in the literature. They give strong confirmation of the model for electron transfer presented here. 

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