Second order kinetics electron-transfer processes

As in chemical systems, however, the requirement that the reaction is thermodynamically favourable is not sufficient to ensure that it occurs at an appreciable rate. In consequence, since the electrode reactions of most organic compounds are irreversible, i.e. slow at the reversible potential, it is necessary to supply an overpotential, >] = E — E, in order to make the reaction proceed at a conveniently high rate. Thus, secondly, the potential of the working electrode determines the kinetics of the electron transfer process. 

A distinction, however, is possible from kinetic studies (see Scheme 11). The slow step of the proton transfer mechanism is the proton transfer process (eqs. 14 and 22), thus the rate law should be first order in the radical species and first order in the base. The slow step of the disproportionation mechanism, on the other hand, is the electron transfer process following the solvent coordination pre-equilibrium, thus the rate law should be second order in the radical species and first order in the solvent under the conditions in which Kgq[S] 1 (preequilibrium favouring the 17-electron species). In addition, stronger donor solvents leads to faster disproportionation processes (e.g. MeCN CH2CI2, THF), while the proton transfer process should be much less solvent dependent. 

Most inner-sphere processes exhibit second order kinetics overall, and interpreting the data is seldom simple. Any one of bridge formation, electron transfer or bridge cleavage can be rate-determining. In the reaction between... 

When the radical cation and radical anion decay completely after laser pulse, the generated radical ion pair returns to the corresponding neutral ground state by the back electron-transfer process [60]. When the solvent is highly polar, the generated radical ions are solvated as free radical ions thus, the back electron transfer obeys second-order kinetics [Eq. (6)]. On the other hand, in the less-polar solvents, the radical ions are present as geminate ion pairs thus, the back electron transfer obeys first-order kinetics [Eq. (7)] ... 

If the EDA and CT pre-equilibria are fast relative to such a (follow-up) process, the overall second-order rate constant is k2 = eda c e In this kinetic situation, the ion-radical pair might not be experimentally observed in a thermally activated adiabatic process. However, photochemical (laser) activation via the deliberate irradiation of the charge-transfer absorption (hvct) will lead to the spontaneous generation of the ion-radical pair (equations 4, 5) that is experimentally observable if the time-resolution of the laser pulse exceeds that of the follow-up processes (kf and /tBet)- Indeed, charge-transfer activation provides the basis for the experimental demonstration of the viability of the electron-transfer paradigm in Scheme l.21... 

The increase in the rate of recombination upon illumination in the CC14 absorption band is due to the CCl photoionization with an electron being transferred to a continuous spectrum and subsequently captured by an arbitrary MP+ particle. As seen from Fig. 16, in this case the process kinetics (curve 1) is described by the second-order equation... 

Fig. 8. Outline of the time-scale of the processes observed during an electron transfer reaction observed through thermal lensing. Processes which occur in times below ca. 0.5 ps are very fast , beyond the temporal resolution of the thermal lensing technique they would appear as a step function in the kinetics of heat release. The slowest processes which would be observed in this case are the second-order recombinations of free ions, which take place in time scales of ps to several ms.

Most aquatic oxidation reactions are attributable to well-defined chemical oxidants. As a result, model systems can be designed where second-order rate constants can be determined precisely for families of organic congeners. The comparatively high quality of these data allows mechanistic models of electron transfer to describe aquatic oxidations of environmental interest. Kinetic studies of these processes have produced many QSARs, mostly simple empirical correlations with common convenient descriptors such as the Hammett constant (a), half-wave oxidation potential ( j/2)> energies of the highest occupied molecular orbital ( HOMO), or rate constants for other oxidation reactions as descriptors (Canonica and Tratnyek, 2003). Their predictive power has lead to engineering applications in water treatment and remediation. 

Similarly, phenothiazine may be oxidized to the cation radical species which then dimerizes forming the 3,10 -diphenothiazinyl species (Tsujino, 1969). The product of the electron-transfer step may react, via a second-order process, with a species in solution to form a new product. An example of this type of mechanism involves the reduction of anthraquinone and its derivatives in the presence of oxygen (Jeziorek etal., 1997). To understand quantitatively an EC and EC2 process, the concentration and scan-rate dependence of the associated cyclic voltammograms is matched with theory deriving from the mass transport/kinetic equations for each species. 

The macromolecular silyl chloride reacts with sodium in a two-electron-transfer reaction to form macromolecular silyl anion. The two-electron-trans-fer process consists of two (or three) discrete steps formation of radical anion, precipitation of sodium chloride and generation of the macromolecular silyl radical (whose presence was proved by trapping experiments), and the very rapid second electron transfer, that is, reduction to the macromolecular silyl anion. Some preliminary kinetic results indicate that the monomer is consumed with an internal first-order-reaction rate. This result supports the theory that a monomer participates in the rate-limiting step. Thus, the slowest step should be a nucleophilic displacement at a monomer by macromolecular silyl anion. This anion will react faster with the more electrophilic dichlorosilane than with a macromolecular silyl chloride. Therefore, polymerization would resemble a chain growth process with a slow initiation step and a rapid multistep propagation (the first and rate-limiting step is the reaction of an anion with degree of polymerization n[DP ] to form macromolecular silyl chloride [DP +J, and the chloride is reduced subsequently to the anion). 

In the EC2i process, an initial electron transfer step is followed by a second-order irreversible chemical reaction (typically a dimerization process, as considered in the practical examples in Sec. III.B). The use of SECM to characterize the kinetics of the second-order chemical reactions is based on the same principles as for the EQ case, discussed in Sec. II, with a generator electrode employed to electrogenerate the species of interest [B, see Eq. (1)], which is collected at a second electrode. The second-order process involving the consumption of B to form electroinactive products occurs in the gap between the two electrodes ... 

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