Precursor complex formation

The voltammograms at the microhole-supported ITIES were analyzed using the Tomes criterion [34], which predicts ii3/4 — iii/4l = 56.4/n mV (where n is the number of electrons transferred and E- i and 1/4 refer to the three-quarter and one-quarter potentials, respectively) for a reversible ET reaction. An attempt was made to use the deviations from the reversible behavior to estimate kinetic parameters using the method previously developed for UMEs [21,27]. However, the shape of measured voltammograms was imperfect, and the slope of the semilogarithmic plot observed was much lower than expected from the theory. It was concluded that voltammetry at micro-ITIES is not suitable for ET kinetic measurements because of insufficient accuracy and repeatability [16]. Those experiments may have been affected by reactions involving the supporting electrolytes, ion transfers, and interfacial precipitation. It is also possible that the data was at variance with the Butler-Volmer model because the overall reaction rate was only weakly potential-dependent [35] and/or limited by the precursor complex formation at the interface [33b]. 

Rates of reductive dissolution of transition metal oxide/hydroxide minerals are controlled by rates of surface chemical reactions under most conditions of environmental and geochemical interest. This paper examines the mechanisms of reductive dissolution through a discussion of relevant elementary reaction processes. Reductive dissolution occurs via (i) surface precursor complex formation between reductant molecules and oxide surface sites, (ii) electron transfer within this surface complex, and (iii) breakdown of the successor complex and release of dissolved metal ions. Surface speciation is an important determinant of rates of individual surface chemical reactions and overall rates of reductive dissolution. 

Similarly, inner-sphere and outer-sphere mechanisms can be postulated for the reductive dissolution of metal oxide surface sites, as shown in Figure 2. Precursor complex formation, electron transfer, and breakdown of the successor complex can still be distinguished. The surface chemical reaction is unique, however, in that participating metal centers are bound within an oxide/hydroxide... 

The kinetic behavior of the reductive dissolution mechanisms given in Figure 2 can be found by applying the Principle of Mass Action to the elementary reaction steps. The rate expression for precursor complex formation via an inner-sphere mechanism is given by ... 

In this case, precursor complex formation depends upon the lability of the incoming metal ion, rather than that of the oxide surface site, since the inner coordination ligands of the surface site are not exchanged (26). 

Surface speciation can be expected to have a tremendous impact on rates of precursor complex formation. Rj, the rate of precursor complex formation, may depend upon the extent of surface protonation, since ligand exchange rates of >MeOH2, >MeOH, and >MeO may vary substantially ... 

Surface Coverage and Reaction Rate. If precursor complex formation is fast relative to electron transfer and product release, it can be treated as a quasi-equilibrium step ... 

The most direct evidence for surface precursor complex formation prior to electron transfer comes from a study of photoreduc-tive dissolution of iron oxide particles by citrate (37). Citrate adsorbs to iron oxide surface sites under dark conditions, but reduces surface sites at an appreciable rate only under illumination. Thus, citrate surface coverage can be measured in the dark, then correlated with rates of reductive dissolution under illumination. Results show that initial dissolution rates are directly related to the amount of surface bound citrate (37). Adsorption of calcium and phosphate has been found to inhibit reductive dissolution of manganese oxide by hydroquinone (33). The most likely explanation is that adsorbed calcium or phosphate molecules block inner-sphere complex formation between metal oxide surface sites and hydroquinone. 

Of course the Co CNHj) breaks down rapidly in acid into Co + and 5NHJ. Precursor complex formation, intramolecular electron transfer, or successor complex dissociation may severally be rate limiting. The associated reaction profiles are shown in Fig. 5.1. A variety of rate laws can arise from different rate-determining steps. A second-order rate law is common, but the second-order rate constant is probably composite. For example, (Fig. 5.1 (b)) if the observed redox rate constant is less than the substitution rate constant, as it is for many reactions of Cr +, Eu +, Cu+, Fe + and other ions, and if little precursor complex is formed, then = k k2kz ). In addition, the breakdown of the successor complex would have to be rapid k > k 2). This situation may even give rise to negative (= A//° +... 

From Eq. 14-30 we see that we may divide a one-electron transfer into various steps (maybe somewhat artificially). First, a precursor complex (PR) has to be formed that is, the reactants have to meet and interact. Hence, electronic as well as steric factors determine the rate and extent at which this precursor complex formation occurs. Furthermore, in many cases, redox reactions take place at surfaces, and therefore, the sorption behavior of the compound may also be important for determining the rate of transformation. In the next step, the actual electron transfer between P and R occurs. The activation energy required to allow this electron transfer to happen depends strongly on the willingness of the two reactants to lose and gain, respectively, an electron. Finally, in the last steps of reaction sequence Eq. 14-30, a successor complex may be postulated which decays into the products. 

As an example, we consider the oxidation of a series of monosubstituted anilines by Mn02 in batch systems. In this case, quite a good correlation between log kK (expressed relative to R of 4-chloroaniline) and E]/2(ArX ) is obtained (Fig. 14.20). The slope of -0.54 indicates that, similar to what we have postulated for the reduction of NACs by surface-bound Fe(II) (see Fig. 14.10 /), the overall reaction rate is determined not solely by the actual electron transfer but also by other steps such as precursor complex formation. Comparable results (slopes of between-0.5 and -0.6) were obtained for the reaction of Mn02 at pH 4 with a series of substituted anilines (Laha and Luthy, 1990), and with a series of substituted phenols at pH 4.4 (Stone, 1987). In all these cases, only initial pseudo-first-order rate constants determined with clean Mn02 were considered. In the presence of solutes such as Mn2+ that may adsorb to the oxide surface, much slower reaction rates and much... 

The kinetics of the reductive dissolution mechanisms shown in Fig. 8.1 can be derived using the principle of mass action. The kinetic expression for precursor complex formation by way of an inner-sphere mechanism (Stone, 1986) is... 

An analogous rate expression can be written for the outer-sphere mechanism. From Hq. (8.2), it can be predicted that high rates of reductive dissolution are enhanced by high rates of precursor complex formation... 

It should also be pointed out that the rate of each of the reaction steps (precursor complex formation, electron transfer, and breakdown of successor complex) is affected by the chemical characteristics of the metal oxide surface sites and the nature of the reductant molecules. These aspects are discussed in detail in an excellent review by Stone (1986), and the reader is encouraged to refer to this article. 

Reaction of Cytochrome cimu with Tris(oxalato)cobalt(III) The cytochrome c protein was also used as reductant in a study of the redox reaction with tris (oxalato)cobalt(III).284 Selection of the anionic cobalt(III) species, [Conl(ox)3]3 was prompted, in part, because it was surmised that it would form a sufficiently stable precursor complex with the positively charged cyt c so that the equilibrium constant for precursor complex formation (K) would be of a magnitude that would permit it to be separated in the kinetic analysis of an intermolecular electron transfer process from the actual electron transfer kinetic step (kET).2S5 The reaction scheme for oxidation of cyt c11 may be outlined ... 

In the case of very effective ion pair (precursor complex) formation, A obs at high [Co(in)] concentration reaches the limiting value /cm. Thus, kEI was found to be 0.158 s and the second-order rate constant for the overall reaction (= kETK) is 40 dm3/(mol s), with K - 253 dm3/mol, all at 298K. Reasonable agreement was found... 

Fig. 7.34. Reaction profiles for inner-sphere redox reactions illustrating three types of behavior (a) precursor complex formation is rate-limiting, (b) precursor-to-successor complex is rate-limiting and (c) breakdown of successor complex is rate-limiting. The situation (b) appears to be most commonly encountered [85].

This expression relates the second-order rate constant, k, for an outer-sphere electron transfer reaction to the free energy of reaction, AG°, with one adjustable parameter, X, known as the reorganization energy. Wis the electrostatic work term for the coulombic interaction of the two reactants, which can be calculated from the collision distance, the dielectric constant, and a factor describing the influence of ionic strength. If one of the reactants is uncharged, Wis zero. In exact calculations, AG should be corrected for electrostatic work. The other terms in equation 46 can be treated as constants (Eberson, 1987) the diffusion-limited reaction rate constant, k, can be taken to be 10 M" is the equilibrium constant for precursor complex formation and Z is the universal collision frequency factor (see Eberson, 1987). 

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