Precursor formation, outer-sphere

A general difficulty encountered in kinetic studies of outer-sphere electron-transfer processes concerns the separation of the precursor formation constant (K) and the electron-transfer rate constant (kKT) in the reactions outlined above. In the majority of cases, precursor formation is a diffusion controlled step, followed by rate-determining electron transfer. In the presence of an excess of Red, the rate expression is given by... 

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... 

At 25°C and p = 0.1 M, the values of are 10 -10 M and those of k are 10 -10 s depending on the identity of L. The internal electron transfer rate in an outer-sphere complex can thus be analyzedwithout considering work terms or, what is equivalent, the equilibrium controlling the formation of precursor complex. This favorable situation is even improved when the metal centers are directly bridged. The relative orientation of the two metal centers in a well-established geometry can be better treated than in the outer-sphere complex (Sec. 5.8). 

Just as we did with outer-sphere reactions, we can dissect an inner sphere redox process into individual steps. Specifically, let us examine the reaction of (HjO) with Co "(NH3)5L. The first step is the formation of the precursor complex > >20.54-56... 

Marcus theory (15) has been applied to the study of the reductions of the jU,2-superoxo complexes [Co2(NH3)8(/u.2-02)(/i2-NH2)]4+ and [Co2(NH3)10(ju.2-O2)]6+ with the well-characterized outer-sphere reagents [Co(bipy)3]2+, [Co(phen)3]2+, and [Co(terpy)2]2+, where bipy = 2,2 -bipyridine, phen = 1,10-phenanthroline, and terpy = 2,2 6, 2"-terpyridine (16a). The kinetics of these reactions could be adequately described using a simple outer-sphere pathway, as predicted by Marcus theory. However, the differences in reactivity between the mono-bridged and di-bridged systems do not appear to be explicable in purely structural terms. Rather, the reactivity differences appear to be caused by charge-dependent effects during the formation of the precursor complex. Some of the values for reduction potentials reported earlier for these species (16a) have been revised and corrected by later work (16b). 

The rate-controlling step in reductive dissolution of oxides is surface chemical reaction control. The dissolution process involves a series of ligand-substitution and electron-transfer reactions. Two general mechanisms for electron transfer between metal ion complexes and organic compounds have been proposed (Stone, 1986) inner-sphere and outer-sphere. Both mechanisms involve the formation of a precursor complex, electron transfer with the complex, and subsequent breakdown of the successor complex (Stone, 1986). In the inner-sphere mechanism, the reductant... 

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... 

This relation will be valid for both inner- and outer-sphere pathways provided that electron transfer, rather than precursor-state formation, is the rate-determining step. The precursor equilibrium constant can be expressed as... 

The outer sphere character of these reactions has encouraged some workers to apply Marcus theory to the rate constants obtained " . Given the uncertainty in the values of the electrode potentials and the considerable electrostatic work function involved in the formation of the precursor complex, the significance of the intrinsic rate parameters obtained is not clear. 

In the absence of ion pairing and rate limitation by solvent dynamics, the volume of activation for adiabatic outer-sphere electron transfer in couples of the type j (z+i)+/z ju principle, be calculated as in equation 2 from an adaptation of Marcus-Hush theory. In equation 2, the subscripts refer respectively to volume contributions from internal (primarily M-L bond length) and solvent reorganization that are prerequisites for electron transfer, medium (Debye-Huckel) effects, the Coulombic work of bringing the reactants together, and the formation of the precursor complex. 

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). 

In this chapter, the adsorption of catalyst precursors on oxidic surfaces will be discussed in terms of a chemical-interaction model, i.e. allowing the formation of inner-sphere complexes, but it is important to realize that other models are being advocated in the literature as well on the one hand, one has the physical adsorption models, allowing only the formation of outer-sphere complexes, and on the other, it is proposed that during adsorption one really has a reaction between the precursor and the support to form a new phase or phases. We will meet the latter situation in our discussion of deposition-precipitation (Section 10.3.3), but we will disregard it when discussing impregnation chemistry (Section 10.3.2). 

The above treatment assumes that the interaction between the reactants is primarily electrostatic, but specific solvent (hydrophobic) interactions also may be important. Additional complications arise in inner-sphere reactions. The formation constant of the precursor complex in such reactions can be expressed as the product of the equilibrium constant for the formation of the outer-sphere complex and the equilibrium constant for the conversion of the outer- to the inner-sphere complex ... 

The reductant and oxidant [M(II) and N(III), respectively] first come together to form a precursor complex. In an outer-sphere reaction this involves a simple diffusional process in an inner-sphere reaction a substitutional step culminating in the formation of... 

The rate of formation of the precursor complex can be rate determining even if its formation does not involve ligand replacement. This occurs in outer-sphere reactions in which the electron transfer rate is rapid. The rate of formation of the precursor complex may then be diffusion controlled i.e., or, more generally, k = Kkj.,j/... 

Inner- or outer-sphere surface complex formation is a. necessary prerequisite for most surface chemical redox reactions. (ESR may provide important information regarding the nature of the precursor complex.) When electron transfer is fast k2 ArJArOH]), overall rates of reaction are influenced by rates of organic reductant adsorption. When electron transfer is slow kl < ArJArOH]), Eq. [18] can be modeled as a pseudoequilibrium reaction, using the equilibrium constant... 

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