Inner-sphere reaction rates

If the reaction(s) obey the predictions of the Marcus theory, then an outer-sphere mechanism is often assumed. This is a dangerous criterion, because it has been observed that inner-sphere reaction rates - also show a correlation with the overall AG of the reaction that is predicted by the Marcus theory for outer-sphere reactions. Murdoch has shown that such linear free-energy correlations may be more general than might originally have been expected. 

Candlin and Halpern comment that the sequence of rapid rates observed for Cr " " as a reductant i.e. Co(NH3)5p > Co(NH3)sBr > Co(NH3)5CI > Co(NH3)5F ) is contrary to that found for the slow reactions of Fe (ref. 126) and Eu (ref. 113). All three reductants would appear to favour inner-sphere mechanisms, but in the case of Fe and Eu the order of reactivity seems to be connected with the stability of the product halide complex (FeX or EuX ) which increases in the order X = 1 to X = F . Or in other words, as pointed out by Halpern and Rabani, in the generalised inner-sphere reaction... 

The Electron Transfer Step. Inner-sphere and outer-sphere mechanisms of reductive dissolution are, in practice, difficult to distinguish. Rates of ligand substitution at tervalent and tetravalent metal oxide surface sites, which could be used to estimate upward limits on rates of inner-sphere reaction, are not known to any level of certainty. 

Examination of the data for (5.49) and (5.50) in Tables 5.7 and 5.8 shows that there is some general order of reactivity for the various ligands L. Containing an unshared electron pair after coordination appears a minimum requirement for a ligand to be potential bridging group, for it has to function as a Lewis base towards two metal cations. Thus CofNHj) and Co(NH3)jpy + oxidize Cr by an outer-sphere mechanism, giving Cr " as the product, at a much slower rate than for the inner-sphere reactions. 

The concept of electrocatalysis and its relation to chemical surface bonding of reactive intermediates is closely related to that of heterogeneous catalysis. Following the previous section, simple Gibbs energy curves can illustrate the essential ideas of how adsorption of intermediates and their associated Gibbs energy affect the rate of an inner-sphere reaction. 

The rate-determining step in most inner sphere reactions is ihe electron transfer step, noi the formation of the bridged complex. If dissociation of a reBcianl complex were rale determining, firsi-order kinelics would be expected 54 Haim. A. Prog. Inorg. Ckem. 19 3,30, 273-357. 

It is important to notice that the rate of a given outer sphere electrode redox reaction should be independent of the nature of the metal electrode if allowance is made for electrostatic work terms or double layer effects which will, of course, be dependent on the nature of the electrode material. Inner sphere reactions, on the other hand, are expected to be catalytic with kinetics strongly dependent on the electrode surface due to specific adsorption interactions. 

In contrast to outer-sphere reactions, the simple observation that a reaction occurs by an inner-sphere mechanism necessarily introduces an element of structural definition. The relative dispositions of the oxidizing and reducing agents are immediately established and, except for structurally flexible bridging ligands such as NC5H4(CH2) C5H4N, the internuclear separation between redox sites can be inferred from known bond distances. Even so, bimolecular inner-sphere reactions necessarily occur by a sequence of elementary steps (Scheme 2) and the observed rate constant may include contributions from any of the series of steps. 

Two separate but somewhat interwoven themes have emerged from the study of inner-sphere reactions. The first is the use of product and rate studies to establish the existence of inner-sphere pathways and then the exploitation of appropriate systems to demonstrate such special features as remote attack . In the second theme the goal has been to assemble the reactants through a chemical bridge and then to study intramolecular electron transfer directly following oxidation or reduction of the resulting dimer (note equation 7). It is convenient to turn first to chemically prepared, intramolecular systems since many of the theoretical ideas and experimental results for outer-sphere reactions can be carried over directly as an initial basis for understanding the experimental observations. 

I k . 2.5. The associative inner-sphere reaction mechanism for Co reduction by Cr or other metals via Cl (thick bars) or other ligands. The overall second-order rate coefficient for the redox reaction (K) varies over 14 orders of magnitude. 

The kinetics of inner-sphere reactions are generally expected to be sensitive to the nature of the electrode material Variations in may arise from several sources. First, the work term, Wp, and hence the precursor stability, Kp, is expected to depend strongly upon the electrode material in view of the specific reactant-electrode interactions involved. Therefore, k p increases as the strength of the reactant-electrode bond increases [Eq. (n) in 12.3.7.2]. However, there is an upper limit to the catalysis thereby induced, corresponding to the onset of monolayer formation. For example, if the adsorbate concentration, corresponding to a monolayer equals 10 mol cm , for the typical bulk-reactant concentration, C, of 10 M, K = F /C = 3 X 10 cm. By comparison, the statistical value of Kp when Wp = 0, is expected to be ca. 10 cm ( 12.3.7.2). Consequently, stabilization of the precursor state via reactant-electrode interactions corresponds to a maximum rate acceleration of ca. 10 under these conditions. 

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