Electrochemical reactions inner-sphere pathways

A major application of eqn. (47) is to diagnose the presence of catalytic, presumably inner-sphere, electrochemical pathways. This utilizes the availability of a number of homogeneous redox couples, such as Ru(NH3)e+/2+ and Cr(bipyridine) +,2+ that must react via inner-sphere pathways since they lack the ability to coordinate to other species [5]. Provided that at least one of the electrochemical reactions also occurs via a well-defined outer-sphere pathway, the observation of markedly larger electrochemical rate constants for a reaction other than that expected from eqn. (47) indicates that the latter utilizes a more expeditious pathway. This procedure can be used not only to diagnose the presence of inner-sphere pathways, but also to evaluate the extent of inner-sphere electrocatalysis (Sect. 4.6) it enables reliable estimates to be made of the corresponding outer-sphere rate parameters [12a, 116, 120c]. 

Equation (a), with set equal to ( >, is surprisingly successful in describing the effect of varying the double-layer structure upon the kinetics of electrochemical reactions at Hg electrodes, at least in the absence of specific adsorption of the supporting electrolyte (i.e., when the inner-layer region adjacent to the electrode contains only solvent molecules). However, this does not necessarily imply that average electrostatic interactions provide the sole contribution to the work terms, because contributions may arise from other sources that remain constant under these conditions. In particular, inner-sphere pathways commonly involve reaction sites within the outer Helmholtz plane. Consequently, the overall work terms consist of separate contributions from transporting the reactant from the bulk solution to this outer plane and from this plane to the reaction site within the inner layer. The latter will then be independent of and, therefore, influence only k j.. in Eq. (a). 

It is also important to develop a theoretical basis for the dependence of the observed rate constant, k ,, for inner- as well as outer-sphere pathways upon the electrode potential, E, thereby relating k to AG ,. An alteration in the electrochemical driving force for the elementary reaction, 8(AG p), will yield a corresponding change in the reorganization free energy, S(AG ), according to ... 

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