Homogeneous redox reaction rates

Despite its complexity, we pay attention to this case because of its potential importance for the determination of rate constants of homogeneous redox reactions. It concerns the electrode reactions... 

For the common circumstance where the transfer coefficient, a, is approximately independent of the electrode potential, a single value of k or k , along with a serves to describe fully the electrochemical kinetics at a given temperature and system composition. As for the rate constants for homogeneous redox reactions, electrochemical rate parameters can be sensitive to electrolyte composition, largely as a result of variations in the structure of the interphasial region (electrochemical double layer) (see 12.3.7.3.). The influence of the electrode material is considered in 12.3.7.5. 

For many electrochemical reactions, values of E, and hence k are unknown so that the intrinsic barrier cannot be obtained experimentally. For example, the reductions of substitutionally inert Co(III)-amine complexes to the corresponding Co(II) species are accompanied by rapid following steps to form [CofOHj) ] . Nevertheless, rate-potential data still can be obtained for such systems which are directly related to corresponding homogeneous redox reactions in thejollowing two ways. 

Another interesting result is a simple relation between the rate constant of a homogeneous redox reaction (isotopic exchange kex) and the rate constant for the same reaction at the electrode (kel) ... 

S.3.3 Electrocatalytic Modified Electrodes Often the desired redox reaction at the bare electrode involves slow electron-transfer kinetics and therefore occurs at an appreciable rate only at potentials substantially higher than its thermodynamic redox potential. Such reactions can be catalyzed by attaching to the surface a suitable electron transfer mediator (45,46). Knowledge of homogeneous solution kinetics is often used to select the surface-bound catalyst. The function of the mediator is to facilitate the charge transfer between the analyte and the electrode. In most cases the mediated reaction sequence (e.g., for a reduction process) can be described by... 

The rate law is of the form of Equation 17.5 in the previous section, and the equivalent law giving the net reaction rate is Equation 17.9. We can, therefore, account for the effect of catalysis on a redox reaction using the same formulation as the case of homogeneous reaction, if we include surface complexes among the promoting and inhibiting species. In Chapter 28, we consider in detail how this law can be integrated into a reaction path simulation. 

Redox reactions in the geochemical environment, as discussed in previous chapters (Chapters 7 and 17), are commonly in disequilibrium at low temperature, their progress described by kinetic rate laws. The reactions may proceed in solution homogeneously or be catalyzed on the surface of minerals or organic matter. In a great many cases, however, they are promoted by the enzymes of the ambient microbial community. 

FIGURE 5.7. Effect of changing the cosubstrate and the pH on the kinetics of an homogeneous redox enzyme reaction as exemplified by the electrochemical oxidation of glucose by glucose oxidase mediated by one-electron redox cosubstrates, ferricinium methanol ( ), + ferricinium carboxylate ( ), and (dimethylammonio)ferricinium ( ). Variation of the rate constant, k3, with pH. Ionic strength, 0.1 M temperature 25°C. Adapted from Figure 3 in reference 11, with permission from the American Chemical Society. 

The reduction of organic halides in the presence of aromatic hydrocarbons, the subject of detailed kinetic studies, provide rate constants for the homogeneous ET [147-150] and the follow-up reaction [151]. The theoretical basis for this kind of experiment ( homogeneous redox catalysis ) was laid by Saveant s group in a series of papers during the years 1978-80 [152-157]. Homogeneous ET also plays an important role in the protonation of anion radicals [158]. 

Values of A , and k may be extracted from the polarographic data, although the treatment is complex. Examples of its use to measure the rate constants for certain redox reactions are given in Refs. 339 and 340 which should be consulted for full experimental details. The values obtained are in reasonable agreement with those from stopped-flow and other methods. The technique has still not been used much to collect rate constants for homogenous reactions. The availability of ultramicroelectrodes has enabled cyclic voltammograms to be recorded at speeds as high as 10 Vs". Transients with very short lifetimes (< ps) and their reaction rates may be characterised. ... 

Comparison of the Rates of Homogeneous and Heterogeneous Redox Reactions... 

It should be seen that Equation 23.37 allows a pathway for the reduction of the reactant, (CO)2Mn(r]2-dppe)2+, separate from that of the heterogeneous pathway of Equation 23.34. Quantification of the extent to which the homogeneous cross-reaction contributes to the redox process almost always requires digital simulations that attempt to fit the shape of the whole CV curve. Such studies allowed Kuchynka and Kochi (25), for example, to obtain values for the rate constants of Equation 23.37 (kf = 200 M 1 s 1, kb = 20 s 1), and to... 

There are several demands that must be more or less fulfilled by the mediator before a successfull amperometric detection of NADH with CMEs can be realized. Despite having a E° lower or comparable with the optimal working potential range for amperometric detection, the mediator should exhibit fast reaction rates both with the electrode proper and NADH, and also be chemically stable at any redox state. Furthermore, the redox reaction of the mediator should involve two electrons and at least one proton making possible, at least theoretically, a fast inner sphere hydride transfer in the homogeneous reaction with NADH. 

Using the Marcus theory, the a value (see -> charge-transfer coefficient) can be predicted, and its dependence on the potential applied. For low - over potentials, and when neither Ox nor Red are specifically adsorbed on the electrode surface, a should be approximately equal to 0.5. Further, the theory describes the relation between homogeneous and heterogeneous rate constants characteristic of the same redox system. An interesting prediction from Marcus theory is the existence of a so-called inverted region for the homogeneous electron transfer reactions, of importance to the phenomenon of... 

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]. 

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