Rate laws for oxidation and reduction

The rate law for a redox reaction predicts the rate at which a species is transformed by a specific reaction mechanism, or combination of mechanisms, from one oxidation state to another. For example, Wehrli and Stumm (1988, 1989) studied the oxidation of vanadyl (Viv) to vanadate (Vv) by reaction with dissolved O2. 

They showed this process can proceed in aqueous solution by the oxidation of the hydroxy complex VO(OH)+, according to the reaction 

To trace a reaction path incorporating redox kinetics, we first set a model in redox disequilibrium by disabling one or more redox couples, then specify the reaction in question and the rate law by which it proceeds. To model the progress of Reaction 17.1, for example, we would disable the redox couple between vanadyl and vanadate species. In a model of the oxidation of Fe++ by manganite (MnOOH), we would likely disable the couples for both iron and manganese. 

The redox reaction may include solvent water, basis and secondary aqueous species, mineral and gas species, and uncomplexed and complexed surface sites. Each such reaction, denoted k, can be written in a generalized form as, 

As before, species with negative reaction coefficients v are reactant species, which 

---