Concentration Profiles in Systems of Limited Lability

As metal ions in aqueous solutions form hydrated aqua complexes, complex-formation processes should be considered as reactions involving replacement of water molecules by ligand particles. Kinetic data for the formation of metal complexes obtained by various methods showed [27] that the formation of ML complexes proceeds via a rapid pre-equilibrium, resulting in the formation of an outer sphere complex M(H20)L. Then, this intermediate loses water in the rate-determining step of inner sphere complex (ML) formation. 

Rates of chemical reactions vary within a wide region of magnitude. Due to diffusion limitations, the rate constant of bimolecular reaction cannot exceed 10 ° mol dm s [28] therefore, this value can be used as an upper limit of Reactions whose half-times are less than 10 s are considered fast [29] then, the rate constant for monomolecular reaction should exceed 0.1 s L In accordance with the reaction rate, metal complexes are classified as labile and inert, but it is not possible to draw a sharp boundary line between the two groups. 

The rate of complex formation depends on various factors, such as the nature of the bond, the constitution of the electronic shells of the central metal atom, stereochemistry of the complex, and so on [29]. It has been suggested [30] that the rate constant for ligand penetration is characteristic of the metal ion alone. However, the exceptions are possible for chelation reactions in which steric effects, 

To reveal the effect of the rate of chemical steps, we consider concentration profiles simulated for the certain model system. To make the mathematics simpler, we explore only a hmited number of components emphasizing that an increase in their number has no effect on general conclusions. Thus, the system to be analyzed would contain only free metal ions (aqua complexes) M , monoUgand complexes ML , and uncharged Ugand L. Then, a single chemical reaction Eq. (3.16) occurs both in the bulk of solution and in the 5-thick diffusion layer. 

When chemical interactions are not infinitely fast, to determine concentration profiles, it is necessary to solve the set of differential equations containing kinetic terms. Hereinafter the results, obtained with the parameters listed in Table 3.4, are referred to the system of limited lability (LL system). The rate constants were varied so that the relation (3.32) was always obeyed. Current densities applied are given next as fractions of the steady-state limiting current density, that is. 

---