Electrically active complex concentration equations

We saw that formal kinetic equations apart from kinetic parameters also contain surface concentrations Cj of electrically active species. It follows from the material presented in previous chapters that differs from the corresponding bulk values because a diffusion layer with certain concentration profiles forms at the electrode surface. Moreover, another reason due to which surface concentrations change is adsorption phenomena, which form a certain structure called a double electrode layer (DEL) at the boundary metal solution. It is clear that in kinetic equations, it is necessary to use local concentrations of reactants and products, that is, concentrations in that region of DEL where electrically active particles are located. The second effect produced by DEL is related to the fact that a potential in the localization of the electrically active complex (EAC) differs from the electrode potential. Therefore, activation energy of the electrochemical process does not depend on the entire jump of the potential at the boundary but on its part only, which characterizes the change in the potential in the reaction zone. In this connection, the so-called Frumkin correction appears in the electrochemical kinetic equations, which is related to the evaluation of the local potential i// [1]. 

Surface concentrations were used in the analysis of experimental voltammo-grams obtained for Cu electrode whose surface was mechanically renewed in the course of measurements [4]. To determine the number of ligand particles in the electrically active complex CuCNp", the following equation was suggested ... 

Another example is processes taking place in the system Cu Cu(II), glycolic acid [8]. Procedures carried out to evaluate surface concentrations in this system are based on the material balance equations written for the surface layer (see [8]). The NTP obtained are shown in Figure 5.3. It can be stated that neither the potential sweep rate nor acidity of the solution (and the composition) has any significant influence on the nature of these dependencies. Thus, the assumption that free Cu " ions (Cu(II) aqua complexes) are electrically active in this case is quite acceptable. Kinetic parameters of the charge transfer process Cu + -F e Cu" " can be determined with reasonable accuracy (Figure 5.3). 

Using surface complexation models is another way to quantitatively describe the ion-exchanges processes. Surface complexation models also apply the law of mass action, combined with surface electric work (Table 1.7). However, there are some theoretical problems with the calculations, namely, that the equations of intrinsic stability use concentrations instead of activities, without discussing... 

In natural waters, other surface reactions will be occurring simultaneously. These include protonation and deprotonation of the >FeOH site at the inner o-plane and complexation of other cations and anions to either the inner (o) or outer (IS) surface planes. Expressions similar to Equation (5) above can be written for each of these reactions. In most studies, the activity coefficients of surface species are assumed to be equal to unity thus, the activities of the surface sites and surface species are equal to their concentrations. Different standard states for the activities of surface sites and species have been defined either explicitly or implicitly in different studies (Sverjensky, 2003). Sveijensky (2003) notes that the use of a hypothetical 1.0 M standard state or similar convention for the activities of surface sites and surface species leads to surface-complexation constants that are directly dependent on the site density and surface area of the sorbent. He defines a standard state for surfaces sites and species that is based on site occupancy and produces equilibrium constants independent of these properties of the solids. For more details about the properties of the electrical double layer, methods to calculate surface specia-tion and alternative models for activity coefficients for surface sites, the reader should refer to the reference cited above and other works cited therein. 

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