Electrode potential, coupled chemical reaction

Determining Equilibrium Constants for Coupled Chemical Reactions Another important application of voltammetry is the determination of equilibrium constants for solution reactions that are coupled to a redox reaction occurring at the electrode. The presence of the solution reaction affects the ease of electron transfer, shifting the potential to more negative or more positive potentials. Consider, for example, the reduction of O to R... 

Additional information on the rates of these (and other) coupled chemical reactions can be achieved by changing the scan rate (i.e., adjusting the experimental time scale). In particular, the scan rate controls the tune spent between the switching potential and the peak potential (during which the chemical reaction occurs). Hence, as illustrated in Figure 2-6, i is the ratio of the rate constant (of the chemical step) to die scan rate, which controls the peak ratio. Most useful information is obtained when the reaction time lies within the experimental tune scale. For scan rates between 0.02 and 200 V s-1 (common with conventional electrodes), the accessible... 

Figure 3,55 Cyclic vollammograms of Re(Bipy)(CO)3CI in CH3CN/0.l M letrabutylammonium hexafluorophosphate as supporting electrolyte at a button Pt electrode, and with a sweep rate of 200 mV s (a) The switching potential characteristics of the coupled chemical reactions in the ahsence of C02. The lettered redox processes are discussed in the text. (b> The effect of saturating the solution with C02. From Sullivan et al. (1985).

In this equation, aua represents the product of the coefficient of electron transfer (a) by the number of electrons (na) involved in the rate-determining step, n the total number of electrons involved in the electrochemical reaction, k the heterogeneous electrochemical rate constant at the zero potential, D the coefficient of diffusion of the electroactive species, and c the concentration of the same in the bulk of the solution. The initial potential is E/ and G represents a numerical constant. This equation predicts a linear variation of the logarithm of the current. In/, on the applied potential, E, which can easily be compared with experimental current-potential curves in linear potential scan and cyclic voltammetries. This type of dependence between current and potential does not apply to electron transfer processes with coupled chemical reactions [186]. In several cases, however, linear In/ vs. E plots can be approached in the rising portion of voltammetric curves for the solid-state electron transfer processes involving species immobilized on the electrode surface [131, 187-191], reductive/oxidative dissolution of metallic deposits [79], and reductive/oxidative dissolution of insulating compounds [147,148]. Thus, linear potential scan voltammograms for surface-confined electroactive species verify [79]... 

The Cottrell equation states that the product it,/2 should be a constant K for a diffusion-controlled reaction at a planar electrode. Deviation from this constancy can be caused by a number of situations, including nonplanar diffusion, convection in the cell, slow charging of the electrode during the potential step, and coupled chemical reactions. For each of these cases, the variation of it1/2 when plotted against t is somewhat characteristic. 

The most popular electroanalytical technique used at solid electrodes is Cyclic Voltammetry (CV). In this technique, the applied potential is linearly cycled between two potentials, one below the standard potential of the species of interest and one above it (Fig. 7.12). In one half of the cycle the oxidized form of the species is reduced in the other half, it is reoxidized to its original form. The resulting current-voltage relationship (cyclic voltammogram) has a characteristic shape that depends on the kinetics of the electrochemical process, on the coupled chemical reactions, and on diffusion. The one shown in Fig. 7.12 corresponds to the reversible reduction of a soluble redox couple taking place at an electrode modified with a thick porous layer (Hurrell and Abruna, 1988). The peak current ip is directly proportional to the concentration of the electroactive species C (mM), to the volume V (pL) of the accumulation layer, and to the sweep rate v (mVs 1). 

According to these results, the characterization of the subsequent coupled chemical reaction of the EC mechanism can be achieved with RPV by examining the oxidative limiting current. The half-wave potential is also interesting in order to determine the formal potential of the electrode process [79]. 

E > E (E less negative). The applied voltage is negative of Ej and as soon as B is produced at the electrode by the chemical reaction B is immediately reduced at a diffusion-controlled rate. This increases the observed height of peak A, for this wave now contains current from the reduction of B as well as from A. When the couple B/B is reversible, the wave for B can be seen if the reverse scan is sufficient to go positive of Eg. In a single CV scan, only the oxidation wave of B in the B/B couple will be seen, but if two successive triangular potentials are applied to the electrode, the full reversible wave of B will be observed (Fig. 2). 

Besides its obvious application to preparative electrolysis, controlled-potential electrolysis (CPE) also can aid in mechanistic analysis of the electrode reaction. The treatment of coupled chemical reactions is simpler theoretically in CPE than in most other electrochemical methods, because the solution can be treated as being homogeneous, rather than having to account for concentration changes as a function of distance from the electrode. The mathematics are more straightforward. 

It is well known that experimental CVs for species in solution phase frequently diverge from theoretical ones for -electron reversible couples. The divergence can be caused by a variety of factors deviations from reversibility, occurrence of coupled chemical reactions and/or surface effects, and resistive and capacitive effects (Nicholson and Shain, 1964 Nicholson, 1965a). These last effects will be briefly treated here because of their potential significance when microheterogenous deposits or more or less homogeneous coatings of microporous materials cover the electrode surface. 

For many electrode processes of interest, the rates of electron transfer, and of any coupled chemical reactions, are high compared with that of steady state mass transport. Therefore during any steady state experiment, Nernstian equilibrium is maintained at the electrode and no kinetic or mechanistic information may be obtained from current or potential measurements. Apart from in a few areas of study, most notably in the field of corrosion, steady state measurements are not therefore widely used by electrochemists. For the majority of electrode processes it is only possible to determine kinetic parameters if the Nernstian equilibrium is disturbed by increasing the rate of mass transport. In this way the process is forced into a mixed control region where the rates of mass transport and of the electrode reaction are comparable. The current, or potential, is then measured as a function of the rate of mass transport, and the data are, then either extrapolated or curve fitted to obtain the desired kinetic parameters. There are basically three different ways in which the rate of mass transport may be enhanced, and these are now discussed. 

In the region where no reverse peak is observed, the pure kinetic zone, it can be shown that the chemical reaction has the effect of of shifting the cathodic peak potential positive of the value for the reversible electron transfer. This is because the coupled chemical reaction reduces the concentration of Rat the surface from the value it would have had for a simple electron transfer reaction. The electrode reaction therefore has to work harder to maintain Nernstian equilibrium... 

In potential sweep methods, the current is recorded while the electrode potential is changed linearly with time between two values chosen as for potential step methods. The initial potential, E, is normally the one where there is no electrochemical activity and the final potential, 2, is the one where the reaction is mass transport controlled. In linear sweep voltammetry, the scan stops at E2, whereas in cyclic voltammetry, the sweep direction is reversed when the potential reaches 2 and the potential remmed to j. This constitutes one cycle of the cyclic voltammogram. Multiple cycles may be recorded, for example, to study film formation. Other waveforms are used to study the formation and kinetics of intermediates when studying coupled chemical reactions (Figure 11.4c). 

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