Simple electrode reaction

Electrode processes are a class of heterogeneous chemical reaction that involves the transfer of charge across the interface between a solid and an adjacent solution phase, either in equilibrium or under partial or total kinetic control. A simple type of electrode reaction involves electron transfer between an inert metal electrode and an ion or molecule in solution. Oxidation of an electroactive species corresponds to the transfer of electrons from the solution phase to the electrode (anodic), whereas electron transfer in the opposite direction results in the reduction of the species (cathodic). Electron transfer is only possible when the electroactive material is within molecular distances of the electrode surface thus for a simple electrode reaction involving solution species of the fonn... 

Similarly to the response at hydrodynamic electrodes, linear and cyclic potential sweeps for simple electrode reactions will yield steady-state voltammograms with forward and reverse scans retracing one another, provided the scan rate is slow enough to maintain the steady state [28, 35, 36, 37 and 38]. The limiting current will be detemiined by the slowest step in the overall process, but if the kinetics are fast, then the current will be under diffusion control and hence obey the above equation for a disc. The slope of the wave in the absence of IR drop will, once again, depend on the degree of reversibility of the electrode process. 

Firstly, it is the electrode potential which determines whether sufficient energy is being supplied for the electron transfer to occur. If we consider the simple electrode reaction (omitting charge designation for the oxidized and reduced species 0 and R)... 

VIII. Structural Effects A. The Rates of Simple Electrode Reactions... 

In Chapter 6 we considered the basic mles obeyed by simple electrode reactions occurring without the formation of intermediates. However, electrochemical reactions in which two or more electrons are transferred more often than not follow a path involving a number of consecutive, simpler steps producing stable or unstable intermediates (i.e., they are multistep reactions). 

As the generality of equations of type (5.2.3) should not be exaggerated (e.g. in the presence of strong adsorption, such as in electrocatalytic processes, they are no longer valid), the basic features of electrochemical kinetics will be explained by using the simple electrode reaction... 

Consider a very simple electrode reaction consisting of a fast one-electron transfer from an electrode to molecules attached to the electrode surface,... 

It was mentioned in Section 2.2 that even in the case of a simple electrode reaction one must take into account both heterogeneous electron transfer and mass transport processes. Let us therefore examine the mathematical relationships which govern the two processes. 

In Sections 4.1 and 4.2, the electron transfer and the mass transport involved in a simple electrode reaction [simple = not complicated by preceding or following reactions, by absorption, or by formation of phases (see Section 2.2)] have been treated separately. However, it is to be expected that in reality both phenomena act in a concerted manner during a faradaic process. Thus, as seen previously, even the simple electrode process ... 

Fig. 9-3. Polarization curves estimated for a simple electrode reaction of metallic ion transfer i = reaction current to - exchange reaction current in reaction equilibrium = symmetric factor (0 < 3 < 1).

The enhancement of SWV net peak current caused by the reactant adsorption on the working electrode surface was utilized for detection of chloride, bromide and iodide induced adsorption of bismuth(III), cadmium(II) and lead(II) ions on mercury electrodes [236-243]. An example is shown in Fig. 3.13. The SWV net peak currents of lead(II) ions in bromide media are enhanced in the range of bromide concentrations in which the nentral complex PbBr2 is formed in the solntion [239]. If the simple electrode reaction is electrochemically reversible, the net peak cnnent is independent of the composition of supporting electrolyte. So, its enhancement is an indication that one of the complex species is adsorbed at the electrode snrface. 

The electrokinetic equation for this simple electrode reaction can be written as... 

First of all, the mathematical background will be developed for the case of a simple electrode reaction O + n e = R. In this treatment, contrasts like potential versus current perturbation, large amplitude versus small amplitude, and single step versus periodical perturbation are emphasized. While discussing these principles, the most common methods derived from them will be briefly mentioned. On the other hand, it will be shown that, by virtue of the method of Laplace transformation, these methods have much in common and contain, in principle, the same information if the detected cell response is of the same order. 

As in the present state of the art the study of electrochemical kinetics is not confined to simple electrode reactions, recent developments of more complex cases will also be discussed. This concerns, in particular, mechanistic studies of multi-step reactions with both unstable and stable intermediates and adsorption processes. Each time, the most suitable methods for such studies will be selected for a discussion of the appropriate methodology and analysis procedure. 

The determination of the kinetic parameters of simple electrode reactions from the jF vs. t1/2 curve resulting from a potential step, was described in 1954 by Gerischer and Vielstich [44], Originally, it was... 

Transport to the electrode surface as described in Chapter 5 assumes that this occurs solely and always by diffusion. In hydrodynamic systems, forced convection increases the flux of species that reach a point corresponding to the thickness of the diffusion layer from the electrode. The mass transfer coefficient kd describes the rate of diffusion within the diffusion layer and kc and ka are the rate constants of the electrode reaction for reduction and oxidation respectively. Thus for the simple electrode reaction O + ne-— R, without complications from adsorption,... 

Potential at half-height — (in voltammetry) This is a diagnostic criterion in -> linear scan voltammetry. The potential at half-height Ep/2 is the potential at which the current is equal to one-half of the peak current fp Ep/2 = h (/=/p/2)- I he first of two potentials at half-height, the one that precedes the peak potential (Ep) is considered only. If a simple electrode reaction is reversible (- reversibility) and controlled by the planar, semi-infinite - diffusion, the absolute value of the difference between Ep/2 and Ep is equal to 56.6/n mV and independent of the - scan rate. If the -> electrode reaction of dissolved reactant is totally irreversible (-> reversibility), the difference Ep/2 - Ep is equal to 47.7/an mV for the cathodic process and -47.7/(l - a)n mV for the anodic process. 

In many simple electrode reactions, the symmetry factor P is found to be close to one-half, and this value is usually assumed in the kinetic analysis of complex reactions. If this is substituted into Eq. 35E, we obtain ... 

So far we have discussed the current-potential relationship for a simple electrode reaction, which occurs in one step and in which a single electron is transferred. We might add here, in parentheses, that there can be only one electron transferred in each elementary step, so that all single-step reactions involve the transfer of only one electron. Real systems are, however, more complex. Most electrode reactions occur in several steps, and the transition from the reactants to the products requires the transfer of several electrons. Even an apparently simple reaction, such as silver plating, cannot be described by the simple equation... 

The separation of the dynamic and energetic effects on the rate of simple electrode reactions may be easier if the activation energy of such reactions could be calculated precisely. 

In Sec. 3.1 we discussed the effect of solvents on simple electrode reactions in which the reactant preserves its first coordination sphere in the course of the electrode process. Now we are going to consider the influence of solvents on reactions which proceed with total breaking of bonds between the central metal ion and the ligands. 

Since Equation 58 is identical in form to Equation 30, the analysis of data for mixed potential systems is the same as that for simple electrode reactions. 

Consider the simple electrode reaction 21.3. Usually, any such primary reaction is accompanied by a side reaction that leads to a reduction of current efficiency. Such a reaction is referred to as a loss reaction in electrochemical terminology. The major loss reaction is the hydrogen evolution reaction... 

Since a and b are constants, plotting the anode and cathode overpotential curves of a simple electrode reaction in semilogarithmic representation results in straight lines when the overpotential is plotted on the linear axis and the current density I o on the logarithmic axis. 

So far the treatment of electron transfer is somewhat pragmatic and gives little insight into the factors which determine their properties. To remedy this to some extent, one should first look at Fig. 1.4 which shows the energy level diagram for a particular but typical simple electrode reaction... 

Standard electrode potentials and kinetic characteristics for some simple electrode reactions... 

The Randles equivalent circuit is used to describe a simple electrode reaction, where the solution resistance Ra) is in series with the charge transfer resistance (Act) and the Warbiug impedance (Zw) expressing the diffusion of the electroactive species, and the double-layer capacitance (Cji) is in parallel with Act and Zw (Zp = Act + is called the Faraday impedance). 

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