Rate of an electrochemical reaction

In addition to electrode kinetics, the rate of an electrochemical reaction can be limited by the rate of mass transfer of reactants to and from the electrode surface. In dilute solutions, four principal equations are used. The flux of species i is... 

Pick s first law and equating the transport flux J with the rate / of an electrochemical reaction... 

The rates of an electrochemical reaction at potentials away from the equilibrium value are given by Eq. (13.5), which in this case can be written as... 

The rate of an electrochemical reaction depends, not only on given system parameters (composition of the catalyst and electrolyte, temperature, state of the catalytic electrode surface) but also on electrode potential. The latter parameter has no analog in heterogeneous catalytic gas-phase reactions. Thus, in a given system, the potential can be varied by a few tenths of a volt, while as a result, the reaction rate will change by several orders of magnitude. 

It is the basic task of electrochemical kinetics to establish the functional relations between the rate of an electrochemical reaction at a given electrode and the various external control parameters the electrode potential, the reactant concentrations, the temperature, and so on. From an analysis of these relations, certain conclusions are drawn as to the reaction mechanism prevailing at a given electrode (the reaction pathway and the nature of the slow step). 

In electrocatalysis, in contrast to electrochemical kinetics, the rate of an electrochemical reaction is examined at constant external control parameters so as to reveal the influence of the catalytic electrode (its nature, its surface state) on the rate constants in the kinetic equations. 

There is no doubt that all the special sites listed above might have adsorptive and other properties differing from those of normal surface atoms. For this reason the rate of an electrochemical reaction could be higher or lower at such sites. The sign and magnitude of the overall effect depends on the relative numbers of special points and normal surface atoms. 

Figure 4 illustrates that our present knowledge about the dependence of the standard potential of very small silver microelectrodes on the agglomeration number is rather fragmentary. Even less is known about this dependence for other metals. The experiments of Fig. 5 prove that the rate of an electrochemical reaction in which a small microelectrode is involved, may strongly depend on the size of the microelectrode. 

The classical electrochemical methods are based on the simultaneous measurement of current and electrode potential. In simple cases the measured current is proportional to the rate of an electrochemical reaction. However, generally the concentrations of the reacting species at the interface are different from those in the bulk, since they are depleted or accumulated during the course of the reaction. So one must determine the interfacial concentrations. There axe two principal ways of doing this. In the first class of methods one of the two variables, either the potential or the current, is kept constant or varied in a simple manner, the other variable is measured, and the surface concentrations are calculated by solving the transport equations under the conditions applied. In the simplest variant the overpotential or the current is stepped from zero to a constant value the transient of the other variable is recorded and extrapolated back to the time at which the step was applied, when the interfacial concentrations were not yet depleted. In the other class of method the transport of the reacting species is enhanced by convection. If the geometry of the system is sufficiently simple, the mass transport equations can be solved, and the surface concentrations calculated. 

Activation Polarization Activation polarization is present when the rate of an electrochemical reaction at an electrode surface is controlled by sluggish electrode kinetics. In other words, activation polarization is directly related to the rates of electrochemical reactions. There is a close similarity between electrochemical and chemical reactions in that both involve an activation barrier that must be overcome by the reacting species. In the case of an electrochemical reaction with riact> 50-100 mV, rjact is described by the general form of the Tafel equation (see Section 2.2.4) ... 

Steady-State Kinetics, There are two electrochemical methods for determination of the steady-state rate of an electrochemical reaction at the mixed potential. In the first method (the intercept method) the rate is determined as the current coordinate of the intersection of the high overpotential polarization curves for the partial cathodic and anodic processes, measured from the rest potential. In the second method (the low-overpotential method) the rate is determined from the low-overpotential polarization data for partial cathodic and anodic processes, measured from the mixed potential. The first method was illustrated in Figures 8.3 and 8.4. The second method is discussed briefly here. Typical current—potential curves in the vicinity of the mixed potential for the electroless copper deposition (average of six trials) are shown in Figure 8.13. The rate of deposition may be calculated from these curves using the Le Roy equation (29,30) ... 

The overall rate of an electrochemical reaction is measured by the current flow through the cell. In order to make valid comparisons between different electrode systems, this current is expressed as cunent density,/, the current per unit area of electrode surface. Tire current density that can be achieved in an electrochemical cell is dependent on many factors. The rate constant of the initial electron transfer step depends on the working electrode potential, Tlie concentration of the substrate maintained at the electrode surface depends on the diffusion coefficient, which is temperature dependent, and the thickness of the diffusion layer, which depends on the stirring rate. Under experimental conditions, current density is dependent on substrate concentration, stirring rate, temperature and electrode potential. 

When one examines the rate of an electrochemical reaction and how it varies with overpotential, it is often found that equations such as (7.150) and (7.150a) (which depend on a Langmuir assumption as to the implied isotherm) are obeyed, and there is no need to modify the kinetic equations to allow for a special isotherm. 

The first knowledge about the relationship between the rate of an electrochemical reaction and the imposed interfacial potential was obtained from the work of Tafel [1] who found empirically that this relationship is exponential if jF is the faradaic current involved, e.g. in the redox reaction 0 + ne=R... 

Diffusion-controlled rate — of an electrochemical reaction is encountered if diffusion of a redox species to the electrode surface is the most hindered (slowest) step in the overall transport process including mass transport, -> chemical reaction and - electrode reaction. 

Therefore, it might be most appropriate to refer to the parameter P as an efficiency factor. We try to accelerate the rate of an electrochemical reaction by applying an amount of electrical energy SAtjtF, but only a fraction P of this electrical energy is used to reduce the free... 

We recall that the current is a very sensitive measure of the rate of an electrochemical reaction. It is therefore quite easy to determine the current-potential relationship without causing a significant change in the concentration of either reactants or products. Thus, measurements in electrode kinetics are conducted effectively under quasi-zero-order kinetic conditions. It would be wrong to infer from this that electrode reactions are independent of concentration. To determine the concentration dependence (i.e., the reaction order), one must obtain a series of HE or //ri plots and derive from them plots of log i versus logC. at different potentials, as shown in Fig. IF. The slopes in Fig. lF(b) yield the parameter p since p = (alog i/alogC.) is measured at constant potential E. Here, and in all further equations, we shall assume that T, P, and the concentration of all other species in solution are kept constant, to permit us to write the equations in a more concise form. 

The rate of an electrochemical reaction is measured as electric current. To allow comparisons between different systems, the rate is usually measured as current density. This is the current flowing through the... 

The rate of an electrochemical reaction p, r (mole/cm catalyst surface area/s), as that of a chemical reaction, depends upon the temperature and activities of reacting species. In addition, in the case of the electrochemical reaction, the electric energy at the electrode-electrolyte interface also strongly influences the rate of the reaction. Thus, the rate of an electrochemical reaction is commonly written as the product of a reaction rate constant and a function of activities of various species, u, ..., involved in the reaction... 

The rate of an electrochemical reaction involving reactant i, expressed as dN /dt, where N, is the number of moles of i electrolyzed at time t, is proportional to the faradaic current (/) flowing across the cell. However, as the electrode process is a heterogeneous reaction, its rate is usually expressed as... 

In Section 26.2, the rate of an electrochemical reaction was shown to be dependent on the electrode potential, the intrinsic rate constants for the forward and backward reactions at the electrode, and the concentrations of oxidized and reduced species at the electrode surface. When the transport of reactants and/or products to and/or from the electrode surface is the rate-controlling step, and in Equation (26.46) will differ from those in the bulk solution. For uncharged species in solution, transport... 

The study of electrochemical systems has always had a major contribution to make to the field of applied science. This has been facilitated by the ease and simplicity with which the rate of an electrochemical reaction can be controlled at the electrode-electrolyte interface by means of the electrode potential. However, it has long been known that many electrochemical reactions take place with complex mechanisms and the importance of techniques that are capable of yielding information on species at or near an electrode has been widely accepted. 

The rate of an electrochemical reaction is usually restricted to a certain (range) of operational current density, j, in order to achieve a high current efficiency together with a suitable form of metal product. At a constant current, I, the mass rate of metal-ion removal is given by Faraday s laws of electrolysis as [28] ... 

Fig. 3. Influence of electric potential on energy barrier for determining rate of an electrochemical reaction, simple picture.

Since the rate of an electrochemical reaction will accelerate as the overpotential applied is increased, the rates can only be meaningfully compared at one point, namely the reversible potential, where the driving force of the overpotential is absent. The rate here is represented by the term /q (exchange current density) = A [reactantse/c., as seen in the equation on p. 64. Unfortunately, such results are almost wholly absent from the electro-organic literature. 

The rate of an electrochemical reaction is usually measured by a current, I, flowing in an external electrical circuit (see below). This current is related to the flux of a reacting species, N., and the flux of a... 

The rates of both chemical and electrochemical reactions are affected by the availability of the reactants and products, and hence their concentrations and rates of diffusion, and by a term known as the activation energy for the reaction. The rate of an electrochemical reaction can also be affected by the various resistances in the system. 

Frumkin has combined this reasoning with his theory of the slow discharge [49] to derive the expression for the rate of an electrochemical reaction [50-52], for example, for the cathodic component of... 

Different variables affecting the rate of an electrochemical reaction are shown in Fig. 2.3. Consider an overall electrode reaction, O + ne R, composed of a series of steps that cause the conversion of the dissolved oxidized species, O, to a reduced form, R, as shown schematically in Fig. 2.4. In general, the current (or electrode reaction rate) is governed by the rates of processes such as ... 

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