Electrochemical rate equations

The rates of electrochemical reactions are directly measurable as currents, I. These rates are related to the chemical reaction rate v by 

V = reaction velocity (mol cm s ) z = number of electrons involved in the reaction F = Faraday constant 

The kinetics of electrochemical reactions distinguish themselves from the kinetics of other reactions by their dependence on the potential, V, of the electrode referred to that of a reference electrode in the same electrolyte. Thus, when a potential is applied to a metal in contact with an electrolyte, the energy of the initial state of the ion or molecule and the electron in the metal at the Fermi level is changed by eV or VF per mole of electrons (i.e., 96,485 C), and the activation energy is altered by a fraction of VF. 

FIGURE 4.2.1. Effect of change of electrode potential, as VF, on energy of activation, A of an electron transfer reaction in relation to the barrier symmetry factor, fS [11]. 

Let us now examine the rate equation for an electrochemical reaction involving the discharge of ions on a metal electrode surface, M, to form a M-H species, as  

---

Electrochemical rate equation, 30 233-236 Electrochemical reactor, 30 309-311 continuity equation, 30 311 engineering, 30 309-321 selectivity function, 30 315-316 Electrocyclic reactions, 20 311-316 Electrodes... 

The behavior of b as f T) for ionic redox reactions at electrodes, especially those processes that involve only outer-sphere changes of state, and both red and ox species which are not specifically adsorbed, is of great interest. From some of Weaver s work information on the dependence of 6 on T for such reactions is available and some attempts have been made, e.g., by Parsons and Passeron, to establish if the potential-dependent factor in the electrochemical rate equation in fact includes a quadratic term in 77 as well as the usual linear one however, this is a different question (cf. Ref. 8) related to the harmonicity or, otherwise, of the fluctuations involved in the activation process. 

Equation 50 will be used subsequently to develop electrochemical rate equations for specific examples of corrosion systems. 

In these equations, the terms and exp(-Z>A-E) have been combined to give a composite rate constant k J. This has been done merely to emphasize the formal similarity between the conventional and electrochemical rate equations. 

Complete electrochemical rate equation, which is an exponential relationship. 

Principles. Since corrosion involves an oxidation and a reduction, we can describe the rates of these reactions, assuming kinetic control, by the electrochemical rate equations described in Section 4.2. Neglecting the backward rates of these component reactions, it can be shown that the corrosion current is a function of the exchange current densities of the anodic (fo,a) and cathodic (/o,c) reactions and the equilibrium potentials of the anodic E ) and the cathodic Ed processes. Assuming the transfer coefficient to be 0.5 results in... 

Following the seminal paper of Butler (37) in 1924 on the kinetic basis of Nernst equilibrium potentials, an electrochemical rate equation was written by Erdey-Gruz and Volmer (14), for a net current-density i, in terms of components of i for the forward and backward directions of the process. They recognized that only some fraction (denoted by a or 3) of the electrical energy change riF associated with change of electrode potential, would exponentially modify the current, giving a potential-dependent rate-equation of the form ... 

Let us consider the electrochemical rate equation and its limiting case of very fast rates, the Nernst equation ... 

Once the local concentration overpotential is known, the activation overpotential, ria, is obtained by subtracting Tjc from total Tj. The local activation overpotential is the actual driving force of the electrochemical reaction. It is related to the local current density at any point of the reaction zone by an electrochemical rate equation such as the Butler-Volmer equation (Eq. (10a)). Therefore, the rate equation, the Nernst equation (Eq. (37)), and the potential balance in combination couple the electric field with the species diffusion field. In addition, the energy balance applies also at the electrode level. Although this introduces another complication, a model including a temperature profile in the electrode is very useful because heat generation occurs mainly by electrochemical reaction and is localised at the reaction zone, while the... 

The complete expression for the current density is obtained as the difference between the anodic and the cathodic current densities. This is the current measured in an external circuit. Now, if we have used Eq. (5.23) to represent the potential dependence of the electrochemical rate equation for the anodic direction, what would we use for the cathodic reaction. Clearly, the term including t] must have the opposite sign, since the same potential that enhances the rate of the reaction in one direction must retard it in the opposite direction. What about the symmetry factor, We noted... 

The values of the parameters derived from the best fit can be related to the fundamental physical constants, such as the electrochemical rate constants, by explicit calculation. From the Butler- Volmer equation,... 

Kinetics, The major factors determining the rate of the partial cathodic reaction are concentrations of metal ions and ligands, pH of the solution, and type and concentration of additives. These factors determine the kinetics of partial cathodic reaction in a general way, as given by the fundamental electrochemical kinetic equations discussed in Chapter 6. 

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]... 

Equation 3.13 predicts a linear dependence of In / on E whose slope depends on the coefficient ana, while the ordinate at the origin depends on the electrochemical rate constant and the net amount of depolarizer deposited on the electrode. Accordingly, both the slope and the ordinate at the origin of Tafel plots become phase-dependent [133, 183]. Since the quantity of depolarizer varies from one... 

In this equation, SLm represents the Tafel slope for the mixture of X plus Y, and Slx,Siy represents the Tafel slopes for the individual components. This equation enables a determination of / from Tafel representations, providing that the quotients between the individual electrochemical rate constants, kx and ky, and the electron transfer coefficients, ocxnax,ocYnaY, are known. 

The possible effect of a coupled chemical reaction on the response to an electrochemical perturbation can be deduced by combination of the j F vs. surface concentration relation with the proper rate equation for the charge transfer process and subsequent elaboration applying to a particular method. Naturally, a complex rate equation will be unfavourable if it is... 

The general rate equation valid for this proposed mechanism can be calculated and verified by experimental evidence. It is clear that if there is one contradiction between calculated results and experimental evidence, the proposed mechanism cannot be valid. Step 3 of the mechanism is proposed as RDS because it is the only electrochemical step in the reaction scheme. Its rate equation can be written as ... 

The electrochemical rate constant for the forward reaction, i.e. reduction, is given by the following equation ... 

---