Electrochemical reactions transfer coefficient

Electrocatalytic reactions often involve several elementary steps some of which are not necessarily electrochemical. The transfer coefficient is, then, related to the symmetry factor of an electron transfer rate-determining step (rds) through (74)... 

V. Marecek, Z. Samec, and J. Weber, The Dependence of the Electrochemical Charge-Transfer Coefficient on the Electrode Potential. Study of the Hexacyanoferrate (III) Hexacyanferrate (IV) Redox Reaction on Polycrystalline Gold Electrode in Potassium Fluoride Solutions, J. Electroanal. Chem. Interfacial Electrochem. 94, 169-185 (1978) cf. also J. Weber, Z. Samec, and V. Marecek, The Effect of Anion Adsorption on the Kinetics of the Iron (3 + )/Iron (2. ) Reaction on Platinum and Gold Electrodes in Perchloric Acid, J. Electroanal. Chem. Interfacial Electrochem. 89, 271-288 (1978). 

Charge of the reactant in the cathodic reaction Transfer coefficient of the anodic partial reaction of an electrochemical process... 

It follows from these kinetic equations that in reactions where the RDS occurs after another step, which is an equilibrium step, the kinetic coefficients and Pg of the overafl reaction are different from the corresponding coefficients of the RDS in fact, in the first case, kg = (k lk i)k2 and Po = 4 + P2 and in the second case, k Q = k 2lk k 1 and Pg = 4 + P i. It is important to note that if the preceding equilibrium step is an electrochemical step (/j > 1), the transfer coefficient pg of the overall reaction will always be larger than unity. The sum of transfer coefficients in the forward and reverse directions of the overaU reaction is given by... 

The smallness of the electron transmission coefficient for the transition from individual energy levels does not mean that aU electrochemical electron transfer reactions should be nonadiabatic. If the inequality opposite to Eq. (34.33) is fulfilled. 

The usual Tafel evaluation yielded a transfer coefficient a = 0.52 and a rate constant k of 4x 10 cm s at the standard potential of the MV /MV couple. This k value corresponds to a moderately fast electrochemical reaction. In this electrode-kinetic treatment the changes in the rate of electron transfer with pH were attributed only to the changes in the overpotential. A more exact treatment should also take into account the electrostatic effect on the rate of reaction which also changes with pH. 

The RHSE has the same limitation as the rotating disk that it cannot be used to study very fast electrochemical reactions. Since the evaluation of kinetic data with a RHSE requires a potential sweep to gradually change the reaction rate from the state of charge-transfer control to the state of mass transport control, the reaction rate constant thus determined can never exceed the rate of mass transfer to the electrode surface. An upper limit can be estimated by using Eq. (44). If one uses a typical Schmidt number of Sc 1000, a diffusivity D 10 5 cm/s, a nominal hemisphere radius a 0.3 cm, and a practically achievable rotational speed of 10000 rpm (Re 104), the mass transfer coefficient in laminar flow may be estimated to be ... 

Hydrogen evolution, the other reaction studied, is a classical reaction for electrochemical kinetic studies. It was this reaction that led Tafel (24) to formulate his semi-logarithmic relation between potential and current which is named for him and that later resulted in the derivation of the equation that today is called "Butler-Volmer-equation" (25,26). The influence of the electrode potential is considered to modify the activation barrier for the charge transfer step of the reaction at the interface. This results in an exponential dependence of the reaction rate on the electrode potential, the extent of which is given by the transfer coefficient, a. 

It follows that the value of the electrochemical transfer coefficient may allow the distinction between stepwise and concerted electron-transfer-bond-breaking reactions when a chemical bond of normal strength is involved (Andrieux and Saveant, 1986b Andrieux et al., 1990b). If the reduction wave possesses the characteristics of a process controlled by slow electron transfer rather than controlled by a follow-up reaction, and if a is significantly larger than 0.5, then one can conclude that the reaction proceeds in a stepwise manner. The same is true when the wave exhibits the characteristics of a process controlled by a follow-up reaction, electron transfer remaining at equilibrium. 

If the reaction (1.1) is controlled by the electrode kinetics, i.e., when the electrode reaction is not electrochemically reversible, the response depends on the dimensionless kinetic parameter k = and the transfer coefficient a [15-17],... 

The physical meaning of the kinetic parameter m is identical as for surface electrode reaction (Chap. 2.5.1). The electrochemical reversibility is primarily controlled by 03 (Fig. 2.71). The reaction is totally irreversible for log(m) < —3 and electrochemically reversible for log(fo) > 1. Between these intervals, the reaction appears quasireversible, attributed with a quasireversible maximum. Though the absolute net peak current value depends on the adsorption parameter. Fig. 2.71 reveals that the quasireversible interval, together with the position of the maximum, is independent of the adsorption strength. Similar to the surface reactions, the position of the maximum varies with the electron transfer coefficient and the amphtude of the potential modrrlation [92]. 

Figure 5. Measurement and analysis of steady-state i— V characteristics, (a) Following subtraction of ohmic losses (determined from impedance or current-interrupt measurements), the electrode overpotential rj is plotted vs ln(i). For systems governed by classic electrochemical kinetics, the slope at high overpotential yields anodic and cathodic transfer coefficients (Ua and aj while the intercept yields the exchange current density (i o). These parameters can be used in an empirical rate expression for the kinetics (Butler—Volmer equation) or related to more specific parameters associated with individual reaction steps.(b) Example of Mn(IV) reduction to Mn(III) at a Pt electrode in 7.5 M H2SO4 solution at 25 Below limiting current the system obeys Tafel kinetics with Ua 1/4. Data are from ref 363. (Reprinted with permission from ref 362. Copyright 2001 John Wiley Sons.)...

Erdey-Gruz and Volmer (2) derived the current-potential relationship in 1930 using the Arrhenius equation (1889) for the reaction rate constant and introduced the transfer coefficient. They also formulated the nucleation model of electrochemical crystal growth. 

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. 

The study of Li28 + DMF solutions [60] also allowed to characterize the electrochemical properties of polysulfides only redox couples of the type 8 /8 are involved. The chemical reactions coupled to charge transfers are classical dissociation and disproportionation equilibria no complex rearrangement reaction or transient species has been necessary. Redox potentials and charge-transfer coefficients of the redox couples involved in sulfur and polysulfide solutions are summarized in Table 2. 

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 electrochemical reaction ox(sin) + 2e- = red(sin) is first order with respect to the reactant ox. The cathodic transfer coefficient is 0.5. How many times is the excliange current density increased when the concentration of ox is increased ten times (Gokjovic)... 

The overpotentia] measured at a current density of 10-5 A/cm2 was +0.236 V. The decay of the overpotential with the cut off of the current was observed as listed Table P.l. Calculate the double-layer capacitance, the exchange current density, and the transfer coefficient for the electrochemical reaction. (Kim)... 

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