Electrochemical reactions rate constants

In 1930, Max Volmer and Tibor Erdey-Griiz used the concept of a slow discharge step for cathodic hydrogen evolntion (slow discharge theory). According to these ideas, the potential dependence of electrochemical reaction rate constants is described by Eq. (6.5). Since hydrogen ions are involved in the slow step A, the reaction rate will be proportional to their concentration. Thus, the overall kinetic equation can be written as... 

Introducing in Equation 4.26 the explicit dependence of the electrochemical reaction rate constants (cf. Equation 4.28) on potential and equalising p to 0.5 results in ... 

Now we seek to relate this expression to the overpotential required to produce that current density at the electrode of interest, so that we can predict electrode overpotential as a function of current density in a similar fashion as with the BV approach for electron-transfer-limited reactions. The electrochemical reaction rate constant % can be written... 

According to Eq. (14.2), the activation energy can be determined from the temperature dependence of the reaction rate constant. Since the overall rate constant of an electrochemical reaction also depends on potential, it must bemeasured at constant values of the electrode s Galvani potential. However, as shown in Section 3.6, the temperature coefficients of Galvani potentials cannot be determined. Hence, the conditions under which such a potential can be kept constant while the temperature is varied are not known, and the true activation energies of electrochemical reactions, and also the true values of factor cannot be measured. 

This article presents a brief account of theory and practical aspects of rotating hemispherical electrodes. The fluid flow around the RHSE, mass transfer correlations, potential profile, and electrochemical application to the investigations of diffusivity, reaction rate constants, intermediate reaction products, passivity, and AC techniques are reviewed in the following sections. 

Similar to the rotating disk, the RHSE has the ability to determine the reaction order and reaction rate constants of an electrode reaction. Consider an electrochemical reaction of the type... 

Thus a plot of 1/i vs. l/fi1/2 would give a straight line, and the reaction rate constant, k, and diffusivity, D, can be respectively determined from the intercept, A, and the slope, B, of the straight line. Equations similar to those of the RDE may be also derived for other type electrochemical reaction using the procedures illustrated in Ref. [48, 50],... 

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 ... 

This value represents the upper limit of a first order reaction rate constant, k, which may be determined by the RHSE. This limit is approximately one order of magnitude smaller that of a rotating electrode. One way to extend the upper limit is to combine the RHSE with an AC electrochemical technique, such as the AC impedance and faradaic rectification metods. Since the AC current distribution is uniform on a RHSE, accurate kinetic data may be obtained for the fast electrochemical reactions with a RHSE. 

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. 

Derivation of the Butler-Volmer equation in terms of electrode reaction rate constants is given in most electrochemical texts.1,3 7 15... 

The current density (or electrochemical reaction rate) that signifies the rate of electric charge flow (e.g., electrons leaving the metal to go to ions in an adjacent layer in solution) is given by, for example, Eq. (7.7) by putting the constant terms kT/h andexp(-AG0 t) together as k ... 

Measuring the Electrochemical Reaction Rate as a Function of Potential (at Constant Concentration and Temperature)... 

When comparing Equations f. 37 and 1.38, it is clear that it is the relation of two parameters, namely the transport coefficient, m, and the formal reaction rate constant k° (incorporated in k(E) in Equation 1.37 see also Equation 1.20), that decides whether the current is determined mainly by the BV relation or by transport. In a voltammogram, the potential area in which the BV relation applies decreases when k° increases relatively in relation to m. In electrochemical terms, one speaks of an increase in the reversible character of the voltammetric wave. When having sufficient positive (negative) potentials for an oxidation (reduction), transport mostly prevails. Providing that the appropriate cell and/or electrode configuration is present, transport-determined currents are very reproducible and suitable for analytical purposes. 

In order to express explicitly the dependence of the reaction rate on potential, it is necessary to re-introduce this dependence for every electrochemical reaction-speed constant. These constants concern reactions where one electron is transferred and to which Equation 4.20 applies. In this relation, the potential of the redox system involved is referred to as the formal potential, so that the anodic and cathodic subcurrent can be expressed as a function of the same rate constant, k0. This is not possible in Equation 4.26 because there are rate constants of different redox systems, or because formal potentials of intermediary redox systems are not known. 

Under these assumptions the electrode potential and the rate of the electrochemical reaction are constant across the catalyst layer and the local current density is... 

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... 

A formally more explicit representation of the effect of electrode potential and associated role of temperature on electrochemical reaction rates follows from the transition-state theory applied by Glasstone et al soon after the appearance of Butler s paper. The rate constant of a chemical process is written as... 

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