Rate constant electrochemical

As a result of polarographic investigations using e.g. a dropping mercury electrode electrochemical rate constants at the half wave potential Ey2 are reported ... 

With the electrochemical rate constant a relationship between the exchange current density, the electrochemical rate constant and the concentration of the reacting species can be derived ... 

FIGURE 34.4 Dependence of electrochemical rate constant on the electrode potential for outer-sphere electron transfer. An exponential increase in the normal region changes for the plateau in the activationless region. 

The rate of MV formation was also dependent on pH. The bimolecular rate constant, as calculated from the first order rate constant of the MV build-up and the concentration of colloidal particles, was substantially smaller than expected for a diffusion controlled reaction Eq. (10). The electrochemical rate constant k Eq. (9) which largely determines the rate of reaction was calculated using a diffusion coefficient of of 10 cm s A plot of log k vs. pH is shown in Fig. 24. 

The partial derivative on the right-hand side represents, in essence, the electrochemical rate constant the larger the change in current with potential the easier charge transfer is and we can define RCT, the charge-transfer resistance, as 1 /(dJ/dE)CoCfl. Given that (1 /i)112 = (1 — i)/J2 and defining the transport part of (2.106) ... 

Evidently, the impedance of the interface consists of two components a charge-transfer resistance Rex, which will depend on the electrochemical rate constants, and a more unusual element arising from the diffusion of the redox couple components to and from the interface. The magnitude of this element... 

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,... 

The electrochemical rate constants for hydrogen peroxide reduction have been found to be dependent on the amount of Prussian blue deposited, confirming that H202 penetrates the films, and the inner layers of the polycrystal take part in the catalysis. For 4-6 nmol cm 2 of Prussian blue the electrochemical rate constant exceeds 0.01cm s-1 [12], which corresponds to the bi-molecular rate constant of kcat = 3 X 103 L mol 1s 1 [114], The rate constant of hydrogen peroxide reduction by ferrocyanide catalyzed by enzyme peroxidase was 2 X 104 L mol 1 s 1 [116]. Thus, the activity of the natural enzyme peroxidase is of a similar order of magnitude as the catalytic activity of our Prussian blue-based electrocatalyst. Due to the high catalytic activity and selectivity, which are comparable with biocatalysis, we were able to denote the specially deposited Prussian blue as an artificial peroxidase [114, 117]. 

The cyclic voltammograms of these systems display quasi-reversible behavior, with AEv/v being increased because of slow electrochemical kinetics. Standard electrochemical rate constants, ( s,h)obs> were obtained from the cyclic voltammograms by matching them with digital simulations. This approach enabled the effects of IR drop (the spatial dependence of potential due to current flow through a resistive solution) to be included in the digital simulation by use of measured solution resistances. These experiments were performed with a non-isothermal cell, in which the reference electrode is maintained at a constant temperature... 

Similar to homogeneous electron-transfer processes, one can consider the observed electrochemical rate constant, k, , to be related to the electrochemical free energy of reorganization for the elementary electron-transfer step, AG, by... 

Consequently, a wealth of information on the energetics of electron transfer for individual redox couples ("half-reactions") can be extracted from measurements of reversible cell potentials and electrochemical rate constant-overpotential relationships, both studied as a function of temperature. Such electrochemical measurements can, therefore, provide information on the contributions of each redox couple to the energetics of the bimolecular homogeneous reactions which is unobtainable from ordinary chemical thermodynamic and kinetic measurements. 

The electrochemical rate constants of the Zn(II)/Zn(Hg) system obtained in propylene carbonate (PC), acetonitrile (AN), and HMPA with different concentrations of tetraethylammonium perchlorate (TEAP) decreased with increasing concentration of the electrolyte and were always lower in AN than in PC solution [72]. The mechanism of Zn(II) electroreduction was proposed in PC and AN the electroreduction process proceeds in one step. In HMPA, the Zn(II) electroreduction on the mercury electrode is very slow and proceeds according to the mechanism in which a chemical reaction was followed by charge transfer in two steps (CEE). The linear dependence of logarithm of heterogeneous standard rate constant on solvent DN was observed only for values corrected for the double-layer effect. 

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. 

Here, kv is an electrochemical rate constant, and F is the faraday, the charge on 1 mol ofunivalentions. It contains the exponential term for the electrode potential (assuming a cathodic reaction in a region in which the rate of the back anodic reaction can be neglected). However, it does take into account the effect of diffusion on the observed current density, i. 

In a series of papers between 1956 and 1965, Marcus solved much of the mystery by outlining a description of the probability of fluctuations in the geometry of reactants and their solvents. These fluctuations lead to changes in the energy barriers that the reactants must surmount before an electron can be transferred from one molecule to another. Marcus extended the theory to other systems, such as electrochemical rate constants at electrodes, and to chemiluminescent electron transfer reactions. The by-now famous inverted effect is a consequence of his theory after a certain point, adding more energy to an electron transfer reaction actually slows the process. Scientists believe photosynthesis can occur because of the inverted effect. 

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

Again neither the electrochemical rate constant ks nor M are known. However, a range of related values is presented in Table II. 

Volmer turned his attention to processes at - nonpo-larizable electrodes [iv], and in 1930 followed the famous publication (together with - Erdey-Gruz) on the theory of hydrogen - overpotential [v], which today forms the background of phenomenological kinetics of electrochemistry, and which resulted in the famous - Butler-Volmer equation that describes the dependence of the electrochemical rate constant on applied overpotential. His major work, Kinetics of Phase Formation , was published in 1939 [v]. See also the Volmer reaction (- hydrogen), and the Volmer biography with selected papers [vi]. 

For solution redox couples uncomplicated by irreversible coupled chemical steps (e.g. protonation, ligand dissociation), a standard (or formal) potential, E°, can be evaluated at which the electrochemical tree-energy driving force for the overall electron-transfer reaction, AG c, is zero. At this potential, the electrochemical rate constants for the forward (cathodic) and backward (anodic) reactions kc and ka (cms-1), respectively, are equal to the so-called "standard rate constant, ks. The relationship between the cathodic rate constant and the electrode potential can be expressed as... 

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