Standard rate constants

TABLE 1-55. STANDARD RATE CONSTANTS FOR THIAZOLES AND 2-THIAZOLONES (377)... 

Sodium-silicate glass, 151 Sol-gel films, 120, 173 Solid electrodes, 110 Solid state devices, 160 Solvents, 102 Speciation, 84 Spectroelectrochenristry, 40 Spherical electrode, 6, 8, 9, 61 Square-wave voltammetry, 72, 92 Staircase voltammetry, 74 Standard potential, 3 Standard rate constant, 12, 18 Stripping analysis, 75, 79, 110 Supporting electrolyte, 102 Surface-active agents, 79... 

It should be kept in mind, that these rate constants are defined based on the volume concentrations of the reacting species. Another standard rate constant hP can be defined with regard to the rate of the reaction at the standard electrode potential of the electrode reaction. This rate constant refers consequently to standard activities instead of concentrations. 

The standard rate constant kP characterizes the rates of both the forward and reverse processes. Its value is independent of the reference electrode selected, in contrast to what holds true for the values of k and and it is also independent of the component concentrations, in contrast to what holds true for the exchange CD. Therefore, this constant is an unambiguous characteristic of the kinetic properties exhibited by a given electrode reaction. 

When the solution is not quite inert, ac techniques are widely used to investigate the capacitance and other surface properties of platinum electrodes as well as of various other electrodes. Their chief advantage is the possibility to apply them in the case of electrodes passing some faradaic current. It is shown in Section 12.5.1 that in this case the electrode s capacitance can be determined by extrapolating results obtained at different ac frequencies to the region of high frequencies. This extrapolation can be used for electrodes where electrode reactions occur that have standard rate constants, of up to 1 cm/s. 

It was shown later that a mass transfer rate sufficiently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r < 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k°) and transfer coefficient (a) were found by fitting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, iii/2, and two quartile potentials, and ii3/4 [8a,27].) A number of voltam-mograms obtained at 5-250 nm pipettes yielded similar values of kinetic parameters, = 1.3 0.6 cm/s, and a = 0.4 0.1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefficient for a 10 nm-radius pipette is > 10 cm/s (assuming D = 10 cm /s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. 

In Ref. 30, the transfer of tetraethylammonium (TEA ) across nonpolarizable DCE-water interface was used as a model experimental system. No attempt to measure kinetics of the rapid TEA+ transfer was made because of the lack of suitable quantitative theory for IT feedback mode. Such theory must take into account both finite quasirever-sible IT kinetics at the ITIES and a small RG value for the pipette tip. The mass transfer rate for IT experiments by SECM is similar to that for heterogeneous ET measurements, and the standard rate constants of the order of 1 cm/s should be accessible. This technique should be most useful for probing IT rates in biological systems and polymer films. 

In electrochemical literature the standard rate constant fe is often designated as fes h or fe9, called the specific heterogeneous rate constant or the intrinsic rate constant. According to eqns. 3.5 and 3.6, we have... 

Here, i is the faradaic current, n is the number of electrons transferred per molecule, F is the Faraday constant, A is the electrode surface area, k is the rate constant, and Cr is the bulk concentration of the reactant in units of mol cm-3. In general, the rate constant depends on the applied potential, and an important parameter is ke, the standard rate constant (more typically designated as k°), which is the forward rate constant when the applied potential equals the formal potential. Since there is zero driving force at the formal potential, the standard rate constant is analogous to the self-exchange rate constant of a homogeneous electron-transfer reaction. 

As the kinetic parameter Ahset decreases, either because the standard rate constant decreases or because the scan rate is increased, the cyclic voltammetric response passes rapidly from the symmetrical reversible Nernstian pattern described in Section 1.2.1 to an asymmetrical irreversible curve, while the cathodic peak shifts in the cathodic direction and the anodic peak shifts in the anodic direction. 

For simplicity, variations of the two rate constants in Figure 1.18 have been restricted to the values in between the standard rate constant k et and... 

The Butler-Volmer rate law has been used to characterize the kinetics of a considerable number of electrode electron transfers in the framework of various electrochemical techniques. Three figures are usually reported the standard (formal) potential, the standard rate constant, and the transfer coefficient. As discussed earlier, neglecting the transfer coefficient variation with electrode potential at a given scan rate is not too serious a problem, provided that it is borne in mind that the value thus obtained might vary when going to a different scan rate in cyclic voltammetry or, more generally, when the time-window parameter of the method is varied. 

FIGURE 1.22. Solvent reorganization energies derived from the standard rate constants of the electrochemical reduction of aromatic hydrocarbons in DMF (with n-Bu4N+ as the cation of the supporting electrolyte) uncorrected from double-layer effects. Variation with the equivalent hard-sphere radii. Dotted line, Hush s prediction. Adapted from Figure 4 in reference 13, with permission from the American Chemical Society. 

These electron transfer reactions are very fast, among the fastest known. This is the reason that impedance methods were used originally to determine the standard rate constant,13,61 at a time when the instrumentation available for these methods was allowing shorter measurement times (high frequencies) to be reached than large-amplitude methods such as cyclic voltammetry. The latter techniques have later been improved so as to reach the same range of fast electron transfer kinetics.22,63... 

Figure 2.29. If the intrinsic barrier for electron transfer is small, the potential range within which the activation control prevails is accordingly narrow and the corresponding asymptote is approximately linear, as represented in the figure, where ks is the standard rate constant (i.e., the rate constant at zero driving force). Under these conditions, redox catalysts that offer a small driving force resulting in counter-diffusion control can be found. This behavior is identified by the value of the slope (F/TIT In 10). The intersection of the counter-diffusion and the diffusion asymptotes provides the value of the standard potential sought, , B.

The Butler-Volmer law may be applied within the potential range of each wave with standard potentials E and E2, transfer coefficients standard rate constants and kc f2. The simulations shown in Figure 2.3527 were carried out as depicted in Section 6.2.6 and led determination of the following parameters ... 

The two successive electron transfer reactions are assumed to obey the Butler-Volmer law with the values of standard potentials, transfer coefficient, and standard rate constants indicated in Scheme 6.1. It is also assumed, matching the examples dealt with in Sections 2.5.2 and 2.6.1, that the reduction product, D, of the intermediate C, is converted rapidly into other products at such a rate that the reduction of B is irreversible. With the same dimensionless variables and parameters as in Section 6.2.4, the following system of partial derivative equations, and initial and boundary conditions, is obtained ... 

Standard rate constant for redox couple measured in 0.1-0.4 M KPF and/or NaClO supporting... 

The largest values for the standard rate constant k° (expressed in metre/second) range from 0.01 m s-1 to 0.1 m s-1, and commonly characterize redox processes which do not involve significant molecular reorganizations. 

The smallest values for the standard rate constant k° are around 10 11 m s-1. 

As will now be discussed, the exchange current is proportional to the standard rate constant, thus resulting in the common practice of using i0 instead of k° in kinetic equations. 

Like the standard rate constant, k°, the exchange current, io, characterizes the rate of the electron transfer process inside a redox couple. 

In the treatment of the kinetics of the electron transfer illustrated in Section 4.1, it has been assumed that the propulsive force for the electron transfer was the electrochemical potential E i.e. a quantity directly related to 4>M — < >s). However, since the solvated ions cannot enter the inner layer of the double layer (IHP), the true propulsive force should be < )M — standard rate constant, k°, and the exchange current, i0, should become respectively ... 

It is commonly assumed that an electron transfer behaves quasi-reversibly when the standard rate constant lies within the values expressed as a function of the highest and lowest scan rates v ... 

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