Rate constant standard redox

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

An alternative electrochemical method has recently been used to obtain the standard potentials of a series of 31 PhO /PhO- redox couples (13). This method uses conventional cyclic voltammetry, and it is based on the CV s obtained on alkaline solutions of the phenols. The observed CV s are completely irreversible and simply show a wave corresponding to the one-electron oxidation of PhO-. The irreversibility is due to the rapid homogeneous decay of the PhO radicals produced, such that no reverse wave can be detected. It is well known that PhO radicals decay with second-order kinetics and rate constants close to the diffusion-controlled limit. If the mechanism of the electrochemical oxidation of PhO- consists of diffusion-limited transfer of the electron from PhO- to the electrode and the second-order decay of the PhO radicals, the following equation describes the scan-rate dependence of the peak potential ... 

The method consists of plotting the forward electron transfer rate constant against the standard potential of a series of redox catalysts as illustrated by Figure 2.29. Three regions appear on the resulting Bronsted plot, which correspond to the following reaction scheme (Scheme 2.14). The... 

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.

FIGURE 4.3. Redox and chemical homogeneous catalysis of trans-1,2 dibromocyclohexane. a cyclic voltammetry in DMF of the direct electrochemical reduction at a glassy carbon electrode (top), of redox catalysis by fhiorenone (middle), of chemical catalysis by an iron(I) porphyrin, b catalysis rate constant as a function of the standard potential of the catalyst couple aromatic anion radicals, Fe(I), a Fe(0), Co(I), Ni(I) porphyrins. Adapted from Figures 3 and 4 of reference lb, with permission from the American Chemical Society. 

Despite the problems that can afflict experimental cyclic voltammograms, when the method for deriving standard redox potentials is used with caution it affords data that may be accurate within a few tens of mV (10 mV corresponds to about 1 kJ mol-1), as remarked by Tilset [335]. Kinetic shifts are usually the most important error source The deviation (A If) of the experimental peak potential from the reversible value can be quite large. However, it is possible to estimate AEp if the rate constant of the chemical reaction is available. For instance, in the case of a second order reaction (e.g., a radical dimerization) with a rate constant k, the value of AEV at 298.15 K is given by equation 16.24 [328,339] ... 

The heterogeneous standard (or conditional) rate constant k° measures the intrinsic ability of a species (say, Ox) to exchange electrons with the electrode in order to convert to its redox partner (say, Red). A species with a large k° will convert to its redox partner on a short time scale a species with a small k° will convert to its redox partner on a long time scale. 

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. 

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

The theory for the reaction of an adsorbed redox couple (2.146) has been exemplified by experiments with methylene blue [92], and azobenzene [79], Both redox couples, methylene blue/leucomethylene, and azobenzene/hydrazobenzene adsorb strongly on the mercury electrode surface. The reduction of methlylene blue involves a very fast two-step redox reaction with a standard rate constants of 3000 s and 6000 s for the first and second step, respectively. Thus, for / < 50 Hz, the kinetic parameter for the first electron transfer is log(m) > 1.8, implying that the reaction appears reversible. Therefore, regardless of the adsorptive accumulation, the net response of methylene blue is a small peak, the peak current of which depends linearly on /J. Increasing the frequency above 50 Hz, the electrochemical... 

Here, cp = (E —E ) is a dimensionless potential and rs = 1 cm is an auxiliary constant. Recall that in units of cm s is heterogeneous standard rate constant typical for all electrode processes of dissolved redox couples (Sect. 2.2 to 2.4), whereas the standard rate constant ur in units of s is typical for surface electrode processes (Sect. 2.5). This results from the inherent nature of reaction (2.204) in which the reactant HgL(g) is present only immobilized on the electrode surface, whereas the product is dissolved in the solution. For these reasons the cathodic stripping reaction (2.204) is considered as an intermediate form between the electrode reaction of a dissolved redox couple and the genuine surface electrode reaction [135]. The same holds true for the cathodic stripping reaction of a second order (2.205). Using the standard rate constant in units of cms , the kinetic equation for reaction (2.205) has the following form ... 

Tab. 16 Standard potential forthe first redox system of each POM and second-order rate constant k derived from DPSC experiments on HPB/NADH systems at pH = 7. Each value of k is the average of at least five experiments. The values of y are not necessary, but have been added to give a better idea of the experimental conditions (taken from Ref. 174)...

The rate constant for the redox step, kr, is unlikely to reflect a simple electron transfer from the monodentate diimine ligand to the metal center because replacement of coordinated water with coordinated hydroxide would be expected to decrease the oxidizing power of the metal-(III) center. This is well documented by the standard reduction potentials of the aqua and hydroxo complexes in Table IV, and it would seem... 

If the rate of electron transfer is low (or the scan rate is too high), electron transfer will not be able to adjust the surface concentrations of -Fc and -Fc+ to values that are at equilibrium with the applied potential (quasireversible or totally irreversible case, see Chap. 3). In this case, the anodic peak and the cathodic peaks will not be at the same potential that is, AEpk will be greater than zero volts. Kinetic information about the surface-bound redox couple can be obtained from such quasireversible or irreversible voltammograms. For example, methods for obtaining the standard heterogeneous rate constant (see Chap. 2) for the surface-confined redox couple have been developed [41,42]. 

Chronoamperometric curves have been used as a standard tool to obtain values of the rate constants of surface-bound molecules and they prove as very useful for validating the Marcus-Hush s formalist, and, indeed, the experimental application of the MH theory to electrode processes has been mainly carried out with surface-bound redox systems. Thus, Chidsey studied the oxidation of ferrocene groups connected to a gold electrode by means of a long alkylthiol chain by using Single Potential Pulse Chronoamperometry (see examples of the experimental responses in Fig. 6.21) [43]. 

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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