Rate constant, standard potential

Dimensionless heterogeneous rate constant Chemical potential Standard chemical potential Sweep rate in CV or LSV (Vs )... 

Montalti M, Credl A, Prod L, Gandolfi MT (2006), Handbook of photochemistry, 3rd edn. CRC Press, Boca Raton. An essential reference book containing data tables for a wide range of compounds, and a variety of reference materials including quantum yields, lifetimes, quenching rate constants, electrochemical potentials and solvent properties as well as information on standard procedures used in chemical actinometry, determination of emission and excitation spectra correction factors, and quantum yield measurements and also information on equipment such as lamps and filters. 

Where refers to the standard rate constant, and alpha (a) is the electron transfer coefficient. The standard rate constant is the value of the rate constants for the forward and backward reactions, at equilibrium, where they are equal. The deviation of these rate constants at potentials differing from equilibrium is an exponential function of potential difference from equilibrium and the transfer coefficient. 

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. 

If no concentration of the educt is given the standard exchange current density y oo is stated. Values of)t are printed in italics values of the apparent rate constant k pp are printed in parentheses in italics. For electrode potentials where the latter rate constant was actually determined the reader is referred to the original literature. 

These equations show that whereas the kinetic coefficients of an individual reaction can assume any value, the coefficients of its forward and reverse process are always interrelated. The relation between the standard equilibrium potential EP and the rate constants and is analogous to the well-known physicochemical relation between equilibrium constant K and the rate constants of the forward and reverse process. 

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. 

Figure 10.11 Arrhenius plots of the ORR rate constants obtained at various electrodes. The symbols are the same as those in Fig. 10.10. Each solid line is the least squares fit of all the data at the constant applied potential. Since the standard potential E° and [RHE(r)] shift to less positive values in a different maimer, the corrected potential E is applied so as to keep a constant overpotential for the ORR at each temperature. The applied potentials of -0.485, -0.525, and -0.585 V vs. E° correspond to 0.80, 0.76, and 0.70 V vs. RHE, respectively, at 30 °C. (From Yano et al. [2006b], reproduced by permission of the PCCP Owner Societies.)...

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 addition to the thermodynamic quantity E°, the electrode reaction is characterized by two kinetic quantities the charge transfer coefficient a and the conditional rate constant k°. These quantities are often sufficient for a complete description of an electrode reaction, assuming that they are constant over the given potential range. Table 5.1 lists some examples of the constant k. If the constant k° is small, then the electrode reaction occurs only at potentials considerably removed from the standard potential. At these potential values practically only one of the pair of electrode reactions proceeds which is the case of an irreversible or one-way electrode reaction. 

The quantity kconv = exp (anFE0,/RT) is the value of the rate constant of the electrode reaction at the potential of the standard reference electrode and will be termed the conventional rate constant of the electrode reaction. It can be found, for example, by extrapolation of the dependence (5.2.36) to E = 0, as... 

Several descriptions of electrode reaction rates discussed on the preceding pages and the difficulty to standardize electrode potential scales with respect to different temperatures imply several definitions of activation energies of electrode reactions. The easiest way to determine this quantity, for example, for an irreversible cathodic process, employs Eqs (5.2.9), (5.2.10) and (5.2.12) at a constant electrode potential,... 

For a particular iron(III) oxidant, the rate constant (log kpe) for electron transfer is strongly correlated with the ionization potential Ip of the various alkylmetal donors in Figure 4 (left) (6). The same correlation extends to the oxidation of alkyl radicals, as shown in Figure 4 (right) (2). [The cause of the bend (curvature) in the correlation is described in a subsequent section.] Similarly, for a particular alkylmetal donor, the rate constant (log kpe) for electron transfer in eq 1 varies linearly with the standard reduction potentials E° of the series of iron(III) complexes FeL33+, with L = substituted phenanthroline ligands (6). 

The complete kinetic expression in eq 16 relates the experimental rate constant ke with the forward rate constant ki, as a direct function of the decomposition rate constant k2 and the standard reduction potential E °. Since an independent measurement of k2f = 1.2 cm s"1 (or k2 = 105 s"1) is available for Me2Co(M)+, it can be used in conjunction with E° = 0.53 V to convert ke to ki, shown in Figure 11 (14). 

The value of E° was hence determined by the reaction of R4M with Fe3+ complexes as outer-sphere SET oxidizers. Using five complexes with a range of different E° values, from 1.15 to 1.42 V, the rate constants were determined193. This was followed up by Eberson who, by application of the Marcus theory, was able to determine from the E° values (shown in Table 18) standard potentials and reorganization energies. Most compounds... 

By use of well-established standard potentials, the reported values for K and kg, and the principle of detailed balancing, one can calculate that the reverse of reaction (10) has a rate constant (k g) of 2x103M-1s-1. Normal ligand substitution reactions at Fe2+ are much faster than this, which raises questions regarding the nature of the transition state for this reaction. 

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 ... 

Here, v is the scan rate, k is the radical self-reaction rate constant, and Ep is the CV wave peak potential. The standard potentials obtained ranged from 1.28 V (4-02NPh0H) to 0.17 V (4-HOPhOH). Good agreement with the literature values was obtained in those cases where the data were available. 

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. 

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... 

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