Standard rate constant ks

Boltzmann s constant (k = 1.38065 10" J K" ) standard rate constant of a charge-transfer adsorption process... 

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. 

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. 

Figure 4 Effect of repeated reaction cycles and catalyst pretreatment in 6.2 M NaOH at 473 K on rate constant and catalyst surface area for ethanolamine dehydrogenation over unpromoted skeletal copper under standard conditions.

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. 

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 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 — exchange current, i0, should become respectively ... 

An inverse correlation occurs between the experimental value < i.expi and the theoretical values of the standard rate constant k,caic when the latter is computed from Eq. (1) using the adiabatic value of the transmission coefficient(i.e.,/c= 1), the solvent-independent frequency factorv = A 77/i (see solid circles in Fig. 18), and the solvent dependence is taken into account only via continuum A., (het) values obtained from Eq. (3). 

Figure 3.12 shows the forward and backward components of square-wave voltam-mograms of mercury(ll)-ferron complex adsorbed on the surface of static mercuiy drop electrode [208]. The ratio of the current and the corresponding SW frequency is reported. At pH 3.5 the electrode reaction involves the direct transfer of two electrons, whereas at pH 5.8 only one electron is exchanged. The simulated responses are presented by symbols. The best fit was achieved by using the following standard rate constants and the transfer coefficients k. = 1550 50 s and a = 0.5 (at pH 3.5), and = 1900 400s and a = 0.55 (at pH 5.8) [208]. 

Sluyters and coworkers [34] have studied the mechanism of Zn(II) reduction on DM E in NaCl04 solutions at different water activity (uw) using faradaic impedance method. Dqx and E p were determined from dc polarographic curves. Hydration numbers of Zn(Il) ion were estimated from the dependence of E[p on In Uw The obtained standard rate constant was changing with a NaCl04 concentration and the slope of the dependence of In k on potential was changing with potential (see Fig. 1). Therefore, the following mechanisms were proposed ... 

V/s, revealing the reversible character of both couples under the experimental conditions of the study. Therefore, we can conclude that CB7 inclusion of methyl viologen does not seem to affect its electrochemical kinetics in a pronounced way. We cannot unequivocally state that there is no change in the kinetics, since a small decrease in the standard rate constant (k") may be possible and go undetected in these experiments. 

Ey2 reversible half-wave potential, k, vxl> experimental standard rate constant, a transfer coefficient, (outer-Helmholtz plane, L ron standard rate constant after correction for the double-layer effect (see 4)), lcex rate constant for the homogeneous self-exchange electron-transfer (see 4) in Chapter 9) obtained with a HMDE in DMF-0.5 M BU4NCIO4 at 22 2°C, except the last two obtained with a DME in DMF-0.1 M Bu4NI at 30°C. 

The mean standard rate constant was k° = (2.1 + 0.2) x 10 3 cm s 1 and showed that SECM is a powerful method to determine the rate constant. The curve fitting and calculation of the offset are crucial for reproducible result. The special advantage of the method is its relative immunity to inaccuracies introduced by uncompensated resistance or limited rise time of potentiostats since the analysis occurs under steady-state conditions and very low total currents. 

Table 7.2 Values of the standard rate constant (k°), the transfer coefficient (a), the reorganization energy (2), and the formal potential (Ef, vs. Ag) corresponding to the theoretical curves shown in Fig. 7.21. Taken from [30]...

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