Standard rate constant determination

Na" >Li+>K >Rb >Cs" ". The standard rate constants determined from steady-state voltammograms were similar for all studied cations ( O.Scm/s) and somewhat lower than those measured with DB18C6 for K and... 

Prepare the solutions and measure the pH at one temperature of the kinetic study. Of course, the pH meter and electrodes must be properly calibrated against standard buffers, all solutions being thermostated at the single temperature of measurement. Carry out the rate constant determinations at three or more tempertures do not measure the pH or change the solution composition at the additional temperatures. Determine from an Arrhenius plot of log against l/T. Then calculate Eqh using Eq. (6-37) or (6-39) and the appropriate values of AH and AH as discussed above. 

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. 

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... 

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 ... 

This equation is of particular importance since it enables estimation of both the interaction product a and the standard rate constant sur, provided the relative surface coverage is known. For this, the quasireversible maximum is to be determined by varying the frequency for various values of the surface coverage 0. Plotting ln(/)... 

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 ... 

In DMSO solution, the standard rate constant and cathodic transfer coefficient of the Cd(II)/Cd(Hg) system decreased with increasing concentration of TEAP [65]. It was found that a chemical reaction, probably partial desolvation of the reactant, precedes the electron transfer, and Cd(II) is reduced according to the CEE mechanism. The kinetic parameters of this process were determined. 

Tab. 8.6 Standard rate constants for electrode reductions of organic compounds determined by...

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. 

As predicted by Eq. (1.120), Fig. 1.18 illustrates how the standard rate constant is independent of vn in the non-adiabatic regime where it is determined by the strength of the electronic interaction the stronger the interaction, the faster the electrode reaction. For weakly adiabatic systems, the increase of the rate constant... 

Activation volume — As in case of homogeneous chemical reactions, also the rate of heterogeneous electron transfer reactions at electrode interfaces can depend on pressure. The activation volume AVZ involved in electrochemical reactions can be determined by studying the pressure dependence of the heterogeneous -> standard rate constant ks AVa = -RT j (p is the molar - gas constant, T absolute temperature, and P the pressure inside the electrochemical cell). If AI4 is smaller than zero, i.e., when the volume of the activated complex is smaller than the volume of the reactant molecule, an increase of pressure will enhance the reaction rate and the opposite holds true when A14 is larger than zero. Refs. [i] Swaddle TW, Tregloan PA (1999) Coord Chem Rev 187 255 [ii] Dolidze TD, Khoshtariya DE, Waldeck DH, Macyk J, van Eldik R (2003) JPhys Chem B 107 7172... 

There are two advantages of the coulostatic method in the study of kinetics of electrode reactions. First, the ohmic drop is not of importance, therefore the measurements can be carried out in highly resistive media. Second, since Ic = IF, Q does not interfere in the measurement. By the help of this technique jo values up to about 0.1 A cm-2 and - standard rate constants up to 0.4cms 1 can be determined. A detailed discussion of coulostatic techniques can be found in Ref. [vi]. 

The current-potential relationship of the totally - irreversible electrode reaction Ox + ne - Red in the techniques mentioned above is I = IiKexp(-af)/ (1+ Kexp(-asteady-state voltammetry, a. is a - transfer coefficient, ks is -> standard rate constant, t is a drop life-time, S is a -> diffusion layer thickness, and

logarithmic analysis of this wave is also a straight line E = Eff + 2.303 x (RT/anF) logzc + 2.303 x (RT/anF) log [(fi, - I) /I -The slope of this line is 0.059/a V. It can be used for the determination of transfer coefficients, if the number of electrons is known. The half-wave potential depends on the drop life-time, or the rotation rate, or the microelectrode radius, and this relationship can be used for the determination of the standard rate constant, if the formal potential is known. 

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