Kinetics standard rate constant

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. 

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. 

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 ... 

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. 

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. 

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... 

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. 

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 ... 

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... 

The charge transfer kinetics of azobenzene at the mercury electrode is slower than that of methylene blue, thus the frequency interval provided by modem instra-mentation (10 < //Hz < 2000) allows variation of the electrochemical reversibility of the electrode reaction over a wide range [79]. The quasireversible maxima measured by the reduction of azobenzene in media at different pH ate shown in Fig. 2.47 in the previous Sect. 2.5.1. The position of the quasireversible maximum depends on pH hence the estimated standard rate constant obeys the following dependence A sur = (62-12pH) S- for pH < 4. These results confirm the quasite-versible maximum can be experimentally observed for a single electrode reaction by varying the frequency, as predicted by analysis in Fig. 2.75. 

For a quasireversible electrode reaction, the kinetic equation for reaction (2.204) can be attributed with a standard rate constant expressed in units of either cms (2.222), or s- (2.223) ... 

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 ... 

SWV has been apphed for the measurements of kinetic parameters of electrode reactions of adsorbed reactant and product. Standard rate constants and trans-... 

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. 

The cadmium electrodeposition on the solid cadmium electrode from the sulfate medium was investigated [217]. The following kinetic parameters were obtained cathodic transfer coefficient a = 0.65, exchange current density Iq = 3.41 mA cm , and standard rate constant kg = 8.98 X 10 cm s . The electrochemical deposition of cadmium is a complex process due to the coexistence of the adsorption and nucleation process involving Cd(II) species in the adsorbed state. 

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. 

Usually the electrode reaction is considered to occur when the reactant reaches the OHP thus, the rate of electrode reaction is influenced by the value of ( ohp- s) For a reduction, Ox2 + ne - Red2 n, the experimental standard rate constant, ksexp, deviates from the standard rate constant expected for ( ohp s) = 0 [curve (b)]. If the latter rate constant is expressed by ks,cori there is a relation ks,exp=ks,con-exp[(an-z)( oHp- s)F/RT], where a is the transfer coefficient. If z=+l, n = 1, a 0.5, and ( ohp- s)<0, then (a-z)( Ohp s)>0 and kSjexp>kSjCon, showing that the electrode reduction of a univalent cation is accelerated by the double-layer effect. On the other hand, if z=0, n= 1, a 0.5, and ( ohp s) <0, ks,expneutral molecule is decelerated by the double-layer effect. In the study of electrode kinetics, it is usual to get kSiCon. by correcting for the double layer effect (see Table 8.6 for an example). 

There is an upper limit to the frequency range useful for kinetic studies due to the presence of double-layer capacity and ohmic resistance [53]. In practical cases, the limit is ca. 10 kHz. Then, from eqns. (64) and (65), it follows that, for p values to be obtained with reasonable accuracy, the condition p > ca. 5 x 10-4 s1/2 should be met. This corresponds to a standard rate constant of ca. 3 cm s 1. 

Under conditions of excess L2(H20)Rh002+, the reaction proceeded to completion and obeyed second-order kinetics. The rate constant kobs was evaluated by standard kinetic analysis. 

The concentrations of species at the interface depend on the mass transport of these species from bulk solution, often described by the mass transfer coefficient /cd. A reversible reaction corresponds to the case where the kinetics of the electrode reaction is much faster than the transport. The kinetics is expressed by a standard rate constant, kQ, which is the rate constant when E = °. So the criterion for a reversible reaction is... 

A complete study of an electrode process requires measurement of kinetic as well as thermodynamic parameters. This means that conditions in which the system is not reversible must be used. Since the standard rate constant, k0, cannot be changed, then the mass transfer coefficient, kd, may have to be increased until the reaction becomes at least quasi-reversible. This can be done in various ways in various types of experiment ... 

We now consider the factors that affect the variation of kc (or ka) and kd. The kinetic rate constants depend on the applied potential and on the value of the standard rate constant, k0. As was seen in Chapter 5, kd is influenced by the thickness of the diffusion layer, which we can control through the type of experiment and experimental conditions, such as varying the forced convection. By altering kc (or ka) and kd we can obtain kinetic information as will be described below. At the moment we note that there are two extremes of comparison between k0 and kd. 

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]. 

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