Electrode standard rate constant

Rate constant for first order chemical process Rate constant for the forward (cathodic) process Rate constant for the reverse (anodic) process Rate constant for an electron transfer process at 0 V vs. the reference electrode Standard rate constant for an electrode process Mass transport coefficient Averaged, overall heat transfer coefficient Kohlrausch constant Selectivity constant for species i Characteristic length Length of a plate electrode Molality of cation Molality of anion... 

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. 

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. 

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. 

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 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. 

Here sur is the surface standard rate constant in units of s. By substitution (2.93) and (2.94) into (2.95), one obtains an integral equation, which is a general solution for a surface electrode reaction ... 

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-... 

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]. 

The electrochemical rate constants of the Zn(II)/Zn(Hg) system obtained in propylene carbonate (PC), acetonitrile (AN), and HMPA with different concentrations of tetraethylammonium perchlorate (TEAP) decreased with increasing concentration of the electrolyte and were always lower in AN than in PC solution [72]. The mechanism of Zn(II) electroreduction was proposed in PC and AN the electroreduction process proceeds in one step. In HMPA, the Zn(II) electroreduction on the mercury electrode is very slow and proceeds according to the mechanism in which a chemical reaction was followed by charge transfer in two steps (CEE). The linear dependence of logarithm of heterogeneous standard rate constant on solvent DN was observed only for values corrected for the double-layer effect. 

Cd(II) reduction at the mercury electrode from aqueous 1 M NaCl04 in the presence of sucrose was described [49] by CEE mechanism. An attempt was made to correlate the individual standard rate constants that became lower with increasing concentration of sucrose, with (1) the surface coverage by sucrose, and (2) the viscosity of the solution layer adjacent to the electrode surface. 

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. 

For the relation between the rate constant for homogeneous self-exchange ET process (kex) and the standard rate constant of the corresponding electrode reaction (kg), see 4) in Chapter 9. 

The strength of metal ion solvation affects not only the half-wave potentials but also the rates of electrode reactions of metal ions. For the reduction of a given metal ion, the reaction rate tends to decrease with increasing strength of solvation. The linear relation in Fig. 8.5 was obtained for the reduction of a sodium ion AG°v(Na+) is the solvation energy of Na+ and ks is the standard rate constant at the formal potential [23 a].2 For alkali metal ions in the same solvent, the rate... 

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). 

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

According to Marcus [19a], the standard rate constant, fcs, for the electrode reaction,... 

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