Reduction rate constant dependence

The cation-radicals ArH+ were detected, but they originated from the fast reaction of a one-electron transfer, which does not affect kinetic constants of the oxidation. The rate constant depends linearly on Brown s a constants of substituents (Dessau et al. 1970). All these data are in agreement with the formation of the strong polar dication of an aromatic hydrocarbon as an intermediate. Because PF salts (in particular the diacetate) are not reductants, the two-electron transfer reaction proceeds irreversibly. 

Kinetics of the reaction of certain Mo02L complexes (L = S-containing salicylaldehyde Schiff base) with PEtPh2 also show the reactions to be first order in complex and in phosphine,145-147,168 The rate constants depend upon the substituent on the aromatic (salicylaldehyde derived) ring and correlate with reduction potentials of the complexes.145... 

Our results do not allow us to decide which of these pH effects is predominant. The experimental observation, however, that in the pH range between 3 and 5 the overall rate constant depends on the concentration of surface protons to the power 1.6 may be an indication that proton catalysis of the detachment of surface Fe(II) is an important factor. In this case, the detachment of surface Fe(II) would be the rate-determining step of the overall process. The experiments presented here serve as an illustrative example, pointing out that reductive dissolution of oxide minerals may be catalyzed by protons, and hence that the rates of proton-catalyzed and of reductive dissolution may not be merely additive. However, more experimental evidence is needed to evaluate the validity of applying the rate expression of the proton-catalyzed dissolution to the overall rate constant of reductive dissolution. 

In aqueous solution, the chemical reduction of the d5/inin5-[Ru(bpy)2L (NO)] + and [Ru(tpy)L(NO)] + complexes releases NO, as attested by measurement based on an NO sensor. For the above-mentioned complexes, the rate constants are similar. For the trans- [RuL(NFl3)4NO] complexes, the NO release rate constant depends on the trans effect exerted by the L ligand, as described previously (15). 

The dependence of the reduction rate constant on bulk ascorbate concentration was found to be logarithmic in the range of investigated ascorbate concentration (0.005-2 mM) (Figure 10.9). 

Since these reductions are of the Michaelis-Menten type(coenzymelike), catalytic rate constants according to Lineweaver-Burk plots which are alteration of first order rate constants depending on the concentration changes of dyes, were calculated and summarized in Table 1. Where, k-cat. Km, and k-cat/Km mean reduction rate constant, dissociation constant, and second order rate constant NB as a mediator has a larger value of k-cat/Km and a smaller value of Km than the other dyes. These results indicate that NB is a better mediator in the reduction of cytochrome c with 3-CD-NAH and is included into the cavity of 3-CD-NAH easily. In the case of NR, Table 1 clearly shows an acceleration effect by adding cyclohexanol. This result can be explained by assuming Scheme 2. 

Establishing these expressions is merely the result of applying the law of mass action to the forward and backward electrode processes. The role of electrons in the process is established by assuming that the magnitudes of the rate constants depend on the electrode potential. The dependence is usually described by assuming that a fraction aE of the electrode potential is involved in driving the reduction process, while the fraction (1 - cx)E is effective in making the reoxidation process more difficult. Mathematically these potential-dependent rate constants are expressed as... 

The free energy on the right-hand side of both of the above equations can be considered as the chemical component of the activation free-energy change that is, it is only dependent upon the chemical species and not the applied voltage. We can now substitute the activation free energy terms above into the expressions for the oxidation and reduction rate constants, which give... 

FIGURE 16.29 Dependence of the Pt oxide reduction rate constant on reducing power of mediator. A stands for the difference hetween the of the mediator and the peak potential for electrochemical reduction of the oxide at the indicated pH. Values for kj as obtained from digital simulations in m moHs. The graph also shows the parabolic curves obtained by the use of Equations 16.20 and 16.21 with different values of A, and adjusted to overlay on the data. (Adapted from Rodrlguez-L6pez, J. et al., J. Phys. Chem. C, 114,18645, 2010.)... 

A metal dipped in an electrolyte solution dissolves as a result of electrode (electrochemical) reactions. Electrochemical reactions differ from other heterogeneous reactions in that their rate constants depend on the value of a. According to the electrochemical nature of metal dissolution, there are anodic or cathodic sites on the dissolving surface, where oxidation of metal M and reduction of species N of the electrolyte take place, respectively. Thus all metals give electrons and pass into the ionized state. 

Multidimensionality may also manifest itself in the rate coefficient as a consequence of anisotropy of the friction coefficient [M]- Weak friction transverse to the minimum energy reaction path causes a significant reduction of the effective friction and leads to a much weaker dependence of the rate constant on solvent viscosity. These conclusions based on two-dimensional models also have been shown to hold for the general multidimensional case [M, 59, and 61]. 

The non-steady-state optical analysis introduced by Ding et al. also featured deviations from the Butler-Volmer behavior under identical conditions [43]. In this case, the large potential range accessible with these techniques allows measurements of the rate constant in the vicinity of the potential of zero charge (k j). The potential dependence of the ET rate constant normalized by as obtained from the optical analysis of the TCNQ reduction by ferrocyanide is displayed in Fig. 10(a) [43]. This dependence was analyzed in terms of the preencounter equilibrium model associated with a mixed-solvent layer type of interfacial structure [see Eqs. (14) and (16)]. The experimental results were compared to the theoretical curve obtained from Eq. (14) assuming that the potential drop between the reaction planes (A 0) is zero. The potential drop in the aqueous side was estimated by the Gouy-Chapman model. The theoretical curve underestimates the experimental trend, and the difference can be associated with the third term in Eq. (14). 

FIG. 10 Potential dependence of the electron-transfer rate constant k i) normalized to the value at the potential of zero charge TCNQ reduction by hexacyanoferrate at the water-DCE... 

FIG. 21 Plot of log ki2 vs. AEi/2 showing the dependence of ET rate on the driving force for the reaction between ZnPor and four aqueous reductants. The difference between the half-wave potentials for an aqueous redox species and ZnPor, AE-i/2 = AE° + A°0, where AE° is the difference in the formal potentials of the aqueous redox species and ZnPor and A° is the potential drop across the ITIES. The solid line is the expected behavior based on Marcus theory for X = 0.55 eV and a maximum rate constant of 50 cm s M . (Reprinted from Ref. 49. Copyright 1999 American Chemical Society.)... 

Electrocatalysis employing Co complexes as catalysts may have the complex in solution, adsorbed onto the electrode surface, or covalently bound to the electrode surface. This is exemplified with some selected examples. Cobalt(I) coordinatively unsaturated complexes of 2,2 -dipyridine promote the electrochemical oxidation of organic halides, the apparent rate constant showing a first order dependence on substrate concentration.1398,1399 Catalytic reduction of dioxygen has been observed on a glassy carbon electrode to which a cobalt(III) macrocycle tetraamine complex has been adsorbed.1400,1401... 

The first step [Eq. (5)] was postulated to be rate determining because of the Tafel slope of 107 mV/ decade and the first-order dependence of the reduction current on the C02 concentration. The second-order rate constant of Eq. (6) was estimated to be 7.5 x 103 M-1 s-1. 

The electrochemical rate constants for hydrogen peroxide reduction have been found to be dependent on the amount of Prussian blue deposited, confirming that H202 penetrates the films, and the inner layers of the polycrystal take part in the catalysis. For 4-6 nmol cm 2 of Prussian blue the electrochemical rate constant exceeds 0.01cm s-1 [12], which corresponds to the bi-molecular rate constant of kcat = 3 X 103 L mol 1s 1 [114], The rate constant of hydrogen peroxide reduction by ferrocyanide catalyzed by enzyme peroxidase was 2 X 104 L mol 1 s 1 [116]. Thus, the activity of the natural enzyme peroxidase is of a similar order of magnitude as the catalytic activity of our Prussian blue-based electrocatalyst. Due to the high catalytic activity and selectivity, which are comparable with biocatalysis, we were able to denote the specially deposited Prussian blue as an artificial peroxidase [114, 117]. 

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