Reaction rates, potential dependence

The role that acid and base catalysts play can be quantitatively studied by kinetic techniques. It is possible to recognize several distinct types of catalysis by acids and bases. The term specie acid catalysis is used when the reaction rate is dependent on the equilibrium for protonation of the reactant. This type of catalysis is independent of the concentration and specific structure of the various proton donors present in solution. Specific acid catalysis is governed by the hydrogen-ion concentration (pH) of the solution. For example, for a series of reactions in an aqueous buffer system, flie rate of flie reaction would be a fimetion of the pH, but not of the concentration or identity of the acidic and basic components of the buffer. The kinetic expression for any such reaction will include a term for hydrogen-ion concentration, [H+]. The term general acid catalysis is used when the nature and concentration of proton donors present in solution affect the reaction rate. The kinetic expression for such a reaction will include a term for each of the potential proton donors that acts as a catalyst. The terms specific base catalysis and general base catalysis apply in the same way to base-catalyzed reactions. 

When the poisoning reaction is analyzed under potential control, the formation rate is dependent on the electrode potential. The hrst experiments that clearly showed that the poison formation reaction was potential-dependent were performed by Clavilier using pulsed voltammetry [Clavilier, 1987] (Fig. 6.15). In this technique, a short pulse at high potential is superimposed on a normal voltammetric potential... 

As already mentioned, the poison formation reaction is potential-dependent, and the poisoning rate for the basal planes is Pt(llO) > Pt(lOO) > Pt(lll) [Sun et al., 1994 Iwasita et al., 1996]. The case of Pt(lll) is special, since the poisoning has been associated with the presence of defects on the surface. Selective covering of the defects on the Pt(l 11) electrode by some adatoms prevents the formation of CO on the electrode surface [Macia et al., 1999, 2001 Smith et al., 2000]. 

Of course, clectrocalalytic reactions are potential dependent in rate, as are all other electrode reactions,87 and one of the subjects to which attention will be given in the following discussion is the reference potential at which a comparison of electrocatalysts should be made. Table 7.17 contains a comparison of chemical (thermal) and electrochemical (electrical) catalysis. 

The exchange current density is the electrode reaction rate at the equilibrium potential (identical forward and reverse reaction rates) and depends on the electrode properties and operation. The typical expression for determining the exchange current density is the Arrhenius law (3.23), where the constant A depends on the gas concentration. Costamagna et al. [40] provide the following expressions for the anodic and cathodic exchange current density, respectively ... 

Given that electrochemical rate constants are usually extremely sensitive to the electrode potential, there has been longstanding interest in examining the nature of the rate-potential dependence. Broadly speaking, these examinations are of two types. Firstly, for multistep (especially multielectron) processes, the slope of the log kob-E plots (so-called "Tafel slopes ) can yield information on the reaction mechanism. Such treatments, although beyond the scope of the present discussion, are detailed elsewhere [13, 72]. Secondly, for single-electron processes, the functional form of log k-E plots has come under detailed scrutiny in connection with the prediction of electron-transfer models that the activation free energy should depend non-linearly upon the overpotential (Sect. 3.2). 

In this text, the conversion rate is used in relevant equations to avoid difficulties in applying the correct sign to the reaction rate in material balances. Note that the chemical conversion rate is not identical to the chemical reaction rate. The chemical reaction rate only reflects the chemical kinetics of the system, that is, the conversion rate measured under such conditions that it is not influenced by physical transport (diffusion and convective mass transfer) of reactants toward the reaction site or of product away from it. The reaction rate generally depends only on the composition of the reaction mixture, its temperature and pressure, and the properties of the catalyst. The conversion rate, in addition, can be influenced by the conditions of flow, mixing, and mass and heat transfer in the reaction system. For homogeneous reactions that proceed slowly with respect to potential physical transport, the conversion rate approximates the reaction rate. In contrast, for homogeneous reactions in poorly mixed fluids and for relatively rapid heterogeneous reactions, physical transport phenomena may reduce the conversion rate. In this case, the conversion rate is lower than the reaction rate. 

Thus, expression (59) enables us to describe the solid-state reaction rate constant dependence on the parameters of the potential barrier and medium properties in a wide temperature range, from liquid helium temperatures when the reaction runs by a tunneling mechanism to high temperatures (naturally, not exceeding the melting point) when the transition is of the activation type. 

As can be seen, the reaction rate v is a function of the Gibbs energy of adsorption, the electrode potential, and the concentration of A. In fact, the reaction rate can be divided into two separate terms one containing the dependence of AGj and Ca and the other one that depends on the electrode potential. If the catalytic activity of several surfaces is compared at constant potential, the reaction rate will depend only on AGj and Ca- In Fig. 2, the term... 

It involves the diffusion of A toward an electrode, a siuface adsorption reaction at an area that is not already occupied by B, desorption of B, and diffusion of C from the electrode. First of all, the system dc behavior must be described by appropriate equations. Because the reactions proceed by an exchange of electrons, the rate constants of forward and backward reactions are potential dependent ... 

The electrode reaction rate constant depends on the difference of potentials (f) between the electrode and the site of the discharging particle. This dependence stems from the fact that the reaction involves a charge (electron) transfer from the electrode to the particle (or in the opposite direction). 

A Posteriori Modei Discrimination. Several discrimination criteria can be used in the case no additional experimental information can be acquired. A first criterion has already been discussed in Section 3.1.2, that is, investigating the total pressure effect on the initial reaction rate potentially allows identifying the RDS in a reaction mechanism. Similar tests can be defined in which the rate equation is rearranged into a particular form to give a linear relationship between dependent and independent variables. 

Under normal circumstances, this occurs by collisions with a third-body species and the reaction rate therefore depends on total pressure. Such a mechanism is impossible in the super-rarified environment of interstellar space. However, the kinetics of such reactions are of indirect interest to astrochemists on two counts. First, treatments of radiative association [22], which is implicated in the formation of molecular species in interstellar clouds, have much in common with those of three-body association [23]. Second, the rate constants for radical association in the limit of high pressure correspond to those for formation of the energised associated molecule, since all such species are collisionally stabilised in the limit of high pressure. Consequently, the values of kggg and how they vary with temperature provide an important test of theories of reactions occurring over attractive potential energy surfaces [6]. 

Electrochemical reaction kinetics is essential in determining the rate of corrosion of a metal M exposed to a corrosive medium (electrolyte). On the other hand, thermodynamics predicts the possibility of corrosion, but it does not provide information on how slow or fast corrosion occurs. The kinetics of a reaction on a electrode surface depends on the electrode potential. Thus, a reaction rate strongly depends on the rate of electron flow to or from a metal-electrolyte interface. If the electrochemical system (electrode and electrolyte) is at equilibrium, then the net rate of reaction is zero. In comparison, reaction rates are governed by chemical kinetics, while corrosion rates are primarily governed by electrochemical kinetics. 

The rate and the degree of reaction of an electrically conductive polymer in repeated redox reaction are important factors in application of the polymer. The fast response of the polymer to an external stimulation may find uses in a sensor or a display. The reaction rate must depend on the mobility of ions in the polymer toward the reactive sites under an applied potential. The degree of the reaction in the cycled oxidation-reduction process predicts applicability of the electrically conductive materials in battery, sensor, transistor, solar cells, etc(6,7). 

In this section we describe the equations required to simulate the electrochemical performance of porous electrodes with concentrated electrolytes. Extensions to this basic model are presented in Section 4. The basis of porous electrode theory and concentrated solution theory has been reviewed by Newman and Tiedemann [1]. In porous electrode theory, the exact positions and shapes of aU the particles and pores in the electrode are not specified. Instead, properties are averaged over a volume small with respect to the overall dimensions of the electrode but large with respect to the pore structure. The electrode is viewed as a superposition of active material, filler, and electrolyte, and these phases coexist at every point in the model. Particles of the active material generally can be treated as spheres. The electrode phase is coupled to the electrolyte phase via mass balances and via the reaction rate, which depends on the potential difference between the phases. AU phases are considered to be electrically neutral, which assumes that the volume of the double layer is smaU relative to the pore volume. Where pUcable, we also indicate boundary conditions that would be used if a Uthium foil electrode were used in place of a negative insertion electrode. 

Because of the general difficulty encountered in generating reliable potentials energy surfaces and estimating reasonable friction kernels, it still remains an open question whether by analysis of experimental rate constants one can decide whether non-Markovian bath effects or other influences cause a particular solvent or pressure dependence of reaction rate coefficients in condensed phase. From that point of view, a purely... 

The reactivity modification or the reaction rate control of functional groups covalently bound to a polyelectrolyte is critically dependent on the strength of the electrostatic potential at the boundary between the polymer skeleton and the water phase ( molecular surface ). This dependence is due to the covalent bonding of the functional groups which fixes the reaction sites to the molecular surface of the polyelectrolyte. Thus, the surface potential of the polyion plays a decisive role in the quantitative interpretation of the reactivity modification on the molecular surface. 

In this chapter we have attempted to summarize and evaluate scientific information available in the relatively young field of microwave photoelectrochemistry. This discipline combines photoelectrochemical techniques with potential-dependent microwave conductivity measurements and succeeds in better characterizing the behavior ofphotoinduced charge carrier reactions in photoelectrochemical mechanisms. By combining photoelectrochemical measurements with microwave conductivity measurements, it is possible to obtain direct access to the measurement of interfacial rate constants. This is new for photoelectrochemistry and promises better insight into the mechanisms of photogenerated charge carriers in semiconductor electrodes. 

Conway, B. E. The Temperature and Potential Dependence of Electrochemical Reaction Rates, and the Real Form of the Tafel Equation 16... 

Figure 8.15. Time dependence of the work function change, AO, the reaction rate, r, and the catalyst potential, Uwr, following galvanostatic steps during C2H4 oxidation on RuCVYSZ.20,21 Catalyst Ru02 (m=0.4 mg A=0.5 cm2), 1=50 pA, Pc2H4=1 14 Pa, po2=17.7 kPa, Fy=175 cm3 STP/min, T = 380°C.25...

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