The rates of heterogeneous processes

In this section consideration is restricted to reactions between gaseous species adsorbed on a solid or liquid surface. Principally, we shall consider the adsorption process, adopting the kinetic viewpoint originally developed by Langmuir. The method is illustrative of kinetic procedures that can also be used to analyze processes involving gas-liquid and gas-solid phase changes. We shall not discuss reactions occurring at surfaces with steps that do not involve adsorption. 

A reaction between gaseous species occurs in an adsorbed gas layer on a surface by means of the following sequence of events (1) Reactant molecules in the gas migrate to the surface, (2) these reactant molecules are adsorbed on the surface, (3) the adsorbed reactants react to form adsorbed products, (4) the product molecules leave the surface, and (5) the product molecules migrate to the bulk of the gas. Since these processes occur in series, the rate of the slowest step determines the overall reaction rate. 

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Like other heterogeneous chemical reactions, electrochemical reactions are always multistep reactions. Some intermediate steps may involve the adsorption or chemisorption of reactants, intermediates, or products. Adsorption processes as a rule have decisive influence on the rates of electrochemical processes. 

Parmon VN. 2007. Thermodynamic analysis of the effect of the nanopaiticle size of the active component on the adsorption equilibrium and the rate of heterogeneous catalytic processes. Dokl Phys Chem 413 42-48. 

Rate Expressions for Heterogeneous Catalytic Reactions Limited by the Rates of Chemical Processes... 

Certain acids with hydroxylic and carboxylic groups have been shown (Schwert-mann and Cornell, 1991) to induce in Fe(HI) solutions the formation of hematite because these acids may act as templates for the nucleation of hematite. These examples illustrate that a complete understanding and quantitative description of the rate of heterogeneous nucleation will have to include surface complexation and other adsorption processes. 

The first reduction process occurring at 1.07 V versus Fc+/Fc is reversible the peripheral fullerene moieties behave independently from an electrochemical point of view in this dendrimer family. On the other hand, the first oxidation process is monoelectronic and it is centered on the Cu(I) complex the rate of heterogeneous electron transfer decreases upon increasing dendrimer generation. 

Electrochemical reactions are heterogeneous chemical reactions accompanied by electrical charge transfer across the interface. Besides ordinary variables of chemical kinetics, such as concentration, temperature, etc., electrochemical kinetics is characterized by an additional independent variable, electrode potential. The rate of electrochemical processes may vary quite significantly (exponentially) with the electrode potential. 

Similarly, the rate of heterogeneous fluid-fluid and gas-liquid reactions depends both on the rate of the chemical reaction and the rate of mass transfer. Since the relative magnitude of the effect of pressure on the two processes can vary greatly we have a large spectrum of possibilities. High pressure can more- or less steeply increase or decrease the overall rate of these reactions. 

If M is unstable then ipb/fpf will be less than unity. Its magnitude will depend upon the scan rate, the value of the first-order constant k, and the conditions of the experiment. At fast scan rates the ratio ipb/ ip, may approach one if the time gate for the decomposition of M is small compared with the half-life of M-, (In 2jk). As the temperature is lowered, the magnitude of k may be sufficiently decreased for full reversible behaviour to be observed. The decomposition of M- could involve the attack of a solution species upon it, e.g. an electrophile. In such cases, ipb/ipf, will of course be dependent upon the concentration of the particular substrate (under pseudo-first-order conditions, k is kapparent). Quantitative cyclic voltammetric and related techniques allow the evaluation of the rate constants for such electrochemical—chemical, EC, processes. At the limit, the electron-transfer process is completely irreversible if k is sufficiently large with respect to the rate of heterogeneous electron transfer the electrochemical and chemical steps are concerted on the time-scale of the cyclic voltammetric experiment.1-3... 

The production of species i (number of moles per unit volume and time) is the velocity of reaction,. In the same sense, one understands the molar flux, jh of particles / per unit cross section and unit time. In a linear theory, the rate and the deviation from equilibrium are proportional to each other. The factors of proportionality are called reaction rate constants and transport coefficients respectively. They are state properties and thus depend only on the (local) thermodynamic state variables and not on their derivatives. They can be rationalized by crystal dynamics and atomic kinetics with the help of statistical theories. Irreversible thermodynamics is the theory of the rates of chemical processes in both spatially homogeneous systems (homogeneous reactions) and inhomogeneous systems (transport processes). If transport processes occur in multiphase systems, one is dealing with heterogeneous reactions. Heterogeneous systems stop reacting once one or more of the reactants are consumed and the systems became nonvariant. 

A further example of the use of this technique to introduce a ferrocene redox centre to a platinum surface is given in equation (32). A comparative survey was made of the rates of heterogeneous charge transfer between the platinum electrode and ferrocene both in solution and immobilized on the surface. Both processes show an Arrhenius temperature dependence but AGact(soIii) / A( ACT(surface bound). Absolute rate theory was unsatisfactory for the surface reaction and the need to involve electron tunnelling and a specific model for the conformation of the surface was indicated.66... 

Although Eq. (23) was derived for a one-step heterogeneous ET reaction, it was shown to be applicable to more complicated substrate kinetics (e.g., liquid-liquid interfacial charge transfer [38, 39, 67], ET through self-assembled monolayers [68, 69], and mediated ET in living cells [70-73]). The effective heterogeneous rate constant obtained by fitting experimental approach curves to Eq. (23) can be related to various parameters, which determine the rates of those processes, as discussed in the referred publications. 

The time range of the electrochemical measurements has been decreased considerably by using more powerful -> potentiostats, circuitry, -> microelectrodes, etc. by pulse techniques, fast -> cyclic voltammetry, -> scanning electrochemical microscopy the 10-6-10-1° s range has become available [iv,v]. The electrochemical techniques have been combined with spectroscopic ones (see -> spectroelectrochemistry) which have successfully been applied for relaxation studies [vi]. For the study of the rate of heterogeneous -> electron transfer processes the ILIT (Indirect Laser Induced Temperature) method has been developed [vi]. It applies a small temperature perturbation, e.g., of 5 K, and the change of the open-circuit potential is followed during the relaxation period. By this method a response function of the order of 1-10 ns has been achieved. 

The final step in removal of any species from the atmosphere involves heterogeneous deposition to the Earth s surface. Removal processes include wet deposition via rain-out (following uptake into tropospheric clouds) and dry deposition to the Earth s surface, principally to the oceans. The rates of these processes are largely determined by the species chemistries in aqueous solution. Heterogeneous lifetimes of the parent HFCs, HCFCs and HFEs are of the order of hundreds of years because of their low aqueous solubility and reactivity. 

If one were to describe the essence of electrode kinetics in one short phrase, it would be the transition from electronic to ionic conduction, and the phenomena associated with and controlling this process. Conduction in the solution is ionic, whereas in the electrodes and the connecting wires it is electronic. The transition from one mode of conduction to the other requires charge transfer across the interfaces. This is a kinetic process. Its rate is controlled by the catalytic properties of the surface, the chemisorption of species, the concentration and the nature of the reacting species and all other parameters that control the rate of heterogeneous chemical reactions. 

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