Rate of a heterogeneous reaction

The speed of a heterogeneous reaction (or its rate) is usually an extremely complex function that depends on physico-chemical and textural variables (shapes and phase dimensions). (Jenerally, the volumetric or areal speed cannot be defined. Despite thus, a certain nrrmber of heterogeneorrs reactions follow the law , which means that the rate can be written as a product of two functions as in the case of the elementary steps  

One of these, ( ), is expressed in mol/m /s and only depends on intensive quantities pressure, temperature, concentrations, light intensity, electric or magnetic fields, etc. It acts as an areal speed. 

The other, E, is expressed in m /mol and only depends on the morphological characteristics of the system. 

In this book, unless explicitly stated otherwise, we will only consider the case of reactions that obey E law. 

Reactions that occur without creation of a new condensed phase and without change in phase dimensions 

---

We have seen that the rates of many reactions increase if we increase the concentration of reactants or the temperature. Similarly, the rate of a heterogeneous reaction can be increased by increasing the surface area of a reactant (Fig. 13.32). But suppose we want to increase the rate for a given concentration or surface area without raising the temperature These sections describe an alternative. 

Electron movement across the electrode solution interface. The rate of electron transfer across the electrode solution interface is sometimes called k. This parameter can be thought of as a rate constant, although here it represents the rate of a heterogeneous reaction. Like a rate constant, its value is constant until variables are altered. The rate constants of chemical reactions, for example, increase exponentially with an increasing temperature T according to the Arrhenius equation. While the rate constant of electron transfer, ka, is also temperature-dependent, we usually perform the electrode reactions with the cell immersed in a thermostatted water bath. It is more important to appreciate that kei depends on the potential of the electrode, as follows ... 

The rate of a heterogeneous reaction may be proportional to the interfacial area of contact between the phases, as well as to the concentrations of reactants within a particular phase, as in the case of many reactions catalyzed at surfaces. 

One can also evaluate the relative change in the rate of a heterogeneous reaction at the substrate by measuring the concentration of the reaction product at the tip. In this setup, the tip is positioned at a fixed distance from the substrate, and the time dependence of concentration is measured. This simpler approach is based on the proportionality between the heterogeneous reaction rate and the product concentration. It is most useful when the substrate flux cannot be measured directly (e.g., the substrate reaction is not an electrochemical process) [76-78]. 

A3.2. The Effects of the Active Phase Dispersion on the Rate of a Heterogeneous Reaction... 

Since chemical adsorption is an exothermic process, the surface coverage decreases with an increase in temperature. The rate of a heterogeneous reaction is proportional to the coverage. As a result the reaction can be treated as a first-order reaction for weakly adsorbed gaseous species. For the strongly adsorbed cases the reaction is the zeroth order because the reaction rate is independent of the partial pressure. For the intermediate case the reaction rate may be a fraction. 

The rate of a heterogeneous reaction was measured in a rotating basket reactor. The volume of the basket was 100 mL and it was filled with 240 g of catalytic particles whose specific surface area was 9.5m /g of... 

The rate of a heterogeneous reaction is defined normally with respect to either l lie reactive surface area or the mass of the solid catalyst as... 

Until now, we have only considered chemical reactions in homogeneous systems. However, the study of heterogeneous systems, in which more than one phase is present, are equally important, particularly in the areas of catalysis and corrosion. For example, the oxidation of a metal is faster when its area exposed to the oxidising medium increases. In general, it is seen that the rate of a heterogeneous reaction is directly proportional to the contact area between the reactants, S. Thus, in the rate law (2.17), these reactions are first order relative to S. ... 

Many parameters influence the rate of a heterogenous reaction The three main ones are temperature, partial pressures of gases (reactants, products, or others), and the shapes and sizes of the samples. 

Remark.- If the condition posed above, namely the rate-determining step being far from equilibrium, is not observed, there is no reason that the rate of a heterogenous reaction follows the law of Arrhenius. However, it is possible that in experiments, the law of Arrhenius seems to be followed and this is quite easy as on one hand the coordinates of Arrhenius support the linearization and on the other hand temperature ranges used are often narrow. In this case, the measured apparent energy does not have any physical significance in connection with the mechanism. This is only a temperature coefficient. 

Before deriving the rate equations, we first need to think about the dimensions of the rates. As heterogeneous catalysis involves reactants and products in the three-dimensional space of gases or liquids, but with intermediates on a two-dimensional surface we cannot simply use concentrations as in the case of uncatalyzed reactions. Our choice throughout this book will be to express the macroscopic rate of a catalytic reaction in moles per unit of time. In addition, we will use the microscopic concept of turnover frequency, defined as the number of molecules converted per active site and per unit of time. The macroscopic rate can be seen as a characteristic activity per weight or per volume unit of catalyst in all its complexity with regard to shape, composition, etc., whereas the turnover frequency is a measure of the intrinsic activity of a catalytic site. 

As well as depending on catalyst porosity, the reaction rate is some function of the reactant concentrations, temperature and pressure. However, this function may not be as simple as in the case of uncatalyzed reactions. Before a reaction can take place, the reactants must diffuse through the pores to the solid surface. The overall rate of a heterogeneous gas-solid reaction on a supported catalyst is made up of a series of physical steps as well as the chemical reaction. The steps are as follows. 

A catalyst is a substance that increases the rate at which a chemical reaction reaches equilibrium. Catalysis is the word used to describe the action of the catalyst. Heterogeneous catalysis describes the enhancement in the rate of a chemical reaction brought about by the presence of an interface between two phases [2],... 

Thus, via the quantum yield, the rate of a heterogeneous photoredox reaction, where the (bulk) solid phase acts as chromophore, depends on the surface concentration of the reductant (or oxidant). 

The rate of a generic reaction j is represented by its absolute velocity Vj, which may be obtained from experiments, provided that the mass of solvent is held constant throughout the experiment and no additional homogeneous or heterogeneous reactions concur to modify the molality of the ion in solution (Delany et al., 1986) ... 

In this case the quantity n indicates how many times the number of reactive particles adsorbed per unit surface increases under illumination (other external conditions remaining the same). Evidently, the rate of the heterogeneous reaction in which these particles participate will be a function of fi and thus will be sensitive to illumination. If An = Ap = 0 (photo-electrically inactive absorption of light), then according to (41) m = 1, and illumination has no effect on the reaction rate. 

Crowley et al. (1994) have measured the absorption cross sections of CH3OCl and calculate a lifetime with respect to photolysis under stratospheric conditions of 4 h at a solar zenith angle of 80°. The rate of the heterogeneous reaction (38) is not known. 

This process can be described in terms of a heterogeneous reaction in which ferri-cyanide (or hexacyanoferrate(III)) ions, [Fe(CN)g], are formed. At the beginning of the voltammetric peak, the current is controlled by the kinetic of the electron transfer across the electrode/electrolyte barrier so that the current increases somewhat exponentially with the applied potential. The value of the current is controlled 150-200 mV after the voltammetric peak by the diffusion rate of ferrocyanide ions from the solution bulk toward the electrode surface. 

From eqn. 3.2-42 it can be concluded that the dependence of the overall rate of a heterogeneous catalytic reaction on the pressure is decreased when the pore-diffusion is rate limiting. 

The effect of diffusion on the rate of a heterogeneous catalytic reaction is characterized by the efficiency factor of a catalyst, tj, defined as the ratio of the actual reaction rate to the rate that would be in the kinetic region under the same conditions. 

A catalyst is a special chemical substance that, when viewed as a microsculpture, has many of the characteristics of a successful three-dimensional sculpture, mainly variety, unity, and interest. A catalyst is a chemical substance that accelerates the rate of a chemical reaction but is not itself changed into a product. The catalyst is not consumed in the chemical change. If the catalyst is viewed as a microsculpture, it is the negative space of this microsculpture that is involved in the catalyst mechanism for changing the rate of a chemical reaction. This can be illustrated with either heterogeneous or homogeneous catalysts. 

It is easy to notice that the usual concepts and laws of the kinetics of homogeneous chemical reactions can hardly be used in analysing the examined heterogeneous process. Indeed, difficulties already arise when employing the main concepts of chemical kinetics, namely, the concentration of a reactant or a product in the system and the rate of a chemical reaction. 

---