Equilibrium constants surface reaction kinetics

A quite analogous treatment may be applied to the kinetics of heterogeneously catalyzed reactions. Consider a surface S that contains so active sites to which reactant A, a gaseous or solute species, may bind reversibly with an equilibrium constant KA ... 

Kr Kinetic equilibrium constant for surface reaction Exam. 10.3... 

Finally, although both temperature-programmed desorption and reaction are indispensable techniques in catalysis and surface chemistry, they do have limitations. First, TPD experiments are not performed at equilibrium, since the temperature increases constantly. Secondly, the kinetic parameters change during TPD, due to changes in both temperature and coverage. Thirdly, temperature-dependent surface processes such as diffusion or surface reconstruction may accompany desorption and exert an influence. Hence, the technique should be used judiciously and the derived kinetic data should be treated with care ... 

Kinetic Term The designation kinetic term is something of a misnomer in that it contains both rate constants and adsorption equilibrium constants. For thfe cases where surface reaction controls the overall conversion rate it is the product of the surface reaction rate constant for the forward reaction and the adsorption equilibrium constants for the reactant surface species participating in the reaction. When adsorption or desorption of a reactant or product species is the rate limiting step, it will involve other factors. 

The equilibrium constant is small but not insignificant. The problem comes with the kinetics of the reaction and it does not proceed without a catalytic surface, even at 500 K. It remains, however, a good example to consider the extent of the reaction as a function of initial reactant concentrations. 

The kinetic studies of the hydrogenolysis of DPM indicate that both the DPM and hydrogen are adsorbed on the same kind of active sites on the catalyst. Also, the rate-determining step of the hydrogenolysis is a surface reaction between adsorbed DPM and dissociatively adsorbed hydrogen. When the rate equation for DPM is applied to asym DAMs, their reactivities can be satisfactorily explained, and it is suggested that the product selectivity is proportional to the ratio of the adsorption equilibrium constants of the two aryl groups. 

MICELLAR CATALYSIS. Chemical reactions can be accelerated by concentrating reactants on a micelle surface or by creating a favorable interfacial electrostatic environment that increases reactivity. This phenomenon is generally referred to as micellar catalysis. As pointed out by Bunton, the term micellar catalysis is used loosely because enhancement of reactivity may actually result from a change in the equilibrium constant for a reversible reaction. Because catalysis is strictly viewed as an enhancement of rate without change in a reaction s thermodynamic parameters, one must exercise special care to distinguish between kinetic and equilibrium effects. This is particularly warranted when there is evidence of differential interactions of substrate and product with the micelle. Micelles composed of optically active detergent molecules can also display stereochemical action on substrates. ... 

The difficulty of dealing with a quantitative theory that involves peaks due to the adsorption or desorption of materials (i.e., 0 > 0) is that one has to know the kinetic rate constants for the surface reactions that are often part of an overall sequence. Equilibrium equations involving the adsorption energies of the intermediates (Gosser 1993) are not enough, i.e., the intermediate may be part of a rate-determining reaction and not at equilibrium. 

A variety of models have been derived to describe the kinetics of semiconductor photocatalysis, but the most commonly used model is the Langmuir-Hinshel-wood (LH) model [77-79]. The LH model relates the rate of surface-catalyzed reactions to the surface covered by the substrate. The simplest representation of the LH model [Eq. (7)] assumes no competition with reaction by-products and is normally applied to the initial stages of photocatalysis under air- or oxygen-saturated conditions. Assuming that the surface coverage is related to initial concentration of the substrate and to the adsorption equilibrium constant, K, tire initial... 

Polarography is valuable not only for studies of reactions which take place in the bulk of the solution, but also for the determination of both equilibrium and rate constants of fast reactions that occur in the vicinity of the electrode. Nevertheless, the study of kinetics is practically restricted to the study of reversible reactions, whereas in bulk reactions irreversible processes can also be followed. The study of fast reactions is in principle a perturbation method the system is displaced from equilibrium by electrolysis and the re-establishment of equilibrium is followed. Methodologically, the approach is also different for rapidly established equilibria the shift of the half-wave potential is followed to obtain approximate information on the value of the equilibrium constant. The rate constants of reactions in the vicinity of the electrode surface can be determined for such reactions in which the re-establishment of the equilibria is fast and comparable with the drop-time (3 s) but not for extremely fast reactions. For the calculation, it is important to measure the value of the limiting current ( ) under conditions when the reestablishment of the equilibrium is not extremely fast, and to measure the diffusion current (id) under conditions when the chemical reaction is extremely fast finally, it is important to have access to a value of the equilibrium constant measured by an independent method. 

Later, it became clear that the concentrations of surface substances must be treated not as an equilibrium but as a pseudo-steady state with respect to the substance concentrations in the gas phase. According to Bodenstein, the pseudo-steady state of intermediates is the equality of their formation and consumption rates (a strict analysis of the conception of "pseudo-steady states , in particular for catalytic reactions, will be given later). The assumption of the pseudo-steady state which serves as a basis for the derivation of kinetic equations for most commercial catalysts led to kinetic equations that are practically identical to eqn. (4). The difference is that the denominator is no longer an equilibrium constant for adsorption-desorption steps but, in general, they are the sums of the products of rate constants for elementary reactions in the detailed mechanism. The parameters of these equations for some typical mechanisms will be analysed below. 

Figure 1.3 shows a plot of 0 versus partial pressure for various values of the adsorption equilibrium constant. These show that as the equilibrium constant increases for a given pressure, we increase the surface fraction covered, up to a value of 1. As the pressure increases, we increase the fraction of the surface covered with A. But we have only a finite amount of catalyst surface area, which means that we will eventually reach a point where increasing the partial pressure of A will have little effect on the amount that can be adsorbed and hence on the rate of any reaction taking place. This is a kind of behavior fundamentally different from that of simple power-law kinetics, where increasing the reactant concentration always leads to an increase in reaction rate proportional to the order in the kinetic expression. 

Another important characteristic of the surface processes is a ratio g of the adspecies migration rate constant to those of the surface reaction, adsorption, and desorption rates. At small coverages the parameter g controls the surface process conditions r 1 in the kinetic and g l in the diffusion mode. A fast surface mobility of the adspecies and their equilibrium distribution on the surface are the most frequently adopted assumptions. At r < 1 the macroscopic concentrations of adspecies 6 cannot be used for calculating the process rates, and a more detailed description of their distribution is essential. 

In summary, it can be seen for the three-step reaction scheme of this example that the net rate of the overall reaction is controlled by three kinetic parameters, KTSi, that depend only on the properties of the transition states for the elementary steps relative to the reactants (and possibly the products) of the overall reaction. The reaction scheme is represented by six individual rate constants /c, and /c the product of which must give the equilibrium constant for the overall reaction. However, it is not necessary to determine values for five linearly independent rate constants to determine the rate of the overall reaction. We conclude that the maximum number of kinetic parameters needed to determine the net rate of overall reaction is equal to the number of transition states in the reaction scheme (equal to three in the current case) since each kinetic parameter is related to a quasi-equilibrium constant for the formation of each transition state from the reactants and/or products of the overall reaction. To calculate rates of heterogeneous catalytic reactions, an addition kinetic parameter is required for each surface species that is abundant on the catalyst surface. Specifically, the net rate of the overall reaction is determined by the intrinsic kinetic parameters Kf s as well as by the fraction of the surface sites, 0, available for formation of the transition states furthermore, the value of o. is determined by the extent of site blocking by abundant surface species. 

For practical heterogeneous catalyst kinetics this principle has the following consequence. Usually, the assumption of a homogeneous surface is not valid. It would be more realistic to assume the existence of a certain distribution in the activity of the sites. From the above, certain sites will, however, contribute most to the reaction, since these sites activate the reactants most optimally. This might result in an apparently uniform reaction behaviour, and can explain why Langmuir adsorption often provides a good basis for the reaction rate description. This also implies that adsorption equilibrium constants determined from adsorption experiments can only be used in kinetic expressions when coverage dependence is explicitly included otherwise they have to be extracted from the rate data. 

Fig. 7. Simulation of linearized plots for kinetics governed by surface concentration of substrates adsorbed on the photocatalyst surface in a Langmuirian fashion, where r, C, k, K, and S are rate of reaction (mols ), concentration of a substrate (molL ), rate constant (10 s ), adsorption equilibrium constant (5 L mol ), and saturated amount of adsorption (2 x 10 mol).

If the system is well represented by Langmuir-Hinshelwood kinetics, then the relative values of the adsorption equilibrium constants of various unsaturated compounds can be obtained from the relative rates determined individually and in competition. The expression for the competitive reaction between two compounds A and B results from the division of the corresponding rate expressions for each compound (equation 3) to give equation (4). The ratio of the individual rates of hydrogenation, k/Jk, permits the abstraction of the ratio K/JK from the competitively determined ratio kkK/Jk K (equation 5). The assumption that the adsorption of the unsaturated compound is rapid and reversible relative to the rates of the surface-catalyzed reactions may not be correct. In that case, KfJK is an apparent relative adsorption equilibrium constant (see Section 3.1.3.2.2). 

---