Rate expressions bimolecular surface reactions

In initial rate studies no products need be present in the feed, and the terms in the rate expression involving the partial pressures of these species may be omitted under appropriate experimental conditions. The use of stoichiometric ratios of reactants may also cause a simplification of the rate expression. If one considers a reversible bimolecular surface reaction between species A and ,... 

Recently, Praharso et al also developed a Langmuir-Hinshelwood type of kinetic model for the SR kinetics of i-Cg over a Ni-based catalyst. In their model, it was assumed that both the hydrocarbon and steam dissociatively chemisorb on two different dual sites on the catalyst surface. The bimolecular surface reaction between dissociated adsorbed species was proposed as the ratedetermining step. The following generalized rate expression was proposed ... 

In the Langmuir-Hinshelwood (L-H) mechanism for surface-catalyzed reactions, the reaction takes place between two surface-adsorbed species [4,5], As a substitute for concentration, we use surface coverage, and the rate is expressed in this term. We consider that the elementary reaction in the L-H mechanism is the bimolecular surface reaction expressed by the following equations ... 

As an extension to concepts discussed earlier, a rate expression for the reaction of A and B to form products can be developed by assuming an irreversible, ratedetermining, bimolecular surface reaction ... 

In catalysis the reasons for all kinetic behaviour lie in the behaviour of surface coverage by the reactants. This means that the kinetics of certain catalytic reactions -and the catalytic oxidation of CO via a bimolecular surface reaction is one of than - do not depend directly on gas phase concentrations. To understand Figures 12.1 and 12.2 we need to examine the behaviour of 6co and dca as expressed by equations 12.4 and 12.5. It is only by understanding the behaviour of the fractions of surface covered by adsorbed species that an understanding of any catalytic reaction can be gained. Since at present there is no way to measure the adsorption isotherms of reacting species at high temperatures, we need a reliable mechanistic rate expression to examine this aspect of the reaction. An appropriate mechanistic rate expression will permit us to reliably simulate the behaviour of the isotherms from kinetic data. 

Adsorption requires the O2 molecule to find a pair of adsorption sites and desorption requires two adsorbed G atoms to be adjacent. Hill [15] and Kisliuk [18,19] discuss lattice statistics and the probability of find-Ing pairs of sites in two-dimensional arrays presented by the regular arrangement of surface atoms illustrated in Figure 5.16. Boudart and pjega-Mariadassou [3],and Hayward andTrapnell [13], describe how the probability of finding pairs of sites is used to develop rate expressions on surfaces. When a bimolecular surface reaction occurs, such as dissociative adsorption, associative desorption, or a bimolecular surface reaction, the rate in the forward direction depends on the probability of finding pairs of reaction centers. This probability, in turn, depends... 

HjS and HjO on type 1 sites and with respect to dissociated oxygen on type 2 sites, and if the bimolecular surface reaction between adsorbed H2S and an adsorbed oxygen atom is the rate-limiting step in this reaction, derive an expression for the expected reaction rate. 

The rate of a bimolecular surface reaction can now be expressed in the form... 

In these expressions is the rate of adsorption of species j, which for A may be written as A + S AS, where A is the gas-phase molecule. S is an empty site on the surface, and AS is the adsorbed molecule. We can consider adsorption as a bimolecular chemical reaction that is proportional to the densities of the two reactants A and S to give... 

To derive the corresponding kinetic expressions for a bimolecular-unimolecular reversible reaction proceeding via an Eley-Rideal mechanism (adsorbed A reacts with gaseous or physically adsorbed B), the term K Pt should be omitted from the adsorption term. When the surface reaction controls the rate the adsorption term is not squared and the term KgKg is omitted. 

As for bimolecular reactions, collision theory can also be used to describe the kinetics of interfacial reactions between a solid surface and solutes in the liquid phase. Astumian and Schelly have described the theory for the kinetics of interfacial reactions in detaiL The complete rate expression, derived by Astumian and Schelly, for solutes reacting with suspended solid spherical particles is given by Eq. (1)... 

Before A and B can react, they must both adsorb on the catalyst surface. The next event is an elementary step that proceeds through a reaction of adsorbed intermediates and is often referred to as a Langmuir-Hinshelwood step. The rate expression for the bimolecular reaction depends on the number density of adsorbed A molecules that are adjacent to adsorbed B molecules on the catalyst surface. This case is similar to the one developed previously for the recombinative desorption of diatomic gases [reverse reaction step in Equation (5.2.20)] except that two different atomic species are present on the surface. A simplified rate expression for the bimolecular reaction is ... 

For 5 not equal to 0, a dividing surface is called a generalized transition state (to distinguish it from the conventional transition state where the gradient is zero). With this choice of dividing surface the generalized TST rate expression given by Eq. (11) reduces for a bimolecular reaction to... 

Many catalyzed surface reactions can be treated as a two-step process with an adsorption equilibrium followed by one rate-determining step (diffusion, surface reaction, or desorption). The surface reaction kinetics are usually discussed in terms of two limiting mechanisms, the Langmuir-Hinshelwood (LH) and Eley-Rideal (ER) mechanisms. In the LH mechanism, reaction takes place directly between species which are chemically bonded (chemisorbed) on the surface. For a bimolecular LH surface reaction. Aawith competitive chemisorption of the reactants, the rate of reaction is given by the following expression ... 

This example demonstrates that the dependence of the initial rate -Ra)o on total pressure Pt gives a clear indication of the rate-controlling step and hence of the form of the LHHW equation. The linear P dependence observed for adsorption-controlling cases and the independence from P of desorption-controlling cases are similar in all reaction types. The Pt dependence of -Ra)o for surface reaction-controlling cases of dual-site or bimolecular reactions is generally expressed by rate equations with a squared term in the denominator ... 

Our recent electronic structure calculations 3deld a potential energy surface adequate to explain, at least qualitatively and within the uncertainties due to an incomplete knowledge of relaxation rates, the available experimental observations for the hydrogen-iodine reaction. The rate expressions, the rate constants, their temperature dependence, the vibrational excitation of HI products, the excitation and/or dissociation of reactant I2, the photochemical rates - all are compatible with the recent ab initio potential energy surface and with the classical trajectory calculations carried out with a similar surface. And all are compatible with either the bimolecular or termolecular mechanisms. It appears most likely that both mechanisms contribute, but the matter is not resolved as yet. 

Finally, to summarize, a variety of the traditional rate expressions for reactions on an ideal surface has been examined, and many of their derivations have been discussed in detail. These include L-H and R-E models describing unimolecular and bimolecular reactions on surfaces with either one type of active site or two types of active sites. If a RDS other than that for a surface reaction is proposed, i.e., either an adsorption or a desorption step, then a H-W rate expression is derived. These standard rate laws, which assume a RDS exists, are frequently referred to and utilized, and they are summarized in Table 7.10. Many other forms of a rate expression, which do not assume a RDS and utilize the SSA, can be derived based on the reaction sequence proposed. 

The expression for the rate of a bimolecular reaction of adsorbed particles when the latter have a rapid surface mobility can be obtained in the traditional way for chemical kinetics if the law of mass action is used for large quasi-particles. Let us consider the reaction AZ+BZ on a homogeneous surface containing three species of particles (s = 3) A, B, and Y (the real properties of the vacant sites Y are taken into account in the final expressions). Particles of A and B are at neighboring sites of a lattice and enter the c.s. of one another. 

Figure 2.12 illustrates schematically the essential features of the thermodynamic formulation of ACT. If it were possible to evaluate A5 ° and A// ° from a knowledge of the properties of aqueous and surface species, the elementary bimolecular rate constant could be calculated. At present, this possibility has been realized for only a limited group of reactions, for example, certain (outer-sphere) electron transfers between ions in solution. The ACT framework finds wide use in interpreting experimental bimolecular rate constants for elementary solution reactions and for correlating, and sometimes interpolating, rate constants within families of related reactions. It is noted that a parallel development for unimolecular elementary reactions yields an expression for k analogous to equation 128, with appropriate AS °. 

With this choice of dividing surfaces, a generalized expression for the transition state theory rate constant for a bimolecular reaction is given by ... 

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