Langmuir-Rideal kinetics

We should warn that the method has been developed for first order reactions for reactions of different order and especially for reactions with Langmuir-Hinshelwood or Eley-Rideal kinetics the method will not work. 

Of course, the Eley-Rideal mechanism is a likely pathway at high reaction temperature, whereas the Langmuir-Hinshelwood mechanism is realized at low temperature, when the precursor concentration remains sufficient. The importance of reactant preadsorption on a given surface can be probed by the use of a Langmuir Hinshelwood kinetic model [91-93]. With the assumptions for this model the surface coverage (0) is related to the initial pressure of reactant (P) and to the apparent adsorption equilibrium constant K ... 

To illustrate tendencies, not to calculate absolute data, some simplified model calculations of reaction a) were made starting with a Langmuir-Hinshelwood kinetic (an Eley-Rideal kinetic would not change the basic conclusion regarding the width of A/F windows) ... 

Langmuir-Hinshelwood models involving the reaction between adsorbed oxygen and adsorbed reactant molecules (Luo and Ollis, 1996 Nimlos et ai, 1996 Feral and Ollis, 1992) and b) Eley-Rideal models, which consider the reaction between adsorbed oxygen and gas phase reactant molecules (Fox, 1988). Cunningham and Hodnett (1981) suggested a combination of the Langmuir-Hinshelwood and Eley-Rideal kinetics. 

The Hougen-Watson kinetic model that is consistent with the Langmuir-Rideal mechanism can be obtained from the rate law in equations (14-63) and (14-64) via the following modification of each generic term ... 

The kinetic rate law for the Langmuir-Rideal single-site mechanism is... 

Figure 8-19. Major kinetic stages of the Langmuir-Rideal heterogeneous recombination mechanism.

A second rule is that the oxidation of higher hydrocarbons, especially on perovskites doped with noble metals for increasing activity, may be described by Langmuir-Hinshelwood kinetics, indicating that both oxygen and CH species are adsorbed on the surface sites. On the contrary, for methane, the oxidation proceeds more or less via Rideal-Eley (RD) mechanism, which is in line with the notorious difficulty of this molecule to be activated. Let us review some cases from the literature. 

Competitive adsorption plays no role in the Eley-Rideal mechanism, but it is a key feature in Langmuir-Hinshelwood kinetics. In (6.59) the rate of reaction reaches its maximum when the surface species A and B are ideally mixed, and both surface concentrations are equal to one-half. Realize that the assumption of ideal mixing in the adsorbate layer is implicitly present in (6.61). The expression for the overall reaction rate becomes... 

Closure. After reading this chapter, the reader should be able to discuss the steps in a heterogeneous reaction (adsorption, surface reaction, and desorption) and describe what is meant by a rate-limiting step. The differences between molecular adsorption and dissociated adsorption should be explained by the reader, as should the different types of surface reactions (single site, dual site, and Eley-Rideal). Given heterogeneous reaction rate data, the reader should be able to analyze the data and to develop a rale law for Langmuir-Hinshelwood kinetics. The reader should be able to discrimi-... 

Mechanistic kinetic expressions are often used to represent the rate data obtained in laboratory studies, and to explain quantitatively the effects observed in the field. Several types of mechanisms have been proposed. These differ primarily in complexity, and on whether the mechanism assumes that one compound that is adsorbed on the catalyst surface reacts with the other compound in the gas phase, eg, the Eley-Rideal mechanism (23) or that both compounds are adsorbed on the catalyst surface before they react, eg, the Langmuir-Hinshelwood mechanism (25). 

Langmuir-Hinshelwood (LH) and Eley-Rideal (ER) kinetic models... 

Whether a catalytic reaction proceeds via a Langmuir-Hinshel vood or Eley-Rideal mechanism has significant implications for the kinetic description, as in the latter case one of the reactants does not require free sites to react. However, Eley-Rideal mechanisms are extremely rare, and we will assume Langmuir-Hinshelwood behavior throughout the remainder of this book. 

Jakdetchai and Nakajima/Wang and coworkers—theoretical models favor redox mechanism. Beginning in 2002, a number of theoretical models were published in Theochem studying the water-gas shift reaction over Cu(110), Cu(lll), and Cu(100) surfaces. Perhaps the first was by Jakdetchai and Nakajima,325 relying on the AMI method. The main goal of the study was (1) to determine whether or not theoretical calculations are consistent with a redox or associative (e.g., formate) mechanism and (2) whether the kinetics are described best by a Langmuir-Hinshel-wood expression or an Eley-Rideal expression. That is, in the case of a redox model, does the adsorbed O adatom react with adsorbed CO or directly with gas phase CO Their approximate A//a[Pg.205]

Using kinetic models of typical catalytic mechanisms (Eley-Rideal and Langmuir-Hinshelwood (LH) mechanisms) as examples, we found parametric domains, in which the hypergeometric representation is an excellent approximation... 

Deviations from this simple expression have been attributed to mechanistic complexity For example, detailed kinetic studies have evaluated the relative importance of the Langmuir-Hinshelwood mechanism in which the reaction is proposed to occur entirely on the surface with adsorbed species and the Eley-Rideal route in which the reaction proceeds via collision of a dissolved reactant with surface-bound intermediates 5 . Such kinetic descriptions allow for the delineation of the nature of the adsorption sites. For example, trichloroethylene is thought to adsorb at Ti sites by a pi interaction, whereas dichloroacetaldehyde, an intermediate proposed in the photo-catalyzed decomposition of trichloroethylene, has been suggested to be dissociatively chemisorbed by attachment of the alpha-hydrogen to a surface site... 

The kinetics of the ethylene oxidation are rather complicated as they depend not only on ethylene and oxygen pressure but also on the concentration of the reaction products. These influence the rate by adsorption competition with the reactants. Moreover, different forms of adsorbed oxygen may occur on the catalyst surface. Consequently, the rate equations proposed in the literature consist of either Langmuir—Hinshelwood and Eley—Rideal types or power rate models with non-integer coefficients. Power rate models are less appropriate as their coefficients inevitably depend on the reaction conditions. 

Interactions 2 and 4 represent a Rideal mechanism and Interactions 2a and 4a a Langmuir-Hinshelwood mechanism. However, to form C03"(adS), by Interaction 1 in Mechanism I, CO must first be adsorbed since Interaction 1 is a fast process, the adsorption of CO would be the slow step of Mechanism I, and the kinetics of the reaction would depend on pco- However, it has been shown (8, 28) that the reaction is zero order with respect to CO, and therefore the adsorption of CO and its conversion to COa udsi are faster processes than Interaction 2 which is the rate-limiting step and hence may be written in the form of 2a (Langmuir-Hinshelwood mechanism). 

As for Mechanism II, for which a choice has to be made between rate-determining steps 4 and 4a, the kinetic results (7) show again that the reaction rate does not depend on pc<>. Here again step 4a has to be preferred (Langmuir-Hinshelwood mechanism) to step 4 (Rideal mechanism). 

From simple measurements of the rate of a photocatalytic reaction as a function of the concentration of a given reactant or product, valuable information can be derived. For example, these measurements should allow one to know whether the active species of an adsorbed reactant are dissociated or not (22), whether the various reactants are adsorbed on the same surface sites or on different sites (23), and whether a given product inhibits the reaction by adsorbing on the same sites as those of the reactants. Referring to kinetic models is therefore necessary. The Langmuir-Hinshelwood model, which indicates that the reaction takes place between both reactants at their equilibrium of adsorption, has often been used to interpret kinetic results of photocatalytic reactions in gaseous or liquid phase. A contribution of the Eley-Rideal mechanism (the reaction between one nonadsorbed reactant and one adsorbed reactant) has sometimes been proposed. 

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