Langmuir-Hinshelwood rate expression

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). 

If the rate of both single reactions is expressed separately, e.g. by means of the equations of Langmuir-Hinshelwood type (when written in a more general way and if the mechanism of both reactions with common reagent X will be the same), we obtain... 

The oxidation of CO on Pt is one of the best studied catalytic systems. It proceeds via the reaction of chemisorbed CO and O. Despite its complexities, which include island formation, surface reconstruction and self-sustained oscillations, the reaction is a textbook example of a Langmuir-Hinshelwood mechanism the kinetics of which can be described qualitatively by a LHHW rate expression. This is shown in Figure 2.39 for the unpromoted Pt( 111) surface.112 For low Pco/po2 ratios the rate is first order in CO and negative order in 02, for high pco/po2 ratios the rate becomes negative order in CO and positive order in 02. Thus for low Pcc/po2 ratios the Pt(l 11) surface is covered predominantly by O, at high pco/po2 ratios the Pt surface is predominantly covered by CO. 

The model considers the noble-metal catalyzed oxidation reactions of CO, two hydrocarbons of differing reactivities and H2, and the reaction kinetics was described by the global rate expressions of the dual-site Langmuir-Hinshelwood type [2]. 

Compare the Michaelis-Menten expression for the rate of an enzyme-catalyzed reaction with the Langmuir-Hinshelwood expression for the same reaction on a metal surface. Are the two expressions equivalent ... 

These should be simple unlmolecular or bimolecular reactions yielding a single or at most two reaction paths. Rates may therefore be fit using Langmuir-Hinshelwood (LH) rate expressions. For A —> products this should be... 

Another problem which can appear in the search for the minimum is intercorrelation of some model parameters. For example, such a correlation usually exists between the frequency factor (pre-exponential factor) and the activation energy (argument in the exponent) in the Arrhenius equation or between rate constant (appears in the numerator) and adsorption equilibrium constants (appear in the denominator) in Langmuir-Hinshelwood kinetic expressions. 

Kinetic orders in CO oxidation on M/A1203 can be explained by the classical Langmuir-Hinshelwood expression for the rate equation, as a function of the rate constant k, the adsorption constants K and the partial pressures P ... 

Since both hydrogen in the solution and the product A are weakly adsorbed species, equilibrium constants ka and k, are very small, which leads to KACA 1 and kh CH 1. Thus, the rate expression for the debenzylation can be simplified as a conventional Langmuir-Hinshelwood model. 

These assumptions are the basis of the simplest rational explanation of surface catalytic kinetics and models for it. The preeminent of these, formulated by Langmuir and Hinshelwood, makes the further assumption that for an overall (gas-phase) reaction, for example, A(g) +...- product(s), the rate-determining step is a surface reaction involving adsorbed species, such as A s. Despite the fact that reality is known to be more complex, the resulting rate expressions find wide use in the chemical industry, because they exhibit many of the commonly observed features of surface-catalyzed reactions. 

By combining surface-reaction rate laws with the Langmuir expressions for surface coverages, we can obtain Langmuir-Hinshelwood (LH) rate laws for surface-catalyzed reactions. Although we focus on the intrinsic kinetics of the surface-catalyzed reaction, the LH model should be set in the context of a broader kinetics scheme to appreciate the significance of this. 

Note the similarity to Langmuir-Hinshelwood kinetics.) The rate is expressed on the basis of the instantaneous number of solid carbon atoms, Nc. The rate r (measured at one gas composition) typically goes through a maximum as the carbon is converted. This is the result of a maximum in the intrinsic activity (related to the fraction of reactive carbon atoms, NCJNC) because of both a change in Nq> and a decrease in Nc. 

To determine Km and Vmax, experimental data for cs versus t are compared with values of cs predicted by numerical integration of equation 10.3-3 estimates of Km and Vmax are subsequently adjusted until the sum of the squared residuals is minimized. The E-Z Solve software may be used for this purpose. This method also applies to other complex rate expressions, such as Langmuir-Hinshelwood rate laws (Chapter 8). 

Langmuir-Hinshelwood mechanism, 19 78 Langmuir-Hinshelwood type rate expressions, 25 192... 

Based on Langmuir-Hinshelwood kinetics the rate expression for a first order reaction (A —> R) that is surface reaction-controlled becomes equal to the following expression [2] ... 

For the same A R reaction, when kinetics are controlled by adsorption of reactant A rather than by surface reaction, the Langmuir-Hinshelwood rate expression becomes equal to the following [2] ... 

We wdl encounter similar rate expressions of this type when we consider surface or enzyme-catalyzed reactions in Chapter 7. These rate expressions are called Langmuir-Hinshelwood and Michaelis-Menten kinetics, respectively. 

Thus we expect the rate to be given by a power dependence on the concentrations and an exponential dependence on temperature k[ (T) = kfoe. This form of the rate expression is not always accurate, especially for catalytic and enzyme reactions for which Langmuir-Hinshelwood and Michaelis-Menten expressions are required to fit experimental data. 

These rate expressions are for Langmuir-Hinshelwood kinetics, which are the simplest forms of surface reaction rates one could possibly find We know of no reactions that are this simple. LH kinetics requires several assumptions ... 

In this rate expression we have lumped C/js into the effective surface rate coefficient by defining k" — CC s- AU sohd reactions have reaction steps similar to those in catalytic reactions, and the rate expressions we need to consider are basically Langmuir-Hinshelwood kinetics, which were considered in Chapter 7. Our use of a first-order irreversible rate expression is obviously a simplification of the more complex rate expressions that can arise from these situations. 

Based on the Langmuir-Hinshelwood expression derived for a unimolecular reaction system (6) Rate =k Ks (substrate) /[I + Ks (substrate)], Table 3 shows boththe apparent kinetic rate and the substrate concentration were used to fit against the model. Results show that the initial rate is zero-order in substrate and first order in hydrogen concentration. In the case of the Schiff s base hydrogenation, limited aldehyde adsorption on the surface was assumed in this analysis. Table 3 shows a comparison of the adsorption equilibrium and the rate constant used for evaluating the catalytic surface. 

For SR of higher hydrocarbons, Rostrup-Nielsen " and Tottrup " postulated a Langmuir-Hinshelwood-Houghen-Watson (LHHW) kinetic model. It was assumed that the hydrocarbon chemisorbs on a dual catalytic site, followed by successive a-scission of the C-C bond. The resulting Ci species react with adsorbed steam to form H2 and CO. The expressions were lit to data for SR of n-Cv on a Ni/MgO catalyst at 500°C the overall rate expression is " " ... 

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 ... 

Such rate expressions are often termed Langmuir-Hinshelwood-Hougen-Watson (LHHW) equations and are widely used in chemical engineering [see Froment and BischofT (79)]. The usual procedure is to postulate plausible mechanisms without considering cycles, as in Example 1. In such cases it may be desirable to develop the complete list of possible direct mechanisms even if further considerations can rule out some as being unlikely. The following example illustrates a typical case. 

A global rate expression for CO methanation over a nickel catalyst is given by Lee (1973) and Vatcha (1976). They report that a Langmuir-Hinshelwood rate law of the form... 

When a simple, fast and robust model with global kinetics is the aim, the reaction kinetics able to predict correctly the rate of CO, H2 and hydrocarbons oxidation under most conditions met in the DOC consist of semi-empirical, pseudo-steady state kinetic expressions based on Langmuir-Hinshelwood surface reaction mechanism (cf., e.g., Froment and Bischoff, 1990). Such rate laws were proposed for CO and C3H6 oxidation in Pt/y-Al203 catalytic mufflers in the presence of NO already by Voltz et al. (1973) and since then this type of kinetics has been successfully employed in many models of oxidation and three-way catalytic monolith converters... 

Mann and Ko [202] likewise examined the selective oxidation of isobutene on bismuth molybdate. With an integral flow reactor, the highest selectivity was obtained at over 30% conversions for an oxygen/olefin ratio of 2/1 and a W/F = 2.5 g h mol-1 (390°C). The data were correlated with a rather complicated Langmuir—Hinshelwood expression inconsistent with a redox mechanism. This was based on a rate-controlling step between adsorbed isobutene and adsorbed oxygen, and included an inhibiting effect of methacrolein by competitive adsorption with isobutene, viz. 

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