Rate Langmuir-Hinshelwood models

Kinetic analysis based on the Langmuir-Hinshelwood model was performed on the assumption that ethylene and water vapor molecules were adsorbed on the same active site competitively [2]. We assumed then that overall photocatalytic decomposition rate was controlled by the surface reaction of adsorbed ethylene. Under the water vapor concentration from 10,200 to 28,300ppm, and the ethylene concentration from 30 to 100 ppm, the reaction rate equation can be represented by Eq.(l), based on the fitting procedure of 1/r vs. 1/ Ccm ... 

Figure 7.18. Dependence of the rate of thiophene hydrodesulfurization on the partial pressures of thiophene at different temperatures, along with fits according to the Langmuir-Hinshelwood model, Eq. (32). [Fron A. Borgna and J.W. Niemantsverdriet, to be published (2003).]...

All of these rates are measured on surfaces shown to be clean by AES, and this Indicates that these processes occur on surfaces containing only submonolayer coverages of reactant species, exactly the situation required for the Langmuir-Hinshelwood model of surface reactions. 

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. 

Propose a rate law based on the Langmuir-Hinshelwood model for each of the following heterogeneously catalyzed reactions ... 

The Michaelis-Menten equatioa 10.2-9, is developed in Section 10.2.1 from the point of view of homogeneous catalysis and the formation of an intermediate complex. Use the Langmuir-Hinshelwood model of surface catalysis (Chapter 8), applied to the substrate in liquid solution and the enzyme as a colloidal particle with active sites, to obtain the same form of rate law. 

Mann, Thurgood, and coworkers—Langmuir-Hinshelwood kinetic model for methanol steam reforming and WGS over Cu/Zn. Mann et al.335 published a complex Langmuir-Hinshelwood model for CuO/ZnO catalysts based on what one would encounter for a methanol steam reformer (MSR) for fuel cell applications. The water-gas shift rate, containing all MSR terms, was determined to be ... 

The ammoxidation of isobutene has not received much attention. The only contribution in this field is by Onsan and Trimm [2.44] for a rather unusual catalyst, a mixture of the oxides of Sn, V and P (ratio 1/9/3) supported on silica. At 520 C, a maximum selectivity to methacrylonitrile + methacrolein of 80% was reached with a Sn—V—P oxide catalyst (ratio 1/9/3), an isobutene/ammonia/oxygen ratio of 1/1.2/2.5 and a contact time of 120 g sec l ]. The kinetics are very similar to those for the pro-pene ammoxidation. Again, the data are initially analysed by means of (parallel) power rate equations, for which the parameters were calculated, while a more detailed analysis proves that a Langmuir—Hinshelwood model with surface reaction as the rate-controlling step provides the best fit with regard to the two main products. At 520° C, the equation which applies for the production of methacrolein plus methacrylonitrile is... 

The next problem of the Langmuir-Hinshelwood kinetics, the validity of the rate-determining step approximation, has not been rigourously examined. However, as has been shown (e.g. refs. 57 and 63), the mathematical forms of the rate equations for the Langmuir-Hinshelwood model and for the steady-state models are very similar and sometimes indistinguishable. This makes the meaning of the constants in the denominators of the rate equations somewhat doubtful in the Langmuir—Hinshelwood model, they stand for adsorption equilibrium constants and in the steady-state models, for rate coefficients or products and quotients of several rate coefficients. 

Moffat and Clark 84> found that a Langmuir-Hinshelwood model applied to a heterogeneous surface can be used to describe both the general kinetics and the rate-temperature maxima reported by Banks and Bailey (Fig. 2) for olefin disproportionation on cobalt molybdate-alumina catalyst. They conclude that the rate-temperature maximum was caused by the reversible deactivation of sites superimposed on the irreversible poisoning of sites. 

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. 

A simple Langmuir-Hinshelwood model explains quantitatively the steady-state behavior (4) but it fails to explain the oscillatory phenomena that were observed. The origin of the limit cycles is not clear. Rate oscillations have not been reported previously for silver catalyzed oxidations. Oxidation of ethylene, propylene and ethylene oxide on the same silver surface and under the same temperature, space velocity and air-fuel ratio conditions did not give rise to oscillations. It thus appears that the oscillations are related specifically to the nature of chemisorbed propylene oxide. This is also supported by the lack of any correlation between the limits of oscillatory behavior and the surface oxygen activity as opposed to the isothermal oscillations of the platinum catalyzed ethylene oxidation where the SEP measurements showed that periodic phenomena occur only between specific values of the surface oxygen activity (6,9). 

Figure 12. Residual rate distribution for the metathesis of pro-pene (left) Langmuir-Hinshelwood model (right) model based on the carbene mechanism [60].

The error model used in the minimization is based on the hypothesis that the residuals have zero mean and are normally distributed. The first is easily checked, the latter is only possible when sufficient data points are available and a distribution histogram can be constructed. An adequate model also follows the experimental data well, so if the residuals are plotted as a function of the dependent or independent variable(s) a random distribution around zero should be observed. Nonrandom trends in the residuals mean that systematic deviations exist and indicate that the model is not completely able to follow the course of the experimental data, as a good model should do. This residual trending can also be evaluated numerically be correlation calculations, but visual inspection is much more powerful. An example is given in Fig. 12 for the initial rate data of the metathesis of propene into ethene and 2-butenc [60], One expression was based on a dual-site Langmuir-Hinshelwood model, whereas the other... 

The behavior of the reaction rate as a function of temperature dispels any notion that the reaction is simple. Figure 3 shows that there is a maximum in the first-order rate constant-temperature curve at approximately 80 °C. At such a low temperature, the rate-temperature maximum cannot be explained by depolymerization, nor can it be explained by deactivation of the catalyst as a result of more rapid polymer accumulation on the catalyst at higher temperatures since the maximum is obtained for initial rates measured as a function of temperature. Theoretical considerations predict that a maximum in the rate-temperature curve may be expected from the Langmuir-Hinshelwood model for polymerization on solid surfaces but not from the Rideal model (5). The rate of reaction for the Langmuir-Hinshelwood model is given by ... 

There are several kinetic implications of the spillover phenomena. As an example, consider a simple reaction A + B - C which occurs with A, B, and C adsorbed and with the surface reaction (A + B, on a single type of active site ) controlling. The reaction rate can be written, following a Langmuir-Hinshelwood model, as... 

For most reaction systems, the intrinsic kinetic rate can be expressed either by a power-law expression or by the Langmuir-Hinshelwood model. The intrinsic kinetics should include both the detailed mechanism of the reaction and the kinetic expression and heat of reaction associated with each step of the mechanism. For catalytic reactions, a knowledge of catalyst deactivation is essential. Film and penetration models for describing the mechanism of gas-liquid and gas-liquid-solid reactions are discussed in Chap. 2. A few models for catalyst deactivation during the hydrodesulfurization process are briefly discussed in Chap. 4. 

Two papers deal with the kinetics of the oxidation on TS-1 andTi,Al- 3 [110, 111]. Equation 18.11 illustrates the general rate law valid for both catalysts, according to a Langmuir-Hinshelwood model. It is consistent with the competition of alcohol/solvent for Ti sites and the adsorption of the substrate and the oxidant on the same site. The inhibitory effect of water, implicit in the competitive adsorption of the solvent, was proved by oxidation tests performed in acetonitrile containing variable quantities of water [77, 111]. 

Different charge-compensating cations in zeolite L have been tested for their promotional effect in n-hexane aromatization. Apparently, high basicity of the alkaline and alkaline earth promoter favors n-hexane aromatization. Basicity and selectivity both increase from Li and Cs 331) and from Mg to Ba (22,25). Bezouhanova et al. studied the FTIR bands of linearly adsorbed CO in the range of 2060-2075 cm . One band at 2075 cm", which is also found on unsupported Pt, is attributed to extrazeolite Pt particles, a second band shifts from 2060 cm" for Li to lower wavenumbers with K and Rb 331). Another criterion, used by Larsen and Haller, is the measured rate of competitive hydrogenation of benzene and toluene, which has been found to correlate with the zeolite basicity (25). As described in a previous section, this method had previously been used by Tri el al. to probe for the electron deficiency of Pt particles in acidic zeolites 332). The rate data are analyzed in terms of a Langmuir-Hinshelwood model and the ratio of the adsorption coefficients of toluene and benzene, A, /b, is determined. It was found to decrease from 8.6 for Pt/Si02, and 5.4 for Pt/MgL, to 4.4 for Pt/BaL. As direct electron transfer from the cations to neutral Pt particles is unlikely, an interaction of Pt with the zeolite framework or with... 

This can be justified if we suppose that the reaction occurred between the two reactants adsorbed on the same catalytic centres and that the bromo-compounds were more strongly adsorbed than the chloro-compounds, the fluoro substituted reactant being less strongly adsorbed than the corresponding monosubstituted halobenzenes. According to the Langmuir-Hinshelwood model the initial reaction rate for the reaction between 3-chlorofluorobenzene and bromobenzene can be written as follows (Equation 2) which is in agreement with the kinetic orders found experimentally. 

Table I summarizes the results of previous investigations on catalytic dehydrogenation of n-butane. In this table 2 models were used to correlate dehydrogenation rate data by various investigators one is a power function model, and the other is a Langmuir-Hinshelwood model. The power function model can be obtained by applying the mass action law to describe rate data. Thus, the model presents the dependence of partial...

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