Langmuir-Hinshelwood equations

Over the usual hmited range of conditions, a power law rate equation often appears to be as satisfactory a fit of the data as a more complex Langmuir-Hinshelwood equation. The example of the hydrogenation of oc tenes is shown in Fig. l-2d and l-2e, and another case follows. 

In comparison with the case of a gas phase molecule that reacts in a monomole-cular reaction on a solid catalyst, the reciprocal of the Michaelis constant takes the place of the equilibrium constant of adsorption in the Langmuir-Hinshelwood equations. 

Kinetics of the photooxidation of organic water impurities on illuminated titania surfaces has been generally regarded to be based on the Langmuir-Hinshelwood equation with first-order reaction kinetics vs. initial substrate concentration was established univocally by many authors... 

With cation-exchanged zeolites [304], the first-order kinetics [eqn. (18)] is explained by the degeneration of the Langmuir—Hinshelwood equation for monomolecular transformation of adsorbed acetylene in the rate-determining step... 

Langmuir—Hinshelwood equations, with a surface reaction as the ratedetermining step, were also found suitable for liquid phase transesterifications [435—437]. With ethyl acetate and 1-propanol in dioxan as a sol-... 

The mechanism of the formation of phosgene according to the reaction, CO (A) + C12(B) =4 C0C12(C), is to be checked with given data at 30.6 C (Potter Baron, CEP 47 473, 1951). Six Langmuir-Hinshelwood equations and a power law model are examined. The rate equations are analyzed in linearized forms. Those that have negative constants are not physically realistic. 

Problem P8.04.01 takes the case where ES is not in equilibrium. Extensions of the M-M equation take into account the presence of additional substrates and inhibitors, and even other mechanisms. Some of these alternates are treated in the Problems. Clearly the M-M equation is a special case of the Langmuir-Hinshelwood equations of Chapter 6. 

Next, the drop in catalytic activity was determined as a function of temperature. The catalyst studied is an improved version of a commercial catalyst on which detailed kinetic experiments were carried out [13 The process occurring over the catalyst is described by a system of the oxidation reactions for o-xylene together with the Langmuir - Hinshelwood equation given by Skrzypek etal[ 3 Their equations (9) - (14) were, however, slightly modified by substituting the product of the activity s and the reaction rate rh R,-s rs> for the reaction rate rt. 

Equation 5.106 can also be transformed into the classic Langmuir-Hinshelwood equation at constant light irradiance (see e.g. eq. 5.91) it demonstrates the interdependence of the reaction rate on light irradiance and concentration of reagent. However, in spite of the similar behaviour of ER and LH kinetics, there is nevertheless a difference in the approximations of the so-called apparent Langmuir constant (A l) in the two mechanistic models, eqs. 5.108 and 5.109 (Emeline et al, 2000b). At very high photon flow (i.e. when [e si °°) 0 in the ER pathway,... 

First-order kinetics was chosen in writing Eq. (11-46), so that an analytical solution could be obtained. Numerical solutions for rj vs have been developed for many other forms of rate equations. Solutions include those for Langmuir-Hinshelwood equations with denominator terms, as derived in Chap. 9 [e.g., Eq. (9-32)]. To illustrate the extreme effects of reaction, Wheeler obtained solutions for zero- and second-order kinetics for a fiat plate of catalyst, and these results are also shown in Fig. 11-7. For many catalytic reactions the rate equation is approximately represented... 

This equation fits the data with an average error of 3%. The data can also be fitted with a Langmuir-Hinshelwood equation based on reaction between adsorbed benzene and adsorbed propylene but with no term for KbCb in the denominator ... 

This equation now has the form of a Langmuir-Hinshelwood equation, except that the rate is shown to be proportional to the concentration of enzyme. If die rate were written per enzyme molecule, the form would be identical to the Langmuir-Hinshelwood form, with cat equal to the rate constant and Ar (= 1/Km) equal to the equilibrium constant for die binding of the reactant to the enzyme. The sequence of steps is then... 

The principal kinetics of propylene polymerization with a magnesium chloride supported Ziegler-Natta catalyst was also developed. The polymerization rate is described by a Langmuir-Hinshelwood equation showing the dependence of die rate on the concentration of the aluminum alkyl ... 

The rate is known and it obeys the Langmuir-Hinshelwood equation ... 

This is the general form of the Langmuir-Hinshelwood equation applicable to heterogeneous chemical catalysis. 

The hydrodenitrogenation of methyicyclohexylamine over NiMoS/Al203 catalysts proceeds via two pathways the elimination of NH3 followed by olefin saturation, and direct hydrogenolysis. In-situ fiuorination promotes the HDN activity by enhancing the elimination step, while little effect is observed for the direct hydrogenolysis path. Kinetic parameters were obtained for the reaction network by fitting the Langmuir-Hinshelwood equations. 

The rate and adsorption constants of CHA and CHE were calculated by fitting the data obtained at four different temperatures (568, 598, 623 and 648 IQ and at different initial partial pressures to Langmuir-Hinshelwood equations. A two-site model was used to describe the surface reactions, one site for the reactions of CHA and the other for the reaction of CHE. The usual kinetic approach is to measure the partial pressures of a reactant and its intermediate and final products as a function of time, and to fit the resulting data with model equations. In our experience, this approach often underestimates the dependency of the concentration of the product on the reactant and may, therefore, give results which are very well acceptable firom a mathematical but not from a chemical point of view. Thus, we studied each reaction step separately in order to determine its chemistry correctly. Kinetic information on the separate reaction steps is then combined in an overaU kinetic scheme. 

This equation, the Langmuir-Hinshelwood equation, was first proposed by Langmuir and Hinshelwood in the 1920-30s for solid-catalyzed gas-phase reactions under the assumption that adsorption and desorption rates are high compared with rates of other chemical transformations on the catalyst surface. In this model, adsorption-desorption steps are considered to be at equilibrium. Later, Hougen, and Watson proposed a similar equation, the Hougen-Watson equation, for a reversible catalytic reaction, again under the assumption that the adsorption-desorption steps are at equilibrium. 

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