Langmuir-Hinshelwood expressions

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 ... 

Two equations have been proposed for correlation of experimental data on pentane isomerizaton the single-site Langmuir-Hinshelwood expression ... 

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 ... 

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. 

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. 

The Langmuir-Hinshelwood expression for the rate of formation of product C is... 

The dehydration of t-butyl alcohol over styrene-divinyl benzene resins containing different combinations of the acid groups -PO(OH)2, -P(OH)2, and -SO3H gave rate data which were best described by a Langmuir-Hinshelwood expression (equation 4), and involved summation of contributions for each site, ie. 

Relatively few kinetic studies have been carried out, but Beranek and Kraus have reported that many catalysts give rise to data which satisfy Langmuir-Hinshelwood expressions of the form (equation 9) ... 

More recently, Lloyd et al.15 pointed out that more theoretically derived Langmuir-Hinshelwood expressions similar to Equation 6.21 provide the best fit of experimental data ... 

Chemisorbed NH3 dissociates much more readily and many authors have studied the kinetics of dissociation. Loffler and Schmidt have studied the kinetics under molecular beam conditions on a polycrystalline specimen and on several low-index faces of a single crystal [(111), (100), (110), (210)]. The rate between 330 and 930 °C is strongly retarded by hydrogen and can be fitted by a Langmuir-Hinshelwood expression with competitive H2 and NH3 adsorption. 

Both groups of workers proposed kinetic equations to fit their results. Nutt and Kapur preferred a Langmuir-Hinshelwood expression for a bimolecular surface reaction with competitive adsorption on single sites where / is the flux... 

While these expressions reproduce the main features of the experimental results well, Pignet and Schmidt suggest that they fail to represent adequately changes in surface chemistry. There was, for example, a lack of reproducibility between 200 and 400 °C in oxygen-deficient conditions. They therefore do not claim any basic significance for the values of the parameters fitted to their Langmuir-Hinshelwood expressions, e.g. the adsorption constants Ko and Ko had different values as did A nh, and A nh3 -... 

Based on the previous assumptions, we can rigorously and explicitly determine an analytical expression of the apparent kinetic constants, between all the lumped families (Fx -> Fy) according to intrinsic elementary kinetic constants as specified in the Single-Events theory (Cochegrue, 2001 Schweitzer, 1998 Valery, 2002). The same applies for the denominator DEN (see next Fig. 26), in which the sum of the terms expresses the competitive chemisorption of all secondary and tertiary carbocations on the acid sites. The apparent kinetics so obtained formally return Langmuir-Hinshelwood expressions, traditional... 

The turnover rate becomes proportional to the surface coverage 0, Equation (1.6) is the Langmuir - Hinshelwood expression and is very similar to the Michaelis - Menten expression used in enzyme catalysis. Consider the following mechanism describing... 

In addition to equations (8-1 a) and (8-1 b), one must establish a specific mathematical form for the rate of photoconversion. For instance, the initial photoconversion rate, which is valuable in the calculation of quantum efficiencies (Ibrahim and de Lasa, 2003), can be represented using a Langmuir-Hinshelwood expression ... 

In Figure 3.15 are some experimental results of Kehoe and Butt [J.P.G. Kehoe and J.B. Butt, J. Appl. Chem. BiotechnoL, 23, (1972)] on the initial rates of the hydrogenation of benzene over a nickel-kieselguhr catalyst in an excess of hydrogen at low temperatures. Determine a consistent form of Langmuir-Hinshelwood expression to correlate these data, and obtain the values of the associated rate and equilibrium constants and their temperature dependence. 

With Equation (2.1.33) this gives the classical Langmuir-Hinshelwood expression (Equation 2.1-40). 

A model was developed to interpret the experimental results, which is similar to the model, Equation (23.27)-Equation (23.30). The Kelvin equation was used to calculate the critical radius of capillary condensation, and the thickness of the adsorbed layer on the walls of vapor-filled pores was calculated using the method of Gregg and Sing [2]. A Langmuir-Hinshelwood expression was assumed to represent the kinetics in vapor filled pores (Equation (23.25a)) and the reaction in liquid-filled pores was taken as first order (Equation 23.25b)). 

In other cases, it is possible to consider the inhibitory effect of certain compounds such as H2S, NH3, organic N-compounds, or even asphaltenes, by competitive adsorption. By factoring out the adsorption term from the lumped rate coefficient, the following Langmuir-Hinshelwood expression can be obtained ... 

The comprehensive work by Xu and Froment [525] established a complex Langmuir—Hinshelwood expression, using a classic approach, on the basis of 280 measurements made with a Ni/MgAl204 catalyst, but it is restricted to a narrow range of parameters temperatures of 500— 575 C, pressures of 3—15 bar and molar H2O/CH4 ratios of 3—5. A... 

This paper describes a mathematical model for a single catalyst particle in which several chemical reactions take place. The model includes transport restrictions against mass and heat transfer in the interior and in the gas film surrounding the particle, and it accepts a general type reaction rate expression such as a power law expression or a Langmuir-Hinshelwood expression. The model is reduced to a number of coupled second order differential equations - one for each reaction - by use of the stoichiometric coefficients. 

This expression, which is identical to Eq. (4.3.31) previously given for first-order kinetics, holds regardless of the value of k in the Langmuir-Hinshelwood expression. 

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