Langmuir-Hinshelwood rate

If reaction XVIII-42 is the slow step, the Langmuir-Hinshelwood rate law is... 

Rate laws have also been observed that correspond to there being two kinds of surface, one adsorbing reactant A and the other reactant B and with the rate proportional to 5a x 5b- For traditional discussions of Langmuir-Hinshelwood rate laws, see Refs. 240-242. Many catalytic systems involve a series of intermediates, and the simplifying assumption of steady-state equilibrium is usually made. See Boudart and co-workers [243-245] for a contemporary discussion of such complexities. 

The reader may verify that the scheme leads to the following Langmuir-Hinshelwood rate equation ... 

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). 

The plots are practically linear and show that the rates are constant. Consequently the order of reaction is zero at both initial pressures. If a Langmuir-Hinshelwood rate equation,... 

All constants of Langmuir-Hinshelwood rate equations are intrinsically positive so any mechanism that results in any negative constants is regarded as invalid. Although such a result may correlate the data adequately over the experimental range, extrapolation usually is not considered safe. 

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] ... 

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... 

The Langmuir—Hinshelwood rate equation (16) used by several authors for other types of catalyst was interpreted by Tanabe and Nitta [290] on the basis of their results with NiS04. The authors assume that the surface reaction of adsorbed ethylene and water molecules, which was found to be the slowest process, may be written in greater detail as... 

Langmuir-Hinshelwood rate expressions of all the reactions of the network were used in the kinetic modeling of the HDN of quinoline by Satterfield et al. (80, 81, 88). Their assumption that there is a single catalytic site for all reactions is too simple. Nevertheless, they collected an impressive body of kinetic data and pinpointed the reactions that were close to equilibrium and those which were kinetically significant. Gioia and Lee (100) extended these studies to higher pressures (up to 15 MPa H2). Only one model survived their regression analysis of the kinetic data. In this model, it was necessary to assume that 1,2,3,4-THQ reacted directly not only to o-propylaniline but also to propylbenzene (PB) and propylcyclohexene (PCHE). Their analysis does not appear to be very reliable, however. First,... 

Steps 3-5 are strictly chemical and consecutive to each other Hougen-Watson-Langmuir-Hinshelwood rate equations describing the rate of the purely chemical phenomenon consisting of steps (3)-(5) have been derived in the chapter on the... 

Once a rate expression is found to be consistent with experimental observations, then rate constants and equilibrium constants are obtained from quantitative rate data. One way to arrive at numerical values for the different constants in a Langmuir-Hinshelwood rate expression is to first invert the rate expression. For Case 2, the rate expression ... 

Preliminary kinetic studies have been performed. The Langmuir-Hinshelwood rate expression was used to correlate results of experiments as it was indicated by the shape of kinetic curves (see Fig. 6). However, the reaction order with respect to hydrogen appeared to be dependent on temperature, while activation energy depends on pressure (9.6 kJ/mol at 11 bar and 35.5 kJ/mol at 21 bar). Therefore the rate of benzaldehyde consumption was approximated using the following simple power law equation ... 

For a more complex expression such as the Langmuir-Hinshelwood rate for gas reaction on heterogeneous catalyst surface with equilibrium adsorption of reactants A and B on two different sites and nonadsorbing products, Eq. (7-85) can be rewritten as... 

An example of a model nonlinear in parameters is Eq. (7-166). Here it is not possible through any number of transformations to obtain a linear form in all the parameters k0, E, K o, Eaa, Km, Ea. Note that for some Langmuir-Hinshelwood rate expressions it is possible to linearize the model in parameters at isothermal conditions and obtain the kinetic constants for each temperature, followed by Arrhenius-type plots to obtain activation energies (see, e.g., Churchill, The Interpretation and Use of Piate Data The Rate Concept, McGraw-Hill, 1974). 

Steps 3-5 are strictly chemical and consecutive to each other Hougen-Watson-Langmuir-Hinshelwood rate equations describing the rate of the purely chemical phenomenon consisting of steps 3-5 have been derived in Chapter 3 on the kinetics of catalysed reactions. In the transport-limited situation the supply of reactant and/or the removal of reaction product will not be sufficiently fast to keep pace with the potential intrinsic rate, and the concentrations of A and B inside the pores will be different from the corresponding concentrations in the bulk of the fluid phase. 

Doraiswamyf presented a very detailed review on the role of heterogeneous catalytic systems on inducing multiplicity and instability. In particular, this review focuses on the role that the Langmuir isotherm and the Langmuir-Hinshelwood rate equations (resulting... 

Problem 9.5 Considering reaction between A and B catalyzed by a solid there are two possible mechanisms by which this reaction could occur. The first is that one of them, say A gets adsorbed on the solid surface and the adsorbed A then reacts chemically with the other component B which is in the gas phase or in solution and is not adsorbed on the surface. The second mechanism is that both A and B are adsorbed, and the adsorbed species undergo chemical reaction on the surface. The reaction rate expression derived for the former mechanism is the Rideal rate law and that for the second mechanism is the Langmuir-Hinshelwood rate law. Obtain simple derivations of these two rate laws. 

Both the Rideal and Langmuir-Hinshelwood rate laws are based upon the Langmuir adsorption equation, which is applicable for gas-solid as well as liquid-solid systems where diffusion of the sorbate to the solid surface is not rate limiting (generally true). The basic assumption of the Langmuir adsorption is that adsorption occurs at adsorption sites and all these sites are equivalent. For gas-solid systems, the rate of adsorption, fo, of the gas A is proportional to the gas pressure, pa, and the number of vacant sites, i.e.. 

If the polymerization centers react with the adsorbed monomer molecules then the Langmuir-Hinshelwood rate equation [Eq. (P9.5.13)] should be used and one would obtain the rate expression in the stationary zone as... 

Problem 9.6 Show that under conditions where Km C [- 2] (see Table 9.5) the Langmuir-Hinshelwood rate equation becomes indistinguishable from the Rideal expression for the stationary zone rate. 

Consequently, we see that for heterogeneous reactions, Langmuir-Hinshelwood rate law s are preferred over power law models. 

The double-line arrow indicates that catalyst decay is second order). The Langmuir-Hinshelwood rate equation, for control by the surface reaction and with q a(t) instead of q-r to account for progressing deactivation, is... 

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