Langmuir-Hinshelwood-Hougen-Watson LHHW rate equations

Langmuir-Hinshelwood-Hougen-Watson (LHHW) Rate Equations (1947) Hougen and Watson analyzed several types of catalytic reactions with different ratedetermining steps (adsorption, surface reaction), different types of adsorption (one or more species, dissociative or molecular adsorption), and different types of reactions (mono- or bimolecular, reversible or irreversible). They derived a general rate equation based on three terms ... 

The first step of the reaction on a solid catalyst is the sorption of at least one reactant. If two reactants are adsorbed, the rate follows the so-called Langmuir-Hinshelwood mechanism, which is based on the assumption that both reactants are adsorbed on the surface (equilibrium). If only one reactant is adsorbed on the surface of the catalyst and reacts with the second species coming from gas phase, the rate follows the Eley-Rideal-mechanism. Other more complex situations may be described by Langmuir-Hinshelwood-Hougen-Watson (LHHW) rate equations. 

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. 

In general, the use of Langmuir-Hinshelwood-Hougen-Watson (LHHW)-type of rate equation for representing the hydrogenation kinetics of industrial feedstocks is complicated, and there are too many coefficients that are difficult to determine. Therefore, simple power law models have been used by most researchers to fit kinetic data and to obtain kinetic parameters. 

The major problem in describing the FT reaction kinetics is the complexity of its reaction mechanism and the large number of species involved. As discussed above, the mechanistic proposals for the FTS used a variety of surface species and different elementary reaction steps, resulting in empirical power law expressions for the kinetics. However, the rate equations of Langmuir—Hinshelwood—Hougen—Watson (LHHW) have been applied based on a reaction mechanism for the hydrocarbon-forming reactions. In most cases, the rate-determining step was assumed to be the formation of the monomer. 

The quasi-equilibrium assumption is frequently used in the heterogeneous catalysis, since the surface reaction steps are often rate-Hmiting, while the adsorption steps are rapid. This is not necessarily true for large molecules. Here we consider the application of the quasi-equilibrium hypothesis on two kinds of reaction mechanisms, an Eley-Rideal mechanism and a Langmuir-Hinshelwood mechanism. The rate expressions obtained with this approach are referred to as Langmuir-Hinshelwood-Hougen-Watson (LHHW) equations in the literature, in honor of the pioneering researchers. 

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