Heterogeneous Langmuir—Hinshelwood model

Examples of Hougen-Watson kinetic models, which are also called Langmuir-Hinshelwood models, can be derived for a great variety of assumed surface mechanisms. See Butt and Perry s Handbook (see Suggestions for Further reading in Chapter 5) for collections of the many possible models. The models usually have numerators that are the same as would be expected for a homogeneous reaction. The denominators reveal the heterogeneous nature of the reactions. They come in almost endless varieties, but all reflect competition for the catalytic sites by the adsorbable species. 

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

Direct reaction between an adsorbed species A(s) and a gas-phase molecule B is sometimes proposed. This reaction pathway is called the Eley-Rideal mechanism. Although such a mechanism may seem as reasonable as the Langmuir-Hinshelwood model discussed above, very few heterogeneous reactions are still thought to occur by the Eley-Rideal mechanism. (An exception seems to be when species B is a very reactive radical species, e.g., a gas-phase H-atom reacting with an adsorbed species, as is discussed in Problem 11.10, in which an Eley-Rideal pathway initiates the growth process.)... 

The Langmuir-Hinshelwood model describes the most common situation in heterogeneous catalysis [15,16]. It assumes that the reactant must be adsorbed on the catalyst surface before it can react. The reaction then takes place at the active site, and the product is then desorbed from the catalyst back to the gas phase (Figure 2.7). 

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. 

The application of Monte-Carlo simulations to non-equilibrium reaction systems in heterogeneous catalysis started by Ziff, Gulari and Barshad on the lattice-gas version of a simple Langmuir-Hinshelwood model of CO oxidation on a transition metal surface. The ZGB-model is a lattice-gas version of the Langmuir-Hinshelwood-model of CO oxidation. 

Models for surface reactions during CVD are based on those used in heterogeneous catalysis and are usually related to the Langmuir-Hinshelwood model, which... 

Langmuir-Hinshelwood model is widely used to define heterogeneous catalytic reactions. This model includes two important steps. The first one describes adsorption of BH on the surface of the catalyst [111]. 

The kinetic behavior of the heterogeneous esterification of acetic acid with amyl alcohol over Dowex 50 Wx8-100 resin and propionic acid with n-butanol over Amberlyst 35 was investigated by Lee and Lin (2000/2002) in a fixed bed reactor at temperatures from 323 K to 393 K and molar ratios of feed (amyl alcohol to acetic acid) from 1 to 10 and the molar ratios of feed (n-butanol to propionic acid) from 0.5 to 2. The equilibrium conversions of acid were found to increase with an increase in the reaction temperature. The kinetic data was correlated with the quasi-homogeneous, Langmuir-Hinshelwood, Eley-Rideal and modified Langmuir-Hinshelwood models. 

Liquid phase hydrogenation catalyzed by Pd/C is a heterogeneous reaction occurring at the interface between the solid catalyst and the liquid. In our one-pot process, the hydrogenation was initiated after aldehyde A and the Schiff s base reached equilibrium conditions (A B). There are three catalytic reactions A => D, B => C, and C => E, that occur simultaneously on the catalyst surface. Selectivity and catalytic activity are influenced by the ability to transfer reactants to the active sites and the optimum hydrogen-to-reactant surface coverage. The Langmuir-Hinshelwood kinetic approach is coupled with the quasi-equilibrium and the two-step cycle concepts to model the reaction scheme (1,2,3). Both A and B are adsorbed initially on the surface of the catalyst. Expressions for the elementary surface reactions may be written as follows ... 

We begin with the simplest model scheme for a heterogeneously catalysed reaction, with Langmuir-Hinshelwood kinetics. A reactant P is adsorbed, reversibly, onto a surface S. There it may react to give a product C. which is immediately and irreversibly desorbed ... 

The second model results from a bimolecular surface reaction, A + B — products, with competitive Langmuir-Hinshelwood kinetics, which occurs in a heterogeneous differential reactor with perfectly mixed gas phase. The reaction is first order in both adsorbed A and B, and two vacant sites are required in the reaction mechanism. If the reaction products desorb immediately, the... 

In heterogeneous catalysis these models are generally referred to as the Langmuir-Hinshelwood-Hougen-Watson (LHHW) models. The term Michaelis-Menten kinetics is often used in homogeneous catalysis, enzyme reactions and reactions of microbial systems. 

In some cases, adsorption of analyte can be followed by a chemical reaction. The Langmuir-Hinshelwood (LH) and power-law models have been used successfully in describing the kinetics of a broad range of gas-solid reaction systems [105,106]. The LH model, developed to describe interactions between dissimilar adsorbates in the context of heterogeneous catalysis [107], assumes that gas adsorption follows a Langmuir isotherm and that the adsorbates are sufficiently mobile so that they equilibrate with one another on the surface on a time scale that is rapid compared to desorpticm. The power-law model assumes a Fre-undlich adsorption isotherm. Bodi models assume that the surface reaction is first-order with respect to the reactant gas, and that surface coverage asymptotically approaches a mmiolayer widi increasing gas concentration. 

In most gas-solid heterogeneous catalyst systems, the effect of pressure often is correlated with an adsorption model of the Langmuir-Hinshelwood type. The over-all rate constant for the first order reaction is related to the adsorption model constants by... 

Wicke et al. [3] were the first to apply a MC simulation to a catalytic reaction based on the Langmuir-Hinshelwood mechanism. They studied the importance of the formation of clusters of adsorbed molecules on a catalyst surface. Many microscopic mathematical models of heterogeneous catalytic systems have been developed since then. However, the time dependence of the reactions in real time could not be followed. Recently more refined MC methods have been developed, so that with these new dynamic Monte Carlo (DMC) methods, the behavior of catalytic systems in real time can be simulated. 

Analysis of such statistical correlations may reveal the significant variables and interactions and may suggest potential mechanisms and kinetic models, say, of the Langmuir-Hinshelwood type, that could be analyzed in greater detail by a regression process. The variables x could be various parameters of heterogeneous processes as well as concentrations. An application of this method to isomerization of n-pentane is given by Kittrel and Erjavec [Ind. Eng. Chem. Proc. Des. Dev. 7 321 (1968)]. 

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

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