Langmuir-Hinshelwood LH Kinetics

By combining surface-reaction rate laws with the Langmuir expressions for surface coverages, we can obtain Langmuir-Hinshelwood (LH) rate laws for surface-catalyzed reactions. Although we focus on the intrinsic kinetics of the surface-catalyzed reaction, the LH model should be set in the context of a broader kinetics scheme to appreciate the significance of this. 

Here A(g) and B(g) denote reactant and product in the bulk gas at concentrations CA and Cg, respectively kAg and kBg are mass-transfer coefficients, s is an adsorption site, and A s is a surface-reaction intermediate. In this scheme, it is assumed that B is not adsorbed. In focusing on step (3) as the rate-determining step, we assume kAg and kBg are relatively large, and step (2) represents adsorption-desorption equilibrium. 

For the overall reaction A - B, if the rds is the unimolecular surface reaction given by equation 8.4-1, the rate of reaction is obtained by using equation 8.4-21 for dA in 8.4-2 to result in  

Some of the problems at the end of the chapter are posed in terms of partial pressure. 

Two common features of catalytic rate laws are evident in this expression. 

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Langmuir-Hinshelwood (LH) kinetics are widely used to quantitatively delineate substrate preadsorption in both solid-gas and solid-liquid reactions. The model assumptions are stated in Table 9.2. Under these... 

There is an intensive literature showing that in the absence of mass transfer limitations, many photocatalytic reactions follow the Langmuir-Hinshelwood (LH) kinetics described in Equation (1) for a one-component... 

For reactions that are catalyzed by solid porous catalyst particles, the sequence of elementary steps may include adsorption on the catalyst surface of one or more reactants and/or desorption of one or more products. In that case, a Langmuir-Hinshelwood (LH) kinetic equation is often found to fit the experimental kinetic data more accurately than the power-law expression of Eq. (6.19). The LH formulation is characterized by a denominator term that includes concentrations of certain reactants and/or products that are strongly adsorbed on the catalyst. The LH equation may also include a prefix, ti, called an overall effectiveness factor that accounts for mass and heat transfer resistances, both external and internal, to die catalyst particles. As an example, laboratory kinetic data for the air-oxidation of SO2 to SO are fitted well by the following LH equation ... 

Langmuir-Hinshelwood (LH) and Eley-Rideal (ER) kinetic models... 

A reason for using microkinetics in heterogeneous catalysis is to have comprehensive kinetics and a transparent reaction mechanism that wonld be useful for re or design or catalyst development. Furthermore, in the long run, the exparimental effort to develop a microkinetics scheme can be less than that for a Langmuir-Hinshelwood (LH) or powa--law scheme because of the more fundamental nature of the reaction kinetics parameters. 

Using kinetic models of typical catalytic mechanisms (Eley-Rideal and Langmuir-Hinshelwood (LH) mechanisms) as examples, we found parametric domains, in which the hypergeometric representation is an excellent approximation... 

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. 

A few of representative kinetic studies in recent years are discussed in this section. Gokon et al49 discussed different kinetics models employed for methane reforming studies, including the Langmuir-Hinshelwood (LH), basic (BA),... 

Many catalyzed surface reactions can be treated as a two-step process with an adsorption equilibrium followed by one rate-determining step (diffusion, surface reaction, or desorption). The surface reaction kinetics are usually discussed in terms of two limiting mechanisms, the Langmuir-Hinshelwood (LH) and Eley-Rideal (ER) mechanisms. In the LH mechanism, reaction takes place directly between species which are chemically bonded (chemisorbed) on the surface. For a bimolecular LH surface reaction. Aawith competitive chemisorption of the reactants, the rate of reaction is given by the following expression ... 

However, as the reaction proceeds, the add adsorption term might have to be introduced and in such an event the reaction kinetics would be represented by a dual site mechanistic, such as Langmuir-Hinshelwood (LH) model. 

The kinetics data of the liquid-solid catalytic esterification are correlated with various kinetic models, over wide ranges of temperature and feed composition. The activity coefficients calculated using the NTRL model are utilized to represent the non-ideality behavior of the species in the liquid solutions. Meanwhile, the effects of film diffusion and pore diffusion appear to be negligible at the experimental conditions. The results reveal that the Langmuir-Hinshelwood (LH) model yielded the best representation for the kinetic behavior of the liquid-solid catalytic esterification ... 

Roduit et al. [1] proposed a global kinetic model for the standard SCR reaction based on V-based catalysts. The kinetic model accounts for three different reactions and intraparticle diffusion. The three reactions are Langmuir-Hinshelwood LH-type SCR, Eley-Rideal ER-type SCR, and direct NH3 oxidation. The main SCR pathway proceeds via the ER-type mechanism, but in the low temperature region T < 200 °C), LH-type reaction occurs. Furthermore, at high temperatures (T > 300 °C), NH3 oxidation and intraparticle mass transfer also takes place [1]. 

In the absence of TCE and chlorine, the possible active species are holes (h+), anion vacancies, or anions (02 ), and hydroxyl radicals (OH ). At constant illumination and oxygen concentration, we may expect h+, and O2 concentrations to be approximately constant, and the dark adsorption to be a dominant variable. If kh+, or ko2- does not vary appreciably with the contaminant structure, the rate would depend clearly on the contaminant coverage as shown in Figme 2a, and the reaction would therefore occur via Langmuir-Hinshelwood mechanism. (Note only rates with conversions below 95% are correlated here (filled circles), as the 100% conversion data contains no kinetic information). This rate vs. d>r LH plot is smoother than those for koH or koH suggesting that non-OH species (holes, anion vacancies, or O2 ) are the active species reacting with an adsorbed contaminant. 

These rate expressions are for Langmuir-Hinshelwood kinetics, which are the simplest forms of surface reaction rates one could possibly find We know of no reactions that are this simple. LH kinetics requires several assumptions ... 

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,... 

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