Catalytic Processes Langmuir-Hinshelwood Mechanism

A classical example of LHHW equations is the bimolecular reaction case, in which the surface reaction between the adsorbed reactants is the rate-limiting step. The adsorption and desorption steps are presumed to be rapid enough to reach quasi-equilibria. For instance, the overall reaction A -h B C comprises the steps 

The adsorption and desorption quasi-equilibria (steps I, II, and IV) are defined as 

The rate expression is rewritten using the concentration of vacant sites, 

A special feature is the dissociative adsorption of a component, for example, hydrogen and oxygen. For this case, we have the adsorption step 

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The Langmuir-Hinshelwood mechanism of heterogeneous catalytic processes (graph 6) ... 

This is a mathematical expression for the steady-state mass balance of component i at the boundary of the control volume (i.e., the catalytic surface) which states that the net rate of mass transfer away from the catalytic surface via diffusion (i.e., in the direction of n) is balanced by the net rate of production of component i due to multiple heterogeneous surface-catalyzed chemical reactions. The kinetic rate laws are typically written in terms of Hougen-Watson models based on Langmuir-Hinshelwood mechanisms. Hence, iR ,Hw is the Hougen-Watson rate law for the jth chemical reaction on the catalytic surface. Examples of Hougen-Watson models are discussed in Chapter 14. Both rate processes in the boundary conditions represent surface-related phenomena with units of moles per area per time. The dimensional scaling factor for diffusion in the boundary conditions is... 

The feed stream is stoichiometric in terms of the two reactants. Diatomic A2 undergoes dissociative adsorption. Components B, C, and D experience single-site adsorption, and triple-site chemical reaction on the catalytic surface is the rate-controlling feature of the overall irreversible process. This Langmuir-Hinshelwood mechanism produces the following Hougen-Watson kinetic model for the rate of reaction with units of moles per area per time ... 

Catalytic reactions are necessarily multi-step processes as indicated schematically in Figure 4. This particular set of steps involves the reversible adsorption of reactants A and 82 on active sites. Here the diatomic compound 82 is shown as being adsorbed in the atomic state. Adsorbed species A and 8 on adjacent sites react to form product P, which is then also involved in a reversible desorption step. This is the classical Langmuir-Hinshelwood mechanism. This particular illustration depicts a commonly accepted sequence of steps for the oxidation of CO on Pt, for which case A represents CO, 82 is oxygen, and P is CO2. 

For most reaction systems, the intrinsic kinetic rate can be expressed either by a power-law expression or by the Langmuir-Hinshelwood model. The intrinsic kinetics should include both the detailed mechanism of the reaction and the kinetic expression and heat of reaction associated with each step of the mechanism. For catalytic reactions, a knowledge of catalyst deactivation is essential. Film and penetration models for describing the mechanism of gas-liquid and gas-liquid-solid reactions are discussed in Chap. 2. A few models for catalyst deactivation during the hydrodesulfurization process are briefly discussed in Chap. 4. 

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