Langmuir—Hinshelwood—Hougen—Watson reaction mechanism

A customized version of the Langmuir-Hinshelwood-Hougen-Watson (LHHW) mechanism is used both for reversible (Figure 4) and irreversible reactions (Figure 5). The main steps in this mechanism are ... 

The rate of oXylene disappearance in Figure 5.10 shows a maximum illustrated when plotted against p-Xylene initial concentration such dependence of reaction rate cannot be explained by a redox mechanism but by a Langmuir-Hinshelwood, Hougen-Watson (LH-HW) model such as equation (5.78) which describes the reaction behaviour with a characteristic maximum as shown in Figure 5.10. 

Microkinetic modeling is a framework for assembling the microscopic information provided by atomistic simulations and electronic structure calculations to obtain macroscopic predictions of physical and chemical phenomena in systems involving chemical transformations. In such an approach the particular catalytic reaction mechanism is expressed in terms of its most elementary steps. In contrast to the Langmuir-Hinshelwood-Hougen-Watson (LHHW) formulations, no rate-determining mechanistic step (RDS) is assumed. 

Fig. 9. Evolution of the initial reaction rate for the reaction A Q + S according to a Langmuir-Hinshelwood/Hougen-Watson mechanism as a function of the reactant concentration depending on the RDS (a) reactant adsorption, (b) surface reaction, and (c) product desorption.

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. 

As pointed out by Levenspid (2000), the usual procedure to study the kinetics of surface-catalyzed reactions is to propose a mechanism based on the Langmuir-Hinshelwood-Hougen-Watson (LHHW) model, derive the corresponding equation, and then fit it to the data at hand. If the fit is good, researchers often claim that thqr have found the actual mechanism. This procedure is questionable, as shown by Topic 4.5.4. It would be better to state that our experimental results are formally described (within the range of the investigated reaction conditions) by the selected kinetic equation (probably out of several possible others). 

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. 

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. 

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. 

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 ... 

The most important characteristic of this problem is that the Hougen-Watson kinetic model contains molar densities of more than one reactive species. A similar problem arises if 5 mPappl Hw = 2CaCb because it is necessary to relate the molar densities of reactants A and B via stoichiometry and the mass balance with diffusion and chemical reaction. When adsorption terms appear in the denominator of the rate law, one must use stoichiometry and the mass balance to relate molar densities of reactants and products to the molar density of key reactant A. The actual form of the Hougen-Watson model depends on details of the Langmuir-Hinshelwood-type mechanism and the rate-limiting step. For example, consider the following mechanism ... 

Since 1 a is only a function of spatial coordinate r, the partial derivative in (19-38) is replaced by a total derivative, and the dimensionless concentration gradient evaluated at the external surface (i.e., ] = 1) is a constant that can be removed from the surface integral in the numerator of the effectiveness factor. In terms of the Hougen-Watson kinetic model and the dimensional scaling factor for chemical reaction that agree with the Langmuir-Hinshelwood mechanism described at the beginning of this chapter ... 

Reactant equilibrium constants Kp and affect the forward kinetic rate constant, and all Ki s affect die adsorption terms in the denominator of the Hougen-Watson rate law via the 0, parameters defined on page 493. However, the forward kinetic rate constant does not appear explicitly in the dimensionless simulations because it is accounted for in Ihe numerator of the Damkohler number, and is chosen independently to initiate the calculations. Hence, simulations performed at larger adsorption/desorption equilibrium constants and the same intrapellet Damkohler number implicitly require that the forward kinetic rate constant must decrease to offset the increase in reactant equilibrium constants. The vacant-site fraction on the internal catalytic surface decreases when adsorption/desorption equilibrium constants increase. The forward rate of reaction for the triple-site reaction-controlled Langmuir-Hinshelwood mechanism described on page 491 is proportional to the third power of the vacant-site fraction. Consequently, larger T, s at lower temperature decrease the rate of reactant consumption and could produce reaction-controlled conditions. This is evident in Table 19-3, because the... 

Postulate a Langmuir-Hinshelwood heterogeneous mechanism for the chemical reaction and develop the corresponding Hougen-Watson kinetic rate law when five-site reaction on the catalytic surface is the slowest step. 

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