Heterogeneously Langmuir-Hinshelwood-Hougen-Watson

The problem posed by Eq. (6.22), without the additional complication of the O dependence, is a classical problem in heterogeneous catalysis. The usual approach it to use Langmuir isotherms to describe reactant (and sometimes product) adsorption. This leads to the well known Langmuir-Hinshelwood-Hougen-Watson (LHHW) kinetics.3 The advantage of this approach is... 

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 Chapters 3 and 4 the Langmuir-Hinshelwood-Hougen-Watson approach to heterogeneous catalysis was discussed. Such an approach supposes that usually there is one rate determining step (adsorption, surface reaction or desorption) and that the other steps are in quasi-equilibria. 

Derive the rate for a heterogeneously catalyzed reaction following Langmuir-Hinshelwood-Hougen-Watson (LHHW) kinetics. 

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. 

Firstly, is a kinetic expression, a rate law, such as, e.g., the Langmuir-Hinshelwood-Hougen-Watson rate expressions in heterogeneous catalysis, and as such has no universal applicability. It is derived on the basis of mass action kinetics and does reduce to the fundamental thermodynamic Nemst equation for i = 0, thus q = 0. ° Nevertheless, experimental deviations can be expected as with any other, even most successful, rate expression. 

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. 

A higher form of interpretation of the effect of solvents on the rate of heterogeneously catalyzed reactions was represented by the Langmuir-Hinshelwood kinetics (7), in the form published by Hougen and Watson (2), where the effect of the solvent on the reaction course was characterized by the adsorption term in the kinetic equation. In catalytic hydrogenations in the liquid state kinetic equations of the Hougen-Watson type very frequently degrade to equations of pseudo-zero order with respect to the concentration of the substrate (the catalyst surface is saturated with the substrate), so that such an interpretation is not possible. At the same time, of course, also in these cases the solvent may considerably affect the reaction. As is shown below, this influence is very adequately described by relations of the LFER type. 

Rate expressions of the form of Equation 5.153 are known as Hougen Watson or Langmuir-Hinshelwood kinetics [17, This form of kinetic expression is often used to describe the species production rates for heterogeneously catalyzed reactions. We complete the section on the kinetics of elementary surface reactions by returning to the methane synthesis reaction listed in Section 5.2. The development proceeds exactly as outlined in Section 5.2. But now it is necessary to add a site-balance expression (Equation 5,129) in Step 3. 

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... 

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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