Langmuir-Hinshelwood kinetics steps

In this rate expression we have lumped C/js into the effective surface rate coefficient by defining k" — CC s- AU sohd reactions have reaction steps similar to those in catalytic reactions, and the rate expressions we need to consider are basically Langmuir-Hinshelwood kinetics, which were considered in Chapter 7. Our use of a first-order irreversible rate expression is obviously a simplification of the more complex rate expressions that can arise from these situations. 

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 ... 

The next problem of the Langmuir-Hinshelwood kinetics, the validity of the rate-determining step approximation, has not been rigourously examined. However, as has been shown (e.g. refs. 57 and 63), the mathematical forms of the rate equations for the Langmuir-Hinshelwood model and for the steady-state models are very similar and sometimes indistinguishable. This makes the meaning of the constants in the denominators of the rate equations somewhat doubtful in the Langmuir—Hinshelwood model, they stand for adsorption equilibrium constants and in the steady-state models, for rate coefficients or products and quotients of several rate coefficients. 

The other approach is based on the Langmuir—Hinshelwood kinetics. In all the work using this approach, the surface reaction of adsorbed olefin and water was found, or postulated, to be the rate-determining step. The corresponding rate equation has the form... 

The Langmuir-Hinshelwood kinetic model describes a reaction in which the rate-limiting step is reaction between two adsorbed species such as chemisorbed CO and 0 reacting to form C02 over a Pt catalyst. The Mars-van Krevelen model describes a mechanism in which the catalytic metal oxide is reduced by one of the reactants and rapidly reoxidizd by another reactant. The dehydrogenation of ethyl benzene to styrene over Fe203 is another example of this model. Ethyl benzene reduces the Fe+3 to Fe+2 whereas the steam present reoxidizes it, completing the oxidation-reduction (redox) cycle. This mechanism is prevalent for many reducible base metal oxide catalysts. There are also mechanisms where the chemisorbed species reacts... 

In most photocatalysis, Langmuir-Hinshelwood kinetics is observed, suggesting the importance of substrate adsorption in key steps of the reaction [83]. That is, the rate of photocatalysis is proportional to the concentration (or pressure) of the reactant, which in turn can be related to the surface coverage by the Langmuir expression, Eq. 8,... 

In this instance it is assumed that either a molecule of A or a molecule of B is adsorbed on each surface atom and that the reaction takes place by the interaction of species adsorbed on adjacent atoms. Reactions of this type in which the rate limiting step involves the reaction of these chemisorbed species are said to follow Langmuir-Hinshelwood kinetics. 

Example 9.1. Langmuir-Hinshelwood kinetics of single-step reversible isomerization. The reaction is... 

Example 9.8. Parallel and sequential deactivation in a hypothetical reaction. The principle of mechanistic modeling can be illustrated by the oversimplified example of a single-step isomerization reaction A — P with Langmuir-Hinshelwood kinetics, rate control by the surface reaction, and slow second-order deactivation. 

Skrzypek el al. mode (19H5) Skrzypek el al. (1985) developed this model based on the Langmuir-Hinshelwood-Hougen-Watson kinetic model to explain the non-monotonic behaviour observed by Calder-bank (1974). They suggested that the reaction rate behaviour can be related to the Langmuir-Hinshelwood kinetic model for bimolecular reactions, where the surface reaction between o-Xylene and oxygen chemisorbed on the active centers is the rate determining step. The rate of appearance of various components can be written as ... 

The Langmuir Hinshelwood kinetic model based on this reaction scheme is formulated assuming that all reactions are in equilibrium except for reaction steps (2), (4), (7) and (11). Reaction steps (2), (4) and (7) are all steps which may be slow during the shift reaction [5,6], whereas reaction step (11) represents the slow step for methanol synthesis [8], The kinetic and thermodynamic parameters are taken from available Cu single crystal experiments. We call this type of model a static microkinetic model since the number of active sites are assumed constant (i.e., independent of reaction conditions) [21]. 

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. 

Langmuir-Hinshelwood kinetics were determined, and the rate-determining step is reduction of the intermediate formaldehyde (Eqs. 13-9 and 13-10). 

To model a catalytic reaction, some knowledge of the elementary reaction steps must be assumed. For ammonia synthesis it is usually accepted that the dissociative chemisorption of nitrogen is the rate-limiting step, a process which requires two adjacent open sites on the catalyst surface. " Using Langmuir-Hinshelwood kinetics the rate of ammonia synthesis (denoted by r) can be written as... 

Langmuir-Hinshelwood kinetics adsorption inhibition, 62 consistency of, 66 rate-controlling step for, 60 two-step model for, 67 Langmuir-Hinshelwood mechanism, 60 Lewis acid, 6 Lewis number definition of, 107 stability as affected by, 266 Local activity factor, 465 Lumping, 81... 

Closure. After reading this chapter, the reader should be able to discuss the steps in a heterogeneous reaction (adsorption, surface reaction, and desorption) and describe what is meant by a rate-limiting step. The differences between molecular adsorption and dissociated adsorption should be explained by the reader, as should the different types of surface reactions (single site, dual site, and Eley-Rideal). Given heterogeneous reaction rate data, the reader should be able to analyze the data and to develop a rale law for Langmuir-Hinshelwood kinetics. The reader should be able to discrimi-... 

The presence of several rate processes occurring in series leads to the development of complex rate expressions, often described as Langmuir-Hinshelwood kinetics. Before going on, we need to separate the chemical steps from the mass transfer steps (a mass transfer step is one in which the species moves into position to react but does not undergo a chemical change). In this section, we consider only the chemical steps that lead to the development of a Langmuir-Hinshelwood rate expression we reserve the mass transfer issues for the following section. 

The reaction mechanism of the SMR reaction strongly depends on the nature of the catalytically active metal and the support (the detailed discussion is provided in the review [14]). The kinetics and mechanism of the SMR reaction over Ni-based catalysts have been extensively studied by several research groups worldwide. For example, Xu and Froment [16] investigated the intrinsic kinetics of the reforming reaction over Ni/MgAl204 catalyst. They arrived at the reaction model based on the Langmuir-Hinshelwood reaction mechanism, which includes several reaction steps as follows ... 

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