Langmuir Hinshelwood kinetics

Writing out the catalytic reaction between A and B in elementary steps according to the Langmuir-Hinshelwood mechanism, we obtain  

Note that in the final desorption step the equilibrium constant for adsorption of AB equals 1 /K4 whereas for the other adsorption steps it is defined as 

In drafting a catalytic cycle as in Eqs. (132)-(135) we naturally have to ensure that the reaction steps are thermodynamically and stoichiometrically consistent. For instance, the number of sites consumed in the adsorption and dissociation steps must be equal to the number of sites liberated in the formation and desorption steps, to fulfill the criterion that a catalyst is unaltered by the catalytic cycle. 

For each step there is a corresponding rate (for convenience we drop the total number of sites from the expressions, i.e. r becomes a rate per site, or a turnover frequency)  

The number of sites on a catalyst is constant and hence all coverages should aWays add up to unity, as expressed by the follo3ving balance of sites  

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Boudart (1956) and Weller (1956) discussed the applicability and need of Langmuir-Hinshelwood kinetics to describe the rate of industrially... 

It is well known that photocatalytic oxidation of or nic pollutants follows Langmuir-Hinshelwood kinetics[6]. Therefore, this kind of reaction can be represented as follows. 

Langmuir s research on how oxygen gas deteriorated the tungsten filaments of light bulbs led to a theory of adsorption that relates the surface concentration of a gas to its pressure above the surface (1915). This, together with Taylor s concept of active sites on the surface of a catalyst, enabled Hinshelwood in around 1927 to formulate the Langmuir-Hinshelwood kinetics that we still use today to describe catalytic reactions. Indeed, research in catalysis was synonymous with kinetic analysis... 

In Langmuir-Hinshelwood kinetics is it assumed that all species are adsorbed and accommodated (in thermal equilibrium) with the surface before they take part in any reactions. Hence, species react in the chemisorbed state on the surface. This is the prevailing situation in heterogeneous catalysis. 

Figure 2 depicts the dependence of N2 rate on Pco at fixed Pno= 0.52 k Pa for three different values of the catalyst potential. Vwr=+KXX) mV corresponds to the clean Pt surface (unpromoted rate) and Vwr=- 200 mV corresponds to a sodium promoted surface. Both CO2 and N2 rates exhibit Langmuir-Hinshelwood behaviour and as can be seen from Figure 2 for N2 rate, increased levels of Na result in a systematic increase in the CO partial pressure (P co) necessary for inhibition. The N2O rate also exhibits Langmuir-Hinshelwood kinetics, but the effect of increased Na is somewhat different in particular, high levels of Na tend to suppress the N2O rate and there is no systematic shift in P co-... 

Figure 3.52 Parity diagram based on Langmuir-Hinshelwood kinetics of the oxygen reaction rate [121].

GP 11] [R 5] Langmuir-Hinshelwood kinetics adequately describe the observed results as a parity diagram (Figure 3.52), comparing experimental with theoretical values (2.0-7.0 mmol 1 hydrogen 3.6 mmol oxygen 48-70 °C) [121]. 

Another problem which can appear in the search for the minimum is intercorrelation of some model parameters. For example, such a correlation usually exists between the frequency factor (pre-exponential factor) and the activation energy (argument in the exponent) in the Arrhenius equation or between rate constant (appears in the numerator) and adsorption equilibrium constants (appear in the denominator) in Langmuir-Hinshelwood kinetic expressions. 

Deactivating catalytic reaction with Langmuir-Hinshelwood kinetics in a completely mixed reactor. 

Lag in the system 509 Langmuir-Hinshelwood kinetics 321 Laplace transformation 80, 536 Latent heat of vapourisation 517 Least squares 112 Level control 509... 

Note the similarity to Langmuir-Hinshelwood kinetics.) The rate is expressed on the basis of the instantaneous number of solid carbon atoms, Nc. The rate r (measured at one gas composition) typically goes through a maximum as the carbon is converted. This is the result of a maximum in the intrinsic activity (related to the fraction of reactive carbon atoms, NCJNC) because of both a change in Nq> and a decrease in Nc. 

In the catalyzed gas-phase decomposition A - B + C, suppose A also acts as an inhibitor of its own decomposition. The resulting rate law (a type of Langmuir-Hinshelwood kinetics, Chapter 8) is ... 

The limitations of analytical solutions may also interfere with the illustration of important features of reactions and of reactors. The consequences of linear behavior, such as first-order kinetics, may be readily demonstrated in most cases by analytical techniques, but those of nonlinear behavior, such as second-order or Langmuir-Hinshelwood kinetics, generally require numerical techniques. 

Mann, Thurgood, and coworkers—Langmuir-Hinshelwood kinetic model for methanol steam reforming and WGS over Cu/Zn. Mann et al.335 published a complex Langmuir-Hinshelwood model for CuO/ZnO catalysts based on what one would encounter for a methanol steam reformer (MSR) for fuel cell applications. The water-gas shift rate, containing all MSR terms, was determined to be ... 

Wheeler, Schmidt, and coworkers—kinetic model for Pt/Ce at short contact times over medium to high T range. In 2004, Wheeler and coworkers422 reported on the water-gas shift reaction over Pt/ceria at short contact times (0.008-0.05 sec) for temperatures between 300 and 1000 °C. The reactant composition for CO, H2, and H20 was 1/2/4. A Langmuir-Hinshelwood kinetic model was used to adequately fit the medium and high temperature shift data ... 

Based on Langmuir-Hinshelwood kinetics the rate expression for a first order reaction (A —> R) that is surface reaction-controlled becomes equal to the following expression [2] ... 

Figure 7-25 Langmuir Hinshelwood kinetics for a unimolecidar surface-catdyzed reaction A products. The rate is first order in at low covauges aid zeroth orda at high coverage.

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 ... 

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 ... 

All the above mechanisms, single or dual site, are known as Langmuir—Hinshelwood kinetics, (e) An adsorbed molecule reacts with a molecule in the gas phase ... 

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