Langmuir-Hinshelwood approach

The theoretical calculations described have recently been supported by an extraordinary kinetic analysis conducted by Vanrysellberghe and Froment of the HDS of dibenzothiophene (104). That work provides the enthalpies and entropies of adsorption and the equilibrium adsorption constants of H2, H2S, dibenzothiophene, biphenyl, and cyclohexylbenzene under typical HDS conditions for CoMo/A1203 catalysts. This work supports the assumption that there are two different types of catalytic sites, one for direct desulfurization (termed a ) and one for hydrogenation (termed t). Table XIV summarizes the values obtained experimentally for adsorption constants of the various reactants and products, using the Langmuir-Hinshelwood approach. As described in more detail in Section VI, this kinetic model assumes that the reactants compete for adsorption on the active site. This competitive adsorption influences the overall reaction rate in a negative way (inhibition). 

Kinetic investigations have been reported for the hydrogenation of a variety of substrates [29,30]. Typically, the reaction is between zero- and first-order for hydrogen and, especially at higher concentrations of nitro arene, zero-order in substrate. A Langmuir-Hinshelwood approach (reversible adsorption of reactants and intermediates on the metal surface) is usually chosen for kinetic analysis, quite often with good agreement. 

The greatest barrier in the application of the Multicomponent Fowler-Guggenheim or Bragg-Williams Lattice gas model to, a practical situation like Pet-reforming, is the absence of experimental interaction parameters. In the simulations of the earlier sections, representative values were used. In general, for an n component system, we need to fix n(n+l) / 2 interaction parameters of the symmetric W matrix (91 for a 13 component Model ). Mobil has used successfully a 13 lump KINPTR model(5), which essentially uses a Hougen-Watson Langmuir-Hinshelwood approach. This results in a psuedo-monomolecular set of reactions, which is amenable to matrix analysis. 

In considering kinetic models which can display oscillatory behaviour, it is useful to recall the Langmuir-Hinshelwood approach to a simple reaction such as the oxidation of CO, taking place in a closed system and consider the commonly adopted assumptions ... 

Langmuir-Hinshelwood approach, with irreversible reaction as further alternative applied to chemical and enzymatic reactions (fc 2 = 0). 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

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... 

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 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... 

For a Langmuir-Hinshelwood reaction in which both reactants are thermally equilibrated on the surface, reaction is initiated by thermal activation of the adsorbate. This thermal sampling can be turned to advantage by invoking detailed balance to equate the rates of adsorption and desorption for a surface at equilibrium [66, 67]. This allows us to relate the final state distributions measured for desorption to the detailed sticking probability for each product quantum state (v, J). This approach has been applied very successfully to hydrogen adsorption/desorption [4, 68] but its use has not been widely explored for reactions of heavier molecules. 

The same approach as for irreversible Langmuir-Hinshelwood-type models can be extended to reversible reactions. Kao and Satterfield [61] developed a graphical method for monomolecular reversible reactions of the type Ai Aj, which is presented here as our last example. The method is based upon the following formulation of the net reaction rate ... 

In a previous publication (4) it was shown that at pressures above 500 p.s.i.g., the rate of reaction ultimately levels out, approaching zero order. This behavior offers evidence that polymerization occurs by reaction of an adsorbed monomer molecule with an adjacently adsorbed monomer molecule or growing polymer chain (Langmuir-Hinshelwood mechanism). If polymerization occurred by reaction of monomer in the gas phase with adsorbed monomer or adsorbed growing polymer chains (Rideal mechanism), the reaction rate should increase without limit as pressure is increased. 

In some cases, adsorption of analyte can be followed by a chemical reaction. The Langmuir-Hinshelwood (LH) and power-law models have been used successfully in describing the kinetics of a broad range of gas-solid reaction systems [105,106]. The LH model, developed to describe interactions between dissimilar adsorbates in the context of heterogeneous catalysis [107], assumes that gas adsorption follows a Langmuir isotherm and that the adsorbates are sufficiently mobile so that they equilibrate with one another on the surface on a time scale that is rapid compared to desorpticm. The power-law model assumes a Fre-undlich adsorption isotherm. Bodi models assume that the surface reaction is first-order with respect to the reactant gas, and that surface coverage asymptotically approaches a mmiolayer widi increasing gas concentration. 

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