Adsorption Langmuir-Hinshelwood-type

Regarding the kinetics, the oxidation of o-xylene and o-tolualdehyde were compared for catalysts with different V/Ti ratios (Table 36). The ratio between partial and complete oxidation (X for o-xylene and Y for o-tolualdehyde) are influenced similarly, indicating that a change in the catalyst structure influences all the reaction steps. The oxidation of o-tolualdehyde in mixtures with o-xylene revealed that o-tolualdehyde reduces the o-xylene oxidation rate by a factor of about 2. The authors conclude that a redox model is inadequate and that hydrocarbon adsorption cannot be rate-determining. Adsorption of various products should be included, and equations of the Langmuir—Hinshelwood type are proposed. It should be noted that the observed inhibition is not necessarily caused by adsorption competition, but may also stem from different... 

A Langmuir-Hinshelwood type of rate expression is often used to describe the effect of the competitive adsorption of components m in the reaction mixture on the rate of hydrotreating of compound i ... 

In most gas-solid heterogeneous catalyst systems, the effect of pressure often is correlated with an adsorption model of the Langmuir-Hinshelwood type. The over-all rate constant for the first order reaction is related to the adsorption model constants by... 

The kinetic model is an application for polymerization reactions, of the deduction of kinetic equations of deactivation of Langmuir Hinshelwood type, equations that fit the real data in a large number of reactions (7, 8). Deactivation mechanism 1. Adsorption and activation step (Initiation)... 

Generally first-order kinetics with respect to the concentration of the pollutant is observed for most AOPs in water. The compounds, which exhibit non-first-order kinetics also show quantum yields greater than one. These apparent higher quantum yields are due to sensitized oxidations. The kinetics for photocatalytic oxidation (PCO) can be expressed as one of Langmuir-Hinshelwood type, thus depending on both the degradation rate and the adsorption rate constant of the pollutant. 

Many kinetic equations have been suggested for the description of catalytic reactions (9, JO). The best approximations are usually seen (77) in relations of the Langmuir-Hinshelwood type (7), which assume the adsorption equilibrium of all the components present in the reaction mixture on the catalyst surface. 

Of the cases described so far, the presence of a third compound had the strongest effect on the selectivity of hydrogenation of two olefinic substrates in the pair olefin-unsaturated alcohol. This influence appeared both in cases where the third compound was unsaturated, was adsorbed competitively and reacted on the catalyst surface, and in cases where the third compound was represented by an inert solvent not undergoing competitive adsorption (was not entering equations of the Langmuir-Hinshelwood type, which were degraded to pseudo-zero order) and obviously operated through interactions of molecules from the bulk phase with adsorbed molecules of the substrate. 

From adsorption measurements during reaction one can also examine whether the reaction rate is correlated with the amounts of adsorbed reactants or with the pressure of the reactants, i.e., whether the mechanism is of Langmuir-Hinshelwood type or of the Eley-Rideal variety. 

For a Langmuir-Hinshelwood type of rate equation, such as Eq. (9-32), Eq. (10-26) is not valid because the adsorption-equilibrium-constant terms in the denominator of the rate expression are also temperature dependent. 

Since the reaction kinetics is of the Langmuir-Hinshelwood type additional informations about the adsorption of reactants is helpful in the development of a kinetic model. Therefore experiments have been carried out by use of an experimental setup for adsorption measurements. Since adsorption and reaction occur simultaneously the change of gas composition in the adsorption cell is registrated by on-line GC-MS. Then the amount of adsorbed substances is calculated as the difference of added substance and substance in the gas phase of the adsorption cell given by the total pressure in the cell and the gas composition. A schematic drawing of the... 

The effect of partial pressure of hydrogen and concentration of p-isobutyl acetophenone on the initial rate of reaction is shown in Fig. (3) at different temperatures. It can be observed that the reaction is first order tending to zero order with respect to partial pressure of hydrogen and close to first order with respect to p-isobutyl acetophenone concentration. This clearly indicates that the reaction proceeds through a Langmuir-Hinshelwood type of mechanism. Moreover, from the typical concentration profile shown in Fig. (2) it can be concluded that the adsorption of the liquid phase components may not be important as the formation of different liquid phase... 

The mechanism of the hydrogenation reaction for hydrogen supplied by the gas phase could be described in terms of a Langmuir-Hinshelwood type of kinetic equation, assuming a fast dissociative adsorption of hydrogen and cyclohexene on two different sites. Following Wallace et al. (1979) and Johnson et al. (1992) it was assumed that these... 

The kinetics of the CO oxidation reaction over all three noble metals exhibit a Langmuir-Hinshelwood type behavior, due to competitive adsorption of CO and oxygen, characterized by the appearance of rate maximum with increasing CO partial pressure. This is a typical behavior which has been described by many investigators for this reaction system [19,20], The catalytic activity, presented as turnover number of CO2 production, was measured by varying either the partial pressures of CO or O2, or temperature, keeping the other parameters constant. 

The kinetics of tiiis reaction were also found to follow a Langmuir-Hinshelwood type behavior, with competitive adsorption of C2H4 and oxygen. A comparative kinetic diagram for all the supported Rh catalysts is given in Fig. 4. The dashed lines indicate an abrupt drop in the ethylene combustion rate which is probably due to surface oxide formation. The same behavior was also observed in the electrochemical promotion (NEMCA) experiments, as briefly discussed below and further described elsewhere [22]. 

The reactant A is further characterized in Eq. (6) by the adsorption coefficient Its value can be determined for each member of the series and the obtained set of equilibrium constants may fit a linear free-energy relationship. However, the correlation of these adsorption coefficients has some weak points. Because of many simplifications in the derivation of Langmuir-Hinshelwood-type rate equations, the exact physical meaning of these coefficients is not clear. Further on, in the evaluation of constants of Eq. (6) and of similar expressions, adsorption coefficients are usually subject to a large error. 

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 ... 

Amadeo and Laborde [51] analyzed five kinetic expressions for low-temperature catalysts two representing redox mechanism and three representing Langmuir-Hinshelwood model. Model I is proposed by Shchibrya et al. [2b]. Model II was a redox type model. Models III and IV were Langmuir-Hinshelwood type models that considered adsorption of four species (CO, H2O, CO2 and H2) and the final model only considered the adsorption of CO and CO2. The results of these authors indicated that only model HI described the reaction behaviour in the conditions investigated. 

The diffusion of adsorbates on the surface is a process which is important for reactions of the Langmuir-Hinshelwood type, where the molecules in question travel some distance on the surface before they react. The surface diffusion process is influenced by the structure and corrugation of the surface. Therefore the information which can be obtained by studying the diffusion process is of importance for the understanding of the surface structure and its influence on a number of processes, as adsorption/desorption, catalytic properties, and epitaxial growth. 

Ref. 205). The two mechanisms may sometimes be distinguished on the basis of the expected rate law (see Section XVni-8) one or the other may be ruled out if unreasonable adsorption entropies are implied (see Ref. 206). Molecular beam studies, which can determine the residence time of an adsorbed species, have permitted an experimental decision as to which type of mechanism applies (Langmuir-Hinshelwood in the case of CO + O2 on Pt(lll)—note Problem XVIII-26) [207,208]. 

The model is intrinsically irreversible. It is assumed that both dissociation of the dimer and reaction between a pair of adjacent species of different type are instantaneous. The ZGB model basically retains the adsorption-desorption selectivity rules of the Langmuir-Hinshelwood mechanism, it has no energy parameters, and the only independent parameter is Fa. Obviously, these crude assumptions imply that, for example, diffusion of adsorbed species is neglected, desorption of the reactants is not considered, lateral interactions are ignored, adsorbate-induced reconstructions of the surface are not considered, etc. Efforts to overcome these shortcomings will be briefly discussed below. 

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). 

The kinetics of the ethylene oxidation are rather complicated as they depend not only on ethylene and oxygen pressure but also on the concentration of the reaction products. These influence the rate by adsorption competition with the reactants. Moreover, different forms of adsorbed oxygen may occur on the catalyst surface. Consequently, the rate equations proposed in the literature consist of either Langmuir—Hinshelwood and Eley—Rideal types or power rate models with non-integer coefficients. Power rate models are less appropriate as their coefficients inevitably depend on the reaction conditions. 

There are only a few recent publications. Anshits et al. [29,30] have carried out adsorption studies with various Cu—O phases and determined kinetics at low pressure in a static system. One of their conclusions is that the kinetics of partial and complete oxidation are very different. The mechanism of the latter is supposed to be of the associative type, contrary to the redox mechanism of the partial oxidation. A kinetic study with a continuously stirred vessel (375—400°C, 1 atm) was carried out by Laksh-manan and Rouleau [185]. In contrast to the redox mechanism, a singlesite Langmuir—Hinshelwood model is proposed, for which the k values and activation energies are determined. 

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