Rate Eley-Rideal models

All four models give a good fit to the data, though with quite different values for the adsorption constants and rate constant. An Eley-Rideal model involving hydrogen from the gas phase gives a poor fit because it predicts first-order behavior for hydrogen. 

Figure 3.10 Test of Eley-Rideal model for benzene alkylation using initial rate data from Example 3.5. 

Altiokka et al. (2003) obtained the kinetics data on the esterification of acetic acid with isobutanol from both homogeneously (autocatalyzed) and heterogeneously catalyzed reactions using dioxane as a solvent in a stirred batch reactor. The uncatalyzed reaction was found to be second-order reversible. In the presence of the catalyst, on the other hand, the reaction was found to occur between an adsorbed alcohol molecule and a molecule of acid in the bulk fluid (Eley-Rideal model). It was also observed that the initial reaction rate decreased with alcohol and water concentrations and linearly increased with that of acid. The temperature dependency of the constants appearing in the rate expression was also determined. 

Steps 1 through 9 constitute a model for heterogeneous catalysis in a fixed-bed reactor. There are many variations, particularly for Steps 4 through 6. For example, the Eley-Rideal mechanism described in Problem 10.4 envisions an adsorbed molecule reacting directly with a molecule in the gas phase. Other models contemplate a mixture of surface sites that can have different catalytic activity. For example, the platinum and the alumina used for hydrocarbon reforming may catalyze different reactions. Alternative models lead to rate expressions that differ in the details, but the functional forms for the rate expressions are usually similar. 

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. 

Equations similar to eqns. (5), (6) and (8) were obtained by Zhdanov [104] to describe the monomolecular adsorption and associative desorption and Eley-Rideal s bimolecular reaction. He examined the dependence of the rate constants of these processes on the surface coverages and discussed various approximations applied previously to describe the effect of lateral interaction of adsorbed molecules on the desorption rate constant. He also considered the effect of the lateral interaction on the pre-exponential factor of the rate constants for various processes, and in terms of the "precursor state model, the effect of ordering the adsorbed molecules on the sticking coefficient and the rate constant of monomolecular desorption. 

From simple measurements of the rate of a photocatalytic reaction as a function of the concentration of a given reactant or product, valuable information can be derived. For example, these measurements should allow one to know whether the active species of an adsorbed reactant are dissociated or not (22), whether the various reactants are adsorbed on the same surface sites or on different sites (23), and whether a given product inhibits the reaction by adsorbing on the same sites as those of the reactants. Referring to kinetic models is therefore necessary. The Langmuir-Hinshelwood model, which indicates that the reaction takes place between both reactants at their equilibrium of adsorption, has often been used to interpret kinetic results of photocatalytic reactions in gaseous or liquid phase. A contribution of the Eley-Rideal mechanism (the reaction between one nonadsorbed reactant and one adsorbed reactant) has sometimes been proposed. 

It is assumed that this is also a rate determining step for the overall reaction. The activation energy of reaction (4) and the site density of oxygen active centers were the only adjustable parameters of the model. In general, a C-H bond scission for reactants and products of the methane dimerization process occurs by an Eley-Rideal (E-R) type mechanism to form a gas-phase alkyl radical and a hydroxyl surface site (HO ) ... 

There are of course a number of directions in which the lattice model derived by Reuter et al could be made more rigorous. The influence of adsorbate-adsorbate interactions, while small, could be quantified, as could the prefactors used in the TST description of diffusion. Reuter et al noted that a small contribution to the total reaction rate may arise from an Eley-Rideal mechanism that is not included in their model. A more challenging task would be to account for the potential role of surface defects. These directions, however, do not diminish the importance of this work, which can reasonably be thought of... 

Naito et al. studied hydrogenation with use of adsorption measurements, mass spectrometry, and microwave spectroscopy for product analysis. In the room temperature deuteriation of propene, butene, and 1,3-butadiene, the main products were [ H2]-propane, [ H2]-butane, and l,2-[ H2]-but-l-ene, respectively. They showed, using mixtures of H2 and D2, that deuterium was added in the molecular form and at a rate proportional to the partial pressure of D2, as opposed to D surface coverage the reaction rates were zero order in hydrocarbon. They proposed, therefore, in contrast to the model of Dent and Kokes for ethene (but note in this case that reaction rate was 0.5 order in hydrogen pressure and proportional to ethene surface coverage), that hydrogenation proceeded by interaction of adsorbed hydrocarbon with gas-phase D2, that is by an Eley-Rideal mechanism. 

C0(ads)+0(ads)— C02(ads)+, 4.C02(ads) — C02(gas)+. The probabilities of steps 1 and 2 are between 0 and 1, while probabilities of other steps are P(3) = 1, P 4) = 1, P(-l)= 0 P(-2)= 0, P(-4)=0. The ZGB-model shows the effect of heterogeneity in the adlayer because of the infinitely fast formation of C02, there is a segregation of the reactants in CO and oxygen islands. The original model has later been extended and modified by numerous people to include desorption of the reactants, diffusion, an Eley Rideal mechanism for the oxidation step, physisorption of the reactants, lateral interactions, an oxidation step with a finite rate constant, surface reconstruction and additional poisoning adsorbates. 

To be able to quantitatively describe and predict the aforementioned phenomena and to be able to relate catalyst properties to unit operation performance, a more detailed description of the species involved as well as a better representation of the fundamental processes that are occurring between the bulk fluid and the catalyst surface than that which is currently employed in pseudo-component, lumped parameter, power law models is required. This more fundamental approach to kinetic modelling has been achieved in many other systems where there are only a few components and reactions by using Langmuir-Hinshelwood and/or Eley-Rideal type rate expressions such expressions are usually developed by considering the... 

The kinetics of methane combustion over a perovskite catalyst (Lao.9Ceo.iCo03) has been studied in Micro-Berty and fixed bed reactors. Discrimination among twenty-three rival kinetic models from Eley-Rideal, LHHW and Mars-van Krevelen (MVK) types has been achieved by means of (a) the initial rate method as well as by (b) integral kinetic data analysis. Two MVK type models could be retained as a result of the two studies, with a steady-state assumption implying the equality of the rate of three elementary steps. 

The initial reaction rates of esterification between acetic add and benzyl alcohol were measured at various conditions, and the Eley-Rideal (ER) model was used to correlate the data and showed a high degree of fit, indicating that the surface reaction between adsorbed alcohol and add in the bulk is the rate-limiting step during the initial stage of the reaction. The ER model of this esterification can be described as follow. 

Figure 9.6 shows examples of the saturation kinetic curves that might be obtained from these three possible alternative explanations. The curves are calculated with and values that are representative of those with Pd in Table 9.3. Different values have been used for the Eley-Rideal and Langmuir-Hinshelwood models in order to scale the curves for clearer presentation. Figure 9.6 shows that any of these models might explain the kinetic observations, but H2 must be >10 atm to clearly show saturation kinetics for the Ph2 dependence of the initial rate. If is smaller than the assumed value of 0.1 atm then this pressure limit would be larger. 

Figure 9.6. Calculated variation of the initial rate of hydrogenation of nitrobenzene, NB, for various models. (— - ) simple Eley-Rideal varying [NB] ( ) full Eley-Rideal varying [NB] (—— —) full Eley-Rideal...

Metkar et al. [9] developed a global kinetic model from a derivation of detailed reaction steps. They used reactions described in (12.11-12.14 [11]) and combined two reactions (see Eqs. 12.15-12.16 [11]). They received the best results when assuming the Eley-Rideal step, during the NO oxidation (Eq. 12.14) as rate determining. The resulting rate expression was ... 

In a global modeling approach, it is assumed that NO and NO2 react with the adsorbed ammonia directly from the gas phase and consequently an Eley-Rideal mechanism-based expression is commonly used to describe the reaction rate ... 

This reaction rate, obtained from the Langmuir-Hinshelwood model, should be compared with that for the direct reaction through the so-called Eley-Rideal mechanism, where a molecule in the gas phase reacts with a surface-bound one, i.e.. 

Miranda et a/. studied the kinetics of TCE oxidation using four different models Langmuir-Hinshelwood (reaction between the two adsorbed species was the rate-controlling step), Rideal-Eley (assuming that oxygen reacts from the gas phase), Mars-van Krevelen (Eq. 4.10), and a CI2 inhibition model (Eq. 4.11). The last of these resulted in the best fit with the experimental laboratory data... 

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