Rideal rate expression

Considering the site balance equation (1 = 0NH3+fi H2O+fi ) and by replacing equation 17 and 18 into equation 16, the following Rideal rate expression is eventually obtained ... 

Modified Kinetics (MB)—A modified Eley-Rideal rate expression... 

This mechanism can be converted to a kinetic scheme to describe the steady state or transient performances of the catalyst. Assuming (i) an Eley-Rideal mechanism (reaction between adsorbed NH3 and gas-phase NO), (ii) that ammonia and water compete for adsorption onto the active sites, and (iii) that adsorption equilibrium is established for both species, the following Rideal rate expression is eventually obtained [6] ... 

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. 

Rate expressions for a Rideal—Eley mechanism may be readily formulated. Assuming A is not adsorbed at all... 

Rate expressions may similarly be derived for a reaction proceeding via a Rideal — Eley mechanism... 

The usual functional expression for the Eley-Rideal rate of formation of product molecule C is... 

In order to explain the mechanism of the Fisher-Tropsch reaction, some authors derived the Langmuir-Hinshelwood or Eley-Rideal types of rate expressions for the reactant consumption, where in the majority of cases the rate-determining step is supposed to be the formation of the building block or monomer, methylene [134],... 

The strategy is to propose a reasonable sequence of steps, derive a rate expression, and then evaluate the kinetic parameters from a regression analysis of the data. As a first attempt at solution, assume both CI2 and CO adsorb (nondissociatively) on the catalyst and react to form adsorbed product in a Langmuir-Hinshelwood step. This will be called Case 1. Another possible sequence involves adsorption of CI2 (nondissociatively) followed by reaction with CO to form an adsorbed product in a Rideal-Eley step. This scenario will be called Case 2. 

Problem 9.5 Considering reaction between A and B catalyzed by a solid there are two possible mechanisms by which this reaction could occur. The first is that one of them, say A gets adsorbed on the solid surface and the adsorbed A then reacts chemically with the other component B which is in the gas phase or in solution and is not adsorbed on the surface. The second mechanism is that both A and B are adsorbed, and the adsorbed species undergo chemical reaction on the surface. The reaction rate expression derived for the former mechanism is the Rideal rate law and that for the second mechanism is the Langmuir-Hinshelwood rate law. Obtain simple derivations of these two rate laws. 

This is the rate expression for the Rideal Mechanism. The other mechanism is the reaction between two adsorbed species ... 

Bernasek and Somorjai proposed that, as the temperature increased and the surface concentration of the D2(ads) species decreased, an Eley— Rideal-type mechanism became important, involving direct reaction of an incident gas phase D2 molecule with H atoms present at the stepped active sites, having (Id ) as the r.d.p. and obeying the rate expression... 

At low temperature, the reaction rate can be expressed by a Rideal-Eley mechanism where dissociatively adsorbed oxygen is assumed to be in equilibrium with gas-phase O2 and to react with gaseous CH4. The kinetic rate expression is given by Arai et al. (1986)... 

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... 

In Eley-Rideal and Langmuir-Hinshelwood type of kinetic rate expressions, the effect of poisons and inhibitors on the reaction rate is accounted for by allowing part of the catalyst surface to become covered with the poisoning compound and so unavailable for desirable reactions. For example, consider the decomposition reaction of A —> B + C that occurs in the presence of an inhibitor, I. If it is assumed that the inhibitor does not participate in the reaction but that it does occupy active catalyst sites and if the surface decomposition is rate controlling then the observed rate of reaction in Langmuir-Hinshelwood terms is given by [13]... 

Previously, for 2-methyl pentane cracking we have used Eley-Rideal kinetic rate expressions to describe the inhibition and poisoning effects of species in the feed, as well as intermediate and product species. In order to utilise such kinetic expressions values for the adsorption equilibrium constants are required. A method for estimating adsorption equilibrium constants has been proposed that uses an integrated form of van t Hoff equation. The heats of adsorption have been calculated using proton affinities and heats of condensation. The entropy of adsorption has been calculated using the Sackur-Tetrode expression. 

This is a so-called Eley-Rideal mechanism, meaning that methane from the gas phase reacts directly with an adsorbed oxygen species (Step 3). The rate expression from the above mechanism is ... 

The MR rate expression Eq. (10.34) differs from the Eley-Rideal rate Eq. (10.18) only in its denominator, which accounts both for the adverse kinetic effect of NH3 and for the favorable O2 dependence at low ammonia coverage (as, e.g., at high temperature), the denominator tends to unity and Eq. (10.34) formally reduces to Eq. (10.18). Indeed, this is consistent with the experimental indications discussed above the ammonia inhibiting effect is particularly evident at low temperatures, but tends to disappear in the runs performed at temperatures of 250 °C and above, where ammonia coverage becomes lower. Likewise, the oxygen dependence is reportedly most manifest at low temperatures. 

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 ... 

The quasi-equilibrium assumption is frequently used in the heterogeneous catalysis, since the surface reaction steps are often rate-Hmiting, while the adsorption steps are rapid. This is not necessarily true for large molecules. Here we consider the application of the quasi-equilibrium hypothesis on two kinds of reaction mechanisms, an Eley-Rideal mechanism and a Langmuir-Hinshelwood mechanism. The rate expressions obtained with this approach are referred to as Langmuir-Hinshelwood-Hougen-Watson (LHHW) equations in the literature, in honor of the pioneering researchers. 

Kircher and Hougen studied NO oxidation, 2NO + O2 —> 2NO2, over activated carbon and Si02 in the presence of water and proposed a Rideal-Eley mechanism between O2 and (N202)ad> which gave a rate expression of ... 

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. 

Mechanistic kinetic expressions are often used to represent the rate data obtained in laboratory studies, and to explain quantitatively the effects observed in the field. Several types of mechanisms have been proposed. These differ primarily in complexity, and on whether the mechanism assumes that one compound that is adsorbed on the catalyst surface reacts with the other compound in the gas phase, eg, the Eley-Rideal mechanism (23) or that both compounds are adsorbed on the catalyst surface before they react, eg, the Langmuir-Hinshelwood mechanism (25). 

Only in one case (the hydration of 2-methylpropene over a H2S04—Si02 catalyst [278]) was the so-called Rideal mechanism proposed as a preferable model and expressed by the rate equation for single-site adsorption with retardation by the product alcohol, viz. 

To derive the corresponding kinetic expressions for a bimolecular-unimolecular reversible reaction proceeding via an Eley-Rideal mechanism (adsorbed A reacts with gaseous or physically adsorbed B), the term K Pt should be omitted from the adsorption term. When the surface reaction controls the rate the adsorption term is not squared and the term KgKg is omitted. 

Salmi (25) set up equations needed to simulate the transient response of both the PFR and the CSTR. The balance equations and the generahzed equations for the rates of the elementary steps are compactly expressed in vector and matrix notation. Details of the computational algorithms are discussed, and they are applied to the N2O decomposition (Eqs. 5 and 6). In another paper (26) these equations are used to simulate (for both PFRs and CSTRs) the responses of sysfems following many mechanisms Eley-Rideal, Langmuir-Hinshelwood. a combination of the two. with and without dissociative adsorption, etc. These curves can be added to those of Kobayashi (22), to expand the general view of how various systems respond. 

The rate of the DeNO, reaction is first order in respect to NO concentration and essentially independent of NH3 concentration when ammonia is in excess. However, in SCR industrial applications a substoichiometric feed ratio (a = NH3/NO < 1) is employed in order to minimize the slip of unconverted ammonia and the formation of ammonium sulfates. A kinetic dependence on ammonia is apparent when NH3 becomes the limiting reactant. Several authors have proposed kinetic expressions for the SCR reaction that account for the observed dependences [31-37]. In particular, the simplest expressions are based on Eley-Rideal kinetics in line with the mechanistic studies, they assume that the reaction occurs between strongly adsorbed ammonia and gas-phase NO. Beckman and Hegedus [36] have proposed and fitted to experimental data obtained over commercial SCR catalysts the following kinetic expression ... 

The speed of a reaction between molecules in a film and those in the underlying solution depends on the rate of approach of the latter to the interface. There are two ways of exactly evaluating the latter, one depending, as we have seen in Section II, on the use of the gas laws and the other using the diffusion coefficient of the molecules in solution. The former method w as suggested by Fosbinder and Rideal (16), who used the Hertz expression,... 

Problem 9.6 Show that under conditions where Km C [- 2] (see Table 9.5) the Langmuir-Hinshelwood rate equation becomes indistinguishable from the Rideal expression for the stationary zone rate. 

A quantitative expression for the rate of coalescence of droplets in a macroemulsion, which includes most of the factors discussed previously, was developed by Davies and Rideal (1963), based on the von Smoluchowski (1916) theory of the coagulation of colloids. 

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