Rate expressions dissociative adsorption

At low concentrations of A2, the fractional surface coverage is proportional to [ 2], which is quite different than the adsorption isotherm derived above for the case without dissociation. In terms of fractional surface coverage, the net rate of dissociative adsorption is expressed by ... 

In a case such as this one where only one species is present in appreciable concentration on the surface, that species is often referred to as the most abundant reaction intermediate, or mari. The overall rate of reaction can be expressed as the rate of dissociative adsorption of N2 ... 

There are a number of limiting forms of the rate expression depending on the magnitudes of the various terms in the denominator relative to unity and to each other. Any species that is weakly adsorbed will not appear in the denominator. If species R undergoes dissociation on adsorption, the term KRPR must be replaced by >JKrPr according to the discussion in Section 6.2.1.3. If an inert specie I is also capable of adsorption, the term KjPj must be added to... 

It has been suggested that the rate limiting step in the mechanism is the chemisorption of propionaldehyde and that the hydrogen undergoes dissociative adsorption on nickel. Determine if the rate expression predicted by a Hougen-Watson model based on these assumptions is consistent with the experimentally observed rate expression. 

The interesting point is that only the ratio of the partial pressures of the reactants enters this equation, but not the total pressure. The physical reason is obvious. Both reactants are competing for free adsorption sites on the surface and since CO inhibits the dissociative adsorption of oxygen the partial pressure of the latter compound enters into the denominator of the rate expression. This result indicates that the actual surface composition and, in addition, the reaction mechanism will not be affected by the total pressure. The only effect of increasing the total pressure (at a fixed p0l pco ratio) will be that rmax will be shifted towards higher temperatures since reduction of... 

In principle it is possible to write down the rate equation for any rate determining chemical step assuming any particular mechanism. To take a specific example, the overall rate may be controlled by the adsorption of A and the reaction may involve the dissociative adsorption of A, only half of which then reacts with adsorbed B by a Langmuir-Hinshelwood mechanism. The basic rate equation which represents such a process can be transposed into an equivalent expression in terms of partial... 

The adsorption group represents the reduction of the number of active sites due to adsorption. The individual terms represent the distribution of the active sites over the different intermediate surface species and vacancies. It may contain square roots of partial pressures, indicating dissociative adsorption. The power n in the rate expression indicates the number of sites involved in the rate determining process, usually 0,1 or 2. 

The value of two before each rate constant in Equation (5.2.14) is a statistical factor that contains the number of nearest neighbors to an adsorption site on a square lattice and accounts for the fact that indistinguishable neighboring sites should not be double counted. For simplicity, this statistical factor will be lumped into the bimolecular rate constant to yield the following rate expression for dissociative adsorption ... 

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. 

One of the first comprehensive kinetic analyses over Au/TS-1 concerned the oxidation of H2 to form water [65]. DPT calculations [63,65] showed the RDS to be the formation of adsorbed H2O2 which ultimately decomposes to form water [65]. In the presence of propylene, the generated H2O2 is expected to perform the epoxidation, therefore similarities between the production of PO and water can likely be drawn. Traditional kinetic analysis [65] produced a power rate law for water production of rn o = h exp[-(37.1 1.1 kj mol- )/RT][H2]° 0.02jqj0.17 0.02 Development of a series of elementary steps [Eqs. (11.1-11.5)] capable of reproducing the observed experimental orders and consistent with DPT calculations proved to require two active sites one capable of nondissociative adsorption of O2 and dissociative adsorption of H2 and a second available for only dissociative adsorption of H2 [65]. The resulting rate expression [65] is presented as Eq. (11.6). 

Although the mechanism is similar to the mechanistic steps presented in reference [65], Taylor et al. [55] used enhanced H2 dissociation in the presence of O2, consisfenf wifh bofh previous experimenfal observation [91] and DFT calculations [63,64], Moreover, the rate determining step (Eq. 11.12) is unique because the fractional propylene order required the inclusion of adsorbed propylene in fhe RDS [55]. This mechanism and ifs associated rate expression (Eq. 11.15) were the simplest means of reproducing fhe observed reaction orders (n = 0.18, m = 0.14). It does imply a relation between H2 and O2 orders m + 1/2, 2rti), however. The addition of a third active site for dissociative H2 adsorption [65] would provide independent control over all three reaction orders. 

The equation for the hydrogen current, was derived by the following considerations At high anodic overpotentials, the dissociative adsorption of H2 onto the available free sites is the rate-determining step, and thus j hj can be expressed as... 

Fits of two principal reaction mechanisms, both of which have the above general form, were made, after initial trials of rate expressions corresponding to mechanisms with other forms of rate expression had resulted in the rejection of these forms. In the above equation the Molecular Adsorption Model (MAM) predicts n=2, m=l while the Dissociative Adsorption Model (DAM) leads to n=2, m=l/2. The two mechanisms differ in that MAM assumes that adsorbed molecular oxygen reacts with adsorbed carbon monoxide molecules, both of which reside on identical sites. Alternatively, the DAM assumes that the adsorbed oxygen molecules dissociate into atoms before reaction with the adsorbed carbon monoxide molecules, once more both residing on identical sites. The two concentration exponents, referred to as orders of reaction, are temperature independent and integral. All the other constants are temperature dependent and follow the Arrhenius relationship. These comprise lq, a catalytic rate constant, and two adsorption equilibrium constants K all subject to the constraints described in Chapter 9. Notice that a mechanistic rate expression always presumes that the rate is measured at constant volume. 

Here, ka, kd and km are the rate coefficients for adsorption, desorption, and migration from the intrinsic precursor state, k m and are the rate coefficients for migration and desorption from the extrinsic precursor state, kv is the rate coefficient for transfer from the chemisorbed state to the intrinsic precursor state, and a and a are the trapping probabilities for molecules incident at intrinsic and extrinsic precursor sites, respectively. Direct transfer from gas phase to chemisorbed state or vice versa is included through the probability, sc, for adsorption and the rate coefficient, ftc, for desorption [427]. In order to generalise the rate expressions, we now introduce a group of terms F(0) which are only functions of the surface coverage 0. For a particular case, such as non-dissociative adsorption, these terms may be evaluated and inserted into the appropriate rate expression. 

In this model, the rates of adsorption, migration and desorption from the intrinsic precursor are fea[A2], km [A ], and fc A ], respectively, and it follows that the normalised rate coefficients defined earlier are identical with the probabilities fc, fm and fd defined by King and Wells [46] and equation (65) is readily transformed into their rate expression for dissociative adsorption derived by the statistical method. 

The kinetics of methanol oxidation over metal oxide catalysts were elegantly derived by Holstein and Machiels [16], The kinetic analysis demonstrated that the dissociative adsorption of water must be included to obtain an accurate kinetic model. The reaction mechanism can be represented by three kinetic steps equilibrated dissociative adsorption of methanol to a surface methoxy and surface hydroxyl (represented by K,), equilibrated dissociative adsorption of water to two surface hydroxyls (represented by K ), and the irreversible hydrogen abstraction of the surface methoxy intermediate to the formaldehyde product and a surface hydroxyl (the rate determining step, represented by kj). For the case of a fully oxidized surface, the following kinetic expression was derived ... 

Adsorption requires the O2 molecule to find a pair of adsorption sites and desorption requires two adsorbed G atoms to be adjacent. Hill [15] and Kisliuk [18,19] discuss lattice statistics and the probability of find-Ing pairs of sites in two-dimensional arrays presented by the regular arrangement of surface atoms illustrated in Figure 5.16. Boudart and pjega-Mariadassou [3],and Hayward andTrapnell [13], describe how the probability of finding pairs of sites is used to develop rate expressions on surfaces. When a bimolecular surface reaction occurs, such as dissociative adsorption, associative desorption, or a bimolecular surface reaction, the rate in the forward direction depends on the probability of finding pairs of reaction centers. This probability, in turn, depends... 

In this mechanism the dihydrogen molecule must dissociatively adsorb prior to reacting with the alkene A. This requires two sites (see Figure 2). When the surface reaction takes place to convert the alkene and two hydrogen atoms into one alkane, the two sites are regenerated. Therefore, we need to examine how the dissociative adsorption step is handled and what ramification this has upon the rate expression, assuming all the adsorption-desorption steps are at equilibrium. 

The dissociative adsorption-desorption of hydrogen follows this rate expression ... 

Dissociative adsorption of reactant A2 on the catalytic surface is the rate-limiting step, and the stable reactive intermediate A2B occupies a significant fraction of surface sites. It is reasonable to assume that reactant B, intermediate A2B, and products C and D experience single-site adsorption. Express your final answer in terms of the partial pressures of... 

The principles underlying this treatment are capable of extension to cover a greater number of reactants, inhibition by products, poisoning by adventitious impurities, dissociation of reactants upon adsorption (Section 3.2.4) and many other situations. The relevant rate expressions were collected and comprehensively evaluated many years ago by O. A. Hougen and K. M. Watson,and monographs on chemical kinetics ° often contain a fuller presentation than is thought necessary here. 

If the reaction proceeds by a mechanism requiring dissociation of one of the reactants (A2) on adsorption, the rate expression corresponding to the termolecular surface reaction between the two symmetric fragments of adsorbed A and an adsorbed B species is given by... 

It was early recognised that the rate limiting step in the ammonia synthesis is the dissociative adsorption of nitrogen (23) and that hydrogenation proceeds at a much faster rate (24). Temkin and Pyzhev (25) proposed a rate expression. 

Sabatier-type volcano plots have been constructed for a number of different commercially relevant systemsl l. A simple kinetic expression that simulates the Sabatier result is found when one realizes that the decomposition of molecules requires a vacant site for molecular fragments to adsorb on. For instance, in the N2O decomposition reaction, the dominant surface species (most abundant reaction intermediate) is atomic oxygen (O), which is in equilibrium with the gas phase. When the slow step in the reaction is dissociative adsorption of N2O, the mean-field kinetic rate expression for N2O decomposition, normalized per unit surface area of catalyst, becomes ... 

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