Rate expressions desorption

Replacing C(. in Etjuation (10-48) by Equation (10-49) an i multipl the numerator anrl denominator by Pp. we obtain the rate expression desorption control ... 

To derive an explicit expression of the rate of desorption we restrict ourselves to nondissociative adsorption, listing references to other systems— such as multicomponent and multilayer adsorbates with and without precursors—for which such a treatment has been given, later. We look at a situation where the gas phase pressure of a molecular species, P, is different from its value, P, which maintains an adsorbate at coverage 6. There is then an excess flux to re-establish equilibrium between gas phase and adsorbate so that we can write [7-10]... 

As discussed in Chapter 7, this form can provide a good fit of the data if the reaction is not too close to equilibrium. However, most reaction engineers prefer a mechanistically based rate expression. This section describes how to obtain plausible functional forms for based on simple models of the surface reactions and on the observation that aU the rates in Steps 2 through 8 must be equal at steady state. Thus, the rate of transfer across the film resistance equals the rate of diffusion into a pore equals the rate of adsorption equals the rate of reaction equals the rate of desorption, and so on. This rate is the pseudohomo-geneous rate shown in Steps 1 and 9. 

Derive the rate expression for temperature-programmed desorption (i.e. the rate versus temperature at a constant heating rate). 

The analyses developed in this section are readily extended to reactions with different stoichiometries. Regardless of whether an adsorption or a desorption process is rate limiting, the resulting rate expressions may be written in the typical Hougen-Watson fashion represented by equation 6.3.30. A comprehensive summary of such relations has been developed by Yang... 

The rate of desorption of an adsorbed species from a surface is usually expressed in the form... 

The rate expression is based on adsorption-desorption equilibrium at the substrate surface with an additional term (k2pH2) representing H2 gas inhibition. The rate constants can be estimated by regression of R with the two partial pressures using experimental data (Roenigk and Jensen, 1985). 

Here La is the rate constant for the adsorption of A. Conversely, desorption control of kinetics for A R leads to the following rate expression [2] ... 

Here /jr is the desorption rate constant for R. Another rate expression that is often appHcable is when kinetics are controlled by impact of gas phase A on adsorbed B for the A -i- B R reaction. For this case ... 

For this estimate, values for the surface diffusion coefficient (D) and the surface exchange coefficient (i) in eq 2 were obtained by linearizing Mitterdorfer s rate expressions for surface transport and adsorption/desorption (ref 84) and re-expressing in terms of the driving forces in eq 2. 

This empirical rate expression considers the active sites of the catalyst as only a fraction of the total adsorption sites for ammonia and is consistent vfith the presence of a reservoir of ammonia adsorbed species which can take part in the reaction. The ammonia reservoir is likely associated vfith poorly active but abundant W and Ti surface sites, which can strongly adsorb ammonia in fact, nhs roughly corresponds to the surface coverage of V. Once the ammonia gas-phase concentration is decreased, the desorption of ammonia species originally adsorbed at the W and Ti sites can occur followed by fast readsorption. When readsorption occurs at the reactive V sites, ammonia takes part in the reaction. Also, the analysis of the rate parameter estimates indicates that at steady state the rate of ammonia adsorption is comparable to the rate of its surface reaction with NO, whereas NH3 desorption is much slower. Accordingly, the assumption of equilibrated ammonia adsorption, which is customarily assumed in steady-state kinetics, may be incorrect, as also suggested by other authors [55]. 

The rate expression is the rate of desorption, which can be regarded as the elementary reaction AS —> A + S, which should have the expression... 

Based on experiments carried out with small catalyst particles under vigorous stirring, experimental data representing intrinsic kinetics were obtained. Rate expressions based on the principle of an ideal surface, rapid adsorption and desorption, but rate-limiting hydrogenation steps were derived. The competiveness... 

With this information in mind, we can construct a model for the deposition rate. In the simplest case, the rate of flux of reactants to the surface (step 2) is equal to the rate at which the reactants are consumed at steady state (step 5). All other processes (decomposition, adsorption, surface diffusion, desorption, and transport away from the substrate) are assumed to be rapid. It is generally assumed that most CVD reactions are heterogeneous and first order with respect to the major reactant species, such that a general rate expression of the form of Eq. (3.2) would reduce to... 

There is the further possibility that the transition C/ + C(0) C(CO)b is either slow (Case 1) or fast (Case 2) in comparison with C(CO)a — CO( ) -f- C/. The rate expression to be derived is the same in either case, but the interpretation of the individual rate constant, is, in Equation (5) will be different. When Case 1 holds, ja represents the rate constant for the surface rearrangement when Case 2 holds, ja represents the rate constant for the desorption of (C0) . It is not possible, on the basis of present experimental evidence, to decide which case is operative. It is conceivable that each case will be operative but in different temperature ranges. Assuming for the moment that Case 1 holds, the general expressions given above can be simplified to... 

Vatcha reports that the rate expression given by Eq. (1) describes the global rate, thus allowing gas phase concentrations to be used in the reaction analysis. Global reaction kinetics will be used in the analysis to follow. Consequently, these kinetics must account for microscopic processes such as adsorption/desorption on the catalyst surface and intraparticle diffusion. Since most available kinetic information is based on steady-state data, a major... 

The overall rate of the reaction, A o B + C, is controlled by the net rate of desorption of B from the surface and by the rate of diffusion of A to the surface. The data available are of the rate against fractional conversion of A at constant pressure and temperature. Find an expression for the rate in terms of the minimum number of constants to be evaluated. 

Figure 2.12 The so-called complete analysis of TDS data is based on the rigorous application of Expression (2-15) for the rate of desorption. The spectra of Figure 2.11 are integrated to determine points on the spectra corresponding to a fixed coverage, in this example 0.15 of a monolayer (b). This procedure gives a pair of (r,T) values for every desorption trace, from which an Arrhenius plot is made (c). The slope yields the activation energy and the intercept equals In v+n In 9 each corresponding to a coverage of 0.15 ML.

The rate expression can be simplified if the assumption is made that methanol desorption is the rate-limiting step on a Cu/Zn0/Al203 catalyst ... 

If the adsorption step itself is rate-limiting, one must have available rate expressions for the adsorption and the desorption steps. The flux in (2.108) is then split into two opposing components. Using the notation of Delahay and Mohilner [201,403], there is a forward flux vj, adding to the adsorbate s surface concentration and backward flux tadsorbed substance. These obey rate equations rather analogous to those for electron transfer, the Butler-Volmer equation, in the sense that there are rate constants that are potential dependent. For the forward and backward rates, we have... 

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