Fractional surface coverage of species

Fractional surface coverages of predominant adsorbed species versus dimensionless distance from the reactor inlet. (Figure adapted from Kinetic Simulation of Ammonia Synthesis Catalysis by J. A. Dumesic and A. A. Trevino, in Journal of Catalysis, Volume 116 119, copyright 1989 by Academic Press, reproduced by permission of the publisher and the authors.)... 

The adsorption/desorption equilibrium constant for each component is Kf = 0.25 atm and forward is the kinetic rate constant for the forward chemical reaction on the catalytic surface with units of moles per area per time. The reason that forward has the same units as Ehw is because rate laws for heterogeneous catalysis are written in terms of fractional surface coverage by the adsorbed species that participate in the reaction. Langmuir isotherms are subsequently used to express fractional surface coverage of the reacting species in terms of their partial pressures. The best value for the pseudo-first-order kinetic rate constant is calculated from... 

Figure 11.7 Fractional surface coverage of adsorbed methoxy species determined with in situ IR during methanol selective oxidation as a function of temperature of reaction (From Burcham, L.J., Badlani, M., and Wachs, I.E. J. Catal. 2001, 203, 104-121. With...

The plateau of the adsorption isotherm indicates the concentration(s) at which all adsorption sites for the adsorbing species are occupied, in surface chemistry terms the fractional surface coverage of the substrate by the adsorbate is unity. Such a specimen provides an ideal opportunity to probe the interfecial chemistry of adhesion directly using what is sometimes referred to as the thin film approach. As the layer of organic material, such as adhesive, is very thin (as a result of monolayer coverage) the contribution of interfacial chemistry at the interface will be maximized in the resultant XPS or ToF-SIMS spectrum. For this reason, the construction of adsorption isotherms is often used as a precursor to direct interphase analysis in this manner. 

Based on the mechanisms proposed in Eqs. (6.53)-(6.56), an expression relating the time-dependent fractional surface coverage of the CO (Oco) species can be shown [79] ... 

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]. 

One feature of this extension is that there are now two different adsorbed species whose concentrations are independent. In tefms of the fractional surface coverages, we have the condition... 

To model the process, a mass balance is made for the adsorbed species, and the partial pressures of the reactants are considered as constant. The surface coverage of each adsorbed species is defined as the fraction of the total number of available adsorption sites occupied by that species and denoted by 0A or 0B. The differential equations for this mechanism are ... 

Several different mathematical relationships (referred to as isotherms) have been developed to describe the relationship of fractional surface coverage with respect to the adsorbing species. Work by Langmuir, Freundlich, Tempkin, and others have attempted to describe the above mentioned pressure differential to fractional surface coverage. The most widely used and accepted isotherm is the BET equation, named after its orignators, Brunauer, Emmett, and Teller, and is as follows 29... 

Finally, we note that the two steps for isobutane activation are kineti-cally significant under the high-temperature reaction conditions. The kinetic model was used to calculate the predicted surface coverage under reaction conditions. Approximately 96% of the surface sites are free under the low-temperature reaction conditions, whereas more than 99% of the sites are free at the higher temperatures. The most abundant surface species are predicted to be adsorbed C3—C. The most abundant heavy species are predicted to be Cg—Cq. The fractional surface coverage by adsorbed Q0—CJ2 is very low (e.g., 10-8), consistent with our decision to neglect surface species heavier than C 2. 

Rates are in units of molecules per second per site, pressures (P) are in pascals, and activation energies are in kilojoules per mole. Concentrations of surface species are represented by fractional surface coverages as discussed in Chapter 5. Kinetic parameters are adapted from the data of Stolze and Norskov [P. Stolze and J. K. Norskov, Phys. Rev. Lett., 55 (1985) 2502 P. Stolze and J. K. Norskov, Surf. Sci. Lett., 197 (1988) L230 P. Stolze and J. K. Norskov,/. Catal., 110 (1988) 1]. 

The fractional order can be explained by means of the surface coverage of adsorbed components which becomes more difficult as it approaches a complete monolayer. The heat of adsorption decreases with the extent of adsorption because of the increasing closeness and interaction of adsorbed species. This can be interpreted by means of an adsorption isotherm such as the Freundlich isotherm which relates the solution concentration to the surface concentration according to Eq. (70),... 

Ammonia adsorption on Lewis sites is stronger than that on Bronsted sites [97]. In situ infrared spectroscopy has been used to monitor surface coverages by various species under reaction conditions. Temperature programmed desorption shows that no NO decomposition occurs in the temperature range 100-600 K. By means of in situ FTIR spectroscopy it was observed that the fractional surface coverages by ammonia on the Bronsted and Lewis acid sites were 0.26 and 0.39, respectively, at 573 K. No adsorption of NO was found. Moreover, it was stated that water does not block the sites for ammonia adsorption. 

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