Surface coverage, partial pressure

The UCKR.ON test problem assumes the simplest uniform surface implicitly, because adsorbed hydrogen coverage is directly proportional to the partial pressure of gaseous hydrogen and adversely affected by the partial pressure of the final products. Such a simple mechanism still amounts to a complex and unaccustomed rate expression of the type solved by second order algebraic equations. 

In a further treatment we shall deal with Eqs. (14) and (14a) under such conditions only, which make the terms with (d2P/dt2)m and d,PJ dQp max negligible as compared with the other terms. Using Eq. (13) we can eliminate from Eq. (14) the unknown value of the surface coverage 0 and thus arrive, for a given pumping speed S and heating rate dT/dt, at a relation between the measured data (i.e. the maximum pressure Pm or the maximum partial pressure Pam, and the corresponding temperature Tm) and the parameters fed, K, Ed, — AH, and x, characteristic of the surface... 

Langmuir was first to model chemisorption and to relate the surface coverage, 0a, of an adsorbate A with the gaseous activity or partial pressure, pA, and temperature ... 

Thus denoting by 0P the coverage of the promoter on the catalyst surface and by pj the partial pressures of reactants, j, of the catalytic reaction we can formulate mathematically the above definition as ... 

Adsorption of reactants on the surface of the catalyst is the first step in every reaction of heterogeneous catalysis. Flere we focus on gases reacting on solid catalysts. Although we will deal with the adsorption of gases in a separate chapter, we need to discuss the relationship between the coverage of a particular gas and its partial pressure above the surface. Such relations are called isotherms, and they form the basis of the kinetics of catalytic reactions. 

Figure 2.10 shows a plot of 0a versus the partial pressure of A, p. . At low pressure, the coverage is small, and increases linearly with pressure the derivative of the plot equals the equilibrium constant, Ka- At high pressure, the surface becomes saturated, and the coverage approaches asymptotically its saturation value of 100 %. 

Note that at low surface coverages where (1 + KaPa + KbPb + ) 1, the fraction of the sites occupied by each species will be proportional to its partial pressure. 

Here Pe and pH are the partial pressures of ethane and hydrogen, respectively, and the parameter a is equal to (6 — x)/2. This analysis was subsequently generalized to include cases in which equilibrium is not established between adsorbed C2H and gas phase ethane (16). Provided that surface coverage by adsorbed species is low, and that equilibrium is maintained between the surface species C2H5 and C2Hx, and H2 in the gas phase, a kinetic analysis leads to the rate expression... 

Definitions for the variables and constants appearing in eqns. 1 and 2 are given in the nomenclature section at the end of this paper. The first of these equations represents a mass balance around the reactor, assuming that it operates in a differential manner. The second equation is a species balance written for the catalyst surface. The rate of elementary reaction j is represented by rj, and v j is the stoichiometric coefficient for component i in reaction j. The relationship of rj to the reactant partial pressures and surface species coverages are given by expressions of the form... 

To further test the model, calculations were performed to simulate the isotopic tracer experiments presented in Figs. 9 and 10. It should be noted that while the tracer experiments were performed at 438K, the rate coefficients used in the model were chosen to fit the experiments in which chemisorbed NO was reduced at 423 K. Figures 21 and 22 illustrate the nitrogen partial pressure and surface coverage responses predicted for an experiment in which 5 0 is substituted for l NO at the same time that H2 is added to the NO flow. Similar plots are shown in Figs. 23 and 24 for an experiment in which NO is substituted for during steady-state reduction. 

With multiple rate controlling steps, a steady state is postulated, that is, all rates are equated to the overall rate. Equations for the individual steps are formulated in terms of variables such as interfacial concentrations and various coverages of the catalyst surface. Any such variables that are not measurable are eliminated in terms of measurable partial pressures and the rate, as well as various constants to be evaluated from the data. The solved problems deal with several cases for instance, P6.03.04 has two participants not in adsorptive equilibrium and P6.06.17 treats a process with five steps. 

Figure 6 shows the dependence of the rate of CO oxidation over single crystal catalysts on the partial pressure of CO. At conditions of relatively high partial pressures of CO, the reaction rate is observed to decrease linearly with increasing CO partial pressure reflecting the domination of reactant surface coverage by CO. For these reaction conditions on Rh, this behavior has been accurately modeled using individual elementary reaction steps established from surface science studies of the interactions of CO and Oj with Rh. 

Consider a surface-catalyzed unimolecular reaction A, — Bg with A and B gases with partial pressures Pas and Pbs above the catalytic surface and coverages 6a and 6b on the surface. The elementary steps and their rates for a simple unimolecular reaction might be... 

In this equation, K represents the equilibrium constant for binding of the analyte to the surface and P is the analyte partial pressure or concentration. When PL changes are at their saturated intensity, PLsat, then 0 = 1 the PL intensity of the reference ambient, PL,.er, corresponds to 0 = 0, and the PL intensity at intermediate surface coverages. Id., allows 0 to be defined as follows ... 

Fig. 12.1. The Langmuir-Hinshelwood adsorption isotherm, showing the fractional coverage of the catalyst surface as a function of the partial pressure of p in the gas phase.

The stationary-state extent of surface coverage for a given partial pressure p is obtained by setting dO/dr equal to zero. This gives... 

Fig. 12.2. The stationary-state fractional coverage of the surface for adsorption with cover-age-dependent parameters and no reaction (a) a = 2, showing unique solution for all partial pressures (b) a = 4.5, typical of all a > 4, showing multiplicity at low pressures,...

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