Coverage-dependent rate constants

Let us consider that Ed corresponding to a peak on the desorption curve is coverage dependent, while kd (and thus the adsorption entropy) remains constant. (For the variability of kd see Section II.A.) When seeking the required function Ed (6) we refer to Eq. (8) in which the term exp (— Edf RT) exhibits the greatest variability. A set of experimental curves of the desorption rate with different initial populations n,B must be available. When plotting ln(— dn,/dt) — x ln(n ) vs 1/T, we obtain the function Ed(ne) from the slope, for the selected n, as has been dealt with in Section V. In the first approximation which is reasonable for a number of actual cases, let us take a simple linear variation of Ed with n ... 

The rate constant k t for the dehydrated adsorption of hydrated anions does not depend on the coverage, whereas the rate constant for... 

Depending on the degree of coverage wifli oxygen the rate constant varied between Uq range between 4.6-10 2-10 cm s. ... 

One notes that the coverage of Cads depends on two important parameters the ratio p of the rate of hydrogenation of Cads to give methane and the rate constant of CO dissociation ... 

As long as there are no important steric contributions to the transition-state energies, the elementary rate constant of Eq. (1.22) does not sensitively depend on the detailed shape of the zeolite cavity. Then the dominant contribution is due to the coverage dependent term 9. 

Table 10.4 lists the rate parameters for the elementary steps of the CO + NO reaction in the limit of zero coverage. Parameters such as those listed in Tab. 10.4 form the highly desirable input for modeling overall reaction mechanisms. In addition, elementary rate parameters can be compared to calculations on the basis of the theories outlined in Chapters 3 and 6. In this way the kinetic parameters of elementary reaction steps provide, through spectroscopy and computational chemistry, a link between the intramolecular properties of adsorbed reactants and their reactivity Statistical thermodynamics furnishes the theoretical framework to describe how equilibrium constants and reaction rate constants depend on the partition functions of vibration and rotation. Thus, spectroscopy studies of adsorbed reactants and intermediates provide the input for computing equilibrium constants, while calculations on the transition states of reaction pathways, starting from structurally, electronically and vibrationally well-characterized ground states, enable the prediction of kinetic parameters. 

FIG. 21 Complex IMPS spectra obtained for the photo-oxidation of DFcET by ZnYPPC" at the water-DCE interface (a). The opposite potential dependencies of the phenomenological ET rate constant and the porph5rin coverage (b) are responsible for the maximum on the flux of electron injection obtained from IMPS responses for DFcET and Fc (c). The potential dependence of the back electron-transfer rate constant is also shown in (d). (From Ref. 83. Reproduced by permission of The Royal Society of Chemistry.)... 

The appearance of capacitive or inductive impedance depends essentially on the value of the rate constants. Low frequency loops, in a general case, are all very sensitive to the pH of the electrolyte. The different time constants are attributed to the relaxation of surface coverage by a corresponding number of reaction Intermediates. 

From this equation it is obvious that while the rate constant, k, generally does not depend on the coverage, the sticking coefficient must depend on the coverage. The value usually reported for the sticking coefficient is the initial sticking coefficient Oo corresponding to 00. 

In some cases experimental data indicate that the Arrhenius expression for the rate constant (Eq. 11.107) is modified by the coverage (concentration) of some surface species. Many functional forms for such coverage-dependence are possible. We describe one such choice that allows both the pre-exponential factor and the activation energy to be functions of the surface coverage of any surface species. The general modification of the Arrhenius rate expression is... 

Equations similar to eqns. (5), (6) and (8) were obtained by Zhdanov [104] to describe the monomolecular adsorption and associative desorption and Eley-Rideal s bimolecular reaction. He examined the dependence of the rate constants of these processes on the surface coverages and discussed various approximations applied previously to describe the effect of lateral interaction of adsorbed molecules on the desorption rate constant. He also considered the effect of the lateral interaction on the pre-exponential factor of the rate constants for various processes, and in terms of the "precursor state model, the effect of ordering the adsorbed molecules on the sticking coefficient and the rate constant of monomolecular desorption. 

The rate constants kx and k for CO and 02 adsorption, respectively, are determined by the respective initial sticking coefficients (i.e., at zero coverage). The coverage dependence of CO adsorption follows a precursor kinetics that can be modeled by the exponent r [being between 3 and 4 for Pt(110) (22)]. The kinetics of oxygen adsorption is modeled by the requirement for two neighboring empty adsorption sites, which can be occupied by either O or CO. We will return to this model later at various points. 

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