Elementary surface

Finally, we will apply transition state theory and collision theory to some elementary surface reactions that are important in catalysis. 

By applying the machinery of statistical thermodynamics we have derived expressions for the adsorption, reaction, and desorption of molecules on and from a surface. The rate constants can in each case be described as a ratio between partition functions of the transition state and the reactants. Below, we summarize the most important results for elementary surface reactions. In principle, all the important constants involved (prefactors and activation energies) can be calculated from the partitions functions. These are, however, not easily obtainable and, where possible, experimentally determined values are used. 

Temperature-programmed reaction spectroscopy offers a straightforward way to monitor the kinetics of elementary surface reactions, provided that the desorption itself is not rate limiting. Figure 7.14 shows the the reaction CO -f O CO2 + 2. ... 

Figure 7.14. The temperature-programmed reaction and corresponding Arrhenius plot based on rate expression (21) enables the calculation of kinetic parameters for the elementary surface reaction between CO and O atoms on a Rh(lOO) surface.

Give at least two reasons why it is important to know the kinetic parameters of elementary surface reactions in catalytic mechanisms. 

Fig. 1.5. (a) Flux through elementary surface, (b) flux as a sum of elementary fluxes, (c) field components due to spherical mass, (d) symmetry of held, (e) the held inside and outside spherical mass. 

Now we establish the second remarkable feature of the attraction field. As before, at the beginning consider the field of a point mass, m(q). By definition, the flux of the field through an elementary surface dS, Fig. 1.5a, is... 

The behavior of g as a function of R is shown in Fig. 1.12c, and, of course, it is a continuous function. Now let us mentally decrease the thickness h and increase the volume density so that the mass remains the same. In such a way we arrive at a distribution of masses with a surface density, and this replacement does not change the field outside the shell, but it leads to a discontinuity of the field at the surface masses. It is instructive to demonstrate why the field inside the shell, R[Pg.46]

Here a is the normal stress equal to the ratio of the force F to the elementary surface dS, provided that this force has only the component normal to dS ... 

The results of these experiments also confirm the conclusions made in the above paper dealing with the mechanism of aggregation. These conditions were based on the data obtained using the method of semiconductor sensors. However, the technique used in [42] was seemingly more sensitive, because it enabled observation of elementary surface processes, such as the appearance of centres of condensation of metal atoms on atomic scale. 

When the absorption and emission transition moments are parallel, 6a = 6e, the common value being denoted 6 hence cos2 6a = cos2 0E = cos2 6. Before excitation, the number of molecules whose transition moment is oriented within angles 6 and 8 + dd, and and 0 I d (Figure 5.6). 

Liquid phase hydrogenation catalyzed by Pd/C is a heterogeneous reaction occurring at the interface between the solid catalyst and the liquid. In our one-pot process, the hydrogenation was initiated after aldehyde A and the Schiff s base reached equilibrium conditions (A B). There are three catalytic reactions A => D, B => C, and C => E, that occur simultaneously on the catalyst surface. Selectivity and catalytic activity are influenced by the ability to transfer reactants to the active sites and the optimum hydrogen-to-reactant surface coverage. The Langmuir-Hinshelwood kinetic approach is coupled with the quasi-equilibrium and the two-step cycle concepts to model the reaction scheme (1,2,3). Both A and B are adsorbed initially on the surface of the catalyst. Expressions for the elementary surface reactions may be written as follows ... 

Handling the experimental data for the temperature range of 470-700°C, we used theoretical expressions for preexponential factors from the theory of absolute rates of surface reactions (Section IV), assuming the elementary surface reactions under consideration to be adiabatic, and also the known K values. Computer calculations were performed by the method of minimization of the sum of the squares of relative deviations of calculated reaction rates from experimental values. 

The more recent theories of chemical conversions [59-61] take into account the fact that the process of overcoming the activation barrier involves a cooperative change of more than one degree of freedom for the starting reagents subsystem. For the surface processes this is expected to lead to a need for considering the dynamics of the solid atom motion and, at least, the model should include information on Debye frequencies for its atoms (see, e.g., Ref. [62]). An additional inconvenience of the models for the elementary surface processes is associated with the fact that the frequencies of the surface atom oscillations differ from those inside the solid. Consideration of the multiphonon contributions to the probabilities that the elementary process can take place results in a significant modification of its rate constant up to the complete disappearance of the activation form of the temperature dependence [63,64]. 

In Section 1 the rates calculating of the elementary surface processes an assumption on the equilibrium distribution of the reagents over the entire surface of the solid body or in the local macroregion was used. Such an assumption is not always true and the theory of surface processes must reflect the possibility of the existence of a wide spectrum of reagent mobilities. Now, the lattice-gas model is used for describing of the systems which have no equilibrium distribution of their components, i.e., 0[Pg.372]

In Eq. (3.67) the quantity pe is determined per unit volume when the observer is at rest. The amount of substance entering through an elementary surface area d. 1 per unit time is pv dA, where dA is a vector with magnitude d. I and pointing in a direction normal to the surface. Along with the substance flow there is a convection flow (p ve), and the amount transported per unit time is -f(pve) dA. The conduction flow Je is a vector with the same direction as the flow, and the amount transported per unit time by means of conduction without a flow of substance is -JJe-dA. 

The other examples of elementary surface reactions can be inspected the same way. Note that in the reaction between sorbates on the active phase sur face, the magnitudes of , and, as a consequence, traditional rate constants k and k may be considered in the first approximation as independent of r. 

Physical Chemistry of Elementary Surface Reaction Steps... 

PHYSICAL CHEMISTRY OF ELEMENTARY SURFACE REACTION STEPS... 

The activation energies of elementary surface reactions that proceed along the same reaction path on similar reaction sites are often found to be linearly related to the corresponding reaction energies, which depend on the nature of the metal. This parallel behavior is expressed in the BEP relationship (20,25), which we used earlier to construct Figure 2. The BEP relationship can be formulated as follows ... 

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