Abstract
Analysis of apparent activation energy is presented for different heterogeneous catalytic reactions with parallel reaction routes. In the case of kinetic coupling between catalytic cycles the activation energy in a particular route depends not only on the activation energies of the elementary steps comprising this route, but also on the frequency of the steps in a parallel route. Expressions were derived for coupling between routes through irreversible adsorption of the substrate, quasi-equilibrated binding as well as different substrate adsorption modes. Theoretical analysis of the apparent activation energy was extended for the reaction network with two routes possessing mechanistically different rate determining steps (i.e. monomolecular vs bimolecular). For structure sensitive reactions an expression for the apparent activation energy for parallel reactions was developed for cases with a continuous distribution of active centers and a cubo-octahedral representation of the metal clusters. A comparison between the theoretical analysis and experimental data on transformations of furfural to furfuryl alcohol and furan on ruthenium clusters shows applicability of the developed theoretical framework.Graphic
Highlights
There was a renewed interest in a theoretical interpretation of apparent activation energy for a single route multi-step reactions, comprising several elementary steps1 3 Vol.:(0123456789)D
In [5] analysis of the apparent activation energy was done for the two step sequence [7, 8] on uniform and nonuniform surfaces [9] as well as for the Langmuir–Hinshelwood mechanism, with the main focus on structure sensitivity [10, 11], e.g. dependence of the rate constants on the cluster size
The physical meaning of Eq (12), which was reported in the literature long time ago [1, 16, 17], is that the apparent activation energy of a two-step sequence can be interpreted as an additive value of the activation energies of steps with the weight factors, which are equal to coverages of intermediates, including the dimensionless concentration of non-occupied active sites [1]
Summary
There was a renewed interest in a theoretical interpretation of apparent activation energy for a single route multi-step reactions, comprising several elementary steps. In [5] analysis of the apparent activation energy was done for the two step sequence [7, 8] on uniform and nonuniform surfaces [9] as well as for the Langmuir–Hinshelwood mechanism, with the main focus on structure sensitivity [10, 11], e.g. dependence of the rate constants on the cluster size. For two first order independent parallel irreversible reactions with the rate constants k+1 and k+2 , the overall activation energy Ea,app is the weighted sum of the individual ones, that is E+1 and E+2 [12]. The main focus was on analyzing the apparent activation energy for several reaction mechanisms typical for heterogeneous catalysis, where the parallel routes are coupled in different ways. The physical meaning of Eq (12), which was reported in the literature long time ago [1, 16, 17], is that the apparent activation energy of a two-step sequence can be interpreted as an additive value of the activation energies of steps with the weight factors, which are equal to coverages (dimensionless concentrations) of intermediates, including the dimensionless concentration of non-occupied active sites [1]
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