Activity apparent turnover frequency

Carbon monoxide oxidation is a relatively simple reaction, and generally its structurally insensitive nature makes it an ideal model of heterogeneous catalytic reactions. Each of the important mechanistic steps of this reaction, such as reactant adsorption and desorption, surface reaction, and desorption of products, has been studied extensively using modem surface-science techniques.17 The structure insensitivity of this reaction is illustrated in Figure 10.4. Here, carbon dioxide turnover frequencies over Rh(l 11) and Rh(100) surfaces are compared with supported Rh catalysts.3 As with CO hydrogenation on nickel, it is readily apparent that, not only does the choice of surface plane matters, but also the size of the active species.18-21 Studies of this system also indicated that, under the reaction conditions of Figure 10.4, the rhodium surface was covered with CO. This means that the reaction is limited by the desorption of carbon monoxide and the adsorption of oxygen. 

The turnover frequency under these conditions is rather low (<20 mol mol-1 h-1) but the kinetic results, in return, are highly accurate. The minus one order in CO and the plus one order in H2 agree very well with the results from Marko [20]. The rate of hydroformylation was proportional to the concentration of the acyl complex. The apparent activation parameters were AH = 49.3 kj/mol and AS = 121 J/mol K. The activation parameters and the reaction order are consistent with reaction 6 and 7 as being rate determining. A low order of 0.1 in alkene was found, which indicates that the rate-determining step is not purely reaction 7 and that either a pre-equilibrium contributes as well or that one of the earlier steps in the cycle is also somewhat slower. 

It was mentioned previously that the rate of a heterogeneously catalyzed reaction is expressed as a turnover frequency (TOF) which is the number of times an active site reacts per unit time. Since active site concentrations have not been available, in most cases the TOF is expressed as the number of molecules formed per unit time per surface atom or unit surface area. The ability to use the STO procedure to measure active site densities also provides a means of determining specific site TOFs. It is apparent that the total number of molecules formed in a catalytic reaction per unit time is the sum of the production from each active site. Thus, the reaction TOF can be expressed as the sum of the products of the specific site TOF and the specific site densities as shown in Eqn. 3.6.21... 

Table V collects values for the activation energies of isomerization and protonation as deduced by De Gauw and van Santen [138] from kinetic measurements. A comparison of the turnover frequency per proton (TOF) and / iso is made in Table V. One notes that the large differences in measured overall TOFs of different zeolites disappear for the elementary rate constant fciso. This implies that the difference in apparent acidity of the zeolite is due mainly to the difference in adsorption isotherms of the different zeolites. One notes the small variation in activation and protonation energy values, which implies a slight dependence of protonation on the micropore channel size and dimension.

The effect of Si substitution on the turnover frequency for WGS is shown in Figure 11. The turnover frequencies plotted in this figure were based on the magnetite surface area as determined by the NO chemisorption technique. The turnover frequencies shown for unsupported Fe O indicate that the factor of 10 decline in activity for the silica-supported catalysts is not a particle size effect, but instead is a consequence of the substitution of Si into the lattice. However, when the adsorption of CO/COo at 663 K was used to titrate the surface sites instead of NO, the resulting turnover frequencies were essentially constant as shown in Figure 12. Accordingly, the CO/CO2 mixture apparently titrates the sites active for WGS. Clearly, the number of active sites is decreased markedly as the particle size decreases in the silica-substituted magnetite catalysts. 

Note that this is the reaction rate or activity. However, this definition takes into account the reaction medium, be it volume, surface, or interface, and not exactly the active sites. Not all mass or surface is active, but part of its outer surface has active sites, which are truly the sites where the chemical reaction occurs. Therefore, rj in fact represents the apparent rate. An important example of reaction that allows to differentiate the apparent from the true rate is the hydrogenation of carbon monoxide to form methane, which is conducted with different catalysts. With iron and cobalt catalysts, the rate per unit of mass of catalyst, used as reference, has shown controversial values. The activity of the catalysts in the Fischer-Tropsch synthesis to form hydrocarbons would decrease according to the order Fe > Co > Ni. However, when the rate per active site was defined, the order of activity was different, i.e., Co > Fe > Ni. This controversy was resolved by Boudart, who defined the intrinsic activity, i.e., the rate per active site. To make it more clear, the turnover frequency (TOF) was defined. Thus, the intrinsic activity is determined, knowing the active sites, i.e. ... 

Ethylene hydrogenation appears to be relatively structure insensitive. The (100) surface has an increase in the surface coverage of about 10% over the (111) surface. This acts to lower the barriers for both the first and second hydrogen addition steps. The reverse path of ethyl reacting back to form ethylene is also increased, thereby countering some of the increased activity. The apparent activation barriers on the (111) and (100) surfaces are 7.1 and 6.5 kcal/mol respectively. There is also little change in the turnover frequency. 

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