Adsorption reactions, turnover rate

The results of adsorption and desorption of CO mentioned above suggest that for the reaction at low temperature, the sites for relatively weakly chemisorbed CO are covered by the deposited carbon and the reaction occurs between molecularly adsorbed CO and oxygen on the carbon-free sites which are the sites for relatively strongly chemisorbed CO. Therefore, the definition of the turnover rate at 445 K remains as given in Equation 1. For the reaction at 518 K, however, this definition becomes inappropriate for the smaller particles. Indeed, to obtain the total number of Pd sites available for reaction, we now need to take into consideration the number Trp of CO molecules under the desorption peak. Furthermore, let us assume that disproportionation of CO takes place through reaction between two CO molecules adsorbed on two adjacent sites, and let us also assume that the coverage is unity for the CO molecules responsible for the LT desorption peak, since this was found to be approximately correct on 1.5 nm Pd on 1012 a-A O (1). Then, the number Np of palladium sites available for reaction at 518 K is given by HT/0 + NC0 LT s nce t ie co molecules under the LT desorption peak count only half of the available sites. Consequently, the turnover rate at 518 K should be defined as ... 

One further example of a structural study of CO adsorption on Ni relates to the rather general issue of the role of coadsorbed CO and alkali metals on metal surfaces. Alkali atoms are known to be promoters of certain catalytic processes, improving turnover rates and/or selectivity in certain reactions, and are used as additives in some commercial catalysts. Indeed, in the specific case of CO on Ni, it... 

As the adsorption reactions (14,16,...) are fast, the turnover rate constant, fct, of the overall process is almost the same as the rate constant of electron transfer reactions (15,17,...). Again, the concentration increases during the reduction (reaction 12), with the consequence of a positive shift for °(q --QH2). However, °(Ag + i-Agn +i) also increases with n, and the autocalytic transfer continues up to the Ag" exhaustion. 

CO oxidation is often quoted as a structure-insensitive reaction, implying that the turnover frequency on a certain metal is the same for every type of site, or for every crystallographic surface plane. Figure 10.7 shows that the rates on Rh(lll) and Rh(llO) are indeed similar on the low-temperature side of the maximum, but that they differ at higher temperatures. This is because on the low-temperature side the surface is mainly covered by CO. Hence the rate at which the reaction produces CO2 becomes determined by the probability that CO desorbs to release sites for the oxygen. As the heats of adsorption of CO on the two surfaces are very similar, the resulting rates for CO oxidation are very similar for the two surfaces. However, at temperatures where the CO adsorption-desorption equilibrium lies more towards the gas phase, the surface reaction between O and CO determines the rate, and here the two rhodium surfaces show a difference (Fig. 10.7). The apparent structure insensitivity of the CO oxidation appears to be a coincidence that is not necessarily caused by equality of sites or ensembles thereof on the different surfaces. 

Figure 53 shows relative rates of C02 formation under steady-state conditions that were recorded with various single-crystal surfaces of Pd as well as with a polycrystalline Pd wire (173). It must be noted that with these experiments no determination of the effective surface areas was performed so that no absolute turnover numbers per cm2 are obtained. Instead, the reaction rates were normalized to their respective maximum values. As can be seen from Fig. 53, all data points are close to a common line which indicates that, in fact, with this reaction the activity is influenced very little by the surface structure. As has been outlined in Section II, the adsorption of CO exhibits essentially quite similar behavior on single-crystal planes with varying orientation. Since the adsorption-desorption equilibrium of CO forms an important step in the overall kinetics of steady-state C02 formation, this effect forms at least a qualitative basis on which the structural insensitivity may be made plausible. 

According to the International Union of Pure and Applied Chemistry (IUPAC O)) the turnover frequency of a catalytic reac tion is defined as the number of molecules reacting per active site in unit time. The term active sites is applied to those sites for adsorption which are effective sites for a particular heterogeneous catalytic reaction. Because it is often impossible to measure the amount of active sites, some indirect method is needed to express the rate data in terms of turnover frequencies In some cases a realistic measure of the number of active sites may be the number of molecules of some compound that can be adsorbed on the catalyst. This measure is frequently used in the literature of the Fischer-Tropsch synthesis, where the amount of adsorption sites is determined by carbon monoxide adsorption on the reduced catalyst. However, it is questionable whether the number of adsorption sites on the reduced catalyst is really an indication of the number of sites on the catalyst active during the synthesis, because the metallic phase of the Fischer-Tropsch catalysts is often carbided or oxidized during the process. 

Applying the Broensted Polanyi correlations is sometimes useful for describing the dependence of the reaction rate on the size of the catalyti caUy active component. A huge amount of experimental data have been compiled to date regarding the effect of the particle size of the catalyst active components on the specific catalytic activity, SCA, as well as on the turnover frequency, TOP, of the active center. Both parameters do not relate to the total surface area of the catalyticaUy active phase or to the total number of active centers and, therefore, characterize directly the properties of the active center. There are also some experimental data on the size dependence of the adsorption properties of small metal parti cles, as well as on the selectivity of a few catalytic processes. 

The break-point temperature in dehydration (above which the rate was temperature insensitive) matched the maximum temperature for dehydrogenation, suggesting that a common intermediate exists for each reaction, and that the product selectivity is determined by interactions with other molecules and the surface. Above 650 K, the catalytic dehydration channel dominates, but the rate-determining step changes above 700 K. Below 700 K, the reaction rate is nearly independent of the partial pressure of formic acid (ca. 0.2 order). Above 700 K, the rate of the reaction is essentially independent of temperature, implying that reaction is limited by formic acid adsorption and dissociation thus, above 700 K, the rate becomes first-order with respect to the partial pressure of formic acid. Higher pressures of formic acid over the crystal surface should therefore increase the transition temperature - this behavior was observed by Iwasawa and coworkers, and the turnover frequency for catalytic dehydration approached the collision frequency of formic acid at high... 

Reuter, Frenkel, and Scheffler have recently used DFT-based calculations to predict the CO turnover frequency on RuO2(110) as a function of 02 pressure, CO pressure, and temperature.31 This was an ambitious undertaking, and as we will see below, remarkably successful. Much of this work was motivated by the earlier success of ab initio thermodynamics, a topic that is reviewed more fully below in section 3.1. The goal of Reuter et al. s work was to derive a lattice model for adsorption, dissociation, surface diffusion, surface reaction, and desorption on defect-free Ru02(l 10) in which the rates of each elementary step were calculated from DFT via transition state theory (TST). As mentioned above, experimental evidence strongly indicates that surface defects do not play a dominant role in this system, so neglecting them entirely is a reasonable approach. The DFT calculations were performed using a GGA full-potential... 

The rate of reaction expressed as molecules reacted (or formed) per unit time per catalytic site (or per exposed atom of active metal for metal catalysts) is called the turnover frequency. For supported metal catalysts the calculation requires knowledge of the dispersion, i.e., the fraction of the active metal available for adsorption of reactants. Boudart coined the term demanding (structure-sensitive) for catalyzed reactions for which the turnover frequency varies with the dispersion. Related to this is the ensemble effect, where the active site requires a specific multiatom grouping.f ... 

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