Turnover frequency/rate

Fig. 7. Turnover frequency (rate) TOF and atomic rate AR versus fraction exposed FE and mean particle size d for a selection of reactions and metal systems (see Table III for details of the studies).

Figure 1.3. Rate and catalyst potential response to step changes in applied current during C2H4 oxidation on Pt deposited on YSZ, an O2 conductor. T = 370°C, p02=4.6 kPa, Pc2H4=0.36 kPa. The catalytic rate increase, Ar, is 25 times larger than the rate before current application, r0, and 74000 times larger than the rate I/2F,16 of 02 supply to the catalyst. N0 is the Pt catalyst surface area, in mol Pt, and TOF is the catalytic turnover frequency (mol O reacting per surface Pt mol per s). Reprinted with permission from Academic Press.

Figure 2.3. Catalysis (0), classical promotion ( ), electrochemical promotion ( , ) and electrochemical promotion of a classically promoted (sodium doped) ( , ) Rh catalyst deposited on YSZ during NO reduction by CO in presence of gaseous 02.14 The Figure shows the temperature dependence of the catalytic rates and turnover frequencies of C02 (a) and N2 (b) formation under open-circuit (o.c.) conditions and upon application (via a potentiostat) of catalyst potential values, UWr, of+1 and -IV. Reprinted with permission from Elsevier Science.

Figure 8.20. Effect of p02 (a) and pC3H6 (b) on the rate and turnover frequency of propylene oxidation on Pt/YSZ.28 Reprinted with permission from Academic Press.

Figure 8.65. Dependence of the catalytic rates and turnover frequencies of C02 on the reaction temperature and on the catalyst potential for the initially sodium free Rh/YSZ catalyst (labeled C2) during NO reduction by CO in presence of gaseous 02. Reprinted with permission from Elsevier Science.

Figure 9.35. Transient effect of applied negative current on the rate and turnover frequency of C2H4 oxidation on Pt/CaZro,9Ino ]03.a (solid curve) and on catalyst potential (dashed curve).45 Reprinted with permission from the Institute of Ionics.

The propane aromatization was conducted under the differential condition by using Ga203/Ga-MOR catalysts thus characterized. The contributions of L, HI, and H2 sites to the propane conversion and the aromatics formation were estimated by assuming that the observed reaction rates are the sum of the reaction rate on each site which is equal to the product of the turnover frequency (TFij) and the amount of active sites per weight of catalyst (Aj) ... 

Before deriving the rate equations, we first need to think about the dimensions of the rates. As heterogeneous catalysis involves reactants and products in the three-dimensional space of gases or liquids, but with intermediates on a two-dimensional surface we cannot simply use concentrations as in the case of uncatalyzed reactions. Our choice throughout this book will be to express the macroscopic rate of a catalytic reaction in moles per unit of time. In addition, we will use the microscopic concept of turnover frequency, defined as the number of molecules converted per active site and per unit of time. The macroscopic rate can be seen as a characteristic activity per weight or per volume unit of catalyst in all its complexity with regard to shape, composition, etc., whereas the turnover frequency is a measure of the intrinsic activity of a catalytic site. 

For each step there is a corresponding rate (for convenience we drop the total number of sites from the expressions, i.e. r becomes a rate per site, or a turnover frequency) ... 

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. 

It is now assumed that each active site consists of four Pt atoms and the reactivity of 1 g of catalyst is tested under conditions where the rate is first order in oxygen concentration. The flow over the reactor is set to 100 mL min with 21% oxygen, the temperature 500 K, the pressure to 1 bar, and the TOE (turnover frequency per site) per Pt site under the chosen conditions is known from surface science experiments to be 0.001 s . The amount of oxygen converted is considered negligible. 

Methanatlon Studies. Because the most effective way to determine the existence of true bimetallic clusters having mixed metal surface sites Is to use a demanding catalytic reaction as a surface probe, the rate of the CO methanatlon reaction was studied over each series of supported bimetallic clusters. Turnover frequencies for methane formation are shown In Fig. 2. Pt, Ir and Rh are all poor CO methanatlon catalysts In comparison with Ru which Is, of course, an excellent methanatlon catalyst. Pt and Ir are completely inactive for methanatlon In the 493-498K temperature range, while Rh shows only moderate activity. 

Fig. 7 Dependence of IR band intensities on H2 partial pressure during ethene hydrogenation catalyzed by Ir4/y-Al203 at 288 K and 760 Torr (40 Torr C2H4, 50-300 Torr H2, and the balance He). The bands at 2990 (diamonds) and 2981 cnr (squares) were chosen to represent di-cr-bonded ethene and that at 1635 cnr (circles) to represent water on the y-AbOs support. These IR bands were chosen as the best ones to minimize error caused by overlap with other bands. The triangles represent the reaction rate expressed as a turnover frequency (TOF), the rate of reaction in units of molecules of ethene converted per Ir atom per second. The data indicate a correlation of the band intensities with the TOF, consistent with the suggestion that the ligands represented by the bands are reaction intermediates (but the data are not sufficient to identify the reaction intermediates) [39]...

Attempts to determine how the activity of the catalyst (or the selectivity which is, in a rough approximation, the ratio of reaction rates) depends upon the metal particle size have been undertaken for many decades. In 1962, one of the most important figures in catalysis research, M. Boudart, proposed a definition for structure sensitivity [4,5]. A heterogeneously catalyzed reaction is considered to be structure sensitive if its rate, referred to the number of active sites and, thus, expressed as turnover-frequency (TOF), depends on the particle size of the active component or a specific crystallographic orientation of the exposed catalyst surface. Boudart later expanded this model proposing that structure sensitivity is related to the number of (metal surface) atoms to which a crucial reaction intermediate is bound [6]. 

The low limit on the rate constant fehetero of 0-0 bond heterolysis in the putative ferric-hydroperoxo intermediate by analyzing the turnover frequency of H2O2 reduction at potentials 0.6-0.4 V (vs. NHE at pH 7). 

Table 20.2. Initial rates and turnover frequencies observed in the hydrogenation of 1-...

Figure 3.9. Transient C02 formation rates on Pd30 (a) and Pd8 (b) mass-selected clusters deposited on a MgO(lOO) film at different reaction temperatures [74]. In these experiments CO was dosed from the gas background while NO was dosed via a pulsed nozzle molecular beam source. The turnover frequencies (TOFs) calculated from the experiments displayed in (a) and (b) are displayed in the last panel (c). C02 formation starts at lower temperatures but reaches lower maximum rates on the larger cluster. (Figure provided by Professor Heiz and reproduced with permission from Elsevier, Copyright 2005).

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