Turnover frequency defined

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. 

Figure 1.25 exemplifies the strucmres of certain efficient precatalysts for asymmetric transfer hydrogenation of ketones. Precatalysts C1-C3 use the NH effect described above. A turnover frequency, defined as moles of product per mol of catalyst per hour, of 30,000 h is achieved by using of C2 and an alkaline base in 2-propanol. A Rh complex C3 is an isolobal to the corresponding arene-Ru complex (see Figure 1.23). The Ru complexes C4 " and C5 without NH group in ligand catalyze the reaction by different mechanisms. A higher than 90% optical yield is achieved by using C5 in reduction of certain aliphatic ketones.

For the sake of consistency and convenience, rates to products quoted throughout this review are given in terms of turnover frequency, defined here as the number of moles of product formed per gram-atom of metal per hour. This provides units of reciprocal hours, rather than the more commonly accepted reciprocal seconds. For the reactions described here, however, use of the former units affords numbers of a magnitude convenient for ready comprehension and comparison. 

Figure 5 compares the activity of the silica-supported SAC-13 with unsupported Nafion particles. Both catalysts show similar product selectivity at identical conditions. As expected, the butene turnover frequency, defined as the butene conversion rate per acid site, is enhanced fourfold when using the supported catalyst. Similar enhancements on supported Nafion have been reported for other reactions as well [10,11,24]. Since hydrated Nafion can conduct protons, acid sites that are hidden within the polymer may not be available for reaction, but may still be measured by the aqueous titration method. 

The simplest scenario to simulate is a homopolymerization during which the monomer concentration is held constant. We assume a constant reaction volume in order to simplify the system of equations. Conversion of monomer to polymer, Xp defined as the mass ratio of polymer to free monomer, is used as an independent variable. Use of this variable simplifies the model by combining several variables, such as catalyst load, turnover frequency, and degradation rate, into a single value. Also, by using conversion instead of time as an independent variable, the model only requires three dimensionless kinetics parameters. 

Another important feature of GAs is that they are tunable. This means that we can define the algorithm s fitness function to reflect the actual requirements from the catalyst. An optimal catalyst exhibits high activity, high stability, and high selectivity. These three figures of merit are directly related to the product yield, the turnover number (TON) and the turnover frequency (TOF), respectively. Often, however, an increase in one comes at the expense of another. Using GAs you can... 

This rate is usually referred to as the turnover frequency and it is the number of molecules reacting per active site per unit time at the conditions of the experiment (Boudart, 1985 McNaught and Wilkinson, 1997 Fogler, 1999). Boudart (1995) used the term turnover frequency to define the number of revolutions of the catalytic cycle per unit time and active site. In each revolution, one mole of reactant is consumed. For example, the revolution of a catalytic cycle for S02 oxidation is shown in Figure 3.1. 

Frequently, the number of active sites is expressed in mole units (the number of active sites divided by the Avogadro number) and thus, turnover frequency is found in s"1 units. For a specific reaction, the turnover frequency depends on the nature of the catalytic active site, the temperature, and the reactants concentration. The above-defined catalytic rate could be described as an active-site level rate. 

The turnover frequency, N, (commonly called the turnover number) defined, as in enzyme catalysis, as molecules reacting per active site in unit time, can be a useful concept if employed with care. In view of the problems in measuring the number of active sites discussed in 1.2.4, it is important to specify exactly the means used to express Q in terms of active sites. A realistic measure of such sites may be the number of surface metal atoms on a supported catalyst but in other cases estimation on the basis of a BET surface area may be the only readily available method. Of course, turnover numbers (like rates) must be reported at specified conditions of temperature, initial concentration or initial partial pressures, and extent of reaction. 

Finally, it is beneficial at this point to define two terms which will be widely alluded to in future discussions, namely, turnover frequency (TOF) and polydisper-sity. TOF is the moles of epoxide consumed per mole catalyst per hour. Because these copolymerization processes occur on a rather slow timescale, TOFs are usually expressed in units of h 1. Polydispersity is also referred to as a molecular weight distribution and is defined as Mw / Mn, where Mw is the weight average molecular... 

A mass-independent quantity of activity, superior to specific activity, is the turnover frequency (tof), defined as ... 

The catalyst turnover number (TON) and the turnover frequency (TOF) are two important quantities used for comparing catalyst efficiency. Their definitions, however, vary slightly among the three catalysis fields. In homogeneous catalysis, the TON is the number of cycles that a catalyst can run through before it deactivates, i.e., the number of A molecules that one molecule of catalyst can convert (or turn over ) into B molecules. The TOF is simply TON/time, i.e., the number of A molecules that one molecule of catalyst can convert into B molecules in one second, minute, or hour. In heterogeneous catalysis, TON and TOF are often defined per active site, or per gram catalyst. This is because one does not know exactly how many... 

The turnover frequency (TOF) is defined as the number of molecules CP that is converted per Pt surface atom per second. The number of accessible Pt surface atoms is based on the total amount of hydrogen chemisorbed. Orders in CP and D2 were determined by varying the applicable partial pressures while the total flow was kept constant. 

Additionally, the rate referred to the number of catalytic sites is known as the turnover rate, vt, or turnover frequency (TOF) [94], The TOF is defined as the number of molecules reacting per active site in unit time, that is, it is the number of revolutions of a catalytic cycle per unit time [95]... 

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. 

The turnover frequency, N, (the term turnover number is discouraged) is defined as the number of molecules reacting per active site in unit time. It is necessary to specify the method used to estimate the number of active sites. Usually, the number of active sites will be assumed to be equivalent to the number of surface atoms, derived, in the case of metals, for example, from measurements of the chemisorption of a specified adsorptive. 

CO to give the engineering thermoplastic polyketone, Carilon [45, 46]. Indeed, when a well-defined complex was used (Fig. 7.12), exceptionally high activities were observed [46], with turnover frequencies (TOFs) higher than the conventional catalyst in methanol as solvent. 

Activity, selectivity, and yield are key catalyst performance characteristics. The recommended measure of catalyst activity is turnover frequency. Turnover frequency (or rate) is defined as the number of molecules that react per active site per unit time. Activity can also be defined as (1) the reaction rate per unit mass or volume of the catalyst, (2) the space velocity at which a given conversion is achieved at a specified temperature, (3) the temperature required to achieve a given conversion level, or (4) the conversion achieved under specified reaction conditions. Alternative 2 is practical for catalyst ranking. Alternatives 3 and 4 are rather uninformative. For rapid catalyst screening the latter two criteria are acceptable, but no catalyst should be eliminated from further consideration if it is only marginally inferior based on these criteria. 

Catalytic activity is generally measured in terms of turnovers. Thus the Turnover Number, TON, is the number of times the catalytic reaction occurs per active site, while the Turnover Frequency (TOF) is the TON per unit of time. The TON is easily understood for defined reactions where the number of active sites is known homogeneous catalyses that occur at clearly understood metal centres, enzymatic catalysts or some heterogeneous catalysts whose active sites are easily determined. If the number of active sites on a heterogeneous catalyst is not easily determined, then that number is often replaced by the total surface area of the catalyst. In industry TOF is sometimes measured as grams of product produced per gram catalyst per hour, as this gives a useful measure of the catalyst cost. 

The reason for measuring the number of exposed metal atoms in a catalyst is that it allows reaction rates to be normalized to the amount of active component. As defined in Chapter 1, the rate expressed per active site is known as the turnover frequency, Tf Since the turnover frequency is based on the number of active sites, it should not depend on how much metal is loaded into a reactor or how much metal is loaded onto a support. Indeed, the use of turnover frequency has made possible the comparison of rates measured on different catalysts in different laboratories throughout the world. 

The intrinsic rate at which a catalytic cycle turns over on an active site is called the turnover frequency, r of a catalytic reaction and is defined as in Chapter 1 [Equation (1.3.9)] as ... 

A parameter, Aq, was defined as the relative change in electron density on nickel resulting from electron transfer between nickel and the second element as compared with that on nickel black. Table 12.2 shows the Aq values for these different nickel catalysts. 29 That for the P-1 nickel boride25 is the most negative and that for the NiP-1 nickel phosphide is the most positive. In Fig. 12.5 is shown the relationship between the areal turnover frequencies for the hydrogenation of styrene over these catalysts and their Aq values. 29 These data... 

The Turnover Frequency (TOP) is often defined as the nurnber of molecules reacting per second per site on the catalyst. Since the number of reaction sites on the catalysts was not known, the Pseudo Turnover Frequency (PTOF), the number of reactions per unit time per unit surface area, PTOF, was used in Figures 2 to 7. 

In order to normalize the polarization measurements with respect to the Ir02 loading, we have defined the turnover frequency (TOE), as given by relation (6) ... 

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