Rate per 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) ... 

Boudart (223) suggested that all reactions might not be equally sensitive to the geometric arrangements in various metal surfaces or to the differences in the electronic structure of sites in different geometric environments (coordination). Boudart divided the reactions into two groups (I) structure insensitive and (II) structure sensitive. The operational criterion of structure sensitivity is the specific activity (the rate per unit surface area) or, the turnover numbers (TONs) (the rate per site) TONs should differ by more than a factor of 5-10 when the dispersion D is varied sufficiently. Bond (224) formulated similar ideas and also suggested several reasons why the variations of TONs with D can monotonically decrease (antipathic), mono-tonically increase (sympathetic), or show a maximum. 

The sum of inlet molecular flow rates per site for a flow reactor, (FT), is equal to the reciprocal of the site time, l/rp, which may be defined as the overall inlet site velocity, //. ... 

All the binary Cu/ZnO catalysts were found highly selective toward methanol without DME, methane, or higher alcohols and hydrocarbons detected in the product by sensitive gas chromatographic methods (59). Several of the composites were also found to be very active when subjected to a standard test with synthesis gas C0/C02/H2 = 24/6/70 at gas hourly space velocity of 5000 hr- pressure 75 atm, and temperature 250°C. The activities, expressed as carbon conversions and yields, are summarized in Table VIII. The end members of the series, pure copper and pure zinc oxide, were inactive under these testing conditions, and maximum activity was obtained for the composition Cu/ZnO = 30/70. The yields per unit weight, per unit area of the catalyst or the individual components, turnover rates per site titratable by irreversible oxygen and by irreversible carbon monoxide, are graphically... 

Within this model all mutation rates can be expressed in terms of only three quantities the chain length of the polymer, X, the single-digit accuracy of replication, q, often expressed as mutation rate per site and replication, p = 1 - q, and the Hamming distance, d(Ij,Ii). Finally, the (dependent) parameter, s = (1 - q)/q is the ratio between single digit mutation rate and accuracy. 

Solving Eq. (6) with explicit expressions for the O2 and CsHg adsorption rates makes it possible to calculate the reaction rate, which is identified below with the O2 adsorption rate per site, i.e., JV = Wq. In particular. Figure 5 shows the reaction rates for the (111) and (100) surfaces. Using these rates and assuming the (111) and (100) facets to operate independently, one can obtain the reaction rate for a catalyst particle with noncommunicating facets. This approach yields (Fig. 6)... 

It is emphasized that each method of measuring active-site density has limitations, and some common techniques are actually invalid. For example, counting the number of chains formed provides no useful information, because Cr/silica is not a living system under industrial conditions and therefore each site produces many chains each second. Nor can kinetics be used in a stand-alone way, because the measured activity is always the product of the number of sites times the rate per site, both of which are unknown. Poisoning experiments give an upper bound. Below is a discussion in more detail of those techniques that the author believes provide most insight into the commercial catalyst. 

Scharifker, B.R. and Mostany, J. (1984) Three-dimensional nucleation with diffusion controlled growth part I. Number density of active sites and nucleation rates per site. Journal of Eiectroanaiyticai Chemistry, 177, 13-23. 

The rate per site or turnover frequency was calculated based on the rate of benzene formation at 373 K and the number of surface sites after CO chemisorption, as presented in Table 3.4. Results show that the turnover frequency (TOF) changed with the different carbon supports. 

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