Surface reaction rate maxima

In Table 2, the relative steady-state surface concentration (with respect to the maximum steady-state concentration defined by the lowest surface reaction rate constant used in the study) as a function of surface reaction rate constant and pseudo-first-order rate constant for the bulk reaction is given. 

The maximum inaccuracy of the this formula does not exceed 5% for any value of the surface reaction rate constant Ks. 

The surface concentration can be calculated by the formulae s = C (1 -j/joo)-The results of numerical solution of appropriate integral equations for the surface concentration (derived in the diffusion boundary layer approximation) in the case of power-law surface reaction for n = 1 /2 and n = 2 was indicated in [133]. The maximum inaccuracy of formula (5.1.7) in these cases is about 10% for any value of the surface reaction rate constant. 

Catalyst Effectiveness. Even at steady-state, isothermal conditions, consideration must be given to the possible loss in catalyst activity resulting from gradients. The loss is usually calculated based on the effectiveness factor, which is the diffusion-limited reaction rate within catalyst pores divided by the reaction rate at catalyst surface conditions (50). The effectiveness factor E, in turn, is related to the Thiele modulus,

first-order rate constant, a the internal surface area, and the effective diffusivity. It is desirable for E to be as close as possible to its maximum value of unity. Various formulas have been developed for E, which are particularly usehil for analyzing reactors that are potentially subject to thermal instabilities, such as hot spots and temperature mnaways (1,48,51). 

In the A sector (lower right), the deposition is controlled by surface-reaction kinetics as the rate-limiting step. In the B sector (upper left), the deposition is controlled by the mass-transport process and the growth rate is related linearly to the partial pressure of the silicon reactant in the carrier gas. Transition from one rate-control regime to the other is not sharp, but involves a transition zone where both are significant. The presence of a maximum in the curves in Area B would indicate the onset of gas-phase precipitation, where the substrate has become starved and the deposition rate decreased. 

This equation gives (0) = 0, a maximum at =. /Km/K2, and (oo) = 0. The assumed mechanism involves a first-order surface reaction with inhibition of the reaction if a second substrate molecule is adsorbed. A similar functional form for (s) can be obtained by assuming a second-order, dual-site model. As in the case of gas-solid heterogeneous catalysis, it is not possible to verify reaction mechanisms simply by steady-state rate measurements. 

Thus, for an almost empty surface, the rate assumes its maximum ivith equal amounts of reactants, at the limit of zero conversion. Again, we need to assess the validity of the approximations under the conditions employed. Nevertheless, the above procedure for determining the reaction rate as a function of mole fraction can be quite useful in the exploration of reaction mechanisms. 

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. 

The reaction was studied for all coinage metal nanoparticles. In the case of GMEs the rate follows zero-order kinetics with IT for all the coinage metal cases. The observed IT for the Cu catalyzed reaction was maximum but its rate of reduction was found to be minimum. Just the reverse was the case for Au and an intermediate value was obtained for the Ag catalyzed reaction (Figure 7). The adsorption of substrates is driven by chemical interaction between the particle surface and the substrates. Here phe-nolate ions get adsorbed onto the particle surface when present in the aqueous medium. This caused a blue shift of the plasmon band. A strong nucleophile such as NaBH4, because of its diffusive nature and high electron injection capability, transfers electrons to the substrate via metal particles. This helps to overcome the kinetic barrier of the reaction. 

The parameter y reflects the sensitivity of the chemical reaction rate to temperature variations. The parameter represents the ratio of the maximum temperature difference that can exist within the particle (equation 12.3.99) to the external surface temperature. For isothermal pellets, / may be regarded as zero (keff = oo). Weisz and Hicks (61) have summarized their numerical solutions for first-order irreversible... 

When the freshly reduced catalyst is suddenly exposed to 10% C2Hit in H2 the result is shown in Fig. 21 (25). Chain growth occurs as with C0/H2, but the reaction rate decreases from an initial maximum as the surface becomes covered with intermediates. 

In this section, methods are described for obtaining a quantitative mathematical representation of the entire reaction-rate surface. In many cases these models will be entirely empirical, bearing no direct relationship to the underlying physical phenomena generating the data. An excellent empirical representation of the data will be obtained, however, since the data are statistically sound. In other cases, these empirical models will describe the characteristic shape of the kinetic surface and thus will provide suggestions about the nature of the reaction mechanism. For example, the empirical model may require a given reaction order or a maximum in the rate surface, each of which can eliminate broad classes of reaction mechanisms. 

Response-surface methodology has been used extensively for determining areas of process operation providing maximum profit. For example, the succinct representation of the rate surface of Eq. (114) indicates that increasing values of X3 will increase the rate r. If some response other than reaction rate is considered to be more indicative of process performance (such as cost, yield, or selectivity), the canonical analysis would be performed on this response to indicate areas of improved process performance. This information... 

Feldspar, among many natural substances such as termite mount-clay, saw dust, kaolinite, and dolomite, offers significant removal ability for phosphate, sulfate, and color colloids. Optimization laboratory tests of parameters such as solution pH and flow rate, resulted in a maximum efficiency for removal of phosphate (42%), sulfate (52%), and color colloids (73%), x-ray diffraction, adsorption isotherms test, and recovery studies suggest that the removal process of anions occurs via ion exchange in conjunction with surface adsorption. Furthermore, reaction rate studies indicated that the removal of these pollutants by feldspar follows first-order kinetics. Percent removal efficiencies, even under optimized conditions, will be expected to be somewhat less for industrial effluents in actual operations due to the effects of interfering substances [58]. 

---