Reaction rates on catalysts

Rate expressions are indispensable in the application of catalysed reactions, in the design of chemical reactors, and their process control. Insight into the dependence of the reaction rate on catalyst variables, the temperature and concentrations of reactants, products and other relevant species are needed to predict the sizes of catalytic reactors and the optimum operating conditions. 

Table 1. Initial reaction rates on catalysts (mol.h. molg ) in ethanol.

For example, if the total pressure in a gas phase reactor is doubled, the average pressure of reactant is approximately doubled also, so from the preceding formula the rate would increase by a factor y/2 only. It appears to be a general statement that fast nth order gas phase reaction rates on catalysts containing small pores, under conditions of bulk diffusion become proportional to ... 

Figure 2. Dependence of Reaction Rates on Catalyst Particle Size.

The fiinctional dependence of tire reaction rate on concentrations may be arbitrarily complicated and include species not appearing in the stoichiometric equation, for example, catalysts, inliibitors, etc. Sometimes, however, it takes a particularly simple fonn, for example, under certain conditions for elementary reactions and for other relatively simple reactions ... 

A catalyst is a material that accelerates a reaction rate towards thennodynamic equilibrium conversion without itself being consumed in the reaction. Reactions occur on catalysts at particular sites, called active sites , which may have different electronic and geometric structures than neighbouring sites. Catalytic reactions are at the heart of many chemical industries, and account for a large fraction of worldwide chemical production. Research into fiindamental aspects of catalytic reactions has a strong economic motivating factor a better understanding of the catalytic process... 

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). 

When water is present, hydrolysis takes place leading to the formation of aggregates. This would explain the low dependence of the reaction rate on the catalyst concentration. 

This characteristic dependence of rate on catalyst concentration was first observed by Bunnett and Randall28 for the reaction of 2,4-dinitrofluorobenzene... 

Catalytic hydrogenation is typically carried out in slurry reactors, where finely dispersed catalyst particles (<100 (tm) are immersed in a dispersion of gas and liquid. It has, however, been demonstrated that continuous operation is possible, either by using trickle bed [24] or monoHth technologies [37]. Elevated pressures and temperatures are needed to have a high enough reaction rate. On the other hand, too high a temperature impairs the selectivity of the desired product, as has been demonstrated by Kuusisto et al. [23]. An overview of some feasible processes and catalysts is shown in Table 8.1. 

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) ... 

Equation (1) consists of various resistance terms. l/Kj a is the gas absorption resistance, while 1/ K,a corresponds to the maleic anhydride diffusion resistance and l/i k represents the chemical reaction resistance. The reaction rate data obtained under the reaction conditions of 250°C and 70 atm were plotted according to equation (1). Although catalytic reaction data with respect to time on stream were not shown here, a linear correlation between reaction rate data and catalyst loading was observed as shown in Fig. 2. The gas absorption resistance (1/ a) was -1.26 h, while the combined reaction-diffusion resistance (lJK,a + 1 T]k) was determined to be 5.57 h. The small negative value of gas absorption resistance indicates that the gas-liquid diffusion resistance was very small and had several orders of magnitude less than the chanical reaction resistance, as similarly observed for the isobutene hydration over Amberlyst-15 in a slurry reactor [6]. This indicates that absorption of malei c anhydride in solvent was a rapid process compared to the reaction rate on the catalyst surface. 

The nonlinear dependence of the reaction rate on the partial pressure of CO suggests that there are stimulated either a single reaction step with the established nonlinearity or at least two steps, one of which has a linear and the other one a nonlinear (nperiodic operation of the reactor at the 180°C level and at a middle oxidation state (pretreatment at p /p = 5,0).has been accomplished (see Figure 9) with a H fl/N testing mixture followed by a C0/N recuperation mixture. After an intermediate activity of the catalyst has been attained by this periodic operation, CO has been added in the testing mixture. 

An example of these pressure studies is provided by the studies of Elsevier et al. [31], who investigated the dependence of the hydrogenation rate of 4-octyne by a Pd-catalyst on the dihydrogen pressure, which was varied between 0 and 40 bar. The hydrogenation rate was shown to depend linearly on the dihydrogen pressure. In order to elucidate the reaction mechanism, the dependence of the reaction rate on substrate and catalyst concentration, and on the temperature, was also measured. NMR experiments with deuterium gas as well as PHIP-ex-periments were also carried out. 

The strong dependence of the reaction rate on the catalyst concentration relative to control experiments in which the amino-hydrogen atoms of 7 were substituted by methyl groups demonstrate that hydrogen bonding represents the major interaction responsible for the observed accelerations. Diels-Alder reactions are also accelerated by hydrogen-bond donors. It was shown that a biphenylenediol 9 is able to catalyse [4 + 2]-cycloadditions of cyclopentadiene, 2,3-dimethylbutadiene and other simple dienes with various a,fi-unsaturated carbonyl compounds (Table 14)175. 

Finally, we note the differences between a Ru(OOOl) catalyst with or without added Cu with respect to attaining steady-state reaction rates. On the Cu-free... 

The kinetics of enzyme-catalyzed reactions (i. e the dependence of the reaction rate on the reaction conditions) is mainly determined by the properties of the catalyst, it is therefore more complex than the kinetics of an uncatalyzed reaction (see p.22). Here we discuss these issues using the example of a simple first-order reaction (see p.22)... 

Supplementary studies of the mechanism were conducted. The dependence of the reaction rate on the nature of environment at the cationic carbon has shown that the concurrent formation of the protic acid proceeds, if the substituents can undergo the isomerization (Scheme 61), and thus the carbenium catalysis is utterly negligible. It was shown that the reaction was still catalyzed, even when a base was added in order to rule out a TfOH catalyzed reaction. Obviously, the protonated base was then a catalyst. 

The presence of 4e as the predominant species during the catalysis is also in accord with the observed kinetic behavior of this catalyst with 1-octene and styrene as the substrates. The observation of this saturated acyl rhodium complex is in line with the positive dependence of the reaction rate on the hydrogen concentration and the zero order in alkene concentration. It was concluded previously that this saturated acyl complex is an unreactive resting state [18]. Before the final hydro-genolysis reaction step can occur, a CO molecule has to dissociate in order to form... 

Strictly speaking, electrocatalysis applies to the dependence of the electrode reaction rate on the nature of the electrode material [152]. In the following, this term will be used in a broader sense and will be admitted to include the possibility that the catalyst be homogeneously dissolved in the electrolyte solution as well as the case where the catalyst is attached to the electrode surface. A short chapter on the electrocatalysis of inorganic chemicals by chemically modified electrodes can also be found in Vol. 10 of this Encyclopedia [9]. 

The initial study on the MeO-TEMPO / Mg(N03)2 / NBS triple catalyst system in the oxidation of 1 indicated the necessity of all three components the TEMPO based catalyst, the nitrate source (MNT) and the bromine source (NBS). A large number of metal nitrates and nitrites were screened initially and the highest activity and aldehyde selectivity under comparable reaction conditions were recorded using Mg(N03)2 as the nitrate component. A number of organic and inorganic bromides soluble in HOAc were also screened and high reaction rates were found when NBS was used as the bromide source. The effect of the concentration of the individual components of the new triple catalyst system on the reaction rate, on the conversion of 1 and on the selectivity to 2 over 60 min reaction time is shown in Figure 1. 

In Figure 7.4 the effectiveness factor is plotted against the Thiele modulus for spherical catalyst particles. For low values of 0, Ef is almost equal to unity, with reactant transfer within the catalyst particles having little effect on the apparent reaction rate. On the other hand, Ef decreases in inverse proportion to 0 for higher values of 0, with reactant diffusion rates limiting the apparent reaction rate. Thus, decreases with increasing reaction rates and the radius of catalyst spheres, and with decreasing effective diffusion coefficients of reactants within the catalyst spheres. 

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