Reaction rate constant, dehydrogenation

Kinetic analysis with a Langmuir-type rate equation (Equation 13.4) [37] gave us the magnitudes of reaction rate constant (k) and retardation constant due to product naphthalene (K) for the superheated liquid film (0.30 g/1.0 mL) and the suspended states (0.30 g/3.0 mL) with the same Pt/C catalyst as summarized in Table 13.2. It is apparent that excellent performance with carbon-supported platinum nanoparticles in the superheated liquid-film state is realized in dehydrogenation catalysis on the basis of reaction rate and retardation constants. 

Corma and co-workers152 have performed a detailed theoretical study (B3PW91/6-31G level) of the mechanism of the reactions between carbenium ions and alkanes (ethyl cation with ethane and propane and isopropyl cation with ethane, propane, and isopentane) including complete geometry optimization and characterization of the reactants, products, reaction intermediates, and transition states involved. Reaction enthalpies and activation energies for the various elemental steps and the equilibrium constants and reaction rate constants were also calculated. It was concluded that the interaction of a carbenium ion and an alkane always results in the formation of a carbonium cation, which is the intermediate not only in alkylation but also in other hydrocarbon transformations (hydride transfer, disproportionation, dehydrogenation). 

Reaction Rate Constants and Activation Energies of Reactions of Dehydrogenation of Alkyl Aromatic Hydrocarbons... 

Example 10.6 A commercial process for the dehydrogenation of ethylbenzene uses 3-mm spherical catalyst particles. The rate constant is 15s , and the diffusivity of ethylbenzene in steam is 4x 10 m /s under reaction conditions. Assume that the pore diameter is large enough that this bulk diffusivity applies. Determine a likely lower bound for the isothermal effectiveness factor. 

Figure 4 Effect of repeated reaction cycles and catalyst pretreatment in 6.2 M NaOH at 473 K on rate constant and catalyst surface area for ethanolamine dehydrogenation over unpromoted skeletal copper under standard conditions.

The dehydrogenation of ethane (A) to ethene (B) is conducted in a 0.5-m3 PFR. The reaction is first-order with respect to A, with a rate constant of 15.2 min-1 at 725°C. The feed contains pure ethane at 725°C, 400 kPa, and a flow rate of 1. 0 kmol min-1. Compare the conversion predicted if isothermal, isobaric conditions are assumed with that if the pressure drop is accounted for with isothermal flow. The diameter of the reactor tube is 0.076 m, and the viscosity of the gas is 2.5 X 10-5 Pa s. 

The residuals discussed thus far have been associated with some dependent variable, such as the reaction rate r. It is particularly advantageous in pinpointing the type of defect present in an inadequate model to expand this definition to include parametric residuals. The parametric residual, then, is simply the difference between a value of a given parameter estimated from the data and that predicted from a model. For example, the dots in Fig. 17 represent the logarithm of the alcohol adsorption constants measured in alcohol dehydrogenation experiments from isothermal data at each of several temperature levels (FI). The solid line represents the expectation that these... 

A kinetic study has been carried out in order to elucidate the mechanism by which the cr-complex becomes dehydrogenated to the alkyl heteroaromatic derivative for the alkylation of quinoline by decanoyl peroxide in acetic acid. The decomposition rates in the presence of increasing amounts of quinoline were determined. At low quinoline concentrations the kinetic course is shown in Fig. 1. The first-order rate constants were calculated from the initial slopes of the graphs and refer to reaction with a quinoline molecule still possessing free 2- and 4-positions. At high quinoline concentration a great increase of reaction rate occurs and both the kinetic course and the composition of the products are simplified. The decomposition rate is first order in peroxide and the nonyl radicals are almost completely trapped by quinoline. The proportion of the nonyl radicals which dimerize to octadecane falls rapidly with increase in quinoline concentration. The decomposition rate in nonprotonated quinoline is much lower than that observed in quinoline in acetic acid. 

A reaction of particular relevance with respect to applied catalysis is the oxidative dehydrogenation (ODH) of hydrocarbon by VmOn ions according to reaction 2, which involves a two-electron reduction of the cluster. By means of a systematic study of the reactions of various YmOn ions as well as the related oxo-vanadium hydroxides VmO H+ ions with a set of C4-hydrocarbons, it was demonstrated recently that the ODH activity of the cluster ions shows a clear correlation with the formal valence of vanadium in the cluster ions with a maximum reactivity for formal vanadium (V) (Fig. 3) [84]. In such a kind of reactivity screening, it is essential to include more than a single reagent as a probe for the reactivity of the different ions in order to reduce interferences by kinetic barriers of one particular combination of neutral and ionic reactants [85]. Accordingly, the sums of the relative rate constants for the ODH reactions of the four different butenes are considered and normalized to the most reactive ion studied, which turns out to be the formally pure vanadium (V) compoimd In addition to isomeric... 

If a diol is oxidatively dehydrogenated to form a diacid via an intermediate with one Off group, then a first order plot based on hydrogen evolution can exhibit some curvature. This is because the slope at any time will reflect the instantaneous concentrations of the diol and intermediate as well as their intrinsic reactivities. First order plots for the reaction of ethylene glycol, 1,4-butanediol and diethanolamine are shown in Figure 2. All plots are reasonably linear, consistent with reaction via an intermediate with a rate constant rather similar to that of the starting diol (or a direct reaction with no intermediate whatsoever). 

The elements of range in value from 0 to 1 and are the ratio of the reformer kinetic constants at time on stream t to the values at start of cycle. At any time on stream t, the deactivation rate constant matrix K(a) is determined by modifying the start-of-cycle K with a. From the catalytic chemistry, it is known that each reaction class—dehydrogenation, isomerization, ring closure, and cracking—takes place on a different combination of metal and acid sites (see Section II). As the catalyst ages, the catalytic sites deactivate at... 

The dependence of selectivity for dehydrogenation on the conversion of alkane shows that for the more selective catalysts known, the reaction proceeds with a sequential mechanism. The first step of the reaction is the breaking of a C—H bond of the alkane molecule, which is also the rate-limiting step. For these more selective catalysts, alkene is the primary product. Therefore, high selectivities can be obtained at low conversions. However, as the conversion increases, the selectivity decreases because of the secondary reaction of the alkene. The rate constant for the reaction of the alkene on the most selective catalyst is still about the same in magnitude as the rate constant for the activation of alkane. It is larger for the less selective catalysts. Thus the maximum yield of alkene among the catalysts known to date is still less than about 35%. To improve this yield, catalysts that react with alkene less rapidly than with alkane need to be found. 

In a series of studies, the variation of the turnover number for the dehydrogenation reaction (the number of product molecules/platinum surface atoms/second) with the hydrogen to hydrocarbon ratio at a constant hydrocarbon pressure of 4 x 10"8 Torr was determined. The results are shown in Fig. 20 for the several stepped surfaces studied. The reaction rates increase with increasing hydrogen to hydrocarbon ratio. If no hydrogen is introduced into the reaction chamber, the catalyst behaves very differently. No benzene... 

Pshezhetskii et al. (17) have recently expressed the view that in the equation for the rate of dehydrogenation, containing the function p in the form of the Langmuir isotherm, z is the ratio of the rate constants of some partial reactions. 

Figure 3 shows a profile of the potential surface of the consecutive stages of (I). Let k be the rate constant of the reaction. Then, in conformity with the results obtained, km. It is clear, however, that the level 4 of the adsorbed butylene in the process of dehydrogenation of butane is the same as the level 6 of the butylene in the dehydrogenation of the latter. Hence, km = ka and consequently km km. Thus, in dehydrogenation the desorption rate constant of the initial substance is considerably larger than that of its dehydrogenation. 

Relative Adsorption Coefficients (zr), Free Energies (A F°), Enthalpies (—AH °), and Entropies (AS°) of Adsorptive Exchange Rate Constants (K), Activation Energies (e), and the h Parameters in Catalytic Dehydrogenation. AF°, AH°, and t cal./mole AS° e.u. Ai Rate of Reactant Supply, andmo Reaction Rate ml. Substance Vapor/min., K-ml./(ml. min.). All Valuesfor N.T.P. Original Data Are Reduced to the Same Units. 

Elementary reaction (5.12) was successfully applied to the kinetic description of the conjugated dehydrogenation of various substrates using corresponding interaction rate constants between H02 and RH. 

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