Efficiency coefficients catalysts

Efficiency coefficients of catalysts 12 and 13 mainly depend on the nature of the nucleophile, and are in the range 2.1-3.3 and 0.07-0.74 for I and Br, respectively (Table IV). This trend is in good agreement with that found for soluble catalysts ( ). 

The regioselectivity benefits from the increased polarisation of the alkene moiety, reflected in the increased difference in the orbital coefficients on carbon 1 and 2. The increase in endo-exo selectivity is a result of an increased secondary orbital interaction that can be attributed to the increased orbital coefficient on the carbonyl carbon ". Also increased dipolar interactions, as a result of an increased polarisation, will contribute. Interestingly, Yamamoto has demonstrated that by usirg a very bulky catalyst the endo-pathway can be blocked and an excess of exo product can be obtained The increased di as tereo facial selectivity has been attributed to a more compact transition state for the catalysed reaction as a result of more efficient primary and secondary orbital interactions as well as conformational changes in the complexed dienophile" . Calculations show that, with the polarisation of the dienophile, the extent of asynchronicity in the activated complex increases . Some authors even report a zwitteriorric character of the activated complex of the Lewis-acid catalysed reaction " . Currently, Lewis-acid catalysis of Diels-Alder reactions is everyday practice in synthetic organic chemistry. 

Diffusion effects can be expected in reactions that are very rapid. A great deal of effort has been made to shorten the diffusion path, which increases the efficiency of the catalysts. Pellets are made with all the active ingredients concentrated on a thin peripheral shell and monoliths are made with very thin washcoats containing the noble metals. In order to convert 90% of the CO from the inlet stream at a residence time of no more than 0.01 sec, one needs a first-order kinetic rate constant of about 230 sec-1. When the catalytic activity is distributed uniformly through a porous pellet of 0.15 cm radius with a diffusion coefficient of 0.01 cm2/sec, one obtains a Thiele modulus y> = 22.7. This would yield an effectiveness factor of 0.132 for a spherical geometry, and an apparent kinetic rate constant of 30.3 sec-1 (106). 

Speed-up of mixing is known not only for mixing of miscible liquids, but also for multi-phase systems the mass-transfer efficiency can be improved. As an example, for a gas/liquid micro reactor, a mini packed-bed, values of the mass-transfer coefficient K a were determined to be 5-15 s [2]. This is two orders of magnitude larger than for typical conventional reactors having K a of 0.01-0.08 s . Using the same reactor filled with 50 pm catalyst particles for gas/Hquid/solid reactions, a 100-fold increase in the surface-to-volume ratio compared with the dimensions of laboratory trickle-bed catalyst particles (4-8 mm) is foimd. 

Lower molecular-weight quaternary ammonium halides, which partition across the two-phase system, transfer anions in measurable concentrations from the aqueous to the organic phase but, in contrast, many of the higher-molecular-weight quaternary ammonium halides with more than ca. 30 carbon atoms are virtually insoluble in aqueous media and their partition coefficients between aqueous and organic phases preclude the transfer of anions efficiently across the interface by the extraction process and yet catalysts, such as Aliquat 336 and Adogen 464, are extremely effective catalysts. 

Die difference from the real value (lm) is mainly due to the approximation made about the mass transfer coefficient as well as the complete wetting of the catalyst, as the actual wetting efficiency is 88%. Furthermore, the problem is more complicated because under incomplete wetting, the gas reactant reaches the catalyst surface more easily than the unwetted part, as Horowitz et al. found out experimentally. 

When reactants of large molecular size, such as oleic acid, were reacted over an ion exchanger catalyst, a direct proportionality between the reaction rate and the surface area of the catalyst was found [433]. The authors explain the result by assuming that, for the bulky reactant molecules, only acid groups at or near the surface of the catalyst particle can be effective catalysts. The efficiency of the catalyst (the rate coefficient with the resin compared to the rate coefficient with the same stoichiometric amount of dissolved inorganic acid) was found to be considerably... 

The experiments were done at 70, 100, and 130°C and at pressures somewhat lower than atmospheric. Under these conditions reaction (368) is practically irreversible. Activated charcoal of the trademark Bayer AKT-4 ground to grain size 0.25-0.5 mm served as a catalyst. Estimation of the efficiency factor on the basis of the determination of the effective difusion coefficient of hydrogen in nitrogen or helium has shown that for this grain size the results of reaction rate measurements refer to the kinetic region. Estimation of relaxation time of the reaction rate from (67) showed the reaction to be quasi-steady at the condition of our experiments in the closed system. 

It is important to have the correct set of variables specified as independent and dependent to meet the modeling objectives. For monitoring objectives observed conditions, including the aforementioned independent variables (FICs, TICs, etc.) and many of the "normally" (for simulation and optimization cases) dependent variables (FIs, TIs, etc.) are specified as independent, while numerous equipment performance parameters are specified as dependent. These equipment performance parameters include heat exchanger heat transfer coefficients, heterogeneous catalyst "activities" (representing the relative number of active sites), distillation column efficiencies, and similar parameters for compressors, gas and steam turbines, resistance-to-flow parameters (indicated by pressure drops), as well as many others. These equipment performance parameters are independent in simulation and optimization model executions. 

Hydrodynamic parameters that are required for trickle bed design and analysis include bed void fraction, phase holdups (gas, liquid, and solid), wetting efficiency (fraction of catalyst wetted by liquid), volumetric gas-liquid mass-transfer coefficient, liquid-solid mass-transfer coefficient (for the wetted part of the catalyst particle surface), gas-solid... 

An appropriate model for trickle-bed reactor performance for the case of a gas-phase, rate limiting reactant is developed. The use of the model for predictive calculations requires the knowledge of liquid-solid contacting efficiency, gas-liquid-solid mass transfer coefficients, rate constants and effectiveness factors of completely wetted catalysts, all of which are obtained by independent experiments. 

The efficiency of the overall recombination reaction is generally expressed in terms of the recombination coefficient (7), defined as the probability that a collision of a gaseous atom with the catalyst will result in recombination, i.e. the absolute rate of recombination is given by yZx and... 

Whenever the kinetics of a chemical transformation can be represented by a single reaction, it is sufficient to consider the conversion of just a single reactant. The concentration change of the remaining reactants and products is then related to the conversion of the selected key species by stoichiometry, and the rates of production or consumption of the various species differ only by their stoichiometric coefficients. In this special case, the combined influence of heat and mass transfer on the effective reaction rate can be reduced to a single number, termed the catalyst efficiency or effectiveness factor rj. From the pioneering work of Thiele [98] on this subject, the expressions pore-efficiency concept and Thiele concept have been coined. 

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