Kinetic parallel reactions

Change of reaction conditions to minimize kinetic complications. For example, if two parallel reactions have substantially different activation energies, their relative rates will depend upon the temperature. The reaction solvent, pH, and concentrations are other experimental variables that may be manipulated for this purpose. 

The study of relative rates by the competitive method can be useful. The principle was discussed in Section 3.1 in the context of parallel reactions, for which the ratio of the product concentrations is equal to the ratio of rate constants (provided the concentrations are under kinetic control). 

Purely parallel reactions are e.g. competitive reactions which are frequently carried out purposefully, with the aim of estimating relative reactivities of reactants these will be discussed elsewhere (Section IV.E). Several kinetic studies have been made of noncompetitive parallel reactions. The examples may be parallel formation of benzene and methylcyclo-pentane by simultaneous dehydrogenation and isomerization of cyclohexane on rhenium-paladium or on platinum catalysts on suitable supports (88, 89), parallel formation of mesityl oxide, acetone, and phorone from diacetone alcohol on an acidic ion exchanger (41), disproportionation of amines on alumina, accompanied by olefin-forming elimination (20), dehydrogenation of butane coupled with hydrogenation of ethylene or propylene on a chromia-alumina catalyst (24), or parallel formation of ethyl-, methylethyl-, and vinylethylbenzene from diethylbenzene on faujasite (89a). 

The studies mentioned in this brief account did not concern the kinetics of complex reactions taking place on the so-called polyfunctional catalysts, which were treated by Weisz (56) the theory of the use of these catalysts has been further worked out for some consecutive or parallel reactions carried out in the reactors with a varying ratio of catalyst components along the catalyst bed [e.g. (90, 91, 91a) ]. Although the description of these reactions, not coupled in the sense defined in Section III, is beyond the scope of this treatment, we mention here at least an experimental... 

The values of the rate constants and adsorption coefficients obtained by the study of isolated reactions agreed well with those obtained by the study of parallel reactions (Table V). The three values of the adsorption coefficient of each acid were obtained independently. In addition to one value from the study of isolated reactions, two additional values were determined by the study of the parallel system one from the kinetics of the consumption of the given acid by reaction (Vila) or (Vllb), and one from the kinetics of reaction (Vile). 

Parallel reactions. Show how the three rate constants that characterize the hydrolysis of isopropyl bromide in alkaline solution, Eqs. (3-68)—(3-70), can be obtained from studies of the kinetics and yields determined over a range of [OH" j. 

For most real systems, particularly those in solution, we must settle for less. The kinetic analysis will reveal the number of transition states. That is, from the rate equation one can count the number of elementary reactions participating in the reaction, discounting any very fast ones that may be needed for mass balance but not for the kinetic data. Each step in the reaction has its own transition state. The kinetic scheme will show whether these transition states occur in succession or in parallel and whether kinetically significant reaction intermediates arise at any stage. For a multistep process one sometimes refers to the transition state. Here the allusion is to the transition state for the rate-controlling step. 

Parallel reactions, 58-64, 129 Partitioning ratios, 79 Perturbation (see Chemical relaxation) pH profiles, 139-145 bell-shaped, 141-142 Phosphorous acid, oxidation of, 186-187 Physical methods for kinetics, 22-25 end point reading unknown, 25-28 sample calculation for, first-order,... 

Methanol oxidation on Pt has been investigated at temperatures 350° to 650°C, CH3OH partial pressures, pM, between 5-10"2 and 1 kPa and oxygen partial pressures, po2, between 1 and 20 kPa.50 Formaldehyde and C02 were the only products detected in measurable concentrations. The open-circuit selectivity to H2CO is of the order of 0.5 and is practically unaffected by gas residence time over the above conditions for methanol conversions below 30%. Consequently the reactions of H2CO and C02 formation can be considered kinetically as two parallel reactions. 

One can add reverse reactions to the parallel reaction model to illustrate what chemists refer to as kinetic and thermodynamic reaction control. Often a reactant A can form two (or more) products, one of which (B) is formed rapidly (the kinetic product) and another (C) which forms more slowly (the thermodynamic... 

When a 1 1 mixture of NO and NO2 (i.e., NO2/NOx=0,5) is fed to the SCR reactor at low temperature (200 °C) where the thermodynamic equilibrium between NO and NO2 is severely constrained by kinetics, the NO2 conversion is much greater than (or nearly twice) the NO conversion for all three catalysts. This observation is consistent with the following parallel reactions of the SCR process [6] Reaction (2) is the dominant reaction due to its reaction rate much faster than the others, resulting in an equal conversion of NO and NO2. On the other hand, Reaction (3) is more favorable than Reaction (1), which leads to a greater additional NO2 conversion by Reaction (3) compared with the NO conversion by Reaction... 

The catalyst performance depends on the H2 to CCI2F2 feed ratio. The selectivities to CH2F2 and CHCIF2 are influenced by the H2 to CCI2F2 feed ratio, while the selectivity to methane is independent of this ratio. We have previously proposed a reaction mechanism with serial reactions on the catalyst surface and minor readsorption of the intermediate products, which is depicted in figure 8 [4,5]. Thus the kinetics of the reaction follows mainly parallel reaction pathways, in which the selectivities are not influenced by the conversion, and a... 

Figure 8. Reaction mechanism with apparent parallel reaction kinetics.

Below some typical kinetic situations for the system of parallel reactions will be considered. 

A cascade of 3 tanks in series is used to optimise the selectivity of a complex sequential-parallel reaction. Depending on the kinetics, distributing the feed of one reactant among the tanks may lead to improved selectivity. 

This concept can be used in the study of other parallel reaction networks, and for designing more efficient catalyst systems in kinetic resolutions. 

The reaction pathway for the gas-phase methylation of m-cresol, as inferred from catalytic data here reported, can be summarized as shown in Scheme 1. Methanol and m-cresol react through two parallel reactions, yielding either 3-MA or DMPs. The relative contribution of the two reactions is a function of the physico-chemical features of the catalysts, and of the reaction temperature as well, C-methylation being kinetically favored at high temperature. Consecutive reactions occur on 3-MA, which acts as a methylating agent yielding DMPs, DMAs and polyalkylates (with co-production of m-cresol in all cases) by reaction with m-cresol, 3-MA and DMPs, respectively. Consecutive reactions may also occur on DMPs to yield polyalkylates. 

Crosslinking of many polymers occurs through a complex combination of consecutive and parallel reactions. For those cases in which the chemistry is well understood it is possible to define the general reaction scheme and thus derive the appropriate differential equations describing the cure kinetics. Analytical solutions have been found for some of these systems of differential equations permitting accurate experimental determination of the individual rate constants. 

Thus mechanism B, which consists solely of bimolecular and unimolecular steps, is also consistent with the information that we have been given. This mechanism is somewhat simpler than the first in that it does not requite a ter-molecular step. This illustration points out that the fact that a mechanism gives rise to the experimentally observed rate expression is by no means an indication that the mechanism is a unique solution to the problem being studied. We may disqualify a mechanism from further consideration on the grounds that it is inconsistent with the observed kinetics, but consistency merely implies that we continue our search for other mechanisms that are consistent and attempt to use some of the techniques discussed in Section 4.1.5 to discriminate between the consistent mechanisms. It is also entirely possible that more than one mechanism may be applicable to a single overall reaction and that parallel paths for the reaction exist. Indeed, many catalysts are believed to function by opening up alternative routes for a reaction. In the case of parallel reaction paths each mechanism proceeds independently, but the vast majority of the reaction will occur via the fastest path. 

The chemical composition of many systems can be expressed in terms of a single reaction progress variable. However, a chemical engineer must often consider systems that cannot be adequately described in terms of a single extent of reaction. This chapter is concerned with the development of the mathematical relationships that govern the behavior of such systems. It treats reversible reactions, parallel reactions, and series reactions, first in terms of the mathematical relations that govern the behavior of such systems and then in terms of the techniques that may be used to relate the kinetic parameters of the system to the phenomena observed in the laboratory. 

In this section we will consider the kinetic implications of both general classes of parallel reactions. 

In this subsection we have treated a variety of higher-order simple parallel reactions. Only by the proper choice of initial conditions is it possible to obtain closed form solutions for some of the types of reaction rate expressions one is likely to encounter in engineering practice. Consequently, in efforts to determine the kinetic parameters characteristic of such systems, one should carefully choose the experimental conditions so as to ensure that potential simplifications will actually occur. These simplifications may arise from the use of stoichiometric ratios of reactants or from the degeneration of reaction orders arising from the use of a vast excess of one reactant. Such planning is particularly important in the early stages of the research when one has minimum knowledge of the system under study. 

Techniques for the Interpretation of Kinetic Data in the Presence of Parallel Reactions... 

In general an analysis of a system in which noncompetitive parallel reactions are taking place is considerably more difficult than analyses of the type discussed in Chapter 3. In dealing with parallel reactions one must deal with the problems of determining reaction orders and rate constants for each of the individual reactions. The chemical engineer must be careful both in planning the experiment and in analyzing the data so as to obtain values of the kinetic con-... 

Illustrations 5.3 and 5.4 indicate how one utilizes the concepts developed in this section in the determination of kinetic parameters for competitive parallel reactions. 

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