Parallel reactions irreversible

A system of parallel reactions as shown in Fig. 5.3-9 was studied by Paul et at. (1992). The reactions are an acid-base neutralization and a base-catalysed hydrolysis of product (C). The labile compound (Q is in solution in an organic solvent, and aqueous NaOH is added to raise the pH from 2 to 7. Enolization occurs under basic conditions and is accompanied by irreversible decomposition (ring opening), which is not shown in the figure. The system was studied in the laboratory using the 6-Iitre reactor shown in Fig. 5.3-10. 

The term parallel reactions describes situations in which reactants can undergo two or more reactions independently and concurrently. These reactions may be reversible or irreversible. They include cases where one or more species may react through alternative paths to give two or more different product species (simple parallel reactions),... 

Simple Parallel Reactions. The simplest types of parallel reactions involve the irreversible transformation of a single reactant into two or more product species through reaction paths that have the same dependence on reactant concentrations. The introduction of more than a single reactant species, of reversibility, and of parallel paths that differ in their reaction orders can complicate the analysis considerably. However, under certain conditions, it is still possible to derive useful mathematical relations to characterize the behavior of these systems. A variety of interesting cases are described in the following subsections. 

Irreversible First-Order Parallel Reactions. Consider the irreversible decomposition of a reactant A into two sets of products by first-order reactions. 

H.3 Higher-Order Irreversible, Simple Parallel Reactions. Many simple parallel reactions... 

There are few short-cut methods for analyzing simple parallel systems. One useful technique, however, is to use stoichiometric ratios of reactants so that the ratio of the time derivatives of the extents of reaction simplifies where possible. For higher-order irreversible simple parallel reactions represented by equations 5.2.41 and 5.2.42, the degenerate form of the ratio of reaction rates becomes... 

ILLUSTRATION 9.1 QUANTITATIVE TREATMENT OF IRREVERSIBLE PARALLEL REACTIONS OCCURING IN THE LIQUID PHASE... 

The following example illustrates a combination of semibatch and semicontinuous operation for an irreversible reaction, with one reactant added intermittently and the other flowing (bubbling) continuously, that is, a combination of Figures 12.3(a) and 12.4(a). Chen (1983, pp. 168-211, 456-460) gives several examples of other situations, including reversible, series-reversible, and series-parallel reactions, and nonisothermal and autothermal operation. 

The following problem is formulated as an optimization problem. A batch reactor operating over a 1-h period produces two products according to the parallel reaction mechanism A — B, A — C. Both reactions are irreversible and first order in A and have rate constants given by... 

When one or more molecular entity(ies) participates in two or more parallel and irreversible reactions in which different products are formed, the faster-forming product will accumulate by the reaction having the lowest activation energy. Thus, kinetically controlled processes are those whose proportion of products is governed by the relative rates of the competing reactions. If the reac-... 

Figure 8.9 shows that the concentration of intermediate in reversible series reactions need not pass through a maximum, while Fig. 8.10 shows that a product may pass through a maximum concentration typical of an intermediate in the irreversible series reaction however, the reactions may be of a different kind. A comparison of these figures shows that many of the curves are similar in shape, making it difficult to select a mechanism of reaction by experiment, especially if the kinetic data are somewhat scattered. Probably the best clue to distinguishing between parallel and series reactions is to examine initial rate data—data obtained for very small conversion of reactant. For series reactions the time-concentration curve for S has a zero initial slope, whereas for parallel reactions this is not so. 

Irreversible series-parallel reactions can be analyzed in terms of their constituent series reactions and parallel reactions in that optimum contacting for favorable product distribution is the same as for the constituent reactions. 

At the same time, as a chemist I was disappointed at the lack of serious chemistry and kinetics in reaction engineering texts. AU beat A B o death without much mention that irreversible isomerization reactions are very uncommon and never very interesting. Levenspiel and its progeny do not handle the series reactions A B C or parallel reactions A B, A —y C sufficiently to show students that these are really the prototypes of aU multiple reaction systems. It is typical to introduce rates and kinetics in a reaction engineering course with a section on analysis of data in which log-log and Anlienius plots are emphasized with the only purpose being the determination of rate expressions for single reactions from batch reactor data. It is typically assumed that ary chemistry and most kinetics come from previous physical chemistry courses. 

Several quantitative analyses of the effect of intraparticle heat and mass transport have been carried out for parallel, irreversible reactions [1]. Roberts and Lamb [2] have worked on the effect of reversibility on the selectivity of parallel reactions in a porous catalyst. The reaction selectivity of a kinetic model of two parallel, first order, irreversible reactions with a second order inhibition kinetic term in one of them has also been investigated [3]. 

Finally, when chemical kinetics contrasts with equilibrium, the parallel scheme is not trivial, since one of the products can be favored in the early stages of the batch cycle by faster kinetics and hindered in the later stages by unfavorable equilibrium. Such a case is shown in Fig. 2.4 for parallel reactions of A to Pi via an equilibrium limited reaction and to P2 via an irreversible reaction. 

Fig. 2.4 Time histories of Ca (continuous line), Cpi (dotted line), and Cp2 ( dashed line) in a batch reactor for parallel reactions of A producing Pi, via an equilibrium limited reaction, and P2, via an irreversible reaction. Initial conditions are Cao = 1 molm-3,...

Consider the following reactions, namely the second order irreversible reaction aA + bB — rR + sS, the series reaction A — B — C, and the parallel reaction A BA->C... 

Competing or Parallel Reactions Some time a given substance reacts or decomposes in more than one way. Then the alternate/parallel reaction must also be taken into consideration in analysing the kinetic data. Consider the simplest case of a first order irreversible reactions A —> B + C leading to the formation of two products through different path ways of first order. 

In its literal form, this reaction is only of academic interest because a molecule is unlikely to break up or isomerize irreversibly in two or more different ways. However, situations frequently encountered in practice are those of multistep parallel first-order decomposition reactions and of parallel reactions that involve coreactants but are pseudo-first order in the reactant A. An example of the first kind is dehydrogenation of paraffins, examples of the second kind include hydration, hydrochlorination, hydroformylation, and hydrocyanation of olefins and some hydrocarbon oxidation reactions. All these reactions are multistep, but the great majority are first order in the respective hydrocarbon, and pseudo-first order if any co-reactant concentration is kept constant. 

Fia. 18, The consequences of disregarding reaction irreversibility, in an abstract example. The species A and E are terminal and all others are intermediates. There are many parallel irreversible mechanisms that transform various intermediates to others (e.g., from A to B, from F to C, and from D to G). The direction of these internal mechanisms, however, is such that they do not participate in the final solution—which requires mechanisms only between A and E. There is actually only one mechanism (shown in thick arrows) that converts A to E in three steps. A method like that of H S, which disregards directionality of steps and treats all steps as reversible initially, will come up with a very large number of mechanisms, going through the intermediates F, C, D, G, B (in that order). Our algorithm would immediately prune out the irrelevant portions of the network (starting with B) and identify the one feasible mechanism. 

Parallel reactions single and consecutive-irreversible reaction steps. 

PARALLEL REACTIONS SINGLE AND CONSECUTIVE IRREVERSIBLE REACTION STEPS... 

Practically any experimental kinetic curve can be reproduced using a model with a few parallel (competitive) or consecutive surface reactions or a more complicated network of chemical reactions (Fig. 4.70) with properly fitted forward and backward rate constants. For example, Hachiya et al. used a model with two parallel reactions when they were unable to reproduce their experimental curves using a model with one reaction. In view of the discussed above results, such models are likely to represent the actual sorption mechanism on time scale of a fraction of one second (with exception of some adsorbates, e.g, Cr that exchange their ligands very slowly). Nevertheless, models based on kinetic equations of chemical reactions were also used to model slow processes. For example, the kinetic model proposed by Araacher et al. [768] for sorption of multivalent cations and anions by soils involves several types of surface sites, which differ in rate constants of forward and backward reaction. These hypothetical reactions are consecutive or concurrent, some reactions are also irreversible. Model parameters were calculated for two and three... 

For a parallel reaction scheme with one key reactant A and with irreversible steps... 

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