Parallel reactions single reactant

In addition to sequential reactions, reactions can occur in parallel and compete with one another. For example, a single reactant A might form two different products, B and C ... 

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. 

Following the treatment of Levenspiel (1) we shall consider a set of parallel reactions in which only a single reactant species has any influence on the corresponding reaction rate expressions. 

The photoinduced reaction of chloranil with various 1,1-diarylethenes is another example of an intramoleclar [2 -I- 2] cycloaddition as reported by Xu and co-workers [86]. Although not interesting from the preparative point of view, the diverse reaction outcomes caused by parallel reaction pathways with and without single-electron transfer and various secondary reactions of the primary products show that the photochemistry involving haloquinones is far from being explored. Another interesting example in this context is the reaction of dichlorobenzoqui-none with various diarylacetylenes in the solid phase via photoinduced electron transfer as reported by Kochi and co-workers [87]. Here, time-resolved spectroscopy revealed the radical ion pair of the two reactants to be the first reactive intermediate that then underwent coupling. 

When the density varies, we need to find another variable to express the progress of a reaction. Earlier we defined the fractional conversion X for a single reaction, and in this chapter we defined the conversion of a reactant species for reactant A and Xj for reaction j. For the conversion in a reaction we need a different variable, and we shall use Xj (bold type), with the index i describing the reaction. We will first work our series and parallel reactions with these variables and then consider a variable-density problem. 

The simplest model of a bubbling fluidized bed, with uniform bubbles exchanging matter with a dense phase of catalytic particles which promote a continuum of parallel first order reactions is considered. It is shown that the system behaves like a stirred tank with two feeds the one, direct at the inlet the other, distributed from the bubble train. The basic results can be extended to cases of catalyst replacement for a single reactant and to Astarita s uniform kinetics for the continuous mixture. 

Common features in the various theoretical explanations of compensation behavior referred to in Section II, A, 1-7 are the occurrence of parallel reactions that are characterized by different values of the kinetic parameters (A, E) and/or a systematic change in the effective concentrations of reactants across the temperature interval used in the measurements of the Arrhenius parameters. Both influences are based on reaction models for which the kinetic behavior cannot be represented as a single desorption step and, indeed, the overall surface interactions could be much more complicated. 

Scheme 4.2 Parallel (competitive) first-order unidirectional reactions of a single reactant.

This set is of the same algebraic form as eqns 5.16 for conversion of a single reactant to two products in parallel steps. Because quasi-equilibrium of isomerization is maintained, the reactant acts as a "homogeneous source" despite being split into two isomers, and the mathematics of product formation is the same as for the simpler reaction with network 5.15. Results from constant-volume batch plotted as lnx versus t for P, Q, and total A give identical straight lines with slope -k, as in Figure 5.6, where... 

Coupled parallel steps are an important combination not covered in any standard texts, and are therefore examined in more detail. Typical examples are isomerization in concert with conversion of the isomers to different products. If isomerization is very fast compared with conversion, the isomers are at quasi-equilibrium and act as "homogeneous source," producing a kinetic behavior like that of a single reactant. If isomerization is very slow compared with conversion, the reactions of the different isomers are essentially uncoupled. If the rates of isomerization and conversion are comparable, a more complex behavior ensues. Most interesting is the case with isomerization being somewhat faster than conversion. The isomer distribution then approaches a steady state (not necessarily close to equilibrium), and from then on the isomers act as homogeneous source. 

In the usual description of solution thermal kinetics, a reactant concentration is designated by [A], Implicit in the use of a single concentration is the assumption that the solvent environment fluctuates rapidly compared to the reaction rates for all possible processes A => B. In this case a single constant, k, sufflces to describe the reaction rate. If the assumption of rapid solvent motion is invalid, then a distribution of solvates. A,-, each with a corresponding rate constant, k,-, must be used to designate the parallel reactions A,- B,. 

These could refer to the main and poisoning reactions, or to reforming or cracking reactions with different compounds in a multicomponent feed stream. Type II selectivity refers to parallel reactions with a single reactant ... 

In this type of reaction a single reactant which is excited by absorption of light is able to start more than one gross reaction. The requirement is that the Bodenstein hypothesis can be applied to all intermediates. Whereas in the previous section in the case of the treated parallel photoreactions the gross... 

Type II selectivity is characterized by parallel (or simultaneous) reactions of a single reactant species. Here the reactant molecule A can be converted into either the desired product B or an undesired product C, symbolized by the reaction scheme ... 

A chemical reaction is a process that results in the interconversion of chemical species Table 4.3 summarizes the base reaction types. Chemical reactions might be elementary reactions or stepwise reactions. A stepwise reaction consists of at least one reaction intermediate and involves at least two consecutive elementary reactions. Parallel reactions are several simultaneous reactions that form different respective products from a single set of reactants (Svehla 1993, Muller 1994). 

The set of all intermediate steps is called the reaction pathway. A given reaction (involving the same reactants and products) may occur by a single pathway or by several parallel pathways. In the case of invertible reactions, the pathway followed in the reverse direction (e.g., the cathodic) may or may not coincide with that of the forward direction (in this example, the anodic). For instance, the relatively simple anodic oxidation of divalent manganese ions which in acidic solutions yields tetrava-lent manganese ions Mn +— Mn -l-2e , can follow these two pathways ... 

In parallel to the bismuth(III)-catalyzed three-component allylation reaction, we have reported the corresponding three-component bismuth(III)-catalyzed Mannich-type reaction. A major merit of the three-component reaction is indeed that many unique structures can be afforded rapidly when three or more reactants are combined in a single step to afford new compounds. The development of an efficient bismuth-catalyzed Mannich-type three-component reaction that combines an aldehyde, an amine, and a silyl enolate to give compounds with a (3-amino carbonyl core... 

Therefore, complex processes are frequently simplified to assume (1) a single reaction in which the major reactant is converted into the major product or for a more accurate estimate (2) simple series or parallel processes in which there is a major desired and a single major undesired product. The fust approximation sets the approximate size of the reactor, while the second begins to examine different reactor types, operating conditions, feed composition, conversion, separation systems required, etc. 

In this section, some analytical solutions of fluidized-bed models are presented. Specifically, model solutions will be given for the case of a gas-phase reactant and a single solid-catalyzed reaction of the form A —> products and bubbling fluidized bed (Type B fluidization). The same analysis holds for a reaction of the form A + B —> products, if the reaction depends only on the concentration of A. Some solutions for the cases of a single reversible reaction, for two reactions in parallel, and two reactions in series will be given as well. 

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