Reversible reaction parallel

To this point we have focused on reactions with rates that depend upon one concentration only. They may or may not be elementary reactions indeed, we have seen reactions that have a simple rate law but a complex mechanism. The form of the rate law, not the complexity of the mechanism, is the key issue for the analysis of the concentration-time curves. We turn now to the consideration of rate laws with additional complications. Most of them describe more complicated reactions and we can anticipate the finding that most real chemical reactions are composites, composed of two or more elementary reactions. Three classifications of composite reactions can be recognized (1) reversible or opposing reactions that attain an equilibrium (2) parallel reactions that produce either the same or different products from one or several reactants and (3) consecutive, multistep processes that involve intermediates. In this chapter we shall consider the first two. Chapter 4 treats the third. 

Parallel and reversible reactions. The isomerization of allyl phenyl sulfide is a degenerate rearrangement made detectable by isotopic labeling of one end of the allyl group, permitting kinetic monitoring by NMR techniques.12... 

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... 

This technique is readily adaptable for use with the generalized additive physical approach discussed in Section 3.3.3.2. It is applicable to systems that give apparent first-order rate constants. These include not only simple first-order irreversible reactions but also irreversible first-order reactions in parallel and reversible reactions that are first-order in both the forward and reverse directions. The technique provides an example of the advantages that can be obtained by careful planning of kinetics experiments instead of allowing the experimental design to be dictated entirely by laboratory convention and experimental convenience. 

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. 

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. 

Reversible First-Order Parallel Reactions. This section extends the analysis developed in the last section to the case where the reactions are reversible. Consider the case where the forward and reverse reactions are all first-order, as indicated by the following mechanistic equations. 

Concentration versus time curves for reversible parallel reactions indicating the possibility of a maximum in the concentration of one product species. 

This section discusses the kinetic implications of series reactions. We will be concerned only with those cases where the progress of the various stages of the overall transformation is not influenced by either parallel or reverse reactions. The discussion will again be limited to constant volume systems. 

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. 

If a particular molecular entity(ies) participates in two or more parallel reactions and the proportion of the resulting products is determined by the relative equilibrium constants for the interconversion of reaction intermediates on or after the rate-determining step(s), then the more prevalent product is said to be thermodynamically controlled (i.e., the more stable product will be the one formed in highest amounts). If the reactions are reversible and the system is allowed to go to equilibrium, the favored product is the thermodynamically controlled species. A synonymous term is equilibrium control. See also Kinetic Control... 

CONSECUTIVE-PARALLEL REACTIONS WITH REVERSIBLE STEPS... 

When reversible steps occur in a reaction scheme, distinctions between consecutive and parallel reactions cannot always be made. For example, the consecutive first-order reactions... 

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. 

Figure 8.10 Concentration-time curves for the elementary reversible parallel reactions...

In this chapter, we examine in depth the kinetics of reversible reactions, chain reactions, parallel reactions, and other reactions. 

The intrinsic stability of the aromatic n system has two major consequences for the course of reactions involving it directly. First, the aromatic ring is less susceptible to electrophilic, nucleophilic, and free-radical attack compared to molecules containing acyclic conjugated n systems. Thus, reaction conditions are usually more severe than would normally be required for parallel reactions of simple olefins. Second, there is a propensity to eject a substituent from the tetrahedral center of the intermediate in such a way as to reestablish the neutral (An + 2)-electron system. Thus, the reaction is two step, an endothermic first step resulting in a four-coordinate carbon atom and an exothermic second step, mechanistically the reverse of the first, in which a group is ejected. The dominant course is therefore a substitution reaction rather than an addition. 

The reversibility of the formation of bromonium ion is a process comparable to the formation of /5-bromo carbocations. In fact, the carbocation formation may be solvent-assisted81 as reported in reaction 8, which parallels reaction 4. 

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]. 

Industrial chemical reactions are often more complex than the earlier types of reaction kinetics. Complex reactions can be a combination of consecutive and parallel reactions, sometimes with individual steps being reversible. An example is the chlorination of a mixture of benzene and toluene. An example of consecutive reactions is the chlorination of methane to methyl chloride and subsequent chlorination to yield carbon tetrachloride. A further example involves the chlorination of benzene to monochlorobenzene, and subsequent chlorination... 

If a reaction has to be divided into more than one elementary reaction, it is called a reaction network. The complexity of such reaction networks can be very different, ranging from just two elementary reactions to a network consisting of parallel-, side-, subsequent-, and equilibrium reactions. Details about more complicated reactions, such as bimolecular reactions, reversible reaction steps and reactions with different kinds of adsorption (chemical, physical, dissociative, etc.), can be found in the typical literature [1-4]. 

This effect is in agreement with the findings of Ashmore et To explain the anomalously fast rate of the decomposition of NO2, these workers postulated that parallel reaction paths were occurring, one the usual molecular path and the other by a free radical mechanism. If this is correct then the principle of microscopic reversibility requires that the oxidation of NO also proceeds by two paths ... 

The derivatives of Meldrum s acid, 59a-b, undergo reductive dimerization in MeCN, and the mechanism has been studied [137,143]. An RS mechanism with rate-determining electron transfer has been invoked either as the only mechanism (for 59b) or as one of two parallel reaction pathways (for 59a) in order to explain the apparent reaction orders found by DCV or LSV in the presence of AcOH [137]. However, AcOH (pA (AcOH) = 12.3 in DMSO [144]) is not likely to be strong enough to protonate the dimer dianion, since the basicity of the dimer dianion is expected to be close to that of the conjugate base of Meldrum s acid (pAT(Meldrum s acid) = 7.3 in DMSO [145]). Consequently, the dimerization may be reversible, and this, in turn, may lead to anomalous apparent reaction orders, although the coupling is of the RR type [76]. 

---