And parallel reactions

The reaction mechanism depends on the chemistry of the active oxidant and chemical contaminants. Multiple sequential and parallel reaction steps occur frequently. Partial oxidation produces noxious byproducts. 

The following details mathematical expressions for instantaneous (point or local) or overall (integral) selectivity in series and parallel reactions at constant density and isotliermal conditions. An instantaneous selectivity is defined as the ratio of the rate of formation of one product relative to the rate of formation of another product at any point in the system. The overall selectivity is the ratio of the amount of one product formed to the amount of some other product formed in the same period of time. 

This reaction cannot be elementary. We can hardly expect three nitric acid molecules to react at all three toluene sites (these are the ortho and para sites meta substitution is not favored) in a glorious, four-body collision. Thus, the fourth-order rate expression 01 = kab is implausible. Instead, the mechanism of the TNT reaction involves at least seven steps (two reactions leading to ortho- or /mra-nitrotoluene, three reactions leading to 2,4- or 2,6-dinitrotoluene, and two reactions leading to 2,4,6-trinitrotoluene). Each step would require only a two-body collision, could be elementary, and could be governed by a second-order rate equation. Chapter 2 shows how the component balance equations can be solved for multiple reactions so that an assumed mechanism can be tested experimentally. For the toluene nitration, even the set of seven series and parallel reactions may not constitute an adequate mechanism since an experimental study found the reaction to be 1.3 order in toluene and 1.2 order in nitric acid for an overall order of 2.5 rather than the expected value of 2. 

TEMPERATURE OPTIMIZATION OF BATCH REACTOR CONSECUTIVE AND PARALLEL REACTION SEQUENCE... 

It is proposed to react 1 t-h-1 of a pure liquid A to a desired product B. Byproducts C and D are formed through series and parallel reactions ... 

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. 

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. 

It has been shown [90] that the homogeneous dissociation of methane is the only primary source of free radicals and it controls the rate of the overall process. This reaction is followed by a series of consecutive and parallel reactions with much lower activation energies. After the formation of acetylene (C2H2), a sequence of very fast reactions occurs, leading to the production of higher unsaturated and aromatic hydrocarbons and finally carbon ... 

As briefly discussed in Section 1.2, chemical-reaction engineers recognized early on the need to predict the influence of reactant segregation on the yield of complex reactions. Indeed, the competitive-consecutive and parallel reaction systems analyzed in the previous section have been studied experimentally by numerous research groups (Baldyga and Bourne 1999). However, unlike the mechanical-engineering community, who mainly focused on the fluid-dynamics approach to combustion problems, chemical-reaction... 

Note that the definition of max is different for the competitive-consecutive and parallel reactions. 

The fact that reaction (12) is much slower than reaction (8), implies that Fe is faster depleted from the solution. As a result, Fenton process is halted because the redox chain cannot be supported itself. In addition, it is accepted that (Pignatello 1992 Boye et al. 2003) the hydroperoxyl radical (HO2 ) has a much lower oxidant power than OH. In the presence of organics, Fenton chemistry is even more complex because hydroxyl radical, both iron cations and the oxidation products enter into a series of consecutive and parallel reactions. An example of the complexity of these reactions is discussed elsewhere (Gozzo 2001) but a brief description is given here. The initial step for an organic substrate (R-H) oxidation starts with the interaction of itself with OH, according to (Walling and Kato 1971) ... 

In some reaction processes, both consecutive and parallel reactions may occur. In a reaction scheme such as... 

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... 

We could write species mass-balance equations (S = 6 in this example) on any such reaction sequence and solve these (/ = 4 are inseparable) to find Cj x), and in most practical examples we must do this. However, there are two simple reaction networks that provide insight into these more complex networks, and we wiU next consider them, namely, series and parallel reaction networks (Figure 4-3). 

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. 

When selectivity and yield of a given product need to be maximized, the design issues become more complicated. While rninimum T is frequently desired, it is usually more important to obtain maximum selectivity to a desired product and niinimiim selectivity to undesired products. For simple series and parallel reaction systems, we can fairly easily summarize the choices. 

As discussed herein, it can be concluded that the mechanistic pathways of the per-oxyoxalate system in the presence of imidazole are well described and that there is a consensus at least in regard to the steps prior to the formation of the HEI. Conventional kinetic studies on this complex transformation, with various consecutive and parallel reaction steps, permit the formulation of a mechanistic scheme, containing the important steps in the Tight-producing pathways, for which rate constants have been determined. Even so, the smdies concerning the EIEI strucmre are still controversial. Many authors favor 3 and/or 48 as the most probable candidates for the HEI, while others have suggested... 

With the addition of Reactions 2-173 and 2-174, the production and consumption of ozone include both chain and parallel reactions. The method of solution is nonetheless similar to the case without anthropogenic ozone destruction. To solve for the concentration of [O3], it is necessary to solve for [XO], [O], and [O3] from three equations d[XO]/df=0, d[O]/df=0, and d[O3]/df=0. 

As described in section 3.3, correlation studies between CS plane defects observed by ETEM and and parallel reaction chemistry (under conditions similar to those used in ETEM) indicate that the CS planes which eliminate supersaturation of anion vacancies are a consequence of catalytic activity and not active oxygen exchange sites for catalysis as was originally believed. They are secondary or detrimental to catalysis. The correlation results strongly suggest that anion point defects are active centres in the rapid diffusion of oxygen in... 

Kinetic models which consider demetallation as a complex reaction network of consecutive and parallel reactions taught by model compound studies have been recognized with real feedstocks. Tamm et al. (1981) suggest a sequential mechanism where the metal compounds are activated by H2S. Model compound reaction pathway studies in the absence of H2S, discussed in Section IV,A,1, and experiments in which H2S was present in excess (Pazos et al., 1983) indicate that sequential reactions are inherent to the chemistry of the metal compounds irrespective of the presence of H2S. However, it is possible that both mechanisms contribute to metal removal. 

All hydroconversion processes involve a complex suite of series and parallel reactions cracking, hydrogenation, sulfur removal, and demetallization. 

This reaction system is a kind of complex van de vusse reaction, a typical reaction process involving consecutive and parallel reactions. It is, therefore, sufficiently complex to illustrate the algorithm. Due to the limit to the space of the article, we only select temperature, concentration and back-mixing to be the object of research to illustrate the use of the algorithm. 

Finally, the eighth reaction mechanism in Table 2.1 includes both series and parallel reactions to the same product P. This scheme is more complete and somewhat more realistic, but it is not so much different from the series scheme, because the side parallel reaction to P only produces small changes in the shape of the concentration profiles. As an example, the initial zero derivative for Cp can be canceled. 

To demonstrate this more clearly, reaction arrows for consecutive and parallel reactions, also displayed in Figure 2.1, converge at a point from which, however, it does not follow that final products formed by all reactive pathways possess equal composition. Remember... 

Note that in some cases, consecutive and parallel reactions may proceed without the formation of an intermediate product of the first kind, when interaction of the initial molecules causes formation of final products excluding the stage of active site formation (these reactions... 

The kinetics of consecutive, consecutive-parallel and parallel reactions of any complexity is discussed in classical monographs on chemical kinetics [1-3,11] and are not considered in the current monograph. The scope of kinetic regularities of these complex reactions mentioned will be minimally required for a clear understanding of their differences from kinetics of conjugated reactions. 

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