Complex system reaction stoichiometry

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The very basis of the kinetic model is the reaction network, i.e. the stoichiometry of the system. Identification of the reaction network for complex systems may require extensive laboratory investigation. Although complex stoichiometric models, describing elementary steps in detail, are the most appropriate for kinetic modelling, the development of such models is time-consuming and may prove uneconomical. Moreover, in fine chemicals manufacture, very often some components cannot be analysed or not with sufficient accuracy. In most cases, only data for key reactants, major products and some by-products are available. Some components of the reaction mixture must be lumped into pseudocomponents, sometimes with an ill-defined chemical formula. Obviously, methods are needed that allow the development of simple... 

The operational interpretation of rA, as opposed to this verbal definition, does depend on the circumstances of the reaction.1 This is considered further in Chapter 2 as a consequence of the application of the conservation of mass to particular situations. Furthermore, rA depends on several parameters, and these are considered in Section 1.4.2. The rate with respect to any other species involved in the reacting system may be related to rA directly through reaction stoichiometry for a simple, single-phase system, or it may require additional kinetics information for a complex system. This aspect is considered in Section 1.4.4, following a preliminary discussion of the measurement of rate of reaction in Section 1.4.3. 

Alternatively, the conservation of atomic species is commonly expressed in the form of chemical equations, corresponding to chemical reactions. We refer to the stoichiometric constraints expressed this way as chemical reaction stoichiometry. A simple system is represented by one chemical equation, and a complex system by a set of chemical equations. Determining the number and a proper set of chemical equations for a specified list of species (reactants and products) is the role of chemical reaction stoichiometry. 

In previous chapters, we deal with simple systems in which the stoichiometry and kinetics can each be represented by a single equation. In this chapter we deal with complex systems, which require more than one equation, and this introduces the additional features of product distribution and reaction network. Product distribution is not uniquely determined by a single stoichiometric equation, but depends on the reactor type, as well as on the relative rates of two or more simultaneous processes, which form a reaction network. From the point of view of kinetics, we must follow the course of reaction with respect to more than one species in order to determine values of more than one rate constant. We continue to consider only systems in which reaction occurs in a single phase. This includes some catalytic reactions, which, for our purpose in this chapter, may be treated as pseudohomogeneous. Some development is done with those famous fictitious species A, B, C, etc. to illustrate some features as simply as possible, but real systems are introduced to explore details of product distribution and reaction networks involving more than one reaction step. 

For a complex system, determination of the stoichiometry of a reacting system in the form of the maximum number (R) of linearly independent chemical equations is described in Examples 1-3 and 14. This can be a useful preliminary step in a kinetics study once all the reactants and products are known. It tells us the minimum number (usually) of species to be analyzed for, and enables us to obtain corresponding information about the remaining species. We can thus use it to construct a stoichiometric table corresponding to that for a simple system in Example 2-4. Since the set of equations is not unique, the individual chemical equations do not necessarily represent reactions, and the stoichiometric model does not provide a reaction network without further information obtained from kinetics. 

A related explanation has to do with the stability of the peroxo dicopper(II) intermediate, since it will either attack the substrate or decompose the kinetics of formation of the intermediate relative to those of the ensuing decomposition reactions will thus be important. Nelson (53) and Sorrell (90) have both described systems that undergo a Cu 02 = 4 1 reaction stoichiometry for dicopper(I) complexes where they propose that degradation of the peroxo dicopperfll) intermediate proceeds by the fast bimolecular two-electron transfer fiom a second dicopper(I) molecule to the putative peroxo-dicopper(II) intermediate to give an aggregated oxo-copper(II) product. [The latter may form hydroxo-Cu(II) species in the presence of protic solvents]. 

These rates are the rates of production of species A, B, and C (rj = Vjr) so these rates are written as negative quantities for reactants and positive quantities for products. This notation quickly becomes cumbersome for complex reaction stoichiometry, and the notation is not directly usable for multiple reaction systems. 

Macroscopic chemical techniques can be used to characterize overall reactions like those in Eqs. 1.3, 1.8, and 1.9. Given the complexity of reaction mechanisms, however, measurements of the composition of the aqueous system in which an overall reaction occurs over the course of time may not always yield data that conform to the expected stoichiometry. For example, if the reaction of carbon dioxide and water to produce protons and bicarbonate ions is initiated at high pH (very low proton concentration), the disappearance of 1 mol C02 need not be accompanied by the disappearance of 1 mol H20 (because of Eq. 1.5) or by the appearance of 1 mol H+ (because of Eq. 1.1).2,7 The unaccounted-for presence of intermediate species (like H2COj in Eq. 1.1) can lead typically to a delay in the formation of one or more final product species relative to the others, such that the expected stoichiometry in an overall reaction is violated when the reaction progress is monitored. This transient feature of mole balance in overall reactions has important ramifications when the kinetics of soil chemical processes are investigated (Section 1.3). 

Complex hydride reductions of Nj, N O, [CN] and nitriles in reactions containing complex mixtures of metal-ion species produce N—H bonded products " by reactions that may relate to those of the biological nitrogenases". Complete reaction stoichiometries are not well established. These reactions are not competitive with other methods for NH or amine synthesis. Nitrogen reacts in H O with a mixture of NaBH, S-donor ligands (e.g., NH CjM SH) and Mo and Fe salts to form NHj and NjH in low yield . In similar systems, nitriles and isonitriles are reduced to NHj and amines in low yield . 

The reaction stoichiometry of permanganate (typically provided as liquid or solid KMnO, but also available in Na, Ca, or Mg salts) in natural systems is complex. Owing to its multiple valence states and mineral forms, Mn can participate in numerous reactions. The reactions proceed at a somewhat slower rate than the previous two reactions, according to second-order kinetics. Depending on pH, the reaction can include destraction by direct electron transfer or free-radical advanced oxidation. Permanganate reactions are effective over a pH range of 3.5-12. 

Model system 86 was designed to evaluate the relative importance of the synclinal vs antiperiplanar geometries (Scheme 10-39 and Table 10-6) [17a,b,cJ. Reaction of 86 with various Lewis acids resulted in the predominant formation of the proximal alcohol (6). The selectivities obtained with model 86 do not correlate with the size of the Lewis acid employed, as previously observed with the allylsilane model 5a. An early transition structure for these reactions is proposed to explain the insensitivity of the cyclization to the size of the Lewis acid-aldehyde complex. The following proposal for Type 2 reactions which proceed by direct addition was advanced (1) there exists a preference for the synclinal orientation of double bonds and (2) the bulk of the Lewis acid-aldehyde complex and the stoichiometry of complexation are stereochemically significant [73]. 

When a metalating agent such as BuLi-TMEDA is present in a much greater molar excess than the aromatic substrate, polymetalation frequently occurs. Polymetalation reactions of toluene, anthracene, biphenyl, fluorene, and indene have been extensively studied by West et ah (14) and Halasa (15). These results, as well as those cited above, illustrate that while metalation can be done conveniently with BuLi-TMEDA, complex metalated intermediates are often obtained, depending frequently on the reaction stoichiometry. This lack of selectivity can obviously limit the synthetic utility of a given reaction system. 

The main problem in applying stoichiometric considerations to bioprocessing (beyond quantification in non-open-reactor systems) arises from the complex metabolic reaction network. In simple reactions stoichiometry is trivial, and complex reactions can only be handled with the aid of a formal mathematical approach analogous to the approach for complex chemical reactions (Schubert and Hofmann, 1975). In such a situation, an elementary balance equation must be set up. Due to complexity, it is not surprising that the approach first used in the quantification of bioprocesses was much simpler— the concept of yield factors Y. This macroscopic parameter Y cannot be considered a biological constant. 

On the other hand, a very unique redox system involving Cu(l)/Cu(II)/Cu(III) oxidation states was reported by Ribas, Stahl, and coworkers [79-81]. They extensively studied the reactivity of the triazamacrocyclic ligand with Cu(II) and successfully characterized C-H activated Ar-Cu(Ill) and Cu(I) complexes. The careful investigation of the reaction stoichiometry revealed that 0.5 eq of Ar-Cu(III) and 0.5 eq of Ar-Cu(I) are formed from 1.0 eq of Cu(II), thus suggesting an disproportionation of Cu(II) into Cuflll) and Cu(I) during the C-H activation event (Eq. 46). Upon treatment of the isolated Ar-Cu(III) complex with MeOH as an oxygen nucleophile, the C-H alkoxylated product and Cu(l) salt are obtained quantitatively (Eq. 47). A similar C-N bond formation occurs when NH pyridone is used as a nitrogen nucleophile. 

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