Reaction, consecutive multiple

The reaction of Example 7.4 is not elementary and could involve shortlived intermediates, but it was treated as a single reaction. We turn now to the problem of fitting kinetic data to multiple reactions. The multiple reactions hsted in Section 2.1 are consecutive, competitive, independent, and reversible. Of these, the consecutive and competitive t5T>es, and combinations of them, pose special problems with respect to kinetic studies. These will be discussed in the context of integral reactors, although the concepts are directly applicable to the CSTRs of Section 7.1.2 and to the complex reactors of Section 7.1.4. 

Eq 2.32 relates changes of the particpants of a reaction. For multiple reactions, the procedure for finding the end concentrations of all participants starts by assuming that the reactions occur consecutively. Key components are identified. Intermediate concentrations are identified by subscripts. The resulting concentration from a particular reaction is the starting concentration for the next reaction in series. The intermediate concentrations are eliminated algebraically.The compositions of the excess... 

In cases where reactions give multiple products, product selectivity is an important issue from a synthetic point of view. Usually much effort is made to increase the amount of a desired product and to decrease the amounts of undesired products. We have already discussed competitive consecutive reactions and competitive parallel reactions in Chapter 6. 

The role of mixing has been studied in systems with more complex reaction schemes or considering more complex fluid-dynamical properties, and in the context of chemical engineering or microfluidic applications (for reviews on microfluidics see e.g. Squires (2005) or Ottino and Wiggins (2004)). Muzzio and Liu (1996) studied bi-molecular and so-called competitive-consecutive reactions with multiple timescales in chaotic flows. Reduced models that predict the global behavior of the competitive-consecutive reaction scheme were introduced by Cox (2004) and by Vikhansky and Cox (2006), and a method for statistical description of reactive flows based on a con-... 

Scheme 6.3 Cascade reactions in glyco-conjugate syntheses. Either one-pot, sequential, or convergent cascade reactions can be applied. Sequential syntheses reactions employ multiple consecutive catalytic steps, whereas in one-pot syntheses multiple catalytic steps are combined in one reaction vessel...

Locklin and coworkers have intensively researched post-polymerization modification via click chemistry for the design of complex surfaces [41, 99-106]. The patterning of polymer-grafted planar surfaces was carried out by consecutive functionalization using the same click-type reaction or multiple click-type reactions. One example is a spatially patterned polymer brush surface fabricated by the combination of surface-initiated free-radical polymerization (Sl-LRP) and... 

In a complex enzyme reaction, multiple substrate-enzyme complexes are formed. Assume the following reaction mechanisms are taking place in three consecutive stages ... 

The carbon-centered radical R, resulting from the initial atom (or group) removal by a silyl radical or by addition of a silyl radical to an unsaturated bond, can be designed to undergo a number of consecutive reactions prior to H-atom transfer. The key step in these consecutive reactions generally involves the intra-or inter-molecular addition of R to a multiple-bonded carbon acceptor. As an example, the propagation steps for the reductive alkylation of alkenes by (TMSfsSiH are shown in Scheme 6. 

Multiple reactions involve two or more stoichiometric equations, each with its own rate expression. They are often classified as consecutive as in... 

Competitive consecutive reactions are combinations of parallel and series reactions that include processes such as multiple halogenation and nitration reactions. For example, when a nitrating mixture of HN03 and H2S04 acts on an aromatic compound like benzene, N02 groups substitute for hydrogen atoms in the ring to form mono-, di-, and tri-substituted nitro compounds. 

There are innumerable industrially significant reactions that involve the formation of a stable intermediate product that is capable of subsequent reaction to form yet another stable product. These include condensation polymerization reactions, partial oxidation reactions, and reactions in which it is possible to effect multiple substitutions of a particular functional group on the parent species. If an intermediate is the desired product, commercial reactors should be designed to optimize the production of this species. This section is devoted to a discussion of this and related topics for reaction systems in which the reactions may be considered as sequential or consecutive in character. 

Multiple Reactions—Choosing a reactor type to obtain the best selectivity can often be made by inspection of generalized cases in reaction engineering books. A quantitative treatment of selectivity as a function of kinetics and reactor type (batch and CSTR) for various multiple reaction systems (consecutive and parallel) is presented in [168]. 

For multiple reactions, material balances must be made for each stoichiometry. An example is the consecutive reactions, A = B = C, for which problem P4.04.52 develops a closed form solution. Other cases of sets of first order reactions are solvable by Laplace Transform, and of course numerically. 

Cobalt, as its CpCo(CO)2 complex, has proven to be especially suited to catalyze [2 + 2 + 2] cycloadditions of two alkyne units with an alkyne or alkene. These cobalt-mediated [2 + 2 + 2] cycloaddition reactions have been studied in great detail by Vollhardt337. The generally accepted mechanism for these cobalt mediated cycloadditions, and similar transition metal mediated cycloadditions in general, has been depicted in equation 166. Consecutive co-ordination of two triple bonds to CpCo(CO)2 with concomitant extrusion of two molecules of carbon monoxide leads to intermediates 578 and 579 via monoalkyne complex 577. These react with another multiple bond to form intermediate 580. The conversion of 578 to 580 is said to be kinetically favored over that of 579 to 580. Because intermediates like 580 have never been isolated, it is still unclear whether the next step is a Diels-Alder reaction to form the final product or an insertion to form 581. The exact circumstances might determine which pathway is followed. 

Quinones [124] and aromatic ketones such as flavones, [116] fluorenone, anthra-quinone, and similar compounds [121] dissociate by competing and consecutive losses of CO and C2H2. Multiple CO losses may also occur subsequent to the RDA reaction of flavones. [116,125] As these molecules all have large 71-electron... 

Fig. 2. Schematic representation of paclitaxel biosynthesis. Dimethylallyl-diphosphate and isopentenyl-diphosphate are condensed through geranylgeranyl diphosphate synthase activity to render geranylgeranyl-diphosphate (GGPP). GGPP is converted into taxa-4(5), 11 (12)-diene in a reaction catalyzed by the taxane synthase (TS). A series of reactions catalyzed by cytochrome P450 monoxygenases lead to the production of a taxane intermediate that is further converted to baccatin III through enzymes-driven oxidation and oxetane ring formation. The side chain moiety of paclitaxel is derived from L-phenylalanine. Three consecutive arrows mean multiple steps. Ac, acetyl Bz, benzoyl.

It is a serious but frequently neglected problem that the analysis of the data obtained with the method (2) or (3) above is only straightforward when each molecule undergoes only a one-step reaction upon one adsorption sojourn on the catalyst surface. If several consecutive reactions (e.g., isomerization combined with hydrogenolysis or two isomerization steps in combination) follow each other before the molecules leave the surface, useful information is still gained (167, 168), but the discussion of data is more complicated. Metals like Pt or Pd do not seem to be a problem in this respect, as is the case with other metals at the lowest possible reaction temperatures. However, metals like Ir or Rh are apparently very active in performing several consecutive steps during one residence of the molecules on the surface, and at temperatures above 200°C it is difficult to avoid the multiple reactions (167). 

Abstract—The question of the multiplicity of the steady states of a chemical reactor was one of the concerns in the pioneering work ofBilous and Amundson. Their diagrams showed quite clearly the geometry of the situation, and this kind of analysis sufficed for many years. It remained for Balakotaiah and Luss, using the methods of singularity theory, to give a comprehensive treatment of the question. After a brief survey, we take up the case of consecutive first-order reactions and show that up to seven steady states are possible. 

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