Reaction, consecutive single

In actual in-situ coal gasification, numerous processes, i.e. oxidation, reduction, thermal cracking and a variety of catalytic as well as non-catalytic reactions, occur in overlapping zones, and to explore the chemistry of these reactions as single or consecutive unit processes is virtually impossible. It is, however, feasible to study the individual reactions under controlled conditions by simulating in-situ gasification in the laboratory. 

Equation (19-22) indicates that, for a nominal 90 percent conversion, an ideal CSTR will need nearly 4 times the residence time (or volume) of a PFR. This result is also worth bearing in mind when batch reactor experiments are converted to a battery of ideal CSTRs in series in the field. The performance of a completely mixed batch reactor and a steady-state PFR having the same residence time is the same [Eqs. (19-5) and (19-19)]. At a given residence time, if a batch reactor provides a nominal 90 percent conversion for a first-order reaction, a single ideal CSTR will only provide a conversion of 70 percent. The above discussion addresses conversion. Product selectivity in complex reaction networks may be profoundly affected by dispersion. This aspect has been addressed from the standpoint of parallel and consecutive reaction networks in Sec. 7. 

The rearrangement of 1-methoxy-substituted bicyclo[2.2.2]octenones (66a-d) follows a mechanistic variant of the ODPM reaction, which includes two consecutive single-step phototransformations, i.e. the ODPM path to (67a-d), again triplet sensitized, and conversion to the final 1,4-diketones (68a-d) cf. Scheme 13).5-1U05-108 jjjg second step involves cleavage of the transient cyclopropane in (67a-d) accompanied by loss of the methoxy methyl, most likely via methyl radicals, and transfer of a hydrogen atom from the solvent. 

There is yet another phenomenon that points to a 1,4-addition of fluorine atoms occurring at least partially The products obtained from the reaction of single-walled carbon nanotubes with fluorine are definite nonconductors (resistance >20 MQ), while the nanotubes employed feature a resistance of 10-15 2 only. Considering the structures that result from a consecutive 1,2- or 1,4-addition of fluorine, respectively, reveals that an electric current via conjugated it-bonds would still be possible in the 1,2-adduct (Figure 3.70). In the 1,4-adduct, on the other... 

Aromatic substituents at the chains of vinyl polymers influence the behavior of these materials. Aromatic units as part of the main chain exert a profound influence on virtually all important properties of the resulting polymer. Aromatic polyamides are formed by the repetitive reaction of aromatic amino group and carboxyl group in the molar ratio of 1 1. In aromatic polyamides as well as aromatic polyesters, the chain-stiffening aromatic rings are separated from each other by three consecutive single bonds ... 

The sequence of various treatments in consecutive cycles should, in principle, simulate natural exposure whilst accelerating its effects in a standardized way. In most test procedures, elevated temperature is applied to accelerate chemical reactions. No single accelerated test can fully simulate the full range of ageing processes and therefore a series of tests of a different character is usually executed, after identification of the main ageing mechanisms, which may be considerably accelerated in that way. 

Electron transfer as an elementary step is a necessary part of the stoichiometric mechanism of all redox and, as has recently been shown, some heterolytic reactions. The most important reactions are those of single-electron transfer (SET). The multi-electron transport in chemical and biochemical transformations consists, as a rule, of a series of consecutive single-electron transfer reactions, while the one-step two-electron transfers are relatively rare. 

However, the polarization curves have a Tafel slope of about 60 mV decade at overvoltages lower than 0.1 V and about 180 mV decade at higher overvoltages. The authors explain this switch from a low to a high Tafel slope by a mechanism with two consecutive single-electron transfer reactions ... 

The bimodal profile observed at low catalyst concentration has been explained by a combination of two light generating reactive intermediates in equihbrium with a third dark reaction intermediate which serves as a way station or delay in the chemiexcitation processes. Possible candidates for the three intermediates include those shown as "pooled intermediates". At high catalyst concentration or in imidazole-buffered aqueous-based solvent, the series of intermediates rapidly attain equihbrium and behave kineticaHy as a single kinetic entity, ie, as pooled intermediates (71). Under these latter conditions, the time—intensity profile (Fig. 2) displays the single maximum as a biexponential rise and fall of the intensity which is readily modeled as a typical irreversible, consecutive, unimolecular process ... 

For a single equation, Eqs. (7-36) and (7-37) relate the amounts of the several participants. For multiple reactions, the procedure for finding the concentrations of all participants starts by assuming that the reactions proceed 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 the series. The final value carries no subscript. After the intermediate concentrations are ehminated algebraically, the compositions of the excess components will be expressible in terms of the key components. 

These statements refer to an elementary reaction, which from this point of view may be defined as a reaction possessing a single transition state. A complex reaction is then a set of elementary reactions, the potential energy surface of the whole being continuous. Thus, for two consecutive reactions the product of the first reaction is the reactant of the second. Each reaction has its own transition state. 

Compared with uncatalyzed reactions, catalysts introduce alternative pathways that, in nearly all cases, involve two nr more consecutive reaction steps. Each of these steps has a lower activation energy than does the uncatalyzed reaction. We can nse as an example the gas phase reaction of ozone and oxygen atoms. In the homogeneons uncatalyzed case, the reaction is represented to occur in a single irreversible step that has a high activation energy ... 

Reactions of this type are mostly performed with internal nucleophiles attached to the carbon atom adjacent to the iminium nitrogen, thus leading to tropane-like azabicyclic systems. Both allyl- and propargylsilanes, activated and unactivated alkenes, and ketones have been successfully used as nucleophiles. The products 1 and 2 are also obtained via two consecutive C —C bond-forming reactions in a single operation. 

The simultaneous determination of a great number of constants is a serious disadvantage of this procedure, since it considerably reduces the reliability of the solution. Experimental results can in some, not too complex cases be described well by means of several different sets of equations or of constants. An example would be the study of Wajc et al. (14) who worked up the data of Germain and Blanchard (15) on the isomerization of cyclohexene to methylcyclopentenes under the assumption of a very simple mechanism, or the simulation of the course of the simplest consecutive catalytic reaction A — B —> C, performed by Thomas et al. (16) (Fig. 1). If one studies the kinetics of the coupled system as a whole, one cannot, as a rule, follow and express quantitatively mutually influencing single reactions. Furthermore, a reaction path which at first sight is less probable and has not been therefore considered in the original reaction network can be easily overlooked. 

The procedure for solving the relations between concentrations has been used in kinetic studies of complex catalytic reactions by many authors, among the first of them being Jungers and his co-workers 17-20), Weiss 21, 22), and others [see, e.g. 23-25a). In many papers this approach has been combined with the solution of time dependencies, at least for some of the single reactions. Also solved were some complicated cases [e.g. six-step consecutive reaction 26,26a) 3 and some improvements of this time-elimination procedure were set forth 27). The elimination of time is... 

In contrast to consecutive reactions, with parallel competitive reactions it is possible to measure not only the initial rate of isolated reactions, but also the initial rate of reactions in a coupled system. This makes it possible to obtain not only the form of the rate equations and the values of the adsorption coefficients, but also the values of the rate constants in two independent ways. For this reason, the study of mutual influencing of the reactions of this type is centered on the analysis of initial rate data of the single and coupled reactions, rather than on the confrontation of data on single reactions with intergal curves, as is usual with consecutive reactions. 

No single mechanistic explanation of the S— T effect has been accepted as possessing general validity the salient features of the several alternative reaction models which remain under discussion are summarized below. There also exist the possibilities that there may be concurrent, consecutive or intermediate behaviour and that different mechanisms may operate for different solids. 

At a fixed temperature, a single, reversible reaction has no interior optimum with respect to reaction time. If the inlet product concentration is less than the equilibrium concentration, a very large flow reactor or a very long batch reaction is best since it will give a close approach to equilibrium. If the inlet product concentration is above the equilibrium concentration, no reaction is desired so the optimal time is zero. In contrast, there will always be an interior optimum with respect to reaction time at a fixed temperature when an intermediate product in a set of consecutive reactions is desired. (Ignore the trivial exception where the feed concentration of the desired product is already so high that any reaction would lower it.) For the normal case of bin i , a very small reactor forms no B and a very large reactor destroys whatever B is formed. Thus, there will be an interior optimum with respect to reaction time. 

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. 

In terms of gross features of mechanism, a redox reaction between transition metal complexes, having adjacent stable oxidation states, generally takes place in a simple one-equivalent change. For the post-transition and actinide elements, where there is usually a difference of two between the stable oxidation states, both single two-equivalent and consecutive one-equivalent changes are possible. 

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