Reaction stoichiometrically-simple

VL stoichiometric reaction, mild, simple high cost limited to NH2 salt heating to ca small specialties, sulfations ... 

The kinetics of a coupled reacting system consisting of n stoichiometrically simple reactions is described generally by a set of n differential equations... 

One of the possibilities is to study experimentally the coupled system as a whole, at a time when all the reactions concerned are taking place. On the basis of the data obtained it is possible to solve the system of differential equations (1) simultaneously and to determine numerical values of all the parameters unknown (constants). This approach can be refined in that the equations for the stoichiometrically simple reactions can be specified in view of the presumed mechanism and the elementary steps so that one obtains a very complex set of different reaction paths with many unidentifiable intermediates. A number of procedures have been suggested to solve such complicated systems. Some of them start from the assumption of steady-state rates of the individual steps and they were worked out also for stoichiometrically not simple reactions [see, e.g. (8, 9, 5a)]. A concise treatment of the properties of the systems of consecutive processes has been written by Noyes (10). The simplification of the treatment of some complex systems can be achieved by using isotopically labeled compounds (8, 11, 12, 12a, 12b). Even very complicated systems which involve non-... 

The three catalyst systems discussed in this section for the reduction of NO by CO underscore the mechanistic complexity of a reaction which is stoichiometrically simple. Extensive bond reorganization is required in the reduction via (113), and each of the catalyst systems appears to proceed by a different mechanism. While two of the three systems possess a common feature in terms of C02 formation, each appears to be different with respect to N20 production. The systematic development of new homogeneous... 

The steps for constructing and interpreting an isothermal, isobaric thermodynamic model for a natural water system are quite simple in principle. The components to be incorporated are identified, and the phases to be included are specified. The components and phases selected "model the real system and must be consistent with pertinent thermodynamic restraints—e.g., the Gibbs phase rule and identification of the maximum number of unknown activities with the number of independent relationships which describe the system (equilibrium constant for each reaction, stoichiometric conditions, electroneutrality condition in the solution phase). With the phase-composition requirements identified, and with adequate thermodynamic data (free energies, equilibrium con-... 

Sh2 substitutions frequently occur in chain reaction sequences, some of which we have already encountered in the earlier discussion. Equations 9.66-9.69 illustrate some reactions the simple stoichiometric equations serve only to emphasize the overall substitution nature of the process and do not reveal the complexities, often considerable, of the actual pathways followed. We shall not attempt to analyze these processes in detail, but in order to give a better idea of the mechanisms will describe more fully two of them, halogenation and autoxidation. 

The individual values of the rates of production Rj of the reaction components in a given reaction, obtained in the way just described, depend, however, on the reaction stoichiometry. In a single (stoichiometrically simple) reaction... 

In a reaction network in which several stoichiometrically simple reactions take place, eqs. 1 to 3 are still used for the primary treatment of the reactor data but the overall rate of production obtained for the y -th component is here equal to the algebraic sum of the rates of production in all the reactions in which the y-th component is formed or consumed. In such a case the evaluation of the reaction rates r of the individual reactions of the network from the rates of production Rj of the key components is more complicated. 

If a step of the sequence can be written as it proceeds at the molecular level, it is denoted as an elementary step (or an elementary reaction), and it represents an irreducible molecular event. Here, elementary steps will be called steps for short. The hydrogenation of dibromine is an example of a stoichiometrically simple reaction ... 

Reactive intermediates may be of numerous different chemical types (e.g., free radicals, free ions, solvated ions, complexes at solid surfaces, complexes in a homogeneous phase, complexes in enzymes). Although many reactive intermediates may be involved in a given reaction (see Scheme 1.1.1), the advancement of the reaction can still be described by a single parameter— the extent of reaction (see Section 1.2). If this is the case, the reaction is said to be single. Why an apparently complex reaction remains stoichiometrically simple or single, and how the kinetic treatment of such reactions can be enumerated are the two questions addressed in this chapter. 

Reaction of chlorine dioxide with hypochlorous acid is not stoichiometrically simple. At a pH of about 5.5, A[C102] > A[HC10] and it is suggested that reaction (2) contributed as well as (1), viz. 

Chemical reactions can be represented by an overall stoichiometric equation which indicates the relative molecular proportions with which the reactants combine to form the products of the particular reaction. Some simple examples from combustion chemistry are... 

Abstract The surfaces of model metal oxides offer many fundamental examples where the outcome of a specific chemical reaction might be linked to the surface structure and local electronic properties. In this work the reaction of simple molecules such as ammonia, alcohols, carboxylic and amino acids is studied on two metal oxide single crystals rutile TiO CllO) and (001) and fluorite UOj(l 11). Studies are conducted with XPS, TPD, and Plane Wave Density Functional Theory (DFT). The effect of surface structure is outlined by comparing the TiOj(llO) rutile surface to those of TiOjCOOl), while the effect of surface point defects is mainly discussed in the case of stoichiometric and substoichiometric UOjClll). 

We have seen that for stoichiometrically simple reactions of the type A-> B, the... 

AE reactions of simple olefins. The Sharpless AE reaction has been supplemented by other approaches to asymmetric epoxide synthesis the most evident goal being to obviate the need for an allylic alcohol. Attempts to carry out asymmetric epoxidation reactions on simple olefins have utilized transition-metal-containing catalysts such as porphyrins as well as stoichiometric chiral reagents (peroxides, dioxiranes, and oxaziridines). These approaches have been summarized [19]. 

Usually, intermolecular ene reactions of simple aldehydes with 1,1-disubstituted alke-nes bearing no additional activating substituents require stoichiometric quantities of powerful Lewis acids. [1] Therefore, catalytic asymmetric variants using milder Lewis acids have previously been restricted to especially reactive aldehydes in intermolecular processes or to intramolecular reactions. For example, Yamamoto et al. described the use of alumi-... 

Higher Order Irreversible Simple Parallel Reactions Many simple parallel reactions do not fit the categories discussed in the last two subsections. Of particular interest are the reactions between different chemical species to give two or more different products (e.g., the formation of orthOy meta, and para derivatives of an aromatic compound). This section is devoted to a discussion of Ihe mathematical relations that govern such reactions. Consider the following two stoichiometric equations as representative of this class of reactions ... 

Each reaction of the network is stoichiometrically simple in the sense that its advancement is described by a single parameter the extent of reaction (see next section). A stoichiometrically simple reaction will be called a single reaction or a reaction for short. The expression simple reaction is best avoided since, in general, a stoichiometrically simple reaction is far from simple. Indeed, in the vast majority of cases, a single reaction docs not lake place as written. It proceeds through a sequence oJ steps involving reactive intermediates that do not appear in the equation for reaction. In what follows, a sequence of steps will be called a sequence. The identification of these intermediates and the definition of the proper sequence arc the central problems of the kinetic analysis. This is logically the second task of the kineticist but it is not the last one. 

This result is very important it indicates the general functional form of the rate r for a stoichiometrically simple reaction. But, in practice, the ponderous solution (3.3.9) will be arrived at, not by blind application of the formulae involving the matrix (3.3.6), but by applying the general condition for the steady state (3.2.8) to every active center and by noting that, with a catalyst of constant activity, the sum of concentrations of active centers is equal to a constant. 

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