Steps, elementary consecutive

Chain Reactions Chain reactions where reactive intermediate substances chain carriers such as atoms, free radicals, or ions) are responsible for the permanent repetition of steps are consecutive reactions of a special type. We distinguish the following elementary steps in a chain reaction ... 

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-... 

In the case of coupled heterogeneous catalytic reactions the form of the concentration curves of analytically determined gaseous or liquid components in the course of the reaction strongly depends on the relation between the rates of adsorption-desorption steps and the rates of surface chemical reactions. This is associated with the fact that even in the case of the simplest consecutive or parallel catalytic reaction the elementary steps (adsorption, surface reaction, and desorption) always constitute a system of both consecutive and parallel processes. If the slowest, i.e. ratedetermining steps, are surface reactions of adsorbed compounds, the concentration curves of the compounds in bulk phase will be qualitatively of the same form as the curves typical for noncatalytic consecutive (cf. Fig. 3b) or parallel reactions. However, anomalies in the course of bulk concentration curves may occur if the rate of one or more steps of adsorption-desorption character becomes comparable or even significantly lower then the rates of surface reactions, i.e. when surface and bulk concentration are not in equilibrium. 

This reaction undergoes conversion in one sequence of consecutive elementary reaction steps and so only one propagating front is formed in a spatially distributed system [68]. Depending on the initial ratio of reactants, iodine as colored and iodide as uncolored product, or both, are formed [145]. 

AI2O3 is initially <3, as expected from reaction (13.37), which indicates that the NO2 uptake at the beginning of the pulse does not obey the overall stoichiometry of the reaction. This has been explained in the literature, considering that the NO2 disproportionation consists of consecutive elementary steps and that the first step is faster than the following ones, which account for the evolution of NO (Equations 13.38-13.40) [94] ... 

An overall reaction includes two or more elementary reactions indeed there is no limit to the number of reactants or elementary reactions comprising an overall reaction. Thus if a single reaction step as written has four or more reactants, it cannot be an elementary process, and it must occur via two or more consecutive steps. If a reaction step contains two to three reactants, it may, or may not, be an elementary reaction. 

Solid-state growth of the layer of any chemical compound ApBq between two mutually insoluble elementary substances A and B is due to two parallel partial chemical reactions proceeding at its interfaces, each of which takes place in the two consecutive, continuously alternating steps ... 

Solid-state growth of the A,BS layer at the interface between elementary substances A and B is due to two partial chemical reactions each of which occurs in two consecutive, alternate steps (see Chapter 1). Firstly, the B... 

Let us now analyse dissociation and recombination in detail. As we saw in the previous sections dissociative adsorption is a process consisting of at least two consecutive elementary steps. Molecular adsorption proceeds dissociation. Dissociation occurs when reaction (4.4) is thermodynamically feasible. We learned in Section 4.2.1 that the surface adatom bond energy varies more than the molecular adsorption bond with variation of metal. Adsorption of atoms is favoured by metals with a partially filled d valence electron band or metals of a low work function. CO will dissociate on the first row transition metals (except... 

There are a considerable number of reactions in which the products contain two electrons, more than the starting compounds, and the consecutive two-step one-electron electron transfer process proves to be energetically unfavorable. In such cases, it is presumed that the two-electron process occurs in one elementary two-electron step. An example of a two-electron process is the hydride transfer, when two electrons are transported together with a proton. BH4, hydroquinones and reduced nicotinamides are typical hydrid donors. A specific feature of quinones is the capacity to accept and then to reversibly release electrons one by one or two electrons as a hydride. Therefore, quinones can serve as a molecular device, which can switch consecutive one-electron process to single two-electron process. 

Nature accomplishes many syntheses-even those of complex molecules-by sequences of elementary steps. In the last few decades, the blueprint of catalyzed cascade reactions has found fertile soil through the advent of transition metal catalysis in laboratories. Scrutinizing catalytic cycles and mechanistic insight has paved the way for designing new sequential transformations catalyzed by transition metal complexes in a consecutive or domino fashion. In particular, transition metal-catalyzed sequences considerably enhance structural complexity by multiple iterations of organometalhc elementary steps. All this has fundamentally revolutionized synthetic strategies and conceptual thinking. 

An important consequence of the preceding consideration is the evident occurrence of the limitation (which is typicaUy not taken into account) for the maximum aUowed number of kineticaUy irreversible steps in the real stationary chemical reactions. Indeed, when the consecutive elementary chemical reactions proceed in the stationary mode, a total of affinity ArS of the stepwise reaction equals the sum of affinities of aU the elementary steps... 

This corresponds to the activation energy Ea2 of the elementary step of the product P elimination from intermediate K-, and equals approximately (to an accuracy of RT) the heat of the formation of the transition state of elementary reaction 2 from the standard state of intermediate Ki (Figure 4.2A). Note that here and in other examples of catalytic reaction schemes with the high occupation of the active center with intermediates the value of the apparent activation energy does not follow the statement in Section 1.4.5 on the apparent activation energies of noncatalytic consecutive processes. 

The initiation process may involve either a single or a few consecutive elementary reactions. In the latter case, the understanding of this process requires knowledge of afl these steps their chemistry and rate constants. NMR spectroscopy proved to be the experimental method of choice in kinetic and mechanistic studies of initiation. However, UV spectroscopy, polarography, conductivity, and the tracer method were also applied. Because of the complexity of initiation, the kinetic studies were performed only for a limited number of systems. The rate constants of the elementary reactions were only determined for a few simpler systems. 

According to Horiuti and Polanyi (111) the hydrogenation reaction of ethylene in the presence of a nickel catalyst consists of the following consecutive elementary steps ... 

The catalytic hydrogenation of ethylene on nickel, as explained by Horiuti, is based on four consecutive elementary reactions, viz., the chemisorption of the reactants to form adsorbed ethylene (la) and adsorbed hydrogen atoms (Ib), the reaction (II) between these adsorbents to give half-hydrogenated molecules, and the addition of another adsorbed hydrogen atom (III) to form ethane. In this mechanism, step (Ib) is... 

The examples of reversible and consecutive reactions presented here give a very modest introduction to the subject of reaction mechanisms. Most reactions are complex, consisting of more than one elementary step. An elementary step is a unimolecular or bimolecular process which is assumed to describe what happens in the reaction on a molecular level. In the gas phase there are some examples of termolecular processes in which three particles meet simultaneously to undergo a reaction but the probability of such an event in a liquid solution is virtually zero. A detailed list of the elementary steps involved in a reaction is called the reaction mechanism. 

When the copper-catalysed reactions (type A and type B) were performed in the cavity of an ESR spectrometer, the presence of phenyl radicals was detected by way of their spin adducts with 2-methyl-2-nitrosopropane and with 2,4,6-tribromonitrosobenzene.98 In view of these observations, Dodonov et al. suggested that a free-radical mechanism was involved in both reaction types, A and B, and explained the formation of the hypervalent copper (HI) intermediate. (Scheme 6.23) The copper (HI) intermediate is formed by two consecutive one-electron oxido-reduction elementary steps. The copper (1) catalytic species is first oxidised to a copper(Il) species which is then oxidised by a phenyl rascal to the active copper (HI) intermediate. This hypervalent species then undergoes a ligand coupling reaction with the substrate, either hydroxylic or an amino derivative. In the type B reaction, the in situ generated phenylcopper (III) diacetate reacts with the substrate to eventually afford the O- or the iV-phenyl derivative. 

In the series of consecutive elementary steps of the selective oxidation of a hydrocarbon molecule, the negatively charged alkyl, formed after abstraction of a proton, must become bonded to a surface oxide ion of the catalyst to form the alkoxy-species, generally accepted, to be next intermediates. Their appearance at the surface of oxide catalysts in the course of the selective oxidation of hydrocarbons has been proved experimentally by many techniques, e.g. in-situ IR and Raman spectroscopies (33). 

Thus, the reason for the stability of the T1(CN) " complexes is obviously their kinetic inertness. It is generally assumed that reduction-oxidation reactions often consist of several elementary, one-electron steps. This assumption is based on the fact that the transfer of several electrons in a single elementary discharge act is less probable than the sequential transfer through one-electron consecutive steps (however, see the discussion in the beginning of this section). In the present case, the reaction... 

Consider the following elementary steps for a consecutive reaction ... 

Extensions of the simple network of consecutive irreversible reactions can easily be expanded to include multiple steps and products, formed by reversible and irreversible elementary reactions. In all complex processes the writing of a reaction network produces the most general description of the kinetic process. Fortunately, in many cases the network is such that the steady state assumptions can be invoked. When this is possible, the kinetic rate expressions for the elementary processes of the reaction mechanism can often be solved analytically, as in the example above, to yield a simpler rate expression for the overall process. The identification of such a mechanistic rate expression, using experimental rate data from a kinetic study, can serve to identify the likely mechanism of that reaction. 

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