Steps, elementary parallel

In many cases one may anticipate several sequences of elementary steps in parallel. Since, in principle, all reaction rates are finite, the contribution of each sequence is finite. In general, only the sequence of steps which yields the greatest contribution in comparison to other sequences is ascertained. In a few cases, however, it is also possible to determine the individual contributions of two or more sequences in parallel, see, e.g.,the reaction 2CO -)- O2 = 2CO2, Section V.D., and the decomposition of formic acid. Section VIII.B. 

It is possible to represent the whole scheme in Fig. 6.46 approximately in the form of a network of elementary steps in parallel and series. If the rate constants... 

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. 

For most real systems, particularly those in solution, we must settle for less. The kinetic analysis will reveal the number of transition states. That is, from the rate equation one can count the number of elementary reactions participating in the reaction, discounting any very fast ones that may be needed for mass balance but not for the kinetic data. Each step in the reaction has its own transition state. The kinetic scheme will show whether these transition states occur in succession or in parallel and whether kinetically significant reaction intermediates arise at any stage. For a multistep process one sometimes refers to the transition state. Here the allusion is to the transition state for the rate-controlling step. 

The strong emphasis placed on concentration dependences in Chapters 2-5 was there for a reason. The algebraic form of the rate law reveals, in a straightforward manner, the elemental composition of the transition state—the atoms present and the net ionic charge, if any. This information is available for each of the elementary reactions that can become a rate-controlling step under the conditions studied. From the form of the rate law, one can deduce the number of steps in the scheme. In most cases, further information can be obtained about the pattern in which parallel and sequential steps are arranged. 

The extent to which such reactions take place in parallel with the dominant reaction (4.1) is, in general, difficult to quantify as the overall reaction (4.3a) may consist of the elementary step (4.1) followed by reaction between adsorbed CO and adsorbed oxygen on the metal surface ... 

In some cases the original reaction with a slow rate-determining step may continue in parallel with the catalyzed reaction. However, the rate is determined by the faster path, which governs the overall rate of formation of products. A very slow elementary reaction does not control the rate if it can be sidestepped by a faster one on an alternative (usually catalyzed) path (Fig. 13.35). 

Complex reactions can be broken into a number of series and parallel elementary steps, possibly involving short-lived intermediates such as free radicals. These individual reactions collectively constitute the mechanism of the complex reaction. The individual reactions are usually second order, and the number of reactions needed to explain an observed, complex reaction can be surprisingly large. For example, a good model for... 

This reaction cannot be elementary. We can hardly expect three nitric acid molecules to react at all three toluene sites (these are the ortho and para sites meta substitution is not favored) in a glorious, four-body collision. Thus, the fourth-order rate expression 01 = kab is implausible. Instead, the mechanism of the TNT reaction involves at least seven steps (two reactions leading to ortho- or /mra-nitrotoluene, three reactions leading to 2,4- or 2,6-dinitrotoluene, and two reactions leading to 2,4,6-trinitrotoluene). Each step would require only a two-body collision, could be elementary, and could be governed by a second-order rate equation. Chapter 2 shows how the component balance equations can be solved for multiple reactions so that an assumed mechanism can be tested experimentally. For the toluene nitration, even the set of seven series and parallel reactions may not constitute an adequate mechanism since an experimental study found the reaction to be 1.3 order in toluene and 1.2 order in nitric acid for an overall order of 2.5 rather than the expected value of 2. 

Each elementary prism is replaced by an infinitely thin line directed along the y-axis with the same mass per unit length as that of the prism. These two steps allow us to replace the two-dimensional body by a system of infinitely thin lines which are parallel to each other, and the distribution of mass on them is defined from the equality... 

Consider the following mechanism for step-change polymerization of monomer M (Px) to P2, P3,..., Pr,. The mechanism corresponds to a complex series-parallel scheme series with respect to the growing polymer, and parallel with respect to M. Each step is a second-order elementary reaction, and the rate constant k (defined for each step)1 is the same for all steps. 

The limitations encountered when obtaining an analytical solution to the conservation equations, as in the present work, differ from those encountered applying direct computational methods. For example, the cost of numerical computations is dependent on the grid and, especially, on the number of species for which conservation equations must be solved additional reactions do not add significantly to the computational effort. With RRA techniques, further limitations arise on the number of different reaction paths that can conveniently be included in the analysis. The analysis typically follows a sequence of reactions that make up the main path of oxidation, the most important reactions, while parallel sequences are treated as perturbations to the main solution and often are sufficiently unimportant to be neglected. The first step thus identifies a skeletal mechanism of 63 elementary steps by omitting the least important steps of the detailed mechanism [44]. 

As an example of a system with a series of reactions, we may look at methane oxidation under conditions of excess oxygen. Following the carbon atom, this process would typically involve the steps CH4 — CH3 — CH2O — HCO — CO —> CO2. We note that each of these steps may involve a number of parallel elementary reactions, but we assume that they do not affect the oxidation pathway. 

A multielectron electrode reaction may also occur by a number of mechanistic routes including sequential and parallel pathways, which in complex electrokinetics may also be analysed individually in terms of elementary chemical and electrochemical steps. Figure 7 depicts plots of log j vs. Tj for (a) sequential and (b) parallel paths for multielectron transfer reactions. It is apparent that, at a given electrode potential, in... 

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 ... 

If a reaction has to be divided into more than one elementary reaction, it is called a reaction network. The complexity of such reaction networks can be very different, ranging from just two elementary reactions to a network consisting of parallel-, side-, subsequent-, and equilibrium reactions. Details about more complicated reactions, such as bimolecular reactions, reversible reaction steps and reactions with different kinds of adsorption (chemical, physical, dissociative, etc.), can be found in the typical literature [1-4]. 

In a Fischer-Tropsch process, some of the elementary steps in the reaction mechanisms that are characterized by "CH2" as the key growth intermediate may occur in parallel to give chain growth. These parallel... 

Almost every chemical reaction in industrial and laboratory practice results not from a single rearrangement or break-up of a molecule or collision of molecules, but from a combination of such molecular events called elementary steps, or steps for short. The steps of a reaction may occur in sequence, reactants reacting to form intermediates which subsequently react to form other intermediates and ultimately a product or products. The sequence of steps then is called a pathway. Almost always, however, one or several of the reactants or intermediates can also undergo alternative reactions that eventually lead to undesired by-products or different but also desired co-products. The combination of steps then is called a network with branches. Pathways from specific reactants to specific products can be defined within networks. Points at which pathways branch are called nodes, and linear portions between nodes or between a node and an end member are called segments. The network may contain parallel pathways from one node to another or to an end member, involving conversion of the same reactants (or intermediates) to the same products (or other intermediates) such pathways form a loop. 

When a reaction rate is measured in a chemical reactor, the reaction is generally a composite reaction comprised of a sequence of elementary reactions. An elementary reaction is a reaction that occurs at the molecular level exactly as written (Laidler, 1987). The mechanism of the reaction is the sequence of elementary reactions that comprise the overall or composite reaction. For example, mineral dissolution reactions generally include transport of reactant to the surface, adsorption of reactant, surface dilfusion of the adsorbate, reaction of the surface complex and release into solution, and transport of product species away from the surface. These reactions occur as sequential steps. Reaction of surface complexes and release to solution may happen simultaneously at many sites on a surface, and each site can react at a different rate depending upon its free energy (e.g., Schott et al., 1989). Simultaneous reactions occurring at different rates are known as parallel reactions. In a series of sequential reactions, the ratedetermining step is the step which occurs most slowly at the onset of the reaction, whereas for parallel steps, the rate-determining step is the fastest reaction. 

The chemical mechanism of a reaction is a proposed set of elementary (molecular) reactions, which provide a sequential path or a number of parallel paths that account for both the stoichiometry and the observed rate law of the overall reaction. If the reaction mechanism is simple, it consists of a single elementary step (apart from molecular diffusion of reactants and products, which is always a step in aqueous reactions) capable of accounting for the rate. 

Experimental rate laws often point to complex mechanisms, that is, a sequence of elementary steps, or two or more such sequences in parallel. Complex mechanisms frequently introduce intermediate species, that is, neither reactants nor products. An energetic or equilibrium description of an overall reaction deals only with reactant and product species, whereas a mechanistic description of reaction kinetics must recognize, in addition, ground-state catalyst species and intermediate species in the ground state and excited electronic states created by photon absorption. 

To illustrate the approach a simple example is given here. Let the main reaction A= fi require dual sites and the parallel coking reaction single sites only The uniform clusters consist of two sites only and these are sufficiently close to each other to allow dual site reactions Decomposed in its elementary steps the process can be written ... 

The kinetics of 1-5 ring closure were investigated in parallel for aliphatic and aromatic hydrocarbons on Pt-C (755-757). The apparent activation energy for dehydrocyclization is always higher (by 7-15 kcal/mol) in the case of monosubstituted benzenes (n-propyl-, sec-butyl-, and isobutyl-benzenes) than in the case of paraffins (ethylpentane, isooctane, n-hexane). The same is not true, however, for dehydrocyclization of o-ethyltoluene and isooctane, which occur with similar activation energies (757). This result is quite understandable if one considers that the first elementary step in the dehydrocyclization of monosubstituted benzenes but not of disubstituted benzenes results in a loss of aromaticity. 

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