Elementary reaction sequence

Although the reaction classes discussed earlier are sufficient to describe the hydrocarbon conversion kinetics, an understanding of the elementary reaction sequence is needed to describe catalyst deactivation. Several of the overall reactions require formation of olefinic intermediates in their elementary reaction sequence. Ultimately, these olefinic intermediates lead to coke formation and subsequent catalyst deactivation. For example, the ring closure reaction... 

Stoichiometric number, a, is the number of times an elementary step may repeat, after an overall reaction in the series of elementary reactions sequence. 

Generalizing on [12], we construct a loop by using a sequence of three elementary reactions. It is emphasized that the reactions comprising the loop must be elementary ones There should not be any other spin pairing combination that connects two anchors. This ensures that the loop in question is indeed the smallest possible one. Inspection of the loops depicted in Figure 4 shows that the H3 and H4 systems are entirely analogous. We include the H3 system in order to introduce the coordinates spanning the plane in which the loop lies, and as a prototype of all three-electron systems. 

Atoms and free radicals are highly reactive intermediates in the reaction mechanism and therefore play active roles. They are highly reactive because of their incomplete electron shells and are often able to react with stable molecules at ordinary temperatures. They produce new atoms and radicals that result in other reactions. As a consequence of their high reactivity, atoms and free radicals are present in reaction systems only at very low concentrations. They are often involved in reactions known as chain reactions. The reaction mechanisms involving the conversion of reactants to products can be a sequence of elementary steps. The intermediate steps disappear and only stable product molecules remain once these sequences are completed. These types of reactions are refeiTcd to as open sequence reactions because an active center is not reproduced in any other step of the sequence. There are no closed reaction cycles where a product of one elementary reaction is fed back to react with another species. Reversible reactions of the type A -i- B C -i- D are known as open sequence mechanisms. The chain reactions are classified as a closed sequence in which an active center is reproduced so that a cyclic reaction pattern is set up. In chain reaction mechanisms, one of the reaction intermediates is regenerated during one step of the reaction. This is then fed back to an earlier stage to react with other species so that a closed loop or... 

Although we treat this reaction as a simple, one-step conversion of A to P, it more likely occurs through a sequence of elementary reactions, each of which is a simple molecular process, as in... 

Each of these variables will be considered in this book. We start with concentrations, because they determine the form of the rate law when other variables are held constant. The concentration dependences reveal possibilities for the reaction scheme the sequence of elementary reactions showing the progression of steps and intermediates. Some authors, particularly biochemists, term this a kinetic mechanism, as distinct from the chemical mechanism. The latter describes the stereochemistry, electron flow (commonly represented by curved arrows on the Lewis structure), etc. 

In the schemes considered to this point, even the complex ones, the products form by a limited succession of steps. In these ordinary reaction sequences the overall process is completed when the products appear from the given quantity of reactants in accord with the stoichiometry of the net reaction. The only exception encountered to this point has been the ozone decomposition reaction presented in Chapter 5, which is a chain reaction. In this chapter we shall consider the special characteristics of elementary reactions that occur in a chain sequence. 

We stressed in Section 13.3 that we cannot in general write a rate law from a chemical equation. The reason is that all but the simplest reactions are the outcome of several, and sometimes many, steps called elementary reactions. Each elementary reaction describes a distinct event, often a collision of particles. To understand how a reaction takes place, we have to propose a reaction mechanism, a sequence of elementary reactions describing the changes that we believe take place as reactants are transformed into products. 

A mechanism is a description of the actual molecular events that occur during a chemical reaction. Each such event is an elementary reaction. Elementary reactions involve one, two, or occasionally three reactant molecules or atoms. In other words, elementary reactions can be unimolecular, bimolecular, or termolecular. A typical mechanism consists of a sequence of elementary reactions. Although an overall reaction describes the starting materials and final products, it usually is not elementary because it does not represent the individual steps by which the reaction occurs. 

In a termolecular reaction, three chemical species collide simultaneously. Termolecular reactions are rare because they require a collision of three species at the same time and in exactly the right orientation to form products. The odds against such a simultaneous three-body collision are high. Instead, processes involving three species usually occur in two-step sequences. In the first step, two molecules collide and form a collision complex. In a second step, a third molecule collides with the complex before it breaks apart. Most chemical reactions, including all those introduced in this book, can be described at the molecular level as sequences of bimolecular and unimolecular elementary reactions. 

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]. 

Second, it may be convenient to assume that one elementary reaction in the sequence occurs at a much slower rate than any of the others. The overall rate of conversion of reactants to products may be correctly calculated on the assumption that this step governs the entire process. The concept of a rate limiting step is discussed in more detail below. 

In the sequence of elementary reactions making up the overall reaction, there often is one step that is very much slower than all the subsequent steps leading to reaction products. In these cases the rate of product formation may depend on the rates of all the steps preceding the last slow step, but will not depend on the rates of any of the subsequent more rapid steps. This last slow step has been termed the rate controlling, rate limiting, or rate determining step by various authors. 

One proposed mechanism involved an intramolecular rearrangement, while a second involved a free radical chain mechanism composed of the following sequence of elementary reactions ... 

Activation Energy Considerations. Activation energy considerations can provide a basis for eliminating certain elementary reactions from a sequence of reactions. Unfortunately, the necessary activation energy data is seldom available, and one must estimate these parameters by empirical rules and generalizations that are of doubtful reliability. 

The collision must be sufficiently energetic that enough energy is available to break the chemical bond linking the two bromine atoms. This type of reaction is called an initiation reaction because it generates a species that can serve as a chain carrier or active center in the following sequence of elementary reactions. 

Equations 4.2.3 and 4.2.4 are the elementary reactions responsible for product formation. Each involves the formation of a chain carrying species (H- for 4.2.3 and Br- for 4.2.4) that propagates the reaction. Addition of these two relations gives the stoichiometric equation for the reaction. These two relations constitute a single closed sequence in the cycle of events making up the chain reaction. They are referred to as propagation reactions because they generate product species that maintain the continuity of the chain. 

Solvent molecules may play a variety of roles in liquid phase reactions. In some cases they merely provide a physical environment in which encounters between reactant molecules take place much as they do in gas phase reactions. Thus they may act merely as space fillers and have negligible influence on the observed reaction rate. At the other extreme, the solvent molecules may act as reactants in the sequence of elementary reactions constituting the mechanism. Although a thorough discussion of these effects would be beyond the scope of this textbook, the paragraphs that follow indicate some important aspects with which the budding ki-neticist should be familiar. 

The following mechanism for a reaction of identical stoichiometry introduces a second complex into the sequence of elementary reactions. 

Presently, the quantitative theory of irreversible polymeranalogous reactions proceeding in a kinetically-controlled regime is well along in development [ 16,17]. Particularly simple results are achieved in the framework of the ideal model, the only kinetic parameter of which is constant k of the rate of elementary reaction A + Z -> B. In this model the sequence distribution in macromolecules will be just the same as that in a random copolymer with parameters P(Mi ) = X =p and P(M2) = X2 = 1 - p where p is the conversion of functional group A that exponentially depends on time t and initial concen-... 

Reaction mechanism a postulated sequence of elementary reactions that is consistent with the observed stoichiometry and rate law these are necessary but not sufficient conditions for the correctness of a mechanism, and are illustrated in Chapter 7. 

The derivation of a rate law from a postulated mechanism is a useful application of reaction mechanisms. It shows how the kinetics of the elementary reaction steps are reflected in the kinetics of the overall reaction. The following example illustrates this for a simple, gas-phase reaction involving an open sequence. The derivations typically employ the stationary-state hypothesis (SSH) to eliminate unknown concentrations of reactive intermediates. 

The catalytic asymmetric hydrogenation with cationic Rh(I)-complexes is one of the best-understood selection processes, the reaction sequence having been elucidated by Halpern, Landis and colleagues [21a, b], as well as by Brown et al. [55]. Diastereomeric substrate complexes are formed in pre-equilibria from the solvent complex, as the active species, and the prochiral olefin. They react in a series of elementary steps - oxidative addition of hydrogen, insertion, and reductive elimination - to yield the enantiomeric products (cf. Scheme 10.2) [56]. 

As a final example, we show how SIMS can be used to identify the ratedetermining step in a sequence of elementary reactions [32], Imagine the situation in which we have an Rh(l 11) surface, partially covered by N atoms, which we heat up to 400 K under a low, constant pressure of H2 with the aim of forming NH3. We expect the following reactions ... 

It is well recognized that specificity is one of the most spectacular aspects of enzymatic action. Thus, the process of alcoholic fermentation of D-glucose by a unicellular organism like yeast has been proved to consist of a sequence of elementary reactions catalyzed by sixteen individual... 

The rate-controlling step is the elementary reaction that has the largest control factor (CF) of all the steps. The control factor for any rate constant in a sequence of reactions is the partial derivative of In V (where v is the overall velocity) with respect to In k in which all other rate constants (kj) and equilibrium constants (Kj) are held constant. Thus, CF = (5 In v/d In ki)K kg. This definition is useful in interpreting kinetic isotope effects. See Rate-Determining Step Kinetic Isotope Effects... 

A sequence of at least two elementary reactions and having at least one reaction intermediate. See... 

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