Sequences of Elementary Reactions

Most stoichiometrically simple reactions proceed via a sequence of elementary reactions, which is referred to as the reaction mechanism. For example, at about 1100 °C, the gas-phase reaction between nitric oxide (NO) and hydrogen is stoichiometrically simple and obeys the stoichiometric equation 

A catalytic version of this reaction takes place in automotive exhaust catalysts at somewhat lower temperatures and is responsible for the removal of oxides of nitrogen from automobile exhaust gases. More generally, the reduction of oxides of nitrogen to N2 is of immense practical importance in the field of air pollution control. 

The mechanism of the uncatalyzed, gas-phase reaction has been of great interest for more than seven decades because it follows a third-order rate equation (—r o = k[NO] [H2]), leading to speculation that a termolecular collision might be involved. However, from the beginning of research on this reaction, it has been hypothesized that the overall reaction proceeds in stages, considered was 

None of the reactions that make up this sequence can be considered elementary. The first probably requires a collision with an inert molecule to activate the N2O2 molecule and to absorb some of the energy associated with the combination of the two NO molecules. The second reaction involves the breaking of three bonds and the formation of three, and the third involves the breaking of two bonds accompanied by the formation of twa Each of the last two reactions probably can be broken into a few simpler reactions that meet the simplicity criteria discussed previously. Nevertheless, this scheme can be used to illustrate some important points about reaction sequences. However, we will not use it to derive a rate equation.  

How is it possible that Reaction (5-C) is stoichiometrically simple and obeys the Law of Definite Proportions, if N2O2 and hydrogen peroxide (H2O2) are produced in the first and second steps Neither hydrogen peroxide nor N2O2 appears in the stoichiometric equation for the reaction of NO with H2. If some H and O atoms are tied up in H2O2 and some N and O atoms are tied up in N2O2, how can reaction (J-C) be stoichiometrically simple  

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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. 

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 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 ... 

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. 

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. 

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. 

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... 

Nonelementary reactions are explained by assuming that what we observe as a single reaction is in reality the overall effect of a sequence of elementary reactions. The reason for observing only a single reaction rather than two or more elementary reactions is that the amount of intermediates formed is negligibly small and, therefore, escapes detection. We take up these explanations later. 

To explain the kinetics of nonelementary reactions we assume that a sequence of elementary reactions is actually occurring but that we cannot measure or observe the intermediates formed because they are only present in very minute quantities. Thus, we observe only the initial reactants and final products, or what appears to be a single reaction. For example, if the kinetics of the reaction... 

Two problems make the search for the correct mechanism of reaction difficult. First, the reaction may proceed by more than one mechanism, say free radical and ionic, with relative rates that change with conditions. Second, more than one mechanism can be consistent with kinetic data. Resolving these problems is difficult and requires an extensive knowledge of the chemistry of the substances involved. Leaving these aside, let us see how to test the correspondence between experiment and a proposed mechanism that involves a sequence of elementary reactions. 

FIGURE 1.4 Typical sequence of elementary reactions in which OH initiates the oxidation of an alkane in the troposphere. 

Most radicals are highly reactive, and there are few examples where one would produce a stable radical product in a reaction. Reference to a radical reaction in synthesis or in Nature, almost always concerns a sequence of elementary reactions that give a composite reaction. Multistep radical sequences are discussed in general terms in this section so that the elementary radical reactions presented later can be viewed in the context of real conversions. The sequences can be either radical chain reactions or radical nonchain reactions. Most synthetic apphcations involve radical chain reactions, and these comprise the bulk of organic synthetic sequences and commercial applications. Nonchain reaction sequences are largely involved in radical reactions in biology. Some synthetic radical conversions are nonchain processes, and some recent advances in commercial polymerization reactions involve nonchain sequences. 

In nonelementary reactions, the reaction order and stoichiometric coefficients are different. A single reaction is observed, but in reality a sequence of elementary reactions occurs. The amount of intermediates formed is negligible and, therefore, not detectable. One famous example is the reaction between hydrogen and bromine. The overall reaction can be described as ... 

A reaction mechanism is the sequence of elementary reactions, or elementary steps, that defines the pathway from reactants to products. Elementary reactions are classified as unimolecular, bimolecular, or termolecular, depending on whether one, two, or three reactant molecules are... 

Sometimes, the rebonding in a chemical transformation occurs in just a single step this will be unimolecular (if we ignore the molecular collisions whereby the reactant molecule gains the necessary energy to react) or bimolecular (if we ignore the initial formation of the encounter complex). Otherwise, a mechanism is a sequence of elementary reactions, each being indivisible into simpler chemical events. 

In the reactions discussed and exemplified above, reactants, transient species and products are related by linear sequences of elementary reactions. The transient species can be regarded as a kinetic product and, if isolable, subject to the usual tests for stability to the reaction conditions. Multiple products, however, may also occur by a mechanism involving branching. Indeed, the case shown earlier in Fig. 9.5b, where the transient is a cul de sac species, is the one in which the branching to the thermodynamic product P and kinetic product T occurs directly from the reactant. In the absence of reversibility, the scheme becomes as that shown in Scheme 9.8a, where the stable products P and Q are formed as, for example, in the stereoselective reduction of a ketone to give diastereoisomeric alcohols. The reduction of 2-norbornanone to a mixture of exo- and cndo-2-norbornanols by sodium borohydride is a classic case. The product ratio is constant over the course of the reaction and reflects directly the ratio of rate constants for the competing reactions. The pseudo-first-order rate constant for disappearance of R is the sum of the component rate constants. 

In this work, we have compared the potential energy profiles of the model catalytic cycle of olefin hydrogenation by the Wilkinson catalyst between the Halpern and the Brown mechanisms. The former is a well-accepted mechanism in which all the intermediates have trans phosphines, while in the latter, proposed very recently, phosphines are located cis to each other to reduce the steric repulsion between bulky olefin and phosphines. Our ab initio calculations on a sterically unhindered model catalytic cycle have shown that the profile for the Halpern mechanism is smooth without too stable intermediates and too high activation barrier. On the other hand, the key cis dihydride intermediate in the cis mechanism is electronically unstable and normally the sequence of elementary reactions would be broken. Possible sequences of reactions can be proposed from our calculation, if one assumes that steric effects of bulky olefin substituents prohibits some intermediates or reactions to be realized. 

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 overall reaction [Equation (7-4)], for which the rate expression is nonele-mentary, consists of the sequence of elementary reactions, Equations (7-5), (7-7), and 7-9. ... 

In developing some of the elementary principles of the kinetics of enzyme reactions, we shall discuss an enzymatic reaction that has been suggested by Levine and LaCourse as part of a system that would reduce the size of an artificial kidney. The desired result is the production of an artificial kidney that could be worn by the patient and would incorporate a replaceable unit for the elimination of tte nitrogenous waste products such as uric acid and creatinine, In the microencapsulation scheme proposed by Levine and LaCourse, the enzyme urease would be used in tire removal of urea from ti)e bloodstream. Here, the catalytic action of urease would cause urea to decompose into ammonia and carbon dioxide. The mechanism of the reaction is believed to proceed by the following sequence of elementary reactions ... 

Nonelementary reaction is seen as a sequence of elementary reactions... 

It is generally accepted that heterogeneous catalysis represents a sequence of elementary reactions such as the adsorption of the reactant on the catalyst surface, atomic rearrangements of the adsorbed particles, and desorption of the products, the overall reaction rate being governed by the slowest step of these elementary reactions. The rate of the slowest... 

A reaction mechanism is a detailed sequence of elementary reactions, with their rates, that are combined to yield the overall reaction. It is often possible to write... 

A reaction mechanism is the detailed sequence of elementary reactions that lead to the overall chemical reaction. 

Sequence of elementary reactions which, when added together, gives the net chemical reaction and reproduces its rate law... 

Rate-determining step The slow step in the sequence of elementary reactions making up a mechanism. 

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