Elementary and Stepwise Reactions

Reactions are of two types. In elementary reactions the reacting molecule or molecules are transformed into products directly, without the formation of intermediates. In a stepwise reaction, one or more intermediate species are produced, which react further to give the products. A stepwise reaction can be split up into two or more elementary reactions. 

As an elementary reaction proceeds, the Gibbs free energy increases up to a maximum value and then goes down to a value corresponding to that of the products. The position of highest energy is called the transition state, and is a key feature of the reaction most of the experimental information about chemical reactions relates to the transition state and will be discussed in the next two chapters. 

In a stepwise reaction, at least one of the products of the first elementary reaction reacts further in a second elementary reaction. This may be followed by further elementary reactions until the reaction is complete. Any molecules produced in the course of a stepwise reaction which react further and are not present at the end of the reaction are known as intermediates. Intermediates are discussed in more detail in Chapters 4, 5 and 6. 

In contrast, the hydrolysis of tm-butyl bromide (2-bromo-2-methylpropane) occurs in a stepwise manner (reaction 1.1b). In the first slow step, the C-Br bond breaks, with the bromine atom taking both electrons from the bond and leaving as a negatively charged bromide ion. The remainder of the molecule is the positively charged tert-butyl cation (2-methylprop-2-yl cation). This is a highly reactive intermediate, which reacts rapidly with the hydroxide ion to form the corresponding alcohol. 

In in elcinemary reaction, reading molecules are transformed into products without going through intermediates. A stepwise reaction involves consecutive elementary reactions where the intermcdiate(s produced in the first elementary reaction react furl her in subsequent elentenla ry reactions. 

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Hence, the correct thermodynamic criterion of the kinetic irreversibility at any step in the chemical transformation chain is a considerable (against quantity RT) change in the chemical potential of the reaction groups related to this step—that is, A j > RT. Note that the criterion is valid for both elementary and stepwise reaction, although in the latter case, one must consider the affinity for the stepwise transformation A,2 > RT. 

Understand the difference between elementary and stepwise reactions, and the role played by transition states and intermediates... 

Figure 1.1 Free energy diagrams for elementary and stepwise reactions...

In Chapter 1, we established some ground rules for writing plausible mechanisms (normally several) for particular reactions, based on the identification of bonds formed and broken in the reaction. In this chapter, we show how kinetics the study of how concentrations of reagents or products vary with time, enable us to rule out some potential mechanisms and provide insight into elementary and stepwise reactions. 

A chemical reaction whose rate expression includes rate constants from more than one elementary reaction. Examples of composite reactions include parallel reactions and stepwise reactions. 

Obviously, the conclusion on proportionahty between the rate of a reaction and its chemical aifinity is vahd, as well as in the cases where an arbitrary complex (not an elementary) stoichiometric stepwise reaction occurs near its equilibrium, the stepwise reaction being characterized by a certain value of chemical aiEnity (see, e.g., expression (1.36)). 

This book starts with a discussion of how covalent bonds break and form, and how these bond-breaking and bond-forming processes provide the basis of reaction mechanisms. The principles governing how to make sensible suggestions about possible mechanisms are set out, and the distinction is made between elementary reactions, which involve just one step, and stepwise reactions which have more than one step and involve the production of intermediates that react further. 

Gibbs energy of activation A G (standard free energy of activation A G ) (Id mol-1) — The standard Gibbs energy difference between the -> transition state of a reaction (either an elementary reaction or a stepwise reaction) and the ground state of the reactants. It is calculated from the experimental rate constant k via the conventional form of the absolute reaction rate equation ... 

For a simple (elementary) reaction, a partial order of reaction is the same as the -> stoichiometric number of the reactant concerned and must, therefore, be a positive integer (see - reaction rate). The overall order is then the same as the molecularity. For stepwise reactions there is no general connection between stoichiometric numbers and partial orders. Such reactions may have more complex rate laws, so that an apparent order of reaction may vary with the concentrations of the chemical species involved and with the progress of the reaction in such cases it is not useful to use the orders of reaction terms, although apparent orders of reaction may be deducible from initial rates. In a stepwise reaction, orders of reaction may in principle always be assigned to the elementary steps. 

In the consideration of chemical transformations, we shall distinguish elementary and combined (stepwise) stoichiometric transformations. The elemen tary chemical transformations are those that run through the formation of only one transition state. The transition state is not thermalized, or at least not thermalized at the reaction coordinate. The stepwise transformations comprise the formation of some intermediate products, which we shall always consider as thermalized. 

Let two stoichiometric stepwise reactions, which involve some combi nation of elementary chemical reactions, be concurrent in the system. Indicate these stepwise reactions by indices 21 and 22. It is evident that for stoichiometric stepwise transformations, the elementary reactions can be omitted in the equation for djS/dt ... 

The simplest example is a stepwise process that proceeds via an arbitrary combination of elementary monomolecular transformations of inter mediates that all exist in their stationary states. When this is the case, the stationary rate of the stepwise process appears to be proportional to the difference between thermodynamic rushes of the initial and final reaction groups—in other words, the stepwise process can be considered from the viewpoint of both kinetics and thermodynamics as a single effective elementary reaction. 

Apparently, thermodynamic rushes for the series of transformations under consideration and, as a result, chemical potentials of the intermediates in their stationary states must decrease progressively while passing from one intermediate to another. When the stepwise transformation may follow sev eral parallel pathways of consecutive elementary transformations, the said relationship between the stationary chemical potentials of the intermediates must be met for each of the possible pathways of the stepwise reaction. 

Hence, the Horiuti Boreskov relationships are always met close to the equilibrium. In terms of the kinetic thermodynamic analysis, it means that close to the equilibrium the stepwise process can be considered as one effective elementary reaction between the initial and final reaction groups. Relationship (1.46) is valid, too, for the reverse process (from right to left) that occurs near the equilibrium point. 

In kinetic diagrams, the kinetic irreversibility is usually indicated with a single arrow ( ), while the potential kinetic reversibility is shown by a double arrow (t ). In any complex pathway with the known drops of chemical potentials at individual stages, the transformation chain can be broken down into kineticaUy reversible and kineticaUy irreversible steps (Figure 1.6). A priori consideration of some elementary steps of a stepwise reaction as kineticaUy irreversible may cause some serious mistakes in making conclusions via classical kinetic analysis of the scheme of chemical transformations. 

Near thermodynamic equilibrium, similar linear relationships are also valid for elementary chemical processes, as well as for stepwise processes where the rates are proportional to the difference between the thermodynamic mshes of the initial and final reaction groups (see Section 1.4.2). Here, the criterion of proximity to thermodynamic equilibrium is relationship jA jl < RT, where Arij is the affinity for the transformation of reaction group i to reaction group j. In fact, while... 

Let us demonstrate this on the preceding example of two parallel reactions. Let transformations Z1 and Z2 be not elementary but stepwise processes described by the simplest scheme ... 

Thus, the rate-determining parameters here are the standard Gibbs energy of the formation of the transition state in elementary reaction 1 (scheme 4.4) and the standard Gibbs potentials of the formation of "external" reactants R as well as of P and intermediate Ki. The apparent activation energy of the stepwise reaction is... 

In catalytic stepwise reactions, which involve more complex elementary transformations than scheme (4.4), the rate-determining parameters can be identified through similar considerations. Several examples of simple model schemes of catalytic transformations are given following. These schemes often are used for the microkinetic analysis of particular catalytic transformations and help to reveal the influence of various factors. 

The phenomenon of self organization occurs at nonstabHities of the sta tionary state and leads to the formation of temporal and spatio temporal dissipative structures. Remember that oscillating instabilities of stationary states of dynamic systems can be observed for the intermediate nonlinear stepwise reactions only, when no fewer than two intermediates are involved (see Section 3.5) and at least one of the elementary steps is kinet icaUy irreversible. The minimal sufficient requirements for the scheme of a process with temporal instabilities are not yet strictly formulated. However, in aU known examples of such reactions, the rate of the kineti caUy irreversible elementary reaction at one of the intermediate steps is at least in a quadratic dependence on the intermediate concentrations. Among these reactions are autocatalytic steps. 

The way in which a plasma polymer is formed has been explained by the rapid step growth polymerization mechanism, which is depicted in Figure 5.3. The essential elementary reactions are stepwise recombination of reactive species (free radicals) and stepwise addition of or intrusion via hydrogen abstraction by impinging free radicals. It is important to recognize that these elementary reactions are essentially oligomerization reactions, which do not form polymers by themselves on each cycle. In order to form a polymeric deposition, a certain number of steps (cycle) must be repeated in gas phase and more importantly at the surface. The number of steps is collectively termed the kinetic pathlength. 

Figure 1.1 shows free energy diagrams for an elementary reaction (1.1a) and for a stepwise reaction with two steps (1.1b). 

First- and second-order reactions may be either elementary or stepwise. Third- and higher-order reactions are almost always stepwise. 

It was already mentioned above that the condition of monodispersity of micelles means that only one kind of aggregates with a fixed aggregation number nj is formed. From the point of view of chemical kinetics the reaction (5.39) is a reaction of ni order. Because typical micelles consist of some tens or hundreds molecules the probability of this elementary step is zero. Therefore, Eq. (5.39) presents only the final result of nj-l stepwise reactions of first order. The corresponding equilibrium constant is then a product of n -l constants for each step of the micellisation process. In our simplest case we can consider that all these constants are the same and we get [ 12]... 

Thus, any complex compound has several stepwise stability constants and only one overall. Stepwise stability constants characterize the complex formation on the account of joining only one ligand. For this reason index a in them defines both the sequential number of elementary reactions and the number of ligands in its product. Overall stability constants characterize the formation of any complex compoxmd directly from dissociated ions, and index a in them defines their number. In order to distinguish overall constants from the stepwise ones they are often denoted by the symbol Overall and stepwise constants are associated between themselves by equations... 

A chemical reaction is a process that results in the interconversion of chemical species Table 4.3 summarizes the base reaction types. Chemical reactions might be elementary reactions or stepwise reactions. A stepwise reaction consists of at least one reaction intermediate and involves at least two consecutive elementary reactions. Parallel reactions are several simultaneous reactions that form different respective products from a single set of reactants (Svehla 1993, Muller 1994). 

Chemical reactions can be classified as either elementary or composite. An elementary reaction is one which, as far as can be determined, goes in a single stage the reactants pass smoothly through an intermediate state and then become products. If a reaction is elementary no specific intermediates can be detected or need to be postulated in order to explain the kinetic behavior. Composite reactions, also known as complex or stepwise reactions, occur in more than one stage, and therefore involve two or more elementary reactions they are considered in more detail in Section IX. 

Chemical reactions n. Reactions between atoms and molecules to produce chemical compounds different from reactants. Chemical reactions may be elementary reactions or stepwise reactions. 

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