Elementary and Complex Reactions

Elementary reactions occur via a single chemical step. If reaction occurs mechanistically as 

There are only a few elementary bimolecular reactions in the gas phase, e.g. the reaction 

Many of the bimolecular reactions for which extensive data are available occur as individual steps in reactions involving radicals, e.g. 

Reactions between light molecules have been extensively studied in the last two decades, generally by molecular beam techniques (see Chapter 4, Section 4.2), and these have allowed detailed testing of the predictions made from calculated potential energy surfaces. There are three typical mechanisms for gas phase reactions. 

The stripping reactions showing forward scattering and large cross sections are typified by reactions such as 

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In Section 1.2 we distinguished between elementary and complex reactions. We now make a distinction between simple and complicated rate equations. A simple rate equation has the form of Eq. (1-11). A complicated rate equation has a form different from Eq. (1-11) it may be a sum of terms like that in (1-11), or it may have quantities in the denominator. We have seen that there is no necessary relationship between the complexity of the reaction and the form of the experimental rate equation. Simple rate equations are treated in Chapter 2 and complicated rate equations in Chapter 3. 

Example 7.11 showed how reaction rates can be adjusted to account for reversibility. The method uses a single constant, Kkinetic or Kthemo and is rigorous for both the forward and reverse rates when the reactions are elementary. For complex reactions with fitted rate equations, the method should produce good results provided the reaction always starts on the same side of equilibrium. 

The reaction is evidently not elementary. Such complex reactions as these, however, are composed of a series or a sequence of elementary reactions. We can determine the reaction order with respect to each reactant (and product) and the influence of the concentration of all species... 

The main problem in applying stoichiometric considerations to bioprocessing (beyond quantification in non-open-reactor systems) arises from the complex metabolic reaction network. In simple reactions stoichiometry is trivial, and complex reactions can only be handled with the aid of a formal mathematical approach analogous to the approach for complex chemical reactions (Schubert and Hofmann, 1975). In such a situation, an elementary balance equation must be set up. Due to complexity, it is not surprising that the approach first used in the quantification of bioprocesses was much simpler— the concept of yield factors Y. This macroscopic parameter Y cannot be considered a biological constant. 

Here, we will not give a review of the phases and systems studies so far (Fig. 5). Instead, we will provide references to the examples discussed in the lecture for our own work on the different reactions spanning elementary and complex systems. Details of the findings can be found in the original references given. 

The collision theory is a useful one not only in the sense that it has provided insight into the nature of chemical reactions, but also because it is a theory that can be readily tested. The mark of a scientific theory is that it can be tested and falsified. So far, collision theory has been supported by experimental evidence, but if new data were produced that could not be explained using the collision theory then it would need to be modified or dismissed in favour of a new theory that did explain all the evidence. Currently collision theory is the best explanation of the experimental data produced so far (at this working level). It should be noted here that we have not begun to distinguish between elementary and complex, multi-step reactions. That discussion is developed in Chapter 16 with the introduction of the idea of the rate-determining step in a sequence of stages. This is an example of how the theory is modified to explain more complex situations. Note that unimolecular reactions are an apparent exception which require special treatment. 

Complex chemical mechanisms are written as sequences of elementary steps satisfying detailed balance where tire forward and reverse reaction rates are equal at equilibrium. The laws of mass action kinetics are applied to each reaction step to write tire overall rate law for tire reaction. The fonn of chemical kinetic rate laws constmcted in tliis manner ensures tliat tire system will relax to a unique equilibrium state which can be characterized using tire laws of tliennodynamics. 

Some reactions apparently represented by single stoichiometric equations are in reahty the result of several reactions, often involving short-hved intermediates. After a set of such elementary reactions is postulated by experience, intuition, and exercise of judgment, a rate equation is deduced and checked against experimental rate data. Several examples are given under Mechanisms of Some Complex Reactions, following. 

In Chapter 1 we distinguished between elementary (one-step) and complex (multistep reactions). The set of elementary reactions constituting a proposed mechanism is called a kinetic scheme. Chapter 2 treated differential rate equations of the form V = IccaCb -., which we called simple rate equations. Chapter 3 deals with many examples of complicated rate equations, namely, those that are not simple. Note that this distinction is being made on the basis of the form of the differential rate equation. 

Equation (1.20) is frequently used to correlate data from complex reactions. Complex reactions can give rise to rate expressions that have the form of Equation (1.20), but with fractional or even negative exponents. Complex reactions with observed orders of 1/2 or 3/2 can be explained theoretically based on mechanisms discussed in Chapter 2. Negative orders arise when a compound retards a reaction—say, by competing for active sites in a heterogeneously catalyzed reaction—or when the reaction is reversible. Observed reaction orders above 3 are occasionally reported. An example is the reaction of styrene with nitric acid, where an overall order of 4 has been observed. The likely explanation is that the acid serves both as a catalyst and as a reactant. The reaction is far from elementary. 

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... 

An irreversible, elementary reaction must have Equation (1.20) as its rate expression. A complex reaction may have an empirical rate equation with the form of Equation (1.20) and with integral values for n and w, without being elementary. The classic example of this statement is a second-order reaction where one of the reactants is present in great excess. Consider the slow hydrolysis of an organic compound in water. A rate expression of the form... 

Chapter 1 treated single, elementary reactions in ideal reactors. Chapter 2 broadens the kinetics to include multiple and nonelementary reactions. Attention is restricted to batch reactors, but the method for formulating the kinetics of complex reactions will also be used for the flow reactors of Chapters 3 and 4 and for the nonisothermal reactors of Chapter 5. 

Note that the Roman numeral subscripts refer to numbered reactions and have nothing to do with iodine. All these examples have involved elementary reactions. Multiple reactions and apparently single but nonelementary reactions are called complex. Complex reactions, even when apparently single, consist of a number of elementary steps. These steps, some of which may be quite fast, constitute the mechanism of the observed, complex reaction. As an example, suppose that... 

Reaction rates almost always increase with temperature. Thus, the best temperature for a single, irreversible reaction, whether elementary or complex, is the highest possible temperature. Practical reactor designs must consider limitations of materials of construction and economic tradeoffs between heating costs and yield, but there is no optimal temperature from a strictly kinetic viewpoint. Of course, at sufficiently high temperatures, a competitive reaction or reversibility will emerge. 

The reaction of Example 7.4 is not elementary and could involve shortlived intermediates, but it was treated as a single reaction. We turn now to the problem of fitting kinetic data to multiple reactions. The multiple reactions hsted in Section 2.1 are consecutive, competitive, independent, and reversible. Of these, the consecutive and competitive t5T>es, and combinations of them, pose special problems with respect to kinetic studies. These will be discussed in the context of integral reactors, although the concepts are directly applicable to the CSTRs of Section 7.1.2 and to the complex reactors of Section 7.1.4. 

Steady-state approximation. Fractional reaction orders may be obtained from kinetic data for complex reactions consisting of elementary steps, although none of these steps are of fractional order. The same applies to reactions taking place on a solid catalyst. The steady-state approximation is very useful for the analysis of the kinetics of such reactions and is illustrated by Example 5.4.2.2a for a solid-catalysed reaction. 

The intermediate reaction complexes (after formation with rate constant, fc,), can undergo unimolecular dissociation ( , ) back to the original reactants, collisional stabilization (ks) via a third body, and intermolecular reaction (kT) to form stable products HC0j(H20)m with the concomitant displacement of water molecules. The experimentally measured rate constant, kexp, can be related to the rate constants of the elementary steps by the following equation, through the use of a steady-state approximation on 0H (H20)nC02 ... 

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