Elementary reaction kinetics

Both unimolecular and bimolecular reactions are common throughout chemistry and biochemistry. Binding of a hormone to a reactor is a bimolecular process as is a substrate binding to an enzyme. Radioactive decay is often used as an example of a unimolecular reaction. However, this is a nuclear reaction rather than a chemical reaction. Examples of chemical unimolecular reactions would include isomerizations, decompositions, and dis-associations. See also Chemical Kinetics Elementary Reaction Unimolecular Bimolecular Transition-State Theory Elementary Reaction... 

For some gas-phase kinetic elementary reactions, the temperature dependence of the rate coefficient is described by the power function k=AT . This can also be... 

At the limit of extremely low particle densities, for example under the conditions prevalent in interstellar space, ion-molecule reactions become important (see chapter A3.51. At very high pressures gas-phase kinetics approach the limit of condensed phase kinetics where elementary reactions are less clearly defined due to the large number of particles involved (see chapter A3.6). 

Elementary reactions are characterized by their moiecuiarity, to be clearly distinguished from the reaction order. We distinguish uni- (or mono-), hi-, and trimoiecuiar reactions depending on the number of particles involved in the essential step of the reaction. There is some looseness in what is to be considered essential but in gas kinetics the definitions usually are clearcut through the number of particles involved in a reactive collision plus, perhaps, an additional convention as is customary in iinimolecular reactions. 

Flere, we shall concentrate on basic approaches which lie at the foundations of the most widely used models. Simplified collision theories for bimolecular reactions are frequently used for the interpretation of experimental gas-phase kinetic data. The general transition state theory of elementary reactions fomis the starting point of many more elaborate versions of quasi-equilibrium theories of chemical reaction kinetics [27, M, 37 and 38]. 

The fimdamental kinetic master equations for collisional energy redistribution follow the rules of the kinetic equations for all elementary reactions. Indeed an energy transfer process by inelastic collision, equation (A3.13.5). can be considered as a somewhat special reaction . The kinetic differential equations for these processes have been discussed in the general context of chapter A3.4 on gas kmetics. We discuss here some special aspects related to collisional energy transfer in reactive systems. The general master equation for relaxation and reaction is of the type [H, 12 and 13, 15, 25, 40, 4T ] ... 

A postulated reaction mechanism is a description of all contributing elementary reactions (we will call this the kinetic scheme), as well as a description of structures (electronic and chemical) and stereochemistry of the transition state for each elementary reaction. (Note that it is common to mean by the term transition state both the region at the maximum in the energy path and the actual chemical species that exists at this point in the reaction.)... 

The overall reaction stoichiometry having been established by conventional methods, the first task of chemical kinetics is essentially the qualitative one of establishing the kinetic scheme in other words, the overall reaction is to be decomposed into its elementary reactions. This is not a trivial problem, nor is there a general solution to it. Much of Chapter 3 deals with this issue. At this point it is sufficient to note that evidence of the presence of an intermediate is often critical to an efficient solution. Modem analytical techniques have greatly assisted in the detection of reactive intermediates. A nice example is provided by a study of the pyridine-catalyzed hydrolysis of acetic anhydride. Other kinetic evidence supported the existence of an intermediate, presumably the acetylpyridinium ion, in this reaction, but it had not been detected directly. Fersht and Jencks observed (on a time scale of tenths of a second) the rise and then fall in absorbance of a solution of acetic anhydride upon treatment with pyridine. This requires that the overall reaction be composed of at least two steps, and the accepted kinetic scheme is as follows. 

The interpretation of kinetic data is largely based on an empirical finding called the Law of Mass Action In dilute solution the rate of an elementary reaction is... 

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. 

From this expression, it is obvious that the rate is proportional to the concentration of A, and k is the proportionality constant, or rate constant, k has the units of (time) usually sec is a function of [A] to the first power, or, in the terminology of kinetics, v is first-order with respect to A. For an elementary reaction, the order for any reactant is given by its exponent in the rate equation. The number of molecules that must simultaneously interact is defined as the molecularity of the reaction. Thus, the simple elementary reaction of A P is a first-order reaction. Figure 14.4 portrays the course of a first-order reaction as a function of time. The rate of decay of a radioactive isotope, like or is a first-order reaction, as is an intramolecular rearrangement, such as A P. Both are unimolecular reactions (the molecularity equals 1). 

According to the definition given, this is a second-order reaction. Clearly, however, it is not bimolecular, illustrating that there is distinction between the order of a reaction and its molecularity. The former refers to exponents in the rate equation the latter, to the number of solute species in an elementary reaction. The order of a reaction is determined by kinetic experiments, which will be detailed in the chapters that follow. The term molecularity refers to a chemical reaction step, and it does not follow simply and unambiguously from the reaction order. In fact, the methods by which the mechanism (one feature of which is the molecularity of the participating reaction steps) is determined will be presented in Chapter 6 these steps are not always either simple or unambiguous. It is not very useful to try to define a molecularity for reaction (1-13), although the molecularity of the several individual steps of which it is comprised can be defined. 

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. 

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. 

In earlier chapters, we have seen how kinetic phenomena can be interpreted, for example, to provide a reaction scheme consisting of a set of elementary reactions. Over the years, several models have been devised to explain and sometimes to predict the rates of elementary reactions. It is these that we now wish to examine on a more fundamental basis in this chapter, plus Chapters 9 and 10. 

That is, the equilibrium constant for a reaction is equal to the ratio of the rate constants for the forward and reverse elementary reactions that contribute to the overall reaction. We can now see in kinetic terms rather than thermodynamic (Gibbs free energy) terms when to expect a large equilibrium constant K 1 (and products are favored) when k for the forward direction is much larger than k for the reverse direction. In this case, the fast forward reaction builds up a high concentration of products before reaching equilibrium (Fig. 13.21). In contrast, K 1 (and reactants are favored) when k is much smaller than k. Now the reverse reaction destroys the products rapidly, and so their concentrations are very low. 

We deal with many reactions that are not elementary. Most industrially important reactions go through a complex kinetic mechanism before the final products are reached. The mechanism may give a rate expression far different than Equation (1.14), even though it involves only short-lived intermediates that never appear in conventional chemical analyses. Elementary reactions are generally limited to the following types. 

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. 

This is the expected form of the kinetic equilibrium constant for elementary reactions. Kkinetic is a function of the temperature and pressure at which the reaction is conducted. 

Solution The elementary reaction steps of adsorption, reaction, and desorption are now reversible. From this point on, we will set ai = a, pi = P, and so on, since the intrinsic kinetics are desired. The relationships between ai, a, and a are addressed using an eflectiveness factor in Section 10.4. The various reaction steps are... 

Recently the polymeric network (gel) has become a very attractive research area combining at the same time fundamental and applied topics of great interest. Since the physical properties of polymeric networks strongly depend on the polymerization kinetics, an understanding of the kinetics of network formation is indispensable for designing network structure. Various models have been proposed for the kinetics of network formation since the pioneering work of Flory (1 ) and Stockmayer (2), but their predictions are, quite often unsatisfactory, especially for a free radical polymerization system. These systems are of significant conmercial interest. In order to account for the specific reaction scheme of free radical polymerization, it will be necessary to consider all of the important elementary reactions. 

In this paper, we first briefly describe both the single-channel 1-D model and the more comprehensive 3-D model, with particular emphasis on the comparison of the features included and their capabilities/limitations. We then discuss some examples of model applications to illustrate how the monolith models can be used to provide guidance in emission control system design and implementation. This will be followed by brief discussion of future research needs and directions in catalytic converter modeling, including the development of elementary reaction step-based kinetic models. 

Chemical vapor deposition (CVD) of carbon from propane is the main reaction in the fabrication of the C/C composites [1,2] and the C-SiC functionally graded material [3,4,5]. The carbon deposition rate from propane is high compared with those from other aliphatic hydrocarbons [4]. Propane is rapidly decomposed in the gas phase and various hydrocarbons are formed independently of the film growth in the CVD reactor. The propane concentration distribution is determined by the gas-phase kinetics. The gas-phase reaction model, in addition to the film growth reaction model, is required for the numerical simulation of the CVD reactor for designing and controlling purposes. Therefore, a compact gas-phase reaction model is preferred. The authors proposed the procedure to reduce an elementary reaction model consisting of hundreds of reactions to a compact model objectively [6]. In this study, the procedure is applied to propane pyrolysis for carbon CVD and a compact gas-phase reaction model is built by the proposed procedure and the kinetic parameters are determined from the experimental results. 

The study of the rates of chemical reactions is called kinetics. Chemists study reaction rates for many reasons. To give just one example, Rowland and Molina used kinetic studies to show the destructive potential of CFCs. Kinetic studies are essential to the explorations of reaction mechanisms, because a mechanism can never be determined by calculations alone. Kinetic studies are important in many areas of science, including biochemistry, synthetic chemistry, biology, environmental science, engineering, and geology. The usefulness of chemical kinetics in elucidating mechanisms can be understood by examining the differences in rate behavior of unimolecular and bimolecular elementary reactions. 

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