Chemical kinetics transition state theory

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]. 

A more general, and for the moment, less detailed description of the progress of chemical reactions, was developed in the transition state theory of kinetics. This approach considers tire reacting molecules at the point of collision to form a complex intermediate molecule before the final products are formed. This molecular species is assumed to be in thermodynamic equilibrium with the reactant species. An equilibrium constant can therefore be described for the activation process, and this, in turn, can be related to a Gibbs energy of activation ... 

After an introductory chapter, phenomenological kinetics is treated in Chapters 2, 3, and 4. The theory of chemical kinetics, in the form most applicable to solution studies, is described in Chapter 5 and is used in subsequent chapters. The treatments of mechanistic interpretations of the transition state theory, structure-reactivity relationships, and solvent effects are more extensive than is usual in an introductory textbook. The book could serve as the basis of a one-semester course, and I hope that it also may be found useful for self-instruction. 

Kinetics on the level of individual molecules is often referred to as reaction dynamics. Subtle details are taken into account, such as the effect of the orientation of molecules in a collision that may result in a reaction, and the distribution of energy over a molecule s various degrees of freedom. This is the fundamental level of study needed if we want to link reactivity to quantum mechanics, which is really what rules the game at this fundamental level. This is the domain of molecular beam experiments, laser spectroscopy, ah initio theoretical chemistry and transition state theory. It is at this level that we can learn what determines whether a chemical reaction is feasible. 

This chapter treats the descriptions of the molecular events that lead to the kinetic phenomena that one observes in the laboratory. These events are referred to as the mechanism of the reaction. The chapter begins with definitions of the various terms that are basic to the concept of reaction mechanisms, indicates how elementary events may be combined to yield a description that is consistent with observed macroscopic phenomena, and discusses some of the techniques that may be used to elucidate the mechanism of a reaction. Finally, two basic molecular theories of chemical kinetics are discussed—the kinetic theory of gases and the transition state theory. The determination of a reaction mechanism is a much more complex problem than that of obtaining an accurate rate expression, and the well-educated chemical engineer should have a knowledge of and an appreciation for some of the techniques used in such studies. 

The transition state theory provides a useful framework for correlating kinetic data and for codifying useful generalizations about the dynamic behavior of chemical systems. This theory is also known as the activated complex theory, the theory of absolute reaction rates, and Eyring s theory. This section introduces chemical engineers to the terminology, the basic aspects, and the limitations of the theory. 

Although the collision and transition state theories represent two important methods of attacking the theoretical calculation of reaction rates, they are not the only approaches available. Alternative methods include theories based on nonequilibrium statistical mechanics, stochastic theories, and Monte Carlo simulations of chemical dynamics. Consult the texts by Johnson (62), Laidler (60), and Benson (59) and the review by Wayne (63) for a further introduction to the theoretical aspects of reaction kinetics. 

Isotope effects on rates (so-called kinetic isotope effects, KIE s) of specific reactions will be discussed in detail in a later chapter. The most frequently employed formalism used to discuss KIE s is based on the activated complex (transition state) theory of chemical kinetics and is analogous to the theory of isotope effects on thermodynamic equilibria discussed in this chapter. It is thus appropriate to discuss this theory here. 

The use of transition state theory as a convenient expression of rate data is obviously complex owing to the presence of the temperature-dependent partition functions. Most researchers working in the area of chemical kinetic modeling have found it necessary to adopt a uniform means of expressing the temperature variation of rate data and consequently have adopted a modified Arrhenius form... 

Recently, transition state theory calculations were applied to a class of reactions involving OH radicals and haloalkanes, again to account systematically for the expected curvature in Arrhenius plots for these reactions (Cohen and Benson, 1987a). Subsequently, empirical relationships were also derived for the a priori determination of pre-exponential factors (A) and activation energies ( ) based on an assumed T dependency of the pre-exponential factor (Cohen and Benson, 1987b). This and related studies clearly illustrate the broad utility of transition state theory in the systematic development of detailed chemical kinetic mechanisms. 

In siunmary, although the application of detailed chemical kinetic modeling to heterogeneous reactions is possible, the effort needed is considerably more involved than in the gas-phase reactions. The thermochemistry of surfaces, clusters, and adsorbed species can be determined in a manner analogous to those associated with the gas-phase species. Similarly, rate parameters of heterogeneous elementary reactions can be estimated, via the application of the transition state theory, by determining the thermochemistry of saddle points on potential energy surfaces. 

Bimolecular processes are very common in biological systems. The binding of a hormone to a receptor is a bimolecular reaction, as is substrate and inhibitor binding to an enzyme. The term bimolecular mechanism applies to those reactions having a rate-limiting step that is bimolecular. See Chemical Kinetics Molecularity Reaction Order Elementary Reaction Transition-State Theory... 

An integer indicating the molecular stoichiometry of an elementary reaction. A fundamental assumption in chemical kinetics is that the kinetic form of a one-step reaction will be identical to its stoichiometric form. In terms of transition-state theory, molecularity equals the number of molecules (or entities) that are used to form the activated complex. For reactions in solution, solvent molecules are counted in the molecularity only if they enter into the overall process, not if they only exert an environmental or solvent effect ". ... 

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... 

State is that assembly of atoms or moieties that closely resembles the reactant(s), such that only a relatively small reorganization will generate the reactant(s). Analogously, a late transition state more closely resembles the structure of the reaction product(s). See Chemical Kinetics Transition State Theory Potential Energy Surface Hammond Principle Transition Structure... 

ELECTROSTATIO BOND ELECTROSTATIO SUREAOE POTENTIAL ELECTROSTRIOTION ELECTROTAXIS ELECTROVALENT BOND ELEMENTARY OHARGE ELEMENTARY REACTION Elementary reaction stoichiometry, MOLECULARITY CHEMICAL KINETICS UNIMOLECULAR BIMOLECULAR TRANSITION-STATE THEORY ELEMENTARY REACTION Element effect,... 

STOICHIOMETRIC NUMBER Stoichiometry of elementary reactions, CHEMICAL KINETICS MOLECULARITY UNIMOLECULAR BIMOLECULAR TRANSITION-STATE THEORY ELEMENTARY REACTION STOKE S SHIFT... 

TRANSITION STATE THEORY POTENTIAL ENERGY SUREACE HAMMOND PRINCIPLE TRANSITION STRUCTURE CHEMICAL KINETICS TRANSITION-STATE ANALOGUES MOLECULAR SIMILARITY... 

TRANSITION-STATE THEORY CHEMICAL KINETICS COLLISION THEORY TEMPERATURE DEPENDENCE... 

The field of chemical kinetics is far reaching and well developed. If the full energy surface for the atoms participating in a chemical reaction is known (or can be calculated), sophisticated rate theories are available to provide accurate rate information in regimes where simple transition state theory is not accurate. A classic text for this field is K. J. Laidler, Chemical Kinetics, 3rd ed., Prentice Hall, New York, 1987. A more recent book related to this topic is I. Chorkendorff and J. W. Niemantsverdriet, Concepts of Modern Catalysis and Kinetics, 2nd ed., Wiley-VCH, Weinheim, 2007. Many other books in this area are also available. 

In this chapter, we discuss the fundamental principles of chemical reactivity and catalysis to understand the organic chemistry of catalysis and how to analyze it. We begin with transition state theory because it provides a simple framework for understanding much about reactivity and kinetics. We progress to structure-activity relationships and also discuss some fundamental concepts in analyzing mechanisms. 

The rate constant, k, for most elementary chemical reactions follows the Arrhenius equation, k = A exp(— EJRT), where A is a reaction-specific quantity and Ea the activation energy. Because EA is always positive, the rate constant increases with temperature and gives linear plots of In k versus 1 IT. Kinks or curvature are often found in Arrhenius plots for enzymatic reactions and are usually interpreted as resulting from complex kinetics in which there is a change in rate-determining step with temperature or a change in the structure of the protein. The Arrhenius equation is recast by transition state theory (Chapter 3, section A) to... 

M Transition state theory is discussed in standard texts on physical chemistry, kinetics, and physical organic chemistry. See, for example, (a) W. J. Moore, Physical Chemistry, 3rd ed., Prentice-Hall, Englewood Cliffs, N.J., 1962, p. 296 (b) S. W. Benson, Thermochemical Kinetics, Wiley, New York, 1968 (c) K. J. Laidler, Chemical Kinetics, 2nd ed., McGraw-Hill, New York, 1965 (d) K. B. Wiberg, Physical Organic Chemistry, Wiley, New York, 1964 (e) L. P. Hammett, Physical Organic Chemistry, 2nd ed., McGraw-Hill, New York, 1970. For a different approach to chemical dynamics, see (f) D. L. Bunker, Accts. Chem. Res., 7, 195 (1974). 

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