Brief Introduction to Chemical Kinetics

This section provides a brief introduction to chemical kinetics, which is needed to understand the basis for kinetic methods of analysis. 

Abstract In this chapter we present a brief introduction to chemical kinetics. Key concepts like reversibility of chemical reactions, reaction rate, reaction rate constant, and chemical equilibrium, are introduced and discussed. The most important of the results here derived is the so-called law of mass action which we discuss from the perspective of chemical kinetics. In this chapter we follow a heuristic rather than a formal approach. We start by analyzing a few simple chemical reactions to gain insight into the chemical kinetics basic concepts. After that, we heuristically derive and discuss the corresponding results for the most general case. The interested reader can consult any of the many available books on the subject. We particularly recommend the book by Houston (Chemical kinetics and reaction dynamics. McGraw-Hill, New York, 2001). 

This chapter is meant as a brief introduction to chemical kinetics. Some central concepts, like reaction rate and chemical equilibrium, have been introduced and their meaning has been reviewed. We have further seen how to employ those concepts to write a system of ordinary differential equations to model the time evolution of the concentrations of all the chemical species in the system. The resulting equations can then be numerically or analytically solved, or studied by means of the techniques of nonlinear dynamics. A particularly interesting result obtained in this chapter was the law of mass action, which dictates a condition to be satisfied for the equilibrium concentrations of all the chemical species involved in a reaction, regardless of their initial values. In the forthcoming chapters we shall use this result to connect different approaches like chemical kinetics, thermodynamics, etc. 

Our objectives in writing this review were to provide a brief introduction to simple methods that are useful for analyses of reaction schemes and to provide several case studies that illustrate different scenarios for the applications of these analysis methods. Finally, we stress that analyses of reaction schemes are not used to prove reaction schemes. Instead, these analyses may be used first to test the feasibility of reaction schemes that have been formulated from chemical experience, intuition, and theoretical methods these analyses may then be used to consolidate and extrapolate the information contained in kinetic models of reaction schemes to help guide the search for better catalytic materials and/or more favorable reaction conditions. 

This section has provided only a brief introduction to the principal concepts in chemical kinetics. Most of the discussion which follows in this chapter relates to fast reactions in solution. Before describing the experimental techniques used to study fast reactions, the important types of solution reactions are outlined and their properties discussed. 

The Brdnsted relations, as presented here, constitute a brief introduction to a vast and well-organized chapter of chemical kinetics acid-base catalysis. A recent survey of the field is The Proton in Chemistry, by R. P. Bell, Methuen Co. Ltd., London, 1959. 

Kinetics, chemical, thermodynamic, and physical principles will all be operating in high-temperature service test environments, requiring each investigator to have an adequate huniliarily of basic mechanisms and corrosion phenomena. A brief introduction to these aspects of service testing is presented here. 

This chapter focuses on the catalytic aspects of methanol chemistry and covers thermodynamic, kinetic, chemical engineering, and materials science aspects. It provides brief introductions into these topics with the aim of establishing an overview of the state of the art of methanol chemistry with only a snapshot of the relevant literature. It highlights what the authors think are the most relevant aspects and future challenges for energy-related catalytic reactions of methanol. It is not meant to provide a complete literature overview on methanol synthesis and reforming. 

The application of kinetics and thermodynamics requires a deeper understanding than the brief introduction given here. Although best suited to simple systems, thermodynamics and kinetics are also unexcelled as tools for the understanding of chemical phenomena in nature. 

The main goal in this chapter is to obtain suitable expressions to represent the kinetics of catalytic processes. Many details of the chemical phenomena are still obscure, and so, just as in Chapter 1, we will only briefly discuss the mechanistic aspects of catalysis. Further details are presented in several books in this area— an entree to this area is provided in books on chemical kinetics and catalysis some texts specifically intended for chemical engineers are by Thomas and Thomas [1], Boudart [2], and a useful brief introduction by Thomson and Webb [3] and a discussion of several important industrial catalytic processes is given in Gates, Katzer and Schuit [62]. For further comprehensive surveys, see Emmett [4] and, for current progress, the series Advances in Catalysis [5],... 

We introduced the concepts of fluctuations and dissipation in Chap. 2, where we discussed the approach of a chemical system to a nonequilibrium stationary state we recommend a review of that chapter. We restricted there the analysis to linear and nonhnear one-variable chemical systems and shall do so again in this chapter, except for a brief referral to extensions to multivariable systems at the end of the chapter. In Chap. 2 we gave some connections between deterministic kinetics, with attending dissipation, and fluctuations, see for example (2.33), which equates the probability of a fluctuation in the concentration X to the deterministic kinetics, see (2.8, 2.9). Here we enlarge on the relations between dissipative, deterministic kinetics, and fluctuations for the purpose of an introduction to the interesting topic of fluctuation dissipation relations. This subject has a long history, more than 100 years [1,2] Reference [1] is a classical review with many references to fundamental earlier work. A brief reminder of one of the early examples, that of Brownian motion, may be helpful. 

In this first chapter, we will outline the scope of this book on the kinetics of chemical processes in the solid state. They are often different from the kinetics of processes in fluids because of structural constraints. After a brief historical introduction, typical situations of non-equilibrium crystals will be described. These will illustrate some basic concepts and our approach to understanding solid state kinetics. 

These ring collision events are now a familiar part of the kinetic theory description of dynamic processes in simple dense fluids. A brief comparison of the theory for the velocity autocorrelation function with that for the chemically reacting fluid will help motivate our description. Recent developments in the theory of the velocity autocorrelation function have arisen out of an attempt to understand the slow t power law decay observed by Alder and Wainwright in a computer simulation of a dense hard-sphere fluid. This work also showed that the translational motion of a small hard sphere in a fluid of similar hard spheres has a significant collective (hydro-dynamic) component. On the theoretical side, this type of behavior was discussed from the kinetic theory point of view in terms of the ring collision events described above and provided a microscopic basis for the introduction of collective effects. In addition, it was shown that mode... 

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