Basic Aspects of Chemical Kinetics

Before we delve into enzyme kinetics, we need to discuss some of the basic principles that apply to the kinetics of both enzymatic and nonenzymatic reactions. Let s first consider a nonenzymatic reaction that converts a single reactant (R) into a product (P)  

To measure the velocity of the reaction (v), we plot the concentration of R as a function of time (fig. 7.2). The rate at any particular time (t) is 

For a simple reaction of this type, the rate at any given time usually is found to be proportional to the remaining concentration of the reactant  

The proportionality constant k is the rate constant. The rate constant is independent of the concentration of the reactant, but it can depend on other parameters, such as temperature or pH, and, as we shall see, it may be altered by a catalyst. It has dimensions of reciprocal seconds (s 1). Combining equations (3) and (4), we have 

A reaction of this type is said to follow first-order kinetics because the rate is proportional to the concentration of a single species raised to the first power (fig. 7.2). An example is the decay of a radioactive isotope such as 14C. The rate of decay at any time (the number of radioactive disintegrations per second) is simply proportional to the amount of l4C present. The rate constant for this extremely slow nuclear reaction is 8 x 10-12 s l. Another example is the initial electron-transfer reaction that occurs when photosyn- 

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Before examining the electrode reaction kinetics it is necessary to recall a few basic aspects of chemical kinetics. Consider the following elementary process ... 

Enzyme kinetics is studied for two reasons (1) it is a practical concern to determine the activity of the enzyme under different conditions (2) frequently the analysis of enzyme kinetics gives information about the mechanism of enzyme action. Chapter 7, Enzyme Kinetics, begins with an introductory section on the discovery of enzymes, basic enzyme terminology and a description of the six main classes of enzymes and the reactions they catalyze. The remainder of the chapter deals with basic aspects of chemical kinetics, enzyme-catalyzed reactions and various factors that affect the kinetics. 

One feature that distinguishes the education of the chemical engineer from that of other engineers is an exposure to the basic concepts of chemical reaction kinetics and chemical reactor design. This textbook provides a judicious introductory level overview of these subjects. Emphasis is placed on the aspects of chemical kinetics and material and energy balances that form the foundation for the practice of reactor design. 

Chapters 3 to 7 treat the aspects of chemical kinetics that are important to the education of a well-read chemical engineer. To stress further the chemical problems involved and to provide links to the real world, I have attempted where possible to use actual chemical reactions and kinetic parameters in the many illustrative examples and problems. However, to retain as much generality as possible, the presentations of basic concepts and the derivations of fundamental equations are couched in terms of the anonymous chemical species A, B, C, U, V, etc. Where it is appropriate, the specific chemical reactions used in the illustrations are reformulated in these terms to indicate the manner in which the generalized relations are employed. 

In this chapter, we will recall some basic aspects of chemical reaction kinetics in solution, starting from an oversimplified point of view and gradually bringing in more complications. We will not discuss theory aimed at explaining reaction rates on a molecular level (molecular reaction dynamics). Other rate processes will be discussed in Chapters 5 and 13. 

Dente and Ranzi (in Albright et al., eds.. Pyrolysis Theory and Industrial Practice, Academic Press, 1983, pp. 133-175) Mathematical modehng of hydrocarbon pyrolysis reactions Shah and Sharma (in Carberry and Varma, eds.. Chemical Reaction and Reaction Engineering Handbook, Dekker, 1987, pp. 713-721) Hydroxylamine phosphate manufacture in a slurry reactor Some aspects of a kinetic model of methanol synthesis are described in the first example, which is followed by a second example that describes coping with the multiphcity of reactants and reactions of some petroleum conversion processes. Then two somewhat simph-fied industrial examples are worked out in detail mild thermal cracking and production of styrene. Even these calculations are impractical without a computer. The basic data and mathematics and some of the results are presented. 

The present chapter will focus on the practical, nuts and bolts aspects of this particular CA approach to modeling. In later chapters we will describe a variety of applications of these CA models to chemical systems, emphasizing applications involving solution phenomena, phase transitions, and chemical kinetics. In order to prepare readers for the use of CA models in teaching and research, we have attempted to present a user-friendly description. This description is accompanied by examples and hands-on calculations, available on the compact disk that comes with this book. The reader is encouraged to use this means to assimilate the basic aspects of the CA approach described in this chapter. More details on the operation of the CA programs, when needed, can be found in Chapter 10 of this book. 

It is useful at this time to review briefly some basic aspects of enzyme inhibition and enzyme inhibitors. For a broader review of enzymatic mechanisms and kinetics consult any of several excellent biochemistry textbooks. Enzyme inhibitors are chemical agents capable of modifying an enzyme s capacity to catalyze the reactions of its normal substrates. Effecting such changes of enzyme function by altering the pH, changing the temperature, or subjecting the system to radiation such as UV should properly be considered a denatu-ration process. 

Through these simulations, students appreciate the energetic and kinetic aspects of chemical reactions and why the composition of the atmosphere is critical to the outcome. For example, the class simulates the effect on the yield of amino acids if the atmospheric composition was CO2 instead of CH4 or the nitrogen source was N2 instead of NH3. The simulations also allow students to investigate the consequences if the pre-biotic atmosphere contained free 02. Through these simulations, basic chemical concepts are discussed including thermodynamics, thermochemistry and bond enthalpies, kinetics, and catalysis. 

The purpose of this book is to present the principles of chemical kinetics along with modem applications. Thus the student will learn not only the basic formulations but also will be stimulated (hopefully) by the exciting current research in chemical kinetics. Obviously a complete description of modem chemical kinetics would require a volume (or volumes) considerably larger than this one. Therefore, only a selection of topics is possible. Many extremely interesting aspects are not covered, but I believe that a student who understands the material presented will have no trouble in going directly to the literature for further informa-, tion. The phenomenology and conunonly used theories of chemical kinetics are presented in a critical manner, with particular emphasis on collision dynamics. How and what mechanistic information can be obtained from various experimental approaches is stressed throughout the book. 

One of my basic goals is to answer questions on stereoselectivity, catalysis, stability and reactivity of reactive intermediates, kinetic and thermodynamic aspects of chemical transformation, and so on. Many of the reactive intermediates of organic chemistry are charged species, such as carbocations (carbenium and carbonium ions) and carbanions, but there is an important subgroup of formally neutral... 

We have taken a quick trip through what we consider essential thermodynamics and for those students who are only going to take one semester of physical chemistry we have to make sure we treat the basics of chemical kinetics. A glance at the table of contents chapter headings will reveal that we can continue to do more with kinetics in an additional chapter or skip to some basic spectroscopy and then return to more kinetics in the second semester with an emphasis on the molecular level. Here, we want to make sure we establish the mathematical basis for the time dependence of chemical reactions at a macroscopic level. Once again we are giving what we believe are the essential aspects of kinetics here and then visit more advanced kinetics in the second semester. 

In his famous book on quantum mechanics, Dirac stated that chemistry can be reduced to problems in quantum mechanics. It is true that many aspects of chemistry depend on quantum mechanical formulations. Nevertheless, there is a basic difference. Quantmn mechanics, in its orthodox form, corresponds to a deterministic time-reversible description. This is not so for chemistry. Chemical reactions correspond to irreversible processes creating entropy. That is, of course, a very basic aspect of chemistry, which shows that it is not reducible to classical dynamics or quantum mechanics. Chemical reactions belong to the same category as transport processes, viscosity, and thermal conductivity, which are all related to irreversible processes.. .. [A]s far back as in 1870 Maxwell considered the kinetic equations in chemistry, as well as the kinetic equations in the kinetic theory of gases, as incomplete dynamics. From his point of view, kinetic equations for... 

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. 

In contrast to our preferred standard mode in this book, we do not develop a Matlab function for the task of numerical integration of the differential equations pertinent to chemical kinetics. While it would be fairly easy to develop basic functions that work reliably and efficiently with most mechanisms, it was decided not to include such functions since Matlab, in its basic edition, supplies a good suite of fully fledged ODE solvers. ODE solvers play a very important role in many applications outside chemistry and thus high level routines are readily available. An important aspect for fast computation is the automatic adjustment of the step-size, depending on the required accuracy. Also, it is important to differentiate between stiff and non-stiff problems. Proper discussion of the difference between the two is clearly outside the scope of this book, however, we indicate the stiffness of problems in a series of examples discussed later. So, instead of developing our own ODE solver in Matlab, we will learn how to use the routines supplied by Matlab. This will be done in a quite extensive series of examples. 

The book presents a review of sixteen important topics in modem homogeneous catalysis. While the focus is on concepts, many key industrial processes and applications that are important in the laboratory synthesis of organic chemicals are used as real world examples. After an introduction to the field, the elementary steps needed for an understanding of the mechanistic aspects of the various catalytic reactions have been described. Chapter 3 gives the basics of kinetics, thus stressing that kinetics, so often neglected, is actually a key part of the foundation of catalysis. 

This chapter deals with the fundamental aspects of redox reactions in non-aque-ous solutions. In Section 4.1, we discuss solvent effects on the potentials of various types of redox couples and on reaction mechanisms. Solvent effects on redox potentials are important in connection with the electrochemical studies of such basic problems as ion solvation and electronic properties of chemical species. We then consider solvent effects on reaction kinetics, paying attention to the role of dynamical solvent properties in electron transfer processes. In Section 4.2, we deal with the potential windows in various solvents, in order to show the advantages of non-aqueous solvents as media for redox reactions. In Section 4.3, we describe some examples of practical redox titrations in non-aqueous solvents. Because many of the redox reactions are realized as electrode reactions, the subjects covered in this chapter will also appear in Part II in connection with electrochemical measurements. 

Creep and fracture in crystals are important mechanical processes which often determine the limits of materials application. Consequently, they have been widely studied and analyzed in physical metallurgy [J. Weertmann, J.R. Weertmann (1983) R.M. Thomson (1983)]. In solid state chemistry and outside the field of metallurgy, much less is known about these mechanical processes [F. Ernst (1995)]. This is true although the atomic mechanisms of creep and fracture are basically independent of the crystal type. Dislocation formation, annihilation, and motion play decisive roles in this context. We cannot give an exhaustive account of creep and fracture in this chapter. Rather, we intend to point out those aspects which strongly influence chemical reactivity and reaction kinetics. Illustrations are mainly from the field of metals and metal alloys. 

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