Chemical kinetics described

Deviation from standard chemical kinetics described in (Section 2.1.1) can happen only if the reaction rate K (t) reveals its own non-monotonous time dependence. Since K(t) is a functional of the correlation functions, it means that these functions have to possess their own motion, practically independent on the time development of concentrations. The correlation functions characterize the intermediate order in the particle distribution in a spatially-homogeneous system. Change of such an intermediate order could be interpreted as a series of structural transitions. 

The rate expressions obtained by chemical kinetics describe file dependency of the reaction rate on kinetic parameters related to the chemical reactions. These rate expressions are commonly referred to as the intrinsic rate expressions of the chemical reactions (or intrinsic kinetics). However, in many instances, file local species concentrations depend also on the rate that the species are transported in the reacting medium. Consequently, the actual reaction rate (also referred to as the global reaction rate) is affected by the transport rates of the reactants and products. 

One of the theories of non-linear phenomena, recently created and being rapidly developed, is catastrophe theory. Catastrophe theory deals with the non-linear phenomena in which a continuous change in control parameters results in a discontinuous alteration of a quantity characterizing the examined system. It is well suited for the investigation of non-linear equations of chemical kinetics, describing chemical reactions. 

Laidler, Keith J. The World of Physical Chemistry. Oxford Oxford University Press, 1993. This book provides highly readable and stimulating coverage of the history of physical chemistry including coverage of the chemical kinetics described in this chapter. 

Chemical kinetics describes the change of species with time under the conditions of nonequilibrium. For qualitative statements, we require a reaction mechanism and the associated kinetic constants of the individual reactions. For special areas, like pyrolysis and flames, there are already sophisticated computer programs, which develop automatically kinetic models [1] and perform a data reduction [2]. Also in the field of geochemistry, such programs are available [3]. 

Chemical kinetics describes the progress of a chemical reaction. The most common description of the progress is given by the term rate of reaction —a positive quantity that expresses how the concentration of a reactant or product changes with time. For the elementary reaction... 

We can now give precise definitions of some words and phrases that are often used loosely. A reaction rate is a rate of change of the concentration of some chemical species at a particular moment it is derived from a set of observations, in which the course of a reaction is monitored over a period of time. Such observations are the basic experimental data. By analysing the relation between these rates and the corresponding concentrations, one obtains a rate law that fits both the data and (often) some standard form (e.g., first-order, in which the rate is proportional to the concentration of one of the reactants). These rate laws, along with known structural data, may be given some interpretation in terms of reaction kinetics, one would describe a scheme of molecular motions that would explain the rate law. Often there are several alternative schemes that would be consistent with a particular set of data further experimentation would then be needed in order to choose between them. Such schemes in terms of chemical kinetics describe events on the microscopic scale, involving atoms and molecules, as distinct from rate laws which are expressed in terms of macromolecular quantities (time and concentration). The schemes may in turn be interpreted in terms of a reaction mechanism, which relates them to chemical dynamics, i.e., to theories of how molecules behave, in terms either of some particular model with limited scope (such as collison theory, or transition-state theory) or of the more fundamental body of theory based upon quantum mechanics. 

The quasi-equilibrium principle gained a widespread practical use in enzyme kinetics, a branch of chemical kinetics describing catalytic reactions involving... 

As these examples have demonstrated, in particular for fast reactions, chemical kinetics can only be appropriately described if one takes into account dynamic effects, though in practice it may prove extremely difficult to separate and identify different phenomena. It seems that more experiments under systematically controlled variation of solvent enviromnent parameters are needed, in conjunction with numerical simulations that as closely as possible mimic the experimental conditions to improve our understanding of condensed-phase reaction kmetics. The theoretical tools that are available to do so are covered in more depth in other chapters of this encyclopedia and also in comprehensive reviews [6, 118. 119],... 

Although the Arrhenius equation does not predict rate constants without parameters obtained from another source, it does predict the temperature dependence of reaction rates. The Arrhenius parameters are often obtained from experimental kinetics results since these are an easy way to compare reaction kinetics. The Arrhenius equation is also often used to describe chemical kinetics in computational fluid dynamics programs for the purposes of designing chemical manufacturing equipment, such as flow reactors. Many computational predictions are based on computing the Arrhenius parameters. 

When a relatively slow catalytic reaction takes place in a stirred solution, the reactants are suppHed to the catalyst from the immediately neighboring solution so readily that virtually no concentration gradients exist. The intrinsic chemical kinetics determines the rate of the reaction. However, when the intrinsic rate of the reaction is very high and/or the transport of the reactant slow, as in a viscous polymer solution, the concentration gradients become significant, and the transport of reactants to the catalyst cannot keep the catalyst suppHed sufficientiy for the rate of the reaction to be that corresponding to the intrinsic chemical kinetics. Assume that the transport of the reactant in solution is described by Fick s law of diffusion with a diffusion coefficient D, and the intrinsic chemical kinetics is of the foUowing form... 

New materials also emerged. Nylon, developed brilliantly by W. H. Carothers and his team of research workers for Du Pont as a fibre in the mid-1930s, was first used as a moulding material in 1941. Also in 1941 a patent taken out by Kinetic Chemical Inc. described how R. J. Plunkett had first discovered polytetrafluoroethylene. This happened when, on one occasion, it was found that on opening the valve of a supposedly full cylinder of the gas tetrafluoroethylene no gas issued out. On subsequently cutting up the cylinder it was found that a white solid, polytetrafluoroethylene (PTFE), had been deposited on the inner walls of the cylinder. The process was developed by Du Pont and, in 1943, a pilot plant to produce their product Teflon came on stream. 

Chemistry can be divided (somewhat arbitrarily) into the study of structures, equilibria, and rates. Chemical structure is ultimately described by the methods of quantum mechanics equilibrium phenomena are studied by statistical mechanics and thermodynamics and the study of rates constitutes the subject of kinetics. Kinetics can be subdivided into physical kinetics, dealing with physical phenomena such as diffusion and viscosity, and chemical kinetics, which deals with the rates of chemical reactions (including both covalent and noncovalent bond changes). Students of thermodynamics learn that quantities such as changes in enthalpy and entropy depend only upon the initial and hnal states of a system consequently thermodynamics cannot yield any information about intervening states of the system. It is precisely these intermediate states that constitute the subject matter of chemical kinetics. A thorough study of any chemical reaction must therefore include structural, equilibrium, and kinetic investigations. 

A large portion of the field of chemical kinetics can be described by, or discussed in terms of, Eq. (5-1), the Arrhenius equation. 

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. 

There are two principal chemical concepts we will cover that are important for studying the natural environment. The first is thermodynamics, which describes whether a system is at equilibrium or if it can spontaneously change by undergoing chemical reaction. We review the main first principles and extend the discussion to electrochemistry. The second main concept is how fast chemical reactions take place if they start. This study of the rate of chemical change is called chemical kinetics. We examine selected natural systems in which the rate of change helps determine the state of the system. Finally, we briefly go over some natural examples where both thermodynamic and kinetic factors are important. This brief chapter cannot provide the depth of treatment found in a textbook fully devoted to these physical chemical subjects. Those who wish a more detailed discussion of these concepts might turn to one of the following texts Atkins (1994), Levine (1995), Alberty and Silbey (1997). 

As described in the first part of this chapter, chemical thermodynamics can be used to predict whether a reaction will proceed spontaneously. However, thermodynamics does not provide any insight into how fast this reaction will proceed. This is an important consideration since time scales for spontaneous reactions can vary from nanoseconds to years. Chemical kinetics provides information on reaction rates that thermodynamics cannot. Used in concert, thermodynamics and kinetics can provide valuable insight into the chemical reactions involved in global biogeochemical cycles. 

First, the simple thermodynamic description of pe (or Eh) and pH are both most directly applicable to the liquid aqueous phase. Redox reactions can and do occur in the gas phase, but the rates of such processes are described by chemical kinetics and not by equilibrium concepts of thermodynamics. For example, the acid-base reaction... 

In chemical kinetics, one finds linked sets of differential equations expressing the rates of change of the interacting species. Overall, mathematical models have been exceedingly successfiil in depicting the broad outlines of an enormously diverse variety of phenomena in nature. Some scientists have even commented in surprise at how well mathematics works in describing nature. So successful have these mathematical models been that their use has spread from the hard sciences to areas as diverse as economics and the analysis of athletic performance [3]. 

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. 

The gas motion near a disk spinning in an unconfined space in the absence of buoyancy, can be described in terms of a similar solution. Of course, the disk in a real reactor is confined, and since the disk is heated buoyancy can play a large role. However, it is possible to operate the reactor in ways that minimize the effects of buoyancy and confinement. In these regimes the species and temperature gradients normal to the surface are the same everywhere on the disk. From a physical point of view, this property leads to uniform deposition - an important objective in CVD reactors. From a mathematical point of view, this property leads to the similarity transformation that reduces a complex three-dimensional swirling flow to a relatively simple two-point boundary value problem. Once in boundary-value problem form, the computational models can readily incorporate complex chemical kinetics and molecular transport models. 

Notice that the word spontaneous has a different meaning in thermodynamics than it does in everyday speech. Ordinarily, spontaneous refers to an event that takes place without any effort or premeditation. For example, a crowd cheers spontaneously for an outstanding performance. In thermodynamics, spontaneous refers only to the natural direction of a process, without regard to whether it occurs rapidly and easily. Chemical kinetics, which we introduce in Chapter 15, describes the factors that determine the speeds of chemical reactions. Thermodynamic spontaneity refers to the direction that a process will take if left alone and given enough time. 

A reaction at steady state is not in equilibrium. Nor is it a closed system, as it is continuously fed by fresh reactants, which keep the entropy lower than it would be at equilibrium. In this case the deviation from equilibrium is described by the rate of entropy increase, dS/dt, also referred to as entropy production. It can be shown that a reaction at steady state possesses a minimum rate of entropy production, and, when perturbed, it will return to this state, which is dictated by the rate at which reactants are fed to the system [R.A. van Santen and J.W. Niemantsverdriet, Chemical Kinetics and Catalysis (1995), Plenum, New York]. Hence, steady states settle for the smallest deviation from equilibrium possible under the given conditions. Steady state reactions in industry satisfy these conditions and are operated in a regime where linear non-equilibrium thermodynamics holds. Nonlinear non-equilibrium thermodynamics, however, represents a regime where explosions and uncontrolled oscillations may arise. Obviously, industry wants to avoid such situations ... 

The effect of chemical kinetics on mass transport in incompressible flows is summarized by the reaction term r in Eq. (89). Applied to a chemical species a, it describes the rate of disappearance of this species per unit volume ... 

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