Kinetics—The Basics

We mentioned in Chapters 6 and 14 the use of catalysts to alter the reaction rate in certain redox reactions the titration reaction of AsCIED with Ce(IV) is catalyzed by OSO4. The catalyst is added in sufficiently high concentration to make the reaction occur immediately. If the catalyst concentration is low and the reaction slow, then we can measure the rate of the reaction and relate it to the catalyst concentration. In this chapter, we describe the basic kinetics of rate-limited reactions. Then we discuss reactions catalyzed by specific catalysts called enzymes and the measurement of the reaction rate to either determine the enzyme activity (concentration) or the concentration of the catalyst s substrate by adding a fixed amount of enzyme to the solution. 

Kinetics is the description of reactirajiates. The order of a reaction defines the dependence of reaction rates on the concentrations of reacting species. Order is determined empirically and is not necessarily related to the stoichiometry of the reaction. Rather, it is governed by the mechanism of the reaction, that is, by the number of species that must collide for the reaction to occur. 

The order of a reaction defines the number of species that must react, not-the ratio in which they react (stoichiometry). 

Reactions in which the rate of the reaction is direcdv proportional to the concentration of a single substance are known as first-order reactions. Consider the reaction 

The rate of reaction slows down with time. 

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The effects of these factors and the means by which they are studied are usually described as enzyme kinetics. The basic information required to study enzyme kinetics is as follows. 

Determining the Best System for a Given Conversion. Suppose we want to find the minimum size of two mixed flow reactors in series to achieve a specified conversion of feed which reacts with arbitrary but known kinetics. The basic performance expressions, Eqs. 5.11 and 5.12, then give, in turn, for the first reactor... 

In chemical reaction kinetics, the basic measurement is that of rate (v) per unit area as a function of temperature, with application of the classical Arrhenius equation, v = Ae E/RT Electrochemical reactions also vaiy with temperature (see Section 7.5.14). However, the basic measurement for electrochemical kinetics is the rate as a function of potential36 at constant temperature, with application of the corresponding Tafel equation, v = A e ar F/RT. 

Volumes 26 and 27 are both concerned with reactions occurring at electrodes arising through the passage of current. They provide an introduction to the study of electrode kinetics. The basic ideas and experimental methodology are presented in Volume 26 whilst Volume 27 deals with reactions at particular types of electrode. 

The Fluctuation-Controlled Kinetics The Basic Formalism of Many-Point Particle Densities... 

Molecular modeling includes a collection of computer-based tools of varying theoretical soundness, which make it possible to explain, and eventually predict, the properties of molecular systems on the basis of their composition, geometry, and electronic structure. The need for such modeling arises while studying and/or developing various chemical products and/or processes. The raison d etre of molecular modeling is provided by chemical thermodynamics and chemical kinetics, the basic facts of which are assumed to be known to the reader.1... 

Although the field of gas-phase kinetics remains hill of challenges it has reached a certain degree of maturity. Many of the fiindamental concepts of kinetics, in general take a particularly clear and rigorous fonn in gas-phase kinetics. The relation between fiindamental quantum dynamical theory, empirical kinetic treatments, and experimental measurements, for example of combustion processes [72], is most clearly established in gas-phase kmetics. It is the aim of this article to review some of these most basic aspects. Details can be found in the sections on applications as well as in the literature cited. 

The basic principle behind TOP mass spectrometry [36] is tire equation for kinetic energy, ze V... 

Even cursory inspection of typical (v,[) data shows tliat tire evolution does not follow tire single exponential approach to saturation implied by, for example, (equation C2.14.22) witli initial concentrations Xq Such data are sometimes described as biphasic , and one encounters attempts to fit and inteiyDret tliem witli two exponentials, even tliough tliere does not seem to be any tlieoretical justification for doing so. The basic kinetics of adsorjDtion are described by ... 

The Hamiltonian again has the basic form of Eq. (63). The system is described by the nuclear coordinates, Q, which are relative to a suitable nuclear configuration Q. In conbast to Section in.C, this may be any point in configmation space. As a diabatic representation has been assumed, the kinetic energy operator matrix, T, is diagonal with elements... 

Many factors affect the mechanisms and kinetics of sorption and transport processes. For instance, differences in the chemical stmcture and properties, ie, ionizahility, solubiUty in water, vapor pressure, and polarity, between pesticides affect their behavior in the environment through effects on sorption and transport processes. Differences in soil properties, ie, pH and percentage of organic carbon and clay contents, and soil conditions, ie, moisture content and landscape position climatic conditions, ie, temperature, precipitation, and radiation and cultural practices, ie, crop and tillage, can all modify the behavior of the pesticide in soils. Persistence of a pesticide in soil is a consequence of a complex interaction of processes. Because the persistence of a pesticide can govern its availabiUty and efficacy for pest control, as weU as its potential for adverse environmental impacts, knowledge of the basic processes is necessary if the benefits of the pesticide ate to be maximized. 

The lack of dependence on ionic strength in the first reaction indicates that it occurs between neutral species. Mono- or dichloramine react much slower than ammonia because of their lower basicities. The reaction is faster with CI2 because it is a stronger electrophile than with HOCl The degree of chlorination increases with decreasing pH and increasing HOCINH mol ratio. Since chlorination rates exceed hydrolysis rates, initial product distribution is deterrnined by formation kinetics. The chloramines hydrolyze very slowly and only to a slight extent and are an example of CAC. 

The development of combustion theory has led to the appearance of several specialized asymptotic concepts and mathematical methods. An extremely strong temperature dependence for the reaction rate is typical of the theory. This makes direct numerical solution of the equations difficult but at the same time accurate. The basic concept of combustion theory, the idea of a flame moving at a constant velocity independent of the ignition conditions and determined solely by the properties and state of the fuel mixture, is the product of the asymptotic approach (18,19). Theoretical understanding of turbulent combustion involves combining the theory of turbulence and the kinetics of chemical reactions (19—23). 

Salt flux across a membrane is due to effects coupled to water transport, usually negligible, and diffusion across the membrane. Eq. (22-60) describes the basic diffusion equation for solute passage. It is independent of pressure, so as AP — AH 0, rejection 0. This important factor is due to the kinetic nature of the separation. Salt passage through the membrane is concentration dependent. Water passage is dependent on P — H. Therefore, when the membrane is operating near the osmotic pressure of the feed, the salt passage is not diluted by much permeate water. 

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. 

Much of the basic theory of reaction kinetics presented in Sec. 7 of this Handbook deals with homogeneous reaclions in batch and continuous equipment, and that material will not be repeated here. Material and energy balances and sizing procedures are developed for batch operations in ideal stirred tanks—during startup, continuation, and shutdown—and for continuous operation in ideal stirred tank batteries and plug flow tubulars and towers. 

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