KINETIC PRINCIPLES

Chemical kinetics is the subject concerned with the study of the rates at which chemical reactions occur and the variables that affect these rates. The objective of this chapter is to develop a working understanding of this subject in order to apply it to chemical reactors. Chemical reactions and rates of reaction are treated from an engineering point of view—in terms of physically measurable quantities. This information is a requisite for the study and analysis of real-world chemical reactor systems. 

Specific topics covered in this chapter include  

Rate vs Equilibrium Considerations Representation of Rate Expressions Solutions to Rate Expressions Reaction Rate Theories 

The first section on reaction rates covers a broad spectrum of related topics. The definition of the rate of reaction, the reaction velocity constant, and the order of reaction are presented. The variables affecting the rate are also discussed. This is followed by a section entitled Rate vs Equilibrium Considerations. The equations for many different types of reactions are developed in the third section. Particular emphasis is placed on notation, nomenclature, and units. The fourth section reviews the solution to numerous rate expressions. The chapter concludes with a section on the present day theories on reaction rates. Although many of the examples are presented in terms of species A, B, C, and so on, real systems are examined throughout the book in later chapters, 

Chemical Reactor Analysis and Applications for the Practicing Engineer. By Louis Theodure 2012 John Wiley Sc Sons, Inc. Published 2012 by John Wiley Sons, Inc. 

Thermodynamic principles can help explain a corrosion situation in terms of the stability of chemical species and reactions associated with corrosion processes. However, thermodynamic calculations cannot be used to predict corrosion rates. When two metals are put in contact, they can produce a voltage, as in a battery or electrochemical cell (see Galvanic Corrosion in Sec. 5.2.1). The material lower in what has been called the galvanic series will tend to become the anode and corrode, while the material higher in the series will tend to support a cathodic reaction. Iron or aluminum, for example, will have a tendency to corrode when connected to graphite or platinum. What the series cannot predict is the rate at which these metals corrode. Electrode kinetic principles have to be used to estimate these rates. 

The exchange current 7o is a fundamental characteristic of electrode behavior that can be defined as the rate of oxidation or reduction at an equilibrium electrode expressed in terms of current. The term exchange current, in fact, is a misnomer, since there is no net current flow. It is merely a convenient way of representing the rates of oxidation and reduction of a given single electrode at equilibrium, when no loss or gain is experienced by the electrode material. For the corrosion of iron, Eq. (1.1), for example, this would imply that the exchange cur- 

Since the net current is zero at equilibrium, this implies that the sum of these two currents is zero, as in Eq. (1.9). Since / is, by convention, always positive, it follows that, when no external voltage or current is applied to the system, the exchange current is as given by Eq. (1.10). 

There is no theoretical way of accurately determining the exchange current for any given system. This must be determined experimentally. For the characterization of electrochemical processes, it is always preferable to normalize the value of the current by the surface area of the electrode and use the current density, often expressed as a small i, i.e., i = 7/surface area. The magnitude of exchange current density is a function of the following main variables  

Electrode composition. Exchange current density depends upon the composition of the electrode and the solution (Table 1.1). For redox reactions, the exchange current density would depend on the composition of the electrode supporting an equilibrium reaction (Table 1.2). 

When a metal is oxidized at elevated temperatures, a stable scale of oxides or other compounds may buildup to cover and protect the exposed metal surface from further corrosion. The corrosion product layer may therefore act as a barrier between the underlying metal and the corrosive environment (air, flue gas, molten salt, or any other corrosive agent). The compound may be a solid, a liquid, or a gas. For instance, if chromium, vanadium, and molybdenum were exposed to air at 1100°C  

In such case, only chromium would not be severely corroded. If the oxide formed serves as an effective barrier, corrosion can be strongly retarded and only a thin oxide layer will form. On the other hand, if the barrier is not very effective, corrosion nay continue at a moderate rate. It could then be concluded that the oxide scale was only slightly protective and that the metal was not corrosion-resistant under these conditions of exposure. 

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For a complete development of these relationships, see M. Boudart, Kinetics of Chemical Processes. Prentice-Hall, Englewood Cliffs, New Jersey, 1968, pp. 35-46 I. Amdur and G. G. Hammes, Chemical Kinetics, Principles and Selected Topics, McGraw-Hill, New Vbrk, 1966, pp. 43-58 J. W. Moore and R. G. Pearson, Kinetics and Mechanism, John Wiley Sons, New Vbrk, 1981, pp. 159-169 M. M. Kreevoy and D. G. Truhlar, in Investigation ofRates and Mechanisms ofReaction, Techniques of Chemistry, 4th ed., Vol. VT, Part 1, C. F. Bemsscoai, ed., John Wiley Sons, New Ybrk, 1986. 

Chemical kinetics involves the study of reaction rates and the variables tliat affect these rates. It is a topic that is critical for the analysis of reacting systems. The objective in tliis sub-section is to develop a working understanding of tliis subject that will penuit us to apply chemical kinetics principles in tlie tu ea of safety. The topic is treated from an engineering point of view, tliat is, in temis of physically measurable quantities. 

The thermodynamic and electrode-kinetic principles of cathodic protection have been discussed at some length in Section 10.1. It has been shown that, if electrons are supplied to the metal/electrolyte solution interface, the rate of the cathodic reaction is increased whilst the rate of the anodic reaction is decreased. Thus, corrosion is reduced. Concomitantly, the electrode potential of the metal becomes more negative. Corrosion may be prevented entirely if the rate of electron supply is such that the potential of the metal is lowered to the value where it is found that anodic dissolution does not occur. This may not necessarily be the potential at which dissolution is thermodynamically impossible. 

A very interesting calculation has been carried out by N. Bjerrum (Zeitschr. Elektrocliem., 1911 Nernst Festschrift, 1912) in which the rotational energy is connected with the frequencies of the infra-red absorption bands of a gas. The chemical constants of gases have also recently been calculated from kinetic principles by Sackur (Nernst Festschrift, 405, 1912 Ann. Phijs., 40, 67, 84, 1918). 

The kinetic principles operating during the initiation and advance of interface-controlled reactions are identical with the behaviour discussed for the decomposition of a single solid (Chaps. 3 and 4). The condition that overall rate control is determined by an interface process is that a chemical step within this zone is slow compared with the rate of arrival of the second reactant. This condition is not usually satisfied during reaction between solids where the product is formed at the contact of a barrier layer with a reactant. Particular systems that satisfy the specialized requirements can, however, be envisaged for example, rate processes in which all products are volatilized or a solid additive catalyzes the decomposition of a solid yielding no solid residue. Even here, however, the kinetic characteristics are likely to be influenced by changing effectiveness of contact as reaction proceeds, or the deactivation of the catalyst surface. 

The important phenomenon of exponential decay is the prototype first-order reaction and provides an informative introduction to first-order kinetic principles. Consider an important example from nuclear physics the decay of the radioactive isotope of carbon, carbon-14 (or C). This form of carbon is unstable and decays over time to form nitrogen-14 ( N) plus an electron (e ) the reaction can be written as... 

Bamford, C. H., and R. G. Compton (Eds), Electrode Kinetics—Principles and Methodology, Elsevier, Amsterdam, 1986. 

Amdur, I., Hammes, G. G. Chem. Kinetics Principles and Selected Topics, p. 148. New York McGraw-Hill 1966. 

I. Amdur and G. G. Hammes, Chemical Kinetics Principles and Selected Topics, McGraw-Hill, New York, 1966. 

This approach assumes that fe is known, the change in CL and k are proportional to CLcr, renal disease does not alter drug metabolism, any metabolites are inactive and nontoxic, the drug obeys first-order (linear) kinetic principles, and the drug is adequately described by a one-compartment model. The kinetic parameter/dosage adjustment factor (Q) can be calculated as ... 

Reactions in a pathway can be divided into two classes those that are very close to equilibrium (near-equilibrium) and those that are far removed from equilibrium (non-equilibrium). This is discussed in Chapter 2 but is summarised here using kinetic principles to explain how enzyme catalysis can give rise to two separate types of reaction in one pathway. 

Kinetic principles that apply to hormone action... 

Althongh many hormones are involved in control of many biochemical and physiological processes, the kinetic principles nnderlying the mechanisms by which this is achieved are similar if not identical for each hormone. These principles are onthned nnder four separate headings. 

KINETIC PRINCIPLES THAT APPLY TO HORMONE ACTION... 

The approach of this work is to measure product compositions and mass balances in much detail in a time resolved manner and to relate this to the controlling kinetic principles and elemental reactions of product formation and catalyst deactivation. Additionally the organic matter, which is entrapped in the zeolite or deposited on it, is determined. The investigation covers a wide temperature range (250 - 500 °C). Four kinetic regimes are discriminated autocatalysis, retardation, reanimation and deactivation. A comprehensive picture of methanol conversion on HZSM5 as a time on stream and temperature function is developed. This also explains consistently individual findings reported in literature [1 4]. 

Geochemists study chemical processes on and in the Earth as well as meteorites and samples from the other planetary bodies. In geochemical kinetics, chemical kinetic principles are applied to Earth sciences. Many theories in geochemical kinetics are from chemical kinetics, but the unique nature of Earth sciences, especially the inference of geological history, requires development of theories that are specific for geochemical kinetics. 

Fig. 8.11. A cyclic voltammogram for a reversible charge-transfer reaction. (Reprinted from V. D. Parker, Linear Sweep and Cyclic Voltammetry, in Comprehensive Chemical Kinetics, Electrode Kinetics, Principles and Methodology, C. H. Bamford and R. C. Compton, eds., copyright 1986, p. 148, with permission from Elsevier Science.)...

Closely related to the problem of the structure of the effective rate constant is the above-mentioned problem of the compensation mechanism. Without a knowledge of this mechanism, it would be impossible to understand why in such a complicated epoxyamine system one can frequently observe relatively simple kinetic principles, viz., a weak dependence of the effective rate constant on conversion, simple dependences of the initial rate on reagent concentrations, a linear dependence of the total heat release on conversion and almost equal values of the heat release and enthalpy of the epoxy ring opening. The latter two aspects have been discussed above, whereas the first two problems can be understood, say, from a consideration of a noncatalytic reaction. 

However, we shall first briefly consider the main kinetic principles of epoxy compound polymerization under the action of TA and the structural peculiarities of the resultant polymers. 

Modern Methods in Kinetics Diffusion-limited Reactions Electrode Kinetics Principles and Methodology... 

Applications of kinetic principles to industrial reactions are often useful. Initial kinetic studies of the esterification reaction are usually conducted on a small scale in a well stirred batch reactor. In many cases, results front batch studies can be used in the evaluation of the esterification reaction in a continuous operating configuration. 

Simple dynamical systems have proved valuable as models of certain classes of physical systems in many branches of science and engineering. In mechanics and electrical engineering Duffing s and van der Pol s equations have played important roles and in physical chemistry and chemical engineering much has been learned from the study of simple, even artificially simple, systems. In calling them simple we mean to imply that their formulation is as elementary as possible their behaviour may be far from simple. Models should have the two characteristics of feasibility and actuality. By the first we mean that a favourable case can be made for the proposed reaction, perhaps by some further elaboration of mechanism but within the framework of accepted kinetic principles. Thus irreversible reactions are acceptable provided that they can be obtained as the limit of a consistent reversible set. By actuality we mean that they are set in an actual context, as taking place in a stirred tank, on a catalytic surface or in a porous medium. It is not usually necessary to assume the reaction to take place in a closed system with certain components held constant presumably by being in excess. 

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