Chemical kinetics empirical rate laws

The primary problem of chemical kinetics is the formulation of an empirical rate law which represents the rate of a reaction as a function of the concentrations or partial pressures of reactants, products, and catalysts present in a gaseous or liquid phase, structure and composition of solid catalysts, temperature, etc. A secondary problem is the ascertainment of the mechanism, which is often represented by a sequence of consecutive steps, or several sequences in parallel. The knowledge of the mechanism of a reaction in turn may be used in order to formulate a rational rate law which may represent the empirical rate data in a more logical form than an empirical rate law. 

There are several aspects to the kinetic study of a chemical reaction. One of these is concerned with the phenomenological, or empirical, rate laws which are obeyed. 

The elucidation of a substitution reaction mechanism depends on reliable kinetic and thermodynamic data obtained by measuring changes in the reaction rate as a function of a chemical property (e.g., concentration, pH, ionic strength, solvent polarity) or physical quantity (e.g., temperature). The determination of an empirical rate law, the observation of steric or electronic effects induced by the entering, spectator, or leaving groups, and the estimation of activation parameters from variable-temperature experiments (i.e.. A// and Aj ) contribute to the adjudication of a plausible mechanism for a given reaction. 

If V depends on the concentration of some species that does not appear in the balanced chemical equation, then that species is called a catalyst if v increases as the concentration of that species increases. If an increase in the concentration of that species leads to a decrease of the reaction velocity v, it is called an inhibitor. If V depends on one or more products, then the reaction is called autocatalytic if the product increases the reaction velocity. If the product decreases the reaction velocity, the reaction is called self-inhibiting. Rate laws are determined experimentally from kinetic data. Such a rate law is called an empirical rate law. Rate laws are often, but not always, found to depend on simple powers of the concentrations ... 

In chemical equilibria, the energy relations between the reactants and the products are governed by thermodynamics without concerning the intermediate states or time. In chemical kinetics, the time variable is introduced and rate of change of concentration of reactants or products with respect to time is followed. The chemical kinetics is thus, concerned with the quantitative determination of rate of chemical reactions and of the factors upon which the rates depend. With the knowledge of effect of various factors, such as concentration, pressure, temperature, medium, effect of catalyst etc., on reaction rate, one can consider an interpretation of the empirical laws in terms of reaction mechanism. Let us first define the terms such as rate, rate constant, order, molecularity etc. before going into detail. 

As well as deceleratory reactions, kineticists often find that some chemical systems show a rate which increases as the extent of reaction increases (at least over some ranges of composition). Such acceleratory, or autocatalytic, behaviour may arise from a complex coupling of more than one elementary kinetic step, and may be manifest as an empirically determined rate law. Typical dependences of R on y for such systems are shown in Figs 6.6(a) and (b). In the former, the curve has a basic parabolic character which can be approximated at its simplest by a quadratic autocatalysis, rate oc y(l - y). 

In the beginnings of classical physical chemistry, starting with the publication of the Zeitschrift fUr Physikalische Chemie in 1887, we find the problem of chemical kinetics being attacked in earnest. Ostwald found that the speed of inversion of cane sugar (catalyzed by acids) could be represented by a simple mathematical equation, the so-called compound interest law. Nernst and others measured accurately the rates of several reactions and expressed them mathematically as first order or second order reactions. Arrhenius made a very important contribution to our knowledge of the influence of temperature on chemical reactions. His empirical equation forms the foundation of much of the theory of chemical kinetics which will be discussed in the following chapter. 

In chemical kinetics, semi-empirical non-linear models for reaction rates are commonly used. For example, Boudart [3] summarizes the laws of reaction rates in the formulae... 

Chemical kinetics is given by constitutive equations (4.470). Their form must be valid in all processes and therefore also in equilibrium (4.471). But simultaneously we have a restriction (4.472) on the constitutive equations (4.470) in equilibrium. We find explicit consequences of this restriction for the approximation of constitutive equations (4.470) by a polynomial in activities [66, 79, 162]. This was motivated by proportionality of activities to concentrations (e.g.(4.469)) and the empirically observed power dependency of reaction rates on concentrations. We denote such powers as reaction orders [132, 157] often they are 1, 2 (rarely 3) but sometimes also fractions (see Rem. 17), cf. also end of this Sect.4.9. Indeed, we show below that such approximation and restriction give the power law of chemical kinetics in activities which is, moreover, consistent with chemical equilibrium and which is then, by the activity-concentration proportionality just mentioned, consistent also with classical power law in concentrations (i.e. with the mass action law of chemical kinetics), cf. examples (4.476), (4.498) below. 

Note that the stoichiometric coefficients in a balanced chemical equation like eq. (2.5) bear no necessary relationship to the orders that appear in the empirical (i.e., experimentally derived) rate law. This statement becomes obvious if one considers that the chemical equation can be multiplied on both sides by any arbitrary number and remain an accurate representation of the stoichiometry even though all the coefficients will change. However, the orders for the new reaction will remain the same as they were for the old one. There are cases in which the rate law depends only on the reactant concentrations and in which the orders of the reactants equal their molecularity. A reaction in which the order of each reactant is equal to its molecularity is said to obey the Law of Mass Action or to behave according to mass action kinetics. 

A distinction has been made between the world of objects/events and the world of laws/theories/models (Logan, 1984 Tiberghien, 2000). Logan (1984) states that chemical kinetics has an unusually complex structure in that it is composed of two distinct but complementary lines of development the empirical and the theoretical . The relationship between chemical phenomena and theories/models is shown in Figure 1. Conceptual analysis of the domain suggested that the rate of chemical reactions can be explained by a qualitative approach (Particulate... 

In Chapters 2 and 3, we will consider, respectively, the factors involved in determining the rates of chemical reaction and the techniques that allow the experimental study of their kinetics. In Chapter 4, we will start from empirical knowledge of the variation of concentration of reactants and products with time to establish the rate laws for the corresponding elementary reactions. Chapters 5-8 will consider some theories that allow us to calculate or rationalise the numerical values in the above rate laws. Chapters 9-14 will discuss in detail some of the most important reactions that have been studied using chemical kinetics. The last two chapters will focus on some less familiar topics in textbooks in this area. 

From a historical perspective, the Chick-Watson model has been the predominant model used to describe the kinetics of using disinfectants to inactivate microorganisms. Chick s law (1908) expresses the rate of destractionof microorganisms using the relationship of a first-order chemical reaction. Watson (1908) refined the equation to produce an empirical relationship that reflected changes in the disinfectant concentration. The Chick-Watson model can be expressed as follows ... 

Kinetic modeling of catalytic reaction systems plays a critical role in the design and optimization of chemical reactors and processes. The models that have been developed over the years have been the result of our understanding of the chemistry, available analytical capabilities, and the desired level of the results. Many of the earliest kinetic models were simply power-law models, i.e. empirical relationships between the measured partial pressures (or compositions) and the reaction rate. The earliest models were based solely on overall composition, conversion and yields since that was all that could be routinely determined. Despite their simplicity, power-law models are still used to model a number of industrial chemical processes. They capture the relevant information and can be used to predict daily operation and control of industrial reactors. 

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