Rates, reaction fundamental concepts

This chapter covers the second fundamental concept used in chemical reaction engineering—chemical kinetics. The kinetic relationships used in the analysis and design of chemical reactors are derived and discussed. In Section 3.1, we discuss the various definitions of the species formation rates. In Section 3.2, we define the rates of chemical reactions and discuss how they relate to the formation (or depletion) rates of individual species. In Section 3.3, we discuss the rate expression that provides the relationship between the reaction rate, the temperature, and species concentrations. Without going into the theory of chemical kinetics, we review the common forms of the rate expressions for homogeneous and heterogeneous reactions. In the last section, we introduce and define a measure of die reaction rate—the characteristic reaction time. In Chapter 4 we use the characteristic reaction time to reduce the reactor design equations to dimensionless forms. 

Chapter 11 deals with free radicals and their reactions. Fundamental structural concepts such as substituent effects on bond dissociation enthalpies (BDE) and radical stability are key to understanding the mechanisms of radical reactions. The patterns of stability and reactivity are illustrated by discussion of some of the absolute rate data that are available for free radical reactions. The reaction types that are discussed include halogenation and oxygenation, as well as addition reactions of hydrogen halides, carbon radicals, and thiols. Group transfer reactions, rearrangements, and fragmentations are also discussed. 

The reaction rate. is a fundamental concept that allows quantitative prediction of rates of conversions of reactants to products.. We define the rate of reaction i, r, to be the net number of times a reaction, event occurs per time per volume. Given the rates of all reactions, we can. calculate directly the production rates of all species,... 

Heat balance calculations are usually carried out when developing new rotary kiln chemical processes or when improving old ones. No thermal process would work if too much heat is released or if there is a lack of sufficient thermal energy to drive the process, in other words, to maintain the reaction temperature. Heat balance can only be calculated with given mass balances as the boundary conditions, hence a quantitative description of the chemical processes on the basis of physical or chemical thermodynamics is required. While chemical thermodynamics establishes the feasibility of a particular reaction under certain reactor conditions, chemical kinetics determines the rate at which the reaction will proceed. Before we establish the global rotary kiln mass and energy balance, it is important to examine some fundamental concepts of thermodynamics that provide the pertinent definitions essential for the design of new rotary kiln bed processes. 

Nuclear reactor physics covers fundamental concepts associated with nuclear reactors including particles, mass, energy, weight fraction, volume fraction, atom fraction, particle interactions, radioactive decay, nuclear cross sections, neutron moderation, flux, reaction rate, and neutron activation. 

The rates of these different reactions vary case by case some of the reactions are relatively fast, whereas others might be considerably slow. The reaction stoichiometry relates the generation and consumption velocities of the various components to the velocities of the corresponding chemical reactions. For a qualitative treatment of the stoichiometry of the chemical reactions and kinetics, some fundamental concepts need to be defined. 

The reaction family concept was exploited by representing the reactions by various reaction families incorporating the metal function (dehydrogenation/hydrogenation) and the acid function (protonation/deprotonation, H/Me-shift, PCP isomerizations, and P-scission). The optimized Cm model provided excellent parity between the predicted and experimental yields for a wide range of operating conditions. This shows that the fundamental nature (feedstock and catalyst acidity independent) of the rate parameters in the model. 

The first step in accounting for a law is to propose a hypothesis, which is essentially a guess at an explanation of the law in terms of more fundamental concepts. Dalton s atomic hypothesis, which was proposed to account for the laws of chemical composition and changes accompanying reactions, is an example. When a hypothesis has become established, perhaps as a result of the success of further experiments it has inspired or by a more elaborate formulation (often in terms of mathematics) that puts it into the context of broader aspects of science, it is promoted to the status of a theory. Among the theories we encounter are the theories of chemical equilibrium, atomic structure, and the rates of reactions. 

This chapter is divided into three sections. In the first section we outline fundamental concepts and explain the relationship between microscopic and macroscopic descriptions of reaction kinetics. The second section is devoted to a priori estimation of bimolecular reaction rate coefficients and their temperature dependence using classical rate theory (Tolman, 1927 Kassel, 1935 Eliason and Hirschfelder, 1959) and transition state theory (TST) (Eyring, 1935 Wigner, 1938 Glasstone et a/., 1941 Marcus, 1965,1974). In the third section a comparison between theoretical concepts and experimental rate data for some selected reactions is made. 

Before considering rate coefficients in terms of theoretical models we introduce the fundamental concepts underlying the rate coefficients of bimolecular gas reactions. 

There are certain limitations to the usefulness of nitration in aqueous sulphuric acid. Because of the behaviour of the rate profile for benzene, comparisons should strictly be made below 68% sulphuric acid ( 2.5 fig. 2.5) rates relative to benzene vary in the range 68-80% sulphuric acid, and at the higher end of this range are not entirely measures of relative reactivity. For deactivated compounds this limitation is not very important, but for activated compounds it is linked with a fundamental limit to the significance of the concept of aromatic reactivity as already discussed ( 2.5), nitration in sulphuric acid cannot differentiate amongst compounds not less than about 38 times more reactive than benzene. At this point differentiation disappears because reactions occur at the encounter rate. 

It is apparent, from the above short survey, that kinetic studies have been restricted to the decomposition of a relatively few coordination compounds and some are largely qualitative or semi-quantitative in character. Estimations of thermal stabilities, or sometimes the relative stabilities within sequences of related salts, are often made for consideration within a wider context of the structures and/or properties of coordination compounds. However, it cannot be expected that the uncritical acceptance of such parameters as the decomposition temperature, the activation energy, and/or the reaction enthalpy will necessarily give information of fundamental significance. There is always uncertainty in the reliability of kinetic information obtained from non-isothermal measurements. Concepts derived from studies of homogeneous reactions of coordination compounds have often been transferred, sometimes without examination of possible implications, to the interpretation of heterogeneous behaviour. Important characteristic features of heterogeneous rate processes, such as the influence of defects and other types of imperfection, have not been accorded sufficient attention. 

The counterflow configuration has been extensively utilized to provide benchmark experimental data for the study of stretched flame phenomena and the modeling of turbulent flames through the concept of laminar flamelets. Global flame properties of a fuel/oxidizer mixture obtained using this configuration, such as laminar flame speed and extinction stretch rate, have also been widely used as target responses for the development, validation, and optimization of a detailed reaction mechanism. In particular, extinction stretch rate represents a kinetics-affected phenomenon and characterizes the interaction between a characteristic flame time and a characteristic flow time. Furthermore, the study of extinction phenomena is of fundamental and practical importance in the field of combustion, and is closely related to the areas of safety, fire suppression, and control of combustion processes. 

Any mathematical function that adequately represents experimental rate data can be used in the rate law. Such a rate law is called an empirical orphenomenologicd rate law. In a broader sense, a rate law may be constructed based, in addition, on concepts of reaction mechanism, that is, on how reaction is inferred to take place at the molecular level (Chapter 7). Such a rate law is called a fundamental rate law. It may be more correct in functional form, and hence more useful for achieving process improvements. 

This chapter presents the underlying fundamentals of the rates of elementary chemical reaction steps. In doing so, we outline the essential concepts and results from physical chemistry necessary to provide a basic understanding of how reactions occur. These concepts are then used to generate expressions for the rates of elementary reaction steps. The following chapters use these building blocks to develop intrinsic rate laws for a variety of chemical systems. Rather complicated, nonseparable rate laws for the overall reaction can result, or simple ones as in equation 6.1-1 or -2. 

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