Chemical kinetics irreversible reactions

The number of nuclei reacting in a specified way with neutrons in unit time is proportional to the number of nuclei present and to the concentration of neutrons. In the language of chemical kinetics, neutron reactions are first-order with respect to concentration of nuclei and neutrons, and it is because neutron reactions are simple first-order Irreversible processes that a very detailed quantitative treatment of the rate processes in a nuclear reactor can be given. 

Exothermic Decompositions These decompositions are nearly always irreversible. Sohds with such behavior include oxygen-containing salts and such nitrogen compounds as azides and metal styphnates. When several gaseous products are formed, reversal would require an unlikely complex of reactions. Commercial interest in such materials is more in their storage properties than as a source of desirable products, although ammonium nitrate is an important explosive. A few typical exampes will be cited to indicate the ranges of reaction conditions. They are taken from the review by Brown et al. ( Reactions in the Solid State, in Bamford and Tipper, Comprehensive Chemical Kinetics, vol. 22, Elsevier, 1980). 

Some chemical reactions are reversible and, no matter how fast a reaction takes place, it cannot proceed beyond the point of chemical equilibrium in the reaction mixture at the specified temperature and pressure. Thus, for any given conditions, the principle of chemical equilibrium expressed as the equilibrium constant, K, determines how far the reaction can proceed if adequate time is allowed for equilibrium to be attained. Alternatively, the principle of chemical kinetics determines at what rate the reaction will proceed towards attaining the maximum. If the equilibrium constant K is very large, for all practical purposes the reaction is irreversible. In the case where a reaction is irreversible, it is unnecessary to calculate the equilibrium constant and check the position of equilibrium when high conversions are needed. 

In the context of chemical kinetics, the eigenvalue technique and the method of Laplace transforms have similar capabilities, and a choice between them is largely dependent upon the amount of algebraic labor required to reach the final result. Carpenter discusses matrix operations that can reduce the manipulations required to proceed from the eigenvalues to the concentration-time functions. When dealing with complex reactions that include irreversible steps by the eigenvalue method, the system should be treated as an equilibrium system, and then the desired special case derived from the general result. For such problems the Laplace transform method is more efficient. 

This chapter is restricted to homogeneous, single-phase reactions, but the restriction can sometimes be relaxed. The formation of a second phase as a consequence of an irreversible reaction will not affect the kinetics, except for a possible density change. If the second phase is solid or liquid, the density change will be moderate. If the new phase is a gas, its formation can have a major effect. Specialized models are needed. Two-phase ffows of air-water and steam-water have been extensively studied, but few data are available for chemically reactive systems. 

Nevertheless, chemical methods have not been used for determining ionization equilibrium constants. The analytical reaction would have to be almost instantaneous and the formation of the ions relatively slow. Also the analytical reagent must not react directly with the unionized molecule. In contrast to their disuse in studies of ionic equilibrium, fast chemical reactions of the ion have been used extensively in measuring the rate of ionization, especially in circumstances where unavoidable irreversible reactions make it impossible to study the equilibrium. The only requirement for the use of chemical methods in ionization kinetics is that the overall rate be independent of the concentration of the added reagent, i.e., that simple ionization be the slow and rate-determining step. 

First law of thermodynamics, 24 645-648 First limiting amino acid, 2 601 First-order irreversible chemical kinetics, 25 286-287, 292-293 First-principle approach, in particle size measurement, 13 153 First sale doctrine, 7 793 Fischer, Emil, 16 768 Fischer carbene reaction, 24 35-36 Fischer esterification, 10 499 Fischer formula, 4 697 Fischer-Indole synthesis, 9 288 Fischer lock and key hypothesis, 24 38 Fischer-Tropsch (FT) synthesis, 6 791, 827 12 431... 

This example also shows that the amount of kinetic information needed to complete the set of equations (one equation in this case) depends on the number of independent irreversible reactions (one) and not on the number of chemical species involved only in the irreversible reactions (two) or on the number of these species appearing as unknowns. 

Most electrode reactions of interest to the organic electrochemist involve chemical reaction steps. These are often assumed to occur in a homogeneous solution, that is, not at the electrode surface itself. They are described by the usual chemical kinetic equations, for example, first- or second-order reactions and may be reversible (chemical reversibility) or irreversible. 

There are several control problems in chemical reactors. One of the most commonly studied is the temperature stabilization in exothermic monomolec-ular irreversible reaction A B in a cooled continuous-stirred tank reactor, CSTR. Main theoretical questions in control of chemical reactors address the design of control functions such that, for instance (i) feedback compensates the nonlinear nature of the chemical process to induce linear stable behavior (ii) stabilization is attained in spite of constrains in input control (e.g., bounded control or anti-reset windup) (iii) temperature is regulated in spite of uncertain kinetic model (parametric or kinetics type) or (iv) stabilization is achieved in presence of recycle streams. In addition, reactor stabilization should be achieved for set of physically realizable initial conditions, (i.e., global... 

For any chemical reaction, whether inorganic or organic, we must choose which kinetic species to include in the elementary reactions that make up the overall process ideally, molecular or chemical information is available to guide this choice. In general, for an elementary (irreversible) reaction among species A and B, to give species C and D, in relative amounts a, b, c, and d, respectively. 

R and S isomers of HDT]acetic acid were synthesized by chemical and enzymatic methods that yield products of known stereochemistry.1819 The two isomers were then distinguished by using the following ingenious enzymatic assays. The acetic acid was first converted to acetyl-coenzyme A (by a reaction of the carboxyl group—and not the methyl—of acetic acid). The acetyl-coenzyme A was then condensed with glyoxylate to form malate in an essentially irreversible reaction catalyzed by malate synthase (equation 8.27). The crucial feature of this reaction is that it is subject to a normal kinetic isotope effect, so that more H than D... 

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. 

The equation relating Kc to kf and kr provides a fundamental link between chemical equilibrium and chemical kinetics The relative values of the rate constants for the forward and reverse reactions determine the composition of the equilibrium mixture. When kf is much larger than kT, Kc is very large and the reaction goes almost to completion. Such a reaction is said to be irreversible because the reverse reaction is often too slow to be detected. When kf and kT have comparable values, Kc has a value near unity, and comparable concentrations of both reactants and products are present at equilibrium. This is the usual situation for a reversible reaction. 

This shows that for an irreversible process, the peak potential is shifted towards more negative (reduction reaction) or more positive (oxidation reaction) potentials by about 0.03 V per decade of increase in the scan rate. For a totally irreversible reaction, no return peak is observed due to the fact that the kinetics are so slow that the opposite reaction cannot occur. The activation energy, overcome by application of a potential, is so high that it is not possible to apply such a potential under experimental conditions. However, the absence of a return peak does not necessarily imply slow electron transfer, but can also be due to a fast following chemical reaction. 

For an electrode process followed up by an irreversible homogeneous chemical reaction (K = 0, Fig. 4.31b), the peak currents are independent of the chemical kinetics whereas the peak potential takes more positive values as xi increases because the chemical reaction facilitates the reduction process by removal of species B. In all cases plotted in this figure, the value of the crossing potential can be evaluated with good accuracy from Eq. (4.255) (error smaller than 3 mV for X2 > 102). With respect to the E mechanism of species A, in the EC response both peak currents are smaller, and this effect is especially noticeable in the minimum which is more affected by the follow-up reaction. 

The chemical kinetics (j2), has no effect on the symmetry of the peaks in the case of the irreversible EC mechanism (K = 0) under kinetic steady-state conditions. On the other hand, for the CE mechanism the /J ane/I/Plane I value does depend on xi and it tends to /Plane — 1 in the limiting case of very fast chemical reactions (see Fig. 4.31a). 

In these electrode processes, the use of macroelectrodes is recommended when the homogeneous kinetics is slow in order to achieve a commitment between the diffusive and chemical rates. When the chemical kinetics is very fast with respect to the mass transport and macroelectrodes are employed, the electrochemical response is insensitive to the homogeneous kinetics of the chemical reactions—except for first-order catalytic reactions and irreversible chemical reactions follow up the electron transfer—because the reaction layer becomes negligible compared with the diffusion layer. Under the above conditions, the equilibria behave as fully labile and it can be supposed that they are maintained at any point in the solution at any time and at any applied potential pulse. This means an independent of time (stationary) response cannot be obtained at planar electrodes except in the case of a first-order catalytic mechanism. Under these conditions, the use of microelectrodes is recommended to determine large rate constants. However, there is a range of microelectrode radii with which a kinetic-dependent stationary response is obtained beyond the upper limit, a transient response is recorded, whereas beyond the lower limit, the steady-state response is insensitive to the chemical kinetics because the kinetic contribution is masked by the diffusion mass transport. In the case of spherical microelectrodes, the lower limit corresponds to the situation where the reaction layer thickness does not exceed 80 % of the diffusion layer thickness. 

In order to analyze the influence of the chemical kinetics on the SWV response of this mechanism when the chemical reaction behaves as irreversible (Keq —> oo), it can be compared with that obtained for a reversible two-electron electrochemical reaction (EE mechanism) at the same values of the difference between the formal potentials of the electrochemical steps, A= E 2 — E (which is always centered atE-mA 1L = (E +E 2)/2). 

Finally, when chemical kinetics contrasts with equilibrium, the parallel scheme is not trivial, since one of the products can be favored in the early stages of the batch cycle by faster kinetics and hindered in the later stages by unfavorable equilibrium. Such a case is shown in Fig. 2.4 for parallel reactions of A to Pi via an equilibrium limited reaction and to P2 via an irreversible reaction. 

The first non-Markovian approach to chemical reactions in solutions, developed by Smoluchowski [1], was designed for contact irreversible reactions controlled by diffusion. Contrary to conventional (Markovian) chemical kinetics in the Smoluchowskii theory, the reaction constant of the bimolecular reaction, k(t), becomes a time-dependent quantity instead of being tmly constant. This feature was preserved in the Collins-Kimball extension of the contact theory, valid not only for diffusional but for kinetic reactions as well [2]. 

Two important questions are asked about every chemical reaction (a) How much product is produced and (b) How fast is it produced The first question involves chemical equilibrium and the second question belongs to the domain of chemical kinetics. (We dealt with kinetics in Experiment 20). Some reactions are irreversible and they go to completion (100% yield). When you ignite methane gas in your gas burner in the presence of air (oxygen), methane burns completely and forms carbon dioxide and water. 

Chemical reactions can be described by thermodynamics (chapter 1.1.2) and kinetics (chapter 1.2). Reactions expressed by the mass-action law (chapter 1.1.2.1), are thermodynamically reversible and independent of time. In contrast, kinetic processes are time dependent reactions. Thus, models that take into account kinetics can describe irreversible reactions such as decay processes that require finite amounts of time and cannot be reversed under a given set of conditions. 

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