Irreversible autocatalytic reaction

A mechanism of this reaction can be represented by the following equation 

This is not a standard kinetic system. In Section 4.3.2 we have shown how equations of this type may appear as slow dynamics of a standard kinetic system. 

Substitution (5.5) yields an exact equation and the eigenvalue is computed from (5.7), (5.8) 

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As a simple illustration, consider the irreversible autocatalytic reaction A + 2B 3B [39]. The reaction transition matrix is... 

For an irreversible autocatalytic reaction A + B— B + B, minimum space time is required for a specified conversion of 4 in a system of CSTR followed by a PFR compared to that in a single CSTR or in a single PFR. Calculate the space time of the CSTR and the PFR connected in series given the feed concentration ao 5 kmol/m, rate constant k = 0.02 m /kmol min and the final conversion Xaj= 0.8. 

The hydrolysis of methyl acetate is an autocatalytic reaction and is first order with respect to both methyl acetate and acetic acid. The reaction is elementary, bimolecular and can be considered irreversible at constant volume for design purposes. The following data are given ... 

It is important to emphasize that the condition A2 > 2Aj is identical to the condition A2 Aj—that is, to the kinetic irreversibility of the autocatalytic reaction or (what is the same) the remoteness of the process under consideration from the point of its equilibrium. 

The phenomenon of self organization occurs at nonstabHities of the sta tionary state and leads to the formation of temporal and spatio temporal dissipative structures. Remember that oscillating instabilities of stationary states of dynamic systems can be observed for the intermediate nonlinear stepwise reactions only, when no fewer than two intermediates are involved (see Section 3.5) and at least one of the elementary steps is kinet icaUy irreversible. The minimal sufficient requirements for the scheme of a process with temporal instabilities are not yet strictly formulated. However, in aU known examples of such reactions, the rate of the kineti caUy irreversible elementary reaction at one of the intermediate steps is at least in a quadratic dependence on the intermediate concentrations. Among these reactions are autocatalytic steps. 

At approximately the same time, Lotka proposed his famous models of oscillating chemical reactions based on irreversible autocatalytic processes. The first model included one autocatalytic step and gave damped oscillations. The second model became a paradigm in oscillating chemistry. It consists of two consecutive autocatalytic steps, resulting in undamped oscillations. The Lotka models attracted great attention from theoretical biologists, because... 

The autocatalytic reaction has been mentioned above and though it is somewhat rare it will serve to complete our description of the shape of reaction rates. Suppose (following Walks and Platt, see Exercise 4.2.5) we have an irreversible reaction A —> B + C, whose rate increases not only with increasing concentration of A (denoted by a) but also with increasing concentration of B (denoted by A). Thus... 

In order to understand the complexity in oscillatory reactions, it would be worthwhile to examine their relationship with different types of chemical reactions [10], which have been summarized in Fig. 9.8 in increasing order of complexity viz., irreversible reactions -> reversible reactions parallel reaction consecutive reaction -> autocatalytic reactions damped oscillations aperiodic oscillations spatio-temporal oscillations chaotic oscillations. Further, Fig. 9.8 shows the concentration... 

Hydrazine is also used in conjunction with HNA to impede hydroxylamine oxidation by nitrous acid, always present in nitric acid media, which increases the HNA availability for the plutonium reduction. Both hydrazine and HNA interact with nitrous acid (HNO2), but the hydrazine oxidation is much faster. On the other hand, the use of HAN in conjunction with nitric acid introduces the possibility of an autocatalytic reaction resulting in the overpressurization of the system or explosion in a reprocessing facility as pointed out in Barney s report (Barney, 1998). The main function of HNA is to reduce plutonium from the tetravalent state to the trivalent state and, thus, separate the plutonium from the uranium, which is retained in the hexavalent oxidation state and, hence, in the organic phase. The reduction reaction by HNA is the result of two irreversible reactions (Equations 14.10 and 14.11) ... 

In the Gray-Scott model PI of this system, both reactions are considered to be irreversible. This reaction scheme is a simplification of the autocatalytic model of the glycolysis cycle (see Chapter 7). A is a feed term and B an inert product. PearsonI °l has shown that as a function of kinetic and diffusion parameters this system leads to the formation of local regions of concentration defined by sharp boundaries. These local regions take on cell-like characteristics, thus undergoing multiplication and division behavior. We discuss some of the results in detail, also because of the discussion in the next chapter on self replication and the origin of protocellular systems. As a function of feed (F) and rate parameter (fc), a state phase diagram can be constructed (see Fig. 8.5). 

Autocatalytic reactions are a type of self-catalytic reaction in which the product produced by the reaction acts as a catalyst for the very same reaction. An irreversible reaction A— in which the product B acts as a catalyst is an autocatalytic reaction represented as... 

Chapter 2 covers the basic principles of chemical kinetics and catalysis and gives a brief introduction on classification and types of chemical reactors. Differential and integral methods of analysis of rate equations for different types of reactions—irreversible and reversible reactions, autocatalytic reactions, elementary and non-elementary reactions, and series and parallel reactions are discussed in detail. Development of rate equations for solid catalysed reactions and enzyme catalysed biochemical reactions are presented. Methods for estimation of kinetic parameters from batch reactor data are explained with a number of illustrative examples and solved problems. 

The chemical reaction kinetics is a class of irreversible processes, which remains outside of the applicability area of the Onsager constitutive theory. Hence, the reaction kinetics is an ideal discipline to test the applicabihty of the generalized Onsager constitutive theory. We shall/are going to study the autocatalytic reactions in a different way other than [ ], [ 7] did it before, emphasizing the following ... 

Let us analyze a model proposed by Lotka in 1910, which explains how a set of consecutive reactions leads to damped oscillations on the way to equilibrium. The model consists of three irreversible steps with one autocatalytic reaction... 

Chlorine-containing polymers such as poly(vinyl chloride) PVC undergo an autocatalytic dehydrochlorination reaction under the influence of elevated temperature and UV radiation. Since the HCl originating from the dehydro chlorination of the PVC chains is believed to sustain this autocatalytic process, stabilizers that irreversibly bond HCl can thus inhibit the degradation. Heavy metal compounds such as cadmium stearate or lead stearate are currently used for this purpose. However, alternatives are required due to environmental problems associated with the use of heavy metals. Indeed, the largest current application of LDH materials is in the polymer industry, mainly to stabilize PVC [3,229-232]. 

Abstract Theoretical models and rate equations relevant to the Soai reaction are reviewed. It is found that in production of chiral molecules from an achiral substrate autocatalytic processes can induce either enantiomeric excess (ee) amplification or chiral symmetry breaking. The former means that the final ee value is larger than the initial value but is dependent upon it, whereas the latter means the selection of a unique value of the final ee, independent of the initial value. The ee amplification takes place in an irreversible reaction such that all the substrate molecules are converted to chiral products and the reaction comes to a halt. Chiral symmetry breaking is possible when recycling processes are incorporated. Reactions become reversible and the system relaxes slowly to a unique final state. The difference between the two behaviors is apparent in the flow diagram in the phase space of chiral molecule concentrations. The ee amplification takes place when the flow terminates on a line of fixed points (or a fixed line), whereas symmetry breaking corresponds to the dissolution of the fixed line accompanied by the appearance of fixed points. The relevance of the Soai reaction to the homochirality in life is also discussed. 

Molecular oxygen is the major cause of irreversible deterioration of hydrocarbon substrates, leading to the loss of useful properties and to the ultimate failure of the substrate. The oxidation process of hydrocarbons is autocatalytic oxidation starts slowly, sometimes with a short induction period, followed by a gradual increase in the rate, concomitant with the build up of hydroperoxides, which eventually subside, giving rise to a sigmoidal oxidation curve. When initiators such as peroxides are present, the length of the induction period is absent, or very short, but it can be prolonged by antioxidants, as shown in Fig. 1. The basic autoxidation theory of hydrocarbons involves a complex set of elementary reaction steps in a free radical-initiated chain reaction mechanism the basic tenets of this theory apply equally to polymer oxidation. 

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