Reaction, autocatalytic

Reactions with such rate-concentration curves lead to interesting optimization problems. In addition, they provide a good illustration of the general design method presented in this chapter. For these reasons let us examine these reactions in some detail. In our approach we deal exclusively with their ll(-rj ) versus curves with their characteristic minima, as shown in Fig. 6.18. 

Plug Flow Versus Mixed Flow Reactor, No Recycle. For any particular rate-concentration curve a comparison of areas in Fig. 6.19 will show which reactor is superior (which requires a smaller volume) for a given job. We thus find 

At low conversion the mixed reactor is superior to the plug flow reactor. 

At high enough conversions the plug flow reactor is superior. 

These findings differ from ordinary nth-order reactions (n 0) where the plug flow reactor is always more efficient than the mixed flow reactor. In addition, we should note that a plug flow reactor will not operate at all with a feed of pure reactant. In such a situation the feed must be continually primed with product, an ideal opportunity for using a recycle reactor. 

An autocatalytic reaction is so called if any of the products catalyze this reaction. This includes, for example, the acid hydrolysis of esters catalyzed by protons  

Note 13.3 - Such S kinetic curves are also conunonly obtained without any autocatalytic effect being required to explain them. Hence, remember that a S curve in is not necessarily due to autocatalysis. 

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 

Let C o snd Cgo be the initial concentration of A and B present in the batch reaction vessel. Note that the autocatalytic reaction requires some amount of B to be present initially for the reaction to get initiated. As the total number of moles of A and B put together does not change with time 

Integrating Equation 2.113 using the method of partial fraction, we get 

An important example of autocatalytic reaction is the fermentation reaction in which a microorganism (B) multiplies on the consumption of organic feed (A). 

As suggested by the name, the products of an autocatalytic reaction accelerate the rate of the reaction. For example, an acid-catalyzed reaction may produce 

Autocatalytic reactions often show higher conversions in a stirred tank than in either a batch flow reactor or a piston flow reactor with the same holding time, tjjatch = i. Since d = agut in a CSTR, the catalyst, B, is present at the 

FIGURE 2.4 Conversion versus dimensionless time, aQkt, for an autocatalytic batch reaction. The parameter is bo/ao. 

FIGURE 2.5 Reaction exotherm for a methyl methacrylate casting system. 

Autocatalysis can cause sustained oscillations in batch systems. This idea originally met with skepticism. Some chemists believed that sustained oscillations would violate the second law of thermodynamics, but this is not true. Oscillating batch systems certainly exist, although they must have some external energy source or else the oscillations will eventually subside. An important example of an oscillating system is the circadian rhythm in animals. A simple model of a chemical oscillator, called the Lotka-Volterra reaction, has the assumed mechanism  

This type of reaction occurs when one of the products of the reactions acts as a catalyst, and is expressed by 

The rate equation for a constant volume batch system is  

When A is consumed, then the total moles of A and B remain unchanged at any time t and can be expressed as Cg = -i- Cg = 

Fig ure 3-11. Rate constants for a homogeneous catalyzed reaction from a series of experiments with different catalyst concentrations. 

Reaction Rate Expression 139 Reananging Equation 3-121 and integrating between tlie limits gives 

Converting the left side of Equation 3-122 into partial fractions gives 

The products of an autocatalytic reaction accelerate the rate of the reaction. For example, an acid-catalyzed reaction may produce additional acid. The rate of most reactions has an initial maximum and then decreases as reaction proceeds. Autocatalytic reactions have an initially increasing rate, although the rate must eventually decline as the reaction goes to completion. A model reaction frequently used to represent autocatalytic behavior is 

Rabbits (R) eat grass (G) to form more rabbits. Lynx (L) eat rabbits to form more lynx. Lynx also die of old age to form dead lynx (D). The grass is assumed to be in constant supply and provides the energy needed to drive the oscillation. The set of ODEs that governs the batch reaction is 

With an autocatalytic reaction the product acts as a catalyst for the reaction, which is thus accelerated. This can be true, for example, for decomposition processes (vid. Sect. 2.2). Autocatalytic reactions may exhibit oscillating behaviour. 

A number of formal kinetic models exist to describe autocatalytic reactions (cf. [1]). In what follows only the simplest model, the Prout-Tompkins model, is described following [1]. It is based on the reaction equation 

Example 3.8 Autocatalytic Reaction On the basis of the data from [1]  

Apparent activation energy Total energy release 

Determination of the variation with time of the conversion, if the conversion at t = 0 amounts to 10 , and of the time-dependent generation of the thermal power 

A reaction in which one of the products of reaction acts as a catalyst is called an autocatal 4 ic reaction. In a n-th order in a batch reactor, the rate of product formation or disappearance of reactant is high initially as concentration of the reactant is high, and reaction slows down as the reactant disappears. However, in an autocatalytic reaction, the rate is low initially as little product is present, the rate increases as more and more product gets formed and then drops again because reactant is consumed. 

The simplest case of such a reaction is given below. 

For this reaction, a reaction rate based on first-order kinetics can be written 

We know from the reaction Equation 3.43 that the total number of moles remains constant, therefore, 

Substituting value of Cr from Equation 3.45 into Equation 3.44 and integrating results in 

Dimethyl-sulfoxide (DMSO) is an aprotic polar solvent often used in organic chemical synthesis. It is known for its limited thermal stability so usually precautions are taken to avoid its exothermal decomposition. The decomposition energy is approximately 500 J g 1, which corresponds to an adiabatic temperature rise of over 250 K. 

This solvent was used for synthesis during a campaign in a pilot plant It was known to be contaminated with an alkyl bromide. Thus, it was submitted to chemical and thermal analysis, which defined safe conditions for its recovery, that is, a maximum heating medium temperature of 130 °C for batch distillation under vacuum. These conditions were established to ensure the required quality and safe operation. A second campaign, which was initially planned, was delayed and in the mean time the solvent was stored in drums. 

Thermal Safety of Chemical Processes Risk Assessment and Process Design. Francis Stoessel Copyright 2008 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim ISBN 978-3-527-31712-7 

The first section of this chapter is an introduction of basic definitions, describing the behavior of autocatalytic reactions, their reaction mechanism, and a phenomenological study. The second section is devoted to their characterization and the last section gives some hints on mastering this category of reaction in the industrial environment. 

Autocatalysis is a term commonly used to describe the experimentally observable phenomenon of a homogeneous chemical reaction which shows a marked increase in rate with time, reaches its peak at about 50 percent conversion, and then drops off. The temperature has to remain constant and all ingredients must be mixed at the start for proper observation. 

Selected for mathematical analysis is the catalytic thermal decomposition of a single compound A into two products B and C, of which B is the autocatalytic agent. Thus, A can decompose via tw o routes, a slow uncatalyzed one ki) and another catalyzed by B kz)- The three essential kinetic steps arc 

These equations show that the autocatalytic agent B forms a complex, AB, with rate k 2- Next, the complex AB decomposes with rate thereby releasing B in addition to forming B and C. 

Reactions k2 and kz together form the path by which most of A decomposes. Reaction k is the starter, but continues concurrently with k2 and kz as long as there is any A. 

The rates of formation of A, B, C, and AB, in accordance with the kinetic steps, are 

Note that initially some (Jmust be present for any reaction to occur, but A could be formed by the reverse reaction. For the irreversible case, = 0, 

both A and ( must be present initially for the reaction to proceed. A plot of CQ i gives an S-shaped curve, starting at Cq(0) = Cqo and ending at Q(oo) = 

Autocatalytic reactions can occur in homogeneous catalytic and enzyme processes, although usually with different specific kinetics. 

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As an example of chemical front instability consider a simple cubic autocatalytic reaction, A + 2B 3B, occurring in... 

C3.6.13 where large diffusion fluxes are indicated by —> and smaller diffusion fluxes by —+. For tire part of tire B front tliat protmdes into tire A region, fast diffusion of B leads to dispersal of B and suppresses tire autocatalytic reaction tliat requires two molecules of B. The front will have difficulty advancing here. In tire region where A protmdes into B, A will react leading to advancement of tire front. The net effect is to remove any initial nonplanarity and give rise to a planar front. 

The effect of temperature on the non-catalysed reaction was difficult to disentangle, for at lower temperatures the autocatalytic reaction intervened. However, from a limited range of results, the reaction appeared to have an experimental activation energy of c. +71 kj moh. ... 

Under the same conditions the even more reactive compounds 1,6-dimethylnaphthalene, phenol, and wt-cresol were nitrated very rapidly by an autocatalytic process [nitrous acid being generated in the way already discussed ( 4.3.3)]. However, by adding urea to the solutions the autocatalytic reaction could be suppressed, and 1,6-dimethyl-naphthalene and phenol were found to be nitrated about 700 times faster than benzene. Again, the barrier of the encounter rate of reaction with nitronium ions was broken, and the occurrence of nitration by the special mechanism, via nitrosation, demonstrated. 

The mechanism of oxidative dyeing involves a complex system of consecutive, competing, and autocatalytic reactions in which the final color depends on the efficiency with which the various couplers compete with one another for the available diimine. In addition, hydrolysis, oxidation, or polymerization of diimine may take place. Therefore, the color of a mixture caimot readily be predicted and involves trial and error. Though oxidation dyes produce fast colors, some off-shade fading does occur, particularly the development of a red tinge by the slow transformation of the blue indamine dye to a red phenazine dye. 

Hydrolysis is a significant threat to phosphate ester stabiHty as moisture tends to cause reversion first to a monoacid of the phosphate ester ia an autocatalytic reaction. In turn, the fluid acidity can lead to corrosion, fluid gelation, and clogged filters. Moisture control and filtration with Fuller s earth, activated alumina, and ion-exchange resias are commonly used to minimise hydrolysis. Toxicity questions have been minimised ia current fluids by avoiding triorthocresyl phosphate which was present ia earlier natural fluids (38). 

There are many reactions in which the products formed often act as catalysts for the reaction. The reaction rate accelerates as the reaction continues, and this process is referred to as autocatalysis. The reaction rate is proportional to a product concentration raised to a positive exponent for an autocatalytic reaction. Examples of this type of reaction are the hydrolysis of several esters. This is because the acids formed by the reaction give rise to hydrogen ions that act as catalysts for subsequent reactions. The fermentation reaction that involves the action of a micro-organism on an organic feedstock is a significant autocatalytic reaction. 

Normally, when a material reacts, its initial rate of disappearance is high and the rate decreases continuously as the reactant is consumed. However, in autocatalytic reaction, the initial rate is relatively slow... 

For an autocatalytic reaction some product B must be present if the reaction is to proceed. Starting with a small concentration of B, the rate rises as B is formed, and when A is used up, the rate must drop to zero. A plot of concentration versus time gives a straight line through the origin as shown in Figure 3-12. 

Autocatalytic reaction A reaetion, the rate of whieh is inereased by the eatalyzing effeet of its reaetion produets. 

T. Aukrust, D. A. Browne, I. Webman. Critical behavior of an autocatalytic reaction model. Phys Rev A 47 5294-5301, 1990. 

This is an autocatalytic reaction, in which a product of the reaction appears in the rate equation for the forward reaction. In this case the mass balance expressions are... 

Consecutive reactions are those in which the product of one reaction is the reactant in the next reaction. These are also called series reactions. Reversible (opposing) reactions, autocatalytic reactions, and chain reactions can be viewed as special types of consecutive reactions. 

The stabilities of the alkaline earth peroxides, M02 2 H202 increased in the sequence Ca > Sr > Ba. Values of E for the autocatalytic reactions... 

This very situation has been encountered during the oxidation of Ta Br2 (= A) to TafiBrJj(= P) by VO, the dioxovanadium(l+) ion (= B), in aqueous solution.19 The autocatalytic reaction of Ta Br and VOJ produces Ta Br l = I), which does not accumulate in the system owing to its rapid reaction with TaeBrfr. 

The general rule is that combinations of isothermal reactors provide intermediate levels of performance compared with single reactors that have the same total volume and flow rate. The second general rule is that a single, piston flow reactor will give higher conversion and better selectivity than a CSTR. Autocatalytic reactions provide the exception to both these statements. 

Since the autocatalytic reaction is third order, a steady-state material balance gives a cubic in bout- This means there are one or three steady states. Suppose binjain = 1/15 and explore the stability of the single or middle steady state for each of the following cases ... 

Iron is the most abundant, useful, and important of all metals. For example, in the 70-kg human, there is approximately 4.2 g of iron. It can exist in the 0, I, II, III, and IV oxidation states, although the II and III ions are most common. Numerous complexes of the ferrous and ferric states are available. The Fe(II) and Fe(III) aquo complexes have vastly different pAa values of 9.5 and 2.2, respectively. Iron is found predominantly as Fe (92%) with smaller abundances of Fe (6%), Fe (2.2%), and Fe (0.3%). Fe is highly useful for spectroscopic studies because it has a nuclear spin of. There has been speculation that life originated at the surface of iron-sulfide precipitants such as pyrite or greigite that could have caused autocatalytic reactions leading to the first metabolic pathways (2, 3). 

At the 24th Combushon Symposium, Shy et al. [26] introduced an experimental aqueous autocatalytic reaction system to simulate the premixed turbulent combustion in a well-known Taylor-Couette (TC) flow field. By electrochemically inifiafing fhis reachon system, the... 

Shy, S.S., Jang, R.H., and Tang, C.Y., Simulation of turbulent burning velocities using aqueous autocatalytic reactions in a near-homogeneous turbulence. Combust. Flame, 105, 54, 1996. 

Shy, S.S., Ronney, R, Buckley, S., and Yahkot, V., Experimental simulation of premixed turbulent combustion using a liquid-phase autocatalytic reaction, Proc. Combust. Inst., 24, 543, 1993. 

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