Chemical reaction autocatalytic

First model for oscillating system was proposed by Volterra for prey-predator interactions in biological systems and by Lotka for autocatalytic chemical reactions. Lotka s model can be represented as... 

Exercise. Show that the autocatalytic chemical reaction... 

In unicellular organisms, the progressive doubling of cell number results in a continually increasing rate of growth in the population. A bacterial culture undergoing balanced growth mimics a first-order autocatalytic chemical reaction (Carberry, 1976 Levenspiel, 1972). Therefore, the rate of the cell population increase at any particular time is proportional to the number density (CN) of bacteria present at that time ... 

Some autocatalytic chemical reactions such as the Brusselator and the Belousov-Zhabotinsky reaction schemes can produce temporal oscillations in a stirred homogeneous solution. In the presence of even a small initial concentration inhomogeneity, autocatalytic processes can couple with diffusion to produce organized systems in time and space. 

This feedback-type behavior has been first considered in the domain of mathematics, with explicit targeting chemistry. In 1910. Alfred Lotka proposed some differential equations that corresponded to the kinetics of an autocatalytic chemical reaction, and then with lto Volterra derived a differential equation that describes a general feedback mechanism (oscillations) known as the Lotka-Volterra model. However, chemistry has not been ready yet for this link. 

Suppose that in a certain autocatalytic chemical reaction a compound A reacts to form a compoxmd B. Further, suppose that the initial concentration of A is Cao and that C t) is the concentration of B at time t. Then Cao - Cb(0 is the concentration of A at time t. Determine Cb(0 if Cb(0) = Cbo-... 

When set up appropriately, autocatalytic chemical reactions (taking the usual meaning of the term) frequently give rise to a "bistability" (in particular bistationarity), and chemical hysteresis as its corollary. Since these reactions are relatively well documented elsewhere, it does not appear necessary to list them all there, particularly since they are quite numerous. Conversely, oscillatory chemical reactions in homogeneous chemical media are rather rarer and, apart from two exceptions, have recently been discovered. Since there is no satisfactory criterion permitting the classification of chemical oscillators at present, we can do little more than record them in a somewhat arbitrary order ... 

A second requirement is that the system contain some sort of feedback, i.e., that the product of some reaction exert an influence upon its own rate of production. Probably the simplest type of feedback and the one most commonly found in chemical oscillators is autocatalysis. The simple model (Lotka, [16]) containing two coupled autocatalytic reactions shown in Table 1 was probably the first chemical" mechanism to give sustained oscillations. While autocatalysis is far more prelavent in biological than in chemical systems, autocatalytic chemical reactions do exist many of them are listed as "clock reactions in collections of lecture demonstrations. 

The vast majority of chemical reactions are sufficiently slow not to observe a dramatic influence of mixing on yields and selectivities. Exceptions are polymerizations, interfacial polycondensations, precipitations, and some fast reactions - usually performed in semibatch mode - such as autocatalytic reactions, neutralizations, nitrations, diazo couplings, brominations, iodinations, and alkaline hydrolysis, which are often encountered in the manufacture of fine chemicals. 

The Belousov-Zhabotinskii reaction is a typical oscillating chemical reaction. Spiral structures form periodically, disappear and reappear as the result of an autocatalytic reaction, the oxidation of Ce3+ and Mn2+ by bromate (lessen, 1978). 

The encapsulation results in a chance collection of molecules that then form an autocatalytic cycle and a primitive metabolism but intrinsically only an isolated system of chemical reactions. There is no requirement for the reactions to reach equilibrium because they are no longer under standard conditions and the extent of reaction, f, will be composition limited (Section 8.2). Suddenly, a protocell looks promising but the encapsulation process poses lots of questions. How many molecules are required to form an organism How big does the micelle or liposome have to be How are molecules transported from outside to inside Can the system replicate Consider a simple spherical protocell of diameter 100 nm with an enclosed volume of a mere 125 fL. There is room within the cell for something like 5 billion molecules, assuming that they all have a density similar to that of water. This is a surprisingly small number and is a reasonable first guess for the number of molecules within a bacterium. 

The dynamics of controlled systems is an open problem that has recently attracted the attention of scientific community [13]. In fact, oscillatory behavior in chemical systems is an interesting topic (which has been typically studied in autocatalytic reactions, e.g., the Lotka system see [44] and references therein). Dynamics of controlled systems can be explained in terms of interconnections. Indeed, by analogy with control systems, autocatalytic chemical systems can be described as examples of chemical feedback [44]. 

Once the door was opened to these new perspectives, the works multiplied rapidly. In 1968 an important paper by Prigogine and Rene Lefever was published On symmetry-breaking instabilities in dissipative systems (TNC.19). Clearly, not any nolinear mechanism can produce the phenomena described above. In the case of chemical reactions, it can be shown that an autocatalytic step must be present in the reaction scheme in order to produce the necessary instability. Prigogine and Lefever invented a very simple model of reactions which contains all the necessary ingerdients for a detailed study of the bifurcations. This model, later called the Brusselator, provided the basis of many subsequent studies. 

The simplest form of flow system is the continuously fed well-stirred tank reactor or CSTR, represented schematically in Fig. 1.11. The behaviour of typical autocatalytic systems in a CSTR will be considered in chapters 4 and 5, but here we may quickly examine how multistability can arise, even with only one overall chemical reaction. We will take a CSTR in which just the... 

Chemical reactions with autocatalytic or thermal feedback can combine with the diffusive transport of molecules to create a striking set of spatial or temporal patterns. A reactor with permeable wall across which fresh reactants can diffuse in and products diffuse out is an open system and so can support multiple stationary states and sustained oscillations. The diffusion processes mean that the stationary-state concentrations will vary with position in the reactor, giving a profile , which may show distinct banding (Fig. 1.16). Similar patterns are also predicted in some circumstances in closed vessels if stirring ceases. Then the spatial dependence can develop spontaneously from an initially uniform state, but uniformity must always return eventually as the system approaches equilibrium. 

The flow diagram technique can also be used to illustrate clearly the rather limited effects on autocatalytic systems which arise from the reversibility of chemical reactions. For this we replace step (6.8) by its reversible counterpart... 

Strictly speaking, except for the explicitly appearing reaction time r or rate mn, the form of the function depends on the concrete kinetics of the chemical reaction, i.e., on whether we are dealing with a first- or second-order reaction or with an autocatalytic reaction, just as, except for the characteristic dimension d, the form of the functions depends on the concrete geometric properties of the system and will be different for a round capillary and a plane slit. 

As has already been indicated, longitudinal heat transfer and diffusion in a detonation wave may be disregarded so that the chemical reaction runs almost adiabatically. In the case of an autocatalytic reaction, the absence of diffusion of the catalyzing products may significantly delay the flow of the reaction in the detonation wave. In the course of reaction along the Todes line, the heat release is tied to a significant increase in temperature. 

As we know, the time of development of an explosion for any reaction whose rate increases with the temperature, and—especially—for an autocatalytic reaction, is determined primarily by the smallest chemical reaction... 

Autocatalytic reaction is a chemical reaction in which a product also functions as a catalyst. In such a reaction, the observed rate of the reaction is often found to increase with time from its initial value [4]. 

A reaction process in which the product directly increases the rate of the chemical reaction is called autocatalysis. In the present case, the reaction product plays the role of a catalyst and of a potent chiral auxiliary at the same time. Hence Soai s discovery described the first example of a chirally autocatalytic reaction in organic chemistry in which the chiral product and the chiral catalyst are identical. 

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