Homogeneous chemical system

V.K. Vanag, L.F. Yang, M. Dolnik, A.M. Zhabotinsky, and l.R. Epstein. Oscillatory cluster patterns in a homogeneous chemical system with global feedback. Nature, 406(6794) 389-391, 2000. 

Figure 6. Buffer capacity vs. pH for some heterogenous and homogeneous chemical systems...

Example 8.8 Entropy production in a homogeneous chemical system The oxidation of sulfur dioxide to trioxide over a vanadium pentoxide catalyst is... 

Sometimes, even spatially homogeneous chemical systems can cause bistability and show complex behavior in time. For example, autocatalysis may occur due to the particular molecular structure and reactivity of certain constituents, and reactions may evolve to new states by amplifying or repressing the effect of a slight concentration perturbation. 

The easily visualized Belousov Zhabotinsky (BZ) reaction is now a classic example of the emergence of temporal and spatio temporal dissipative struc tures in homogeneous chemical systems. The reaction was discovered by Soviet military chemist B. P. Belousov in 1951 when he was studying homo geneous oxidation of citric acid by potassium bromide, KBrOq, in the presence of cerium sulfate Ce(S04)2 as the catalyst for redox processes. In the dissolved mixture of these compounds under certain process conditions, Belousov discovered a time-oscillating synchronous reduction of cerium(4+) ions ... 

Thus, from the 1920s until the mid-1960s, it was the unfortunate custom to ascribe all concentration oscillations observed in chemical and biochemical systems to some invisible but important heterogeneous processes or simply to technical errors. The majority of chemists believed that oscillations were impossible in homogeneous chemical systems. They believed this in spite of the clear statement by Bonhoeffer in 1948 that there is no fundamental difference between homogeneous and heterogeneous systems. Bonhoeffer pointed out that heterogeneous systems are more convenient for oscillations, but no more than that. 

Although the oscillatory behavior of continuously stirred tank reactor had been discussed in chemical engineering long before the current studies on homogeneous chemical systems, [see G G], it is recently that the role of stirring and of a CSTR environment in reactions such as the B-Z and others has been recognized and used extensively in experiments. 

Lenin prize. The B-Z reaction, as it is now known, has been studied intensivety and many other cases of oscillations in homogeneous chemical systems have been identified. Figure 8.3 shows an example from the combustion of hydrogen. Similar fluctuations during the oxidation of hydrocarbon fuels are responsible for knock in internal combustion engines. 

Phenomena in homogeneous chemical systems far from equilibrium. Acc. Chem. Res. 9 438-45. 

Example 8.7 Entropy production in a homogeneous chemical system... 

Korzukhin, M. D. (1971a). II. Mathematical modelling of the kinetics of homogeneous chemical systems. In Oscillatory processes in biological and chemical systems, pp. 231-42. Chast 2-aya, Pushchino na Oke (in Russian). 

When solving the problem on controlling the chemical reaction, the spatially homogeneous chemical system under isothermal conditions is described by a set of ordinary differential equations. Unlike equation (3.1), in the following system of kinetic equations the control parameters u(t) are separated... 

For a number of years, there was considerable controversy over whether true chaos existed in homogeneous chemical systems, and in the BZ reaction in particular. Interestingly, some of the skeptics included those who had fought hardest to convince the chemical community that periodic oscillation was a genuine property of chemical systems and not an artifact (Ganapathisubranianian and Noyes, 1982a). It now seems safe to declare that the argument has been clearly settled in favor of those who hold that chaos can arise from pure chemical processes. On the... 

Pacault, A. Hanusse, P. De Kepper, P. Vidal, C. Boissonade, J. 1976. Phenomena in Homogeneous Chemical Systems far from Equilibrium, Acc. Chem. Res. 9,438-445. Pagola, A. Vidal, C. 1987. Wave Profile and Speed near the Core of a Target Pattern in the Belousov Zhabotinsky Reaction, J. Phys. Chem. 91, 501-503. 

Here X is the nonequilibrium constraint. If the system under consideration is a homogeneous chemical system, then Zk is specified by the rates of chemical reactions. For an inhomogeneous system, Zk may contain partial derivatives to account for diffusion and other transport processes. It is remarkable that, whatever the complexity of Zk, the loss of stability of a solution of (19.2.4) at a particular value of A, and bifurcation of new solutions at this point are similar to those of (19.2.1). As in the case of (19.2.1), the symmetries of (19.2.4) are related to the multiplicity of solutions. For example, in an isotropic system, the equations should be invariant under the inversion r —r. In this case, if Xk[r,t) is a solution then Xk -r,t) will also be a solution if Xk(r,t) Xk —r,t) then there are two distinct solutions which are mirror images of each other. 

The reaction between hydrogen gas and iodine vapor to produce hydrogen iodide gas is an exampie of a homogeneous reaction, a reaction whose reactants and products exist in a singie phase—in this case, the gas phase. This reaction system is also an example of a homogeneous chemical system, because all reactants and products in all intermediate steps are in the same phase. 

P. de Kepper and J. Boissonnade, From bistability to sustained oscillations in homogeneous chemical systems in a flow reactor. in "Oscillations and Travelling Waves in Chemical Systems,"... 

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