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The Belousov-Zhabotinskii Reaction

The reactants include malonic acid, sodium bromate, and sulfuric acid, which are mixed together at initial concentrations far from equilibrium. Energy is released by the oxidation of malonic acid by bromate. The net reaction is as follows:

3 [Graphics:../Images/index_gr_6.gif]([Graphics:../Images/index_gr_7.gif]H[Graphics:../Images/index_gr_8.gif]+ 2 [Graphics:../Images/index_gr_9.gif]+ 2 [Graphics:../Images/index_gr_10.gif] -> 2 BrCH([Graphics:../Images/index_gr_11.gif]H[Graphics:../Images/index_gr_12.gif] + 3 [Graphics:../Images/index_gr_13.gif] + 4 H[Graphics:../Images/index_gr_14.gif]O

The direct chemical reaction between bromate and malonic acid is kinetically slow. Thus, cerium ions at much lower concentrations are added to the reaction mixture. The cerium ions catalyze the overall reaction by acting as an electron relay between malonic acid and bromate. During the course of the reaction, the color of the solution oscillates between clear and yellow with a period of about two minutes because the dominant chemical speciation of cerium oscillates between the +3 and +4 oxidation states. The oscillatory reaction can be represented in 21 steps, but the following 6 elementary steps and 1 empirical step retain the essential features of the system [4]:

[Graphics:../Images/index_gr_15.gif] [Graphics:../Images/index_gr_16.gif]
[Graphics:../Images/index_gr_17.gif] [Graphics:../Images/index_gr_18.gif]
[Graphics:../Images/index_gr_19.gif] [Graphics:../Images/index_gr_20.gif]
[Graphics:../Images/index_gr_21.gif] [Graphics:../Images/index_gr_22.gif]
[Graphics:../Images/index_gr_23.gif] [Graphics:../Images/index_gr_24.gif]
[Graphics:../Images/index_gr_25.gif] [Graphics:../Images/index_gr_26.gif]
[Graphics:../Images/index_gr_27.gif] [Graphics:../Images/index_gr_28.gif]

To simulate this system by numerical methods, we write a rate equation for each reactant. The list of nine reactant species includes: [Graphics:../Images/index_gr_29.gif], HOBr, [Graphics:../Images/index_gr_30.gif], [Graphics:../Images/index_gr_31.gif], [Graphics:../Images/index_gr_32.gif], [Graphics:../Images/index_gr_33.gif], Ce(III), Ce(IV), and "organic" (namely malonic acid). We then specify initial conditions and seek a numerical solution.


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