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Understanding the Chemical Oscillations

The complex kinetics diagram can be employed to understand the oscillatory behavior shown in Figure 1. At the beginning of a chemical cycle, [[Graphics:../Images/index_gr_150.gif]] and [[Graphics:../Images/index_gr_151.gif]] are low, as shown at 309 sec in Figure 4. Although the overall reaction is slow ([Graphics:../Images/index_gr_152.gif] in Figure 5), reactions 5 and 6 together combine to make an autocatalytic sequence for [Graphics:../Images/index_gr_153.gif], as follows.

[Graphics:../Images/index_gr_154.gif]

[[Graphics:../Images/index_gr_155.gif]] is thus increasing at an accelerating rate. The production of [Graphics:../Images/index_gr_156.gif] from [Graphics:../Images/index_gr_157.gif], [Graphics:../Images/index_gr_158.gif], and Ce(III) (reaction 6) is shown by the red lines surrounding [Graphics:../Images/index_gr_159.gif] in Figure 5. In turn, the red lines surrounding [Graphics:../Images/index_gr_160.gif] indicate production from [Graphics:../Images/index_gr_161.gif], [Graphics:../Images/index_gr_162.gif], and [Graphics:../Images/index_gr_163.gif] (reaction 5). [[Graphics:../Images/index_gr_164.gif]] and [[Graphics:../Images/index_gr_165.gif]] are increasing by 20% per second, as shown in the bar chart. By 325 sec, [[Graphics:../Images/index_gr_166.gif]] has dramatically increased by the autocatalytic process (Figure 4). Accompanying the increase in [[Graphics:../Images/index_gr_167.gif]], [[Graphics:../Images/index_gr_168.gif]] is high enough that reaction 6 is depleting Ce(III) at about 20% per second, as shown in the bar chart. Consequently, Ce(IV) is forming (Figure 4). However, a limit is being approached because the disproportionation reaction (4) limits [[Graphics:../Images/index_gr_169.gif]], as indicated by the red line representing production of [Graphics:../Images/index_gr_170.gif] from [Graphics:../Images/index_gr_171.gif]. The continuing increase of [Ce(IV)] leads to the formation of [Graphics:../Images/index_gr_172.gif] via reaction 7, as shown by the 20% per second increase in [[Graphics:../Images/index_gr_173.gif]] at 332 sec. At this point, the overall reaction rate has increased to [Graphics:../Images/index_gr_174.gif]. The formation of [Graphics:../Images/index_gr_175.gif] leads to the depletion of [Graphics:../Images/index_gr_176.gif] via reaction 2. This relationship is apparent in Figure 4 and in the bar chart at 332 sec in Figure 5. The red lines indicate the formation of HOBr from the reactants for reaction 2 (i.e., [Graphics:../Images/index_gr_177.gif], [Graphics:../Images/index_gr_178.gif], and [Graphics:../Images/index_gr_179.gif]). The removal of [Graphics:../Images/index_gr_180.gif] shifts the system away from reactions 5, 6, and 7, as shown by the absence at 342 sec of red lines corresponding to these reactions (cf. 325 sec). [Ce(IV)] continues to fall (Figures 4 and 5), and the red lines show the accompanying production of Ce(III) and [Graphics:../Images/index_gr_181.gif]. Overall, however, [[Graphics:../Images/index_gr_182.gif]] is decreasing via reactions 1 through 3. When [Graphics:../Images/index_gr_183.gif] is depleted to trace levels, the overall reaction rate is slow (viz. 360 sec in Figure 3). The low concentration of [Graphics:../Images/index_gr_184.gif] keeps reaction 2 slow while allowing [Graphics:../Images/index_gr_185.gif] to begin forming via reaction 3. [[Graphics:../Images/index_gr_186.gif]] and [[Graphics:../Images/index_gr_187.gif]] are again low (cf. 309 sec), and the chemical cycle then repeats.


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