After the user enters the chemical system as shown above, the subsequent steps of setting up the differential equations and numerically solving the coupled equations are fully automated. After the numerical engine has finished the computations, the user is presented with graphs of the solutions, as shown in Figures 1 and 2. Following an initial induction period, the oscillatory behavior of chemical intermediates is apparent in Figure 1. In particular, [Ce(IV)] oscillates from nearly zero to 2 mM, with accompanying changes from clear to yellow. Figure 2 shows that the concentrations of the reactants are much higher than those of the chemical intermediates, and the concentrations monotonically decrease during the course of the reaction. There are some periods when the overall reaction rate is apparently slow (i.e., the nearly flat regions in Figure 2) and other periods when the reaction rate appears to accelerate.
Figure 1. The concentrations of , , and Ce(IV) as a function of time from 0 to 1200 sec. After an initial induction period, an oscillatory behavior with a period of about 2 minutes is observed.
The following two conditions must be satisfied for a reaction to oscillate.
1.The concentrations of reactants and products must be far from their equilibrium conditions.
2.There must be chemical feedback in the chemical mechanism (implying a complex kinetic mechanism).
At sufficiently long time periods (i.e., when reactant and product concentrations are sufficiently close to equilibrium), the chemical system reverts to a single mode and all chemical species approach equilibrium concentrations monotonically. Throughout the course of the reaction, the free energy of the system declines as the extent of reaction continues.
Figure 2. The concentrations of , , and organic as a function of time from 0 to 1200 sec. The concentrations of these reactant species decrease monotonically through the course of the reaction, proceeding stepwise through periods of slow and fast reaction rates.
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