Oregonator model of Oscillating Chemical Reactions
Reference : R.J. Field and R.M. Noyes, J. Chem. Phys. 60, 1877 (1974).
A simplified form of this model uses the following mechanism.
step 
reaction 
contributions to the rate equation 
1 
A+Y X 

2 
X+Y P 

3 
B+X 2X+Z 

4 
2X Q 

5 
Z Y 
The overall reaction, obtained by adding reactions 1, 2, 4 and twice 3 and 5, is A + 2B P + Q.
Problem: Use the following definitions
for dimensionless concentration variables (a,
h, and r) and rate
constants (q, s) to solve Oregonator model for the BZ reaction:
[HBrO_{2}] = 5.025 x 10^{11} a,
[Br^{}] = 3.0 x 107 h,
[Ce(IV)] = 2.412 x 10^{8} r,
q = 8.375 x 10^{6},
s = 77.27 .
The time variable is also the dimensionless variable t
= t/w with w = 0.1610sec. Take the initial concentrations to be a=1,
h=1000, and r=1000.
(a )Set up the differential rate equations for a, h, and r.
(b) Solve the d.e. from time 0 to t1=1000, and plot concentrations (better to plot the log(conc.)) versus time.
(c) Also plot the trajectories of a and r versus h in concentration (or log(conc.)) space. Be careful, this system of differential equations is "stiff" and requires special treatement.
See an interactive mathcad solution of this problem in the file oregonat.mcd .
Return to oscillating reactions CONTENTS , Lotka model , Brusselator
With the advent of HTML5, Javascript is now ready for prime time
for mathematical applications. There are
new Javascript demos
illustrating how we might use interactive web objects to
help students learn Calculus.