Department of Mathematics

IDEA: Internet Differential Equations Activities

Oregonator model of Oscillating Chemical Reactions

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:
[HBrO2] = 5.025 x 10-11 a,
[Br-] = 3.0 x 10-7 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

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