Chemistry 6, 9 AM section, graphic

Lotka-Volterra Rate Expressions

We can write the steps in the Lotka-Volterra mechanism as

A + X -> 2 X (Rate constant k1)

X + Y -> 2 Y (Rate constant k2)

Y -> B (Rate constant k3)

so that the rate laws for the intermediates are

d[X]/dt = k1[A][X] – k2[X][Y]

d[Y]/dt = k2[X][Y] – k3[Y]

If [A] is a constant ([A]0) and if we assume steady state for X and Y, we can write

d[X]/dt = k1[A]0[X] – k2[X][Y] = 0

d[Y]/dt = k2[X][Y] – k3[Y] = 0

or

[Y] = k1[A]0/k2 = constant

[X] = k3/k2 = constant

which is what a steady-state assumption should give, but we know this assumption misses the key feature of this reaction mechanism: the oscillation in time of the intermediates' concentrations.

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