Suppose we have a reversible chemical reaction, where 2 molecules of A can react to form a single molecule of B, as shown in the chemical reaction diagram One common example would be the dimerisation of oxygen, where two oxygen molecules combine to form O2.

A + A k1

−→

←−

k2 B.

If the reactions obey the law of mass action then the concentrations of A and B obey the differential equationsa. Show that [A] + 2[B] is constant.

b. Without actually solving for [A], show that there is a single

(scientifically valid) stable steady state.

Wolfram Alpha will happily solve this equation, but the solution is rather long and complicated, and not really very helpful at all.

c. Describe how the solution will behave.