Chapter 14, Problem 86E

Consider the reaction:
${\text{2O}}_{\text{3}}\left(\text{g}\right)\to {\text{3O}}_{\text{2}}\left(\text{g}\right)$
The rate law for this reaction is:
$\text{rate}=k\frac{{[O_3]}^2}{[O_2]}$
Suppose that a 1.0 L reaction vessel initially contains 1.0 mol of ${\text{O}}_{\text{3}}$ and 1.0 mol of ${\text{O}}_2$ . What fraction of the ${\text{O}}_{\text{3}}$ has reacted when the rate falls to one-half of its initial value?