decomposition:

$O_3(g){}_{k_{-1}}^{k_1}{O}_2(g)+O(g)$

$O_3(g)+O(g)k_{2}2O_2(g)$

a$.$ Derive the rate law expression for the loss of $O_3(g).$

b$.$ Under what conditions will the rate law expression for $O_3(g)$ decomposition be first order with respect to $O_3(g)?$