Chapter 15, Problem 65E

The reaction

$5{\text{Br}}^{-}\left(aq\right)+{\text{BrO}}_3{}^{-}\left(aq\right)+6{\text{H}}^{+}\left(aq\right)\to 3{\text{Br}}_2\left(l\right)+3{\text{H}}_2\text{O}\left(l\right)$

is expected to obey the mechanism

$\begin{array}{l}{\text{BrO}}_3{}^{-}\left(aq\right)+{\text{H}}^{+}\left(aq\right)\underset{k_{-1}}{\overset{k_1}{\rightleftharpoons }}{\text{HBrO}}_3\left(aq\right)\text{}\text{ Fast equilibrium}\\ {\text{HBrO}}_3\left(aq\right)+{\text{H}}^{+}\left(aq\right)\underset{k_{-2}}{\overset{k_2}{\rightleftharpoons }}{\text{H}}_2{\text{BrO}}_3{}^{+}\left(aq\right)\text{ Fast equilibrium}\\ {\text{Br}}^{-}\left(aq\right)+{\text{H}}_2{\text{BrO}}_3{}^{+}\left(aq\right)\stackrel{k_3}{\to }\left({\text{Br—BrO}}_2\right)\left(aq\right)+{\text{H}}_2\text{O}\left(l\right)\text{ Slow}\\ \left({\text{Br—BrO}}_2\right)\left(aq\right)+4{\text{H}}^{+}\left(aq\right)+4{\text{Br}}^{-}\left(aq\right)\to \text{products Fast}\end{array}$

Write the rate law for this reaction.