Chapter 13, Problem 82E

Consider the reaction.

${\text{2NH}}_{\text{3}}(aq)+{\text{OCl}}^{\text{-}}(aq)\to {\text{N}}_{\text{2}}{\text{H}}_{\text{4}}(aq)+{\text{H}}_{\text{2}}\text{O}(l)+{\text{Cl}}^{\text{-}}(aq)$

This three-step mechanism is proposed.

${\text{NH}}_{\text{3}}(aq)+{\text{OCl}}^{\text{-}}(aq)\underset{h_2}{\overset{k_1}{\rightleftharpoons }}{\text{NH}}_{\text{2}}\text{Cl}(aq)+{\text{OH}}^{\text{-}}(aq)$ Fast
${\text{NH}}_{\text{2}}\text{Cl}(aq)+{\text{NH}}_{\text{3}}(aq)\underset{k_{.3}}{\to }{\text{N}}_{\text{2}}{\text{H}}_{\text{5}}{}^{+}(aq)+{\text{Cl}}^{\text{-}}(aq)$ Slow
${\text{N}}_{\text{2}}{\text{H}}_{\text{5}}{}^{\text{+}}(aq)+{\text{OH}}^{\text{-}}(aq)\underset{k_4}{\to }{\text{N}}_{\text{2}}{\text{H}}_{\text{4}}(aq)+{\text{H}}_{\text{2}}\text{O}(l)$ Fast

a. Show that the mechanism sums to the overall reaction.
b. What is the rate law predicted by this mechanism?