Chapter 14, Problem 106E

Consider the reaction:
${\text{2NH}}_{\text{3}}\left(\text{aq}\right)+{\text{OCl}}^{-}\left(\text{aq}\right)\to {\text{N}}_{\text{2}}{\text{H}}_{\text{4}}\left(\text{aq}\right)+{\text{H}}_{\text{2}}\text{O}\left(\text{l}\right)+{\text{Cl}}^{-}\left(\text{aq}\right)$
This three-step mechanism is proposed:
$\begin{array}{l}{\text{NH}}_{\text{3}}\left(aq\right)+{\text{OCl}}^{-}\left(aq\right)\underset{k_2}{\overset{k_1}{\rightleftharpoons }}{\text{NH}}_2\text{Cl}\left(aq\right){\text{+OH}}^{-}\left(aq\right)\text{ Fast}\\ {\text{NH}}_{\text{2}}\text{Cl}\left(aq\right)+{\text{NH}}_{\text{3}}\left(aq\right)\underset{k_3}{\to }{\text{ N}}_2{\text{H}}_5{}^{+}\left(aq\right){\text{+Cl}}^{-}\left(aq\right)\text{ Slow}\\ {\text{N}}_{\text{2}}{\text{H}}_{\text{5}}{}^{\text{+}}\left(aq\right)+{\text{OH}}^{-}\left(aq\right)\underset{k_4}{\to }{\text{N}}_2{\text{H}}_4\left(aq\right){\text{+H}}_2\text{O Fast}\end{array}$
a. Show that the mechanism sums to the overall reaction.
b. What is the rate law predicted by this mechanism?