Chapter 11, Problem 78QAP

For the reaction

${\text{2H}}_2\left(g\right)+2\text{NO}\left(g\right)\to {\text{N}}_2\left(g\right)+2{\text{H}}_2\text{O}\left(g\right)$

the experimental rate expression is rate $\text{rate}=k{\left[\text{NO}\right]}^2\left[{\text{H}}_2\right]$. The following mechanism is proposed:

$\begin{array}{l}\text{2NO}\rightleftharpoons {\text{N}}_2{\text{O}}_2\left(\text{fast}\right)\\ {\text{N}}_2{\text{O}}_2+{\text{H}}_2\to {\text{H}}_2\text{O}+{\text{N}}_2\text{O}\left(\text{slow}\right)\\ {\text{N}}_2\text{O}+{\text{H}}_2\to {\text{N}}_2+{\text{H}}_2\text{O}\left(\text{fast}\right)\end{array}$

Is this mechanism consistent with the rate expression?