Chapter 11, Problem 77QAP

For the reaction between hydrogen and iodine,

${\text{H}}_2\left(g\right)+{\text{I}}_2\to 2\text{HI}\left(g\right)$

the experimental rate expression is $\text{rate}=k\left[{\text{H}}_2\right]\left[{\text{I}}_2\right]$. Show that this expression is consistent with the mechanism

$\begin{array}{l}{\text{I}}_2\left(g\right)\rightleftharpoons 2\text{I}\left(g\right)\left(\text{fast}\right)\\ {\text{H}}_2\left(g\right)+\text{I}\left(g\right)+\text{I}\left(g\right)\to 2\text{HI}\left(g\right)\left(\text{slow}\right)\end{array}$