Chapter 14, Problem 105E

Consider the gas-phase reaction:
${\text{H}}_{\text{2}}\left(\text{g}\right)+{\text{I}}_{\text{2}}\left(\text{g}\right)\to \text{2HI}\left(\text{g}\right)$
The reaction was experimentally determined to be first order in ${\text{H}}_{\text{2}}$ and first order in ${\text{ I}}_{\text{2}}$ . Consider the proposed mechanisms.
Proposed mechanism I:
${\text{H}}_{\text{2}}\left(\text{g}\right)+{\text{I}}_{\text{2}}\left(\text{g}\right)\to \text{2HI}\left(\text{g}\right)$ Single step
Proposed mechanism II:
$\begin{array}{l}{\text{I}}_{\text{2}}\left(g\right)\underset{k_{-1}}{\overset{k_1}{\rightleftharpoons }}\text{2 I}\left(g\right)\text{ Fast}\\ {\text{H}}_{\text{2}}\left(\text{g}\right){\text{+ 2 I}}_{\text{2}}\left(g\right)\underset{k_2}{\to }\text{2HI}\left(g\right)\text{ Slow}\end{array}$
a. Show that both of the proposed mechanisms are valid.
b. What kind of experimental evidence might lead you to favor mechanism II over mechanism I?