Chapter 14, Problem 61QP

The rate law for the reaction:

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

is rate $=k\left[{\text{H}}_{\text{2}}\right]{\left[\text{NO}\right]}^2.$ Which of the following mechanisms can be ruled out on the basis of the observed rate expression?

Mechanism I

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

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

${\text{O + H}}_{\text{2}}\to {\text{H}}_{\text{2}}\text{O }\left(\text{fast}\right)$

Mechanism II

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

${\text{N}}_{\text{2}}{\text{O + H}}_{\text{2}}\to {\text{N}}_{\text{2}}{\text{+ H}}_{\text{2}}\text{O }\left(\text{fast}\right)$

Mechanism III

$\text{2NO}\rightleftarrows {\text{N}}_{\text{2}}{\text{O}}_{\text{2}}\left(\text{fast equilibrium}\right)$

${\text{N}}_{\text{2}}{\text{O}}_{\text{2}}{\text{ + H}}_{\text{2}}\to {\text{N}}_{\text{2}}{\text{O + H}}_{\text{2}}\text{O }\left(\text{slow}\right)$

${\text{N}}_{\text{2}}{\text{O}}_{}{\text{ + H}}_{\text{2}}\to {\text{N}}_{\text{2}}{\text{ + H}}_{\text{2}}\text{O }\left(\text{fast}\right)$