Chapter 13, Problem 13.58QP

The rate law for the reaction

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

is rate = k[H₂][NO]². Which of the following mechanisms can be ruled out on the basis of the observed rate expression?

Mechanism I

$\begin{array}{cc}\begin{array}{c}{\text{H}}_2+\text{NO}\stackrel{}{\to }{\text{H}}_2\text{O}+\text{N}\\ \text{N}+\text{NO}\stackrel{}{\to }{\text{N}}_2+\text{O}\\ \text{O}+{\text{H}}_2\stackrel{}{\to }{\text{H}}_2\text{O}\end{array}& \begin{array}{l}(\text{slow})\hfill \\ (\text{fast})\hfill \\ (\text{fast})\hfill \end{array}\end{array}$

Mechanism II

$\begin{array}{ll}\begin{array}{c}{\text{H}}_2+2\text{NO}\stackrel{}{\to }{\text{N}}_2\text{O}+{\text{H}}_2\text{O}\\ {\text{N}}_2\text{O}+{\text{H}}_2\stackrel{}{\to }{\text{N}}_2+{\text{H}}_2\text{O}\end{array}\hfill & \begin{array}{l}(\text{slow})\hfill \\ (\text{fast})\hfill \end{array}\hfill \end{array}$

Mechanism III

$\begin{array}{ll}\begin{array}{c}2\text{NO}\stackrel{}{\rightleftharpoons }{\text{N}}_2{\text{O}}_2\\ {\text{N}}_2{\text{O}}_2+{\text{H}}_2\stackrel{}{\to }{\text{N}}_2\text{O}+{\text{H}}_2\text{O}\\ {\text{N}}_2\text{O}+{\text{H}}_2\stackrel{}{\to }{\text{N}}_2+{\text{H}}_2\text{O}\end{array}\hfill & \begin{array}{l}(\text{fast equilibrium})\hfill \\ (\text{slow})\hfill \\ (\text{fast})\hfill \end{array}\hfill \end{array}$