The termolecular reaction
`2NO(g) + H_(2)(g) rarr 2NOH(g)` is found to be third order obeying the rate law `r = k[NO]^(2)[H_(2)]`. Show that it is conisstent with either of the following mechanisms:
(a) `2NO(g) overset(k_(eq))hArr N_(2)O_(2)(g) ("fast equilibrium")`
`N_(2)O_(2)(g) + H_(2)(g) overset(k')rarr 2NOH(g)` (slow)
(b) `2NO(g) +H_(2)(g) overset(k'_(eq))hArr NOH_(2)(g) ("fast equilibrium")`
`NOH_(2)(g) + NO(g) overset(k'')rarr 2NOH(g)` (slow)

Explanation

To show that the termolecular reaction \(2NO(g) + H_2(g) \rightarrow 2NOH(g)\) is consistent with the given mechanisms, we will analyze each mechanism step by step.

### Step 1: Understanding the Rate Law
The rate law for the reaction is given as:
\[ r = k[NO]^2[H_2] \]
This indicates that the reaction is third order: second order with respect to \(NO\) and first order with respect to \(H_2\).
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