The termolecular reaction `2NO(g) + H_2(g) to 2NOH(g) ` is found to be third-order obeying the rate law `r = k[NO]^2[H_2]`. Show that it is consistent with either of the following mechanisms :
`2NO(g) overset(k_(eq))hArr N_2O_2(g)` (fast equilibrium)
`N_2O_2 (g) H_2(g) oveerset(k')to 2NOH (g)` (slow)

Explanation

To demonstrate that the given termolecular reaction \(2NO(g) + H_2(g) \to 2NOH(g)\) is consistent with the proposed mechanisms, we will analyze the rate law and the steps of the mechanisms.

### Step 1: Write 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 overall, with respect to the concentration of \(NO\) and \(H_2\).
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