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The termolecular reaction 2NO(g) + H(2...

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 consistent 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) `NO(g) +H_(2)(g) overset(k'_(eq))hArr NOH_(2)(g) ("fast equilibrium")`
`NOH_(2)(g) + NO(g) overset(k'')rarr 2NOH(g)` (slow)

Text Solution

Verified by Experts

Since the slow step is the rate determining step, hence
`r = k'[ N_2O_2][H_2]`
and from the fast equilibrium step,
`K_(eq)= ([N_2O_2])/([NO]^(2))or [N_2O_2]= K_(eq)[NO]^2`
`rArr r =k' K[NO_2][H_2] = k[NO]^2[H_2]` where k = k' K
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