129. The reaction:
2NO + Br₂ → 2NOBr
is supposed to follow the following mechanism.
(i) $\mathrm{NO}+{\mathrm{Br}}_2 \stackrel{\mathrm{fast}}{\rightleftharpoons } {\mathrm{NOBr}}_2$
(ii) ${\mathrm{NOBr}}_2+\mathrm{NO}\stackrel{\mathrm{slow}}{\to } 2\mathrm{NOBr}$
Suggest the rate law expression.

The rate expression is derived by step II of the mechanism, as it is the slower one

rate = k[NOBr₂][NO] ...(i)

However, NOBr₂ is an intermediate and thus its concentration should be replaced from equation (i)
From step (i),

Equilibrium constant, ${\mathrm{K}}_{\mathrm{c}} = \frac{\left[{\mathrm{NOBr}}_2\right]}{{\left[\mathrm{NO}\right]}_2 \left[{\mathrm{Br}}_2\right]}$

$\therefore$          $\left[{\mathrm{NOBr}}_2\right] = {\mathrm{k}}_{\mathrm{c}} \left[\mathrm{NO}\right] \left[{\mathrm{Br}}_2\right]$                  ...(ii)

Then by equation (i) and (ii)

              $\mathrm{rate} = \mathrm{k}\text{'} - {\left[\mathrm{NO}\right]}^2 \left[{\mathrm{Br}}_2\right]$

Order of the reaction is 2+1 =3