Write the overall reaction and the rate law equation from the following elementary steps.
$N O + {B r}_{2} ⇌ N O {B r}_{2}$
$N O {B r}_{2} + N O \to 2 N O B r$

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Solution

Adding both the steps, we get overall reaction,
$2 N O + {B r}_{2} \to 2 N O B r$ .
The second step is slow and, therefore, a rate determining step.
$r = k^{^{'}} [N O {B r}_{2}] [N O]$
$K = \frac{[N O {B r}_{2}]}{[N O] [{B r}_{2}]}$ or $[N O {B r}_{2}] = K [N O] [{B r}_{2}]$
$r = k^{^{'}} K {[N O]}^{2} [{B r}_{2}]$

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