Question

The chemical reaction, $2O_3\to 3O_2$ proceeds as follows:
$O_3\rightleftharpoons O_2+O$ ....(fast)
$O+O_3\to 2O_2$ ....(slow)

The rate law expression should be:

• A. $r=K[O_3{]}^2$
• B. $r=K\left[O_3{]}^2\right[O_2{]}^{-1}$
• C. $r=K\left[O_3\right]\left[O_2\right]$
• D. Unpredictable

Answer 1

The correct option is B $r=K\left[O_3{]}^2\right[O_2{]}^{-1}$

$O_3\rightleftharpoons O_2+O....\left(fast\right)$

$O+O_3\to 2O_2$ ....(slow)

The rate of reaction depends on slowest step.
So rate would be: $r=k\left[O\right]\left[O_3\right]$

From the fast step, we have
$K=\frac{\left[O\right]\left[O_2\right]}{\left[O_3\right]}$

So,
$r=k\times K\left[O_3{]}^2\right[O_2{]}^{-1}=K^{\prime }\left[O_3{]}^2\right[O_2{]}^{-1}$