The chemical reaction `2O_(3) overset(k_(1))rarr 3O_(2)` proceeds as follows:
`O_(3) overset(k_(eq))hArr O_(2)+O` (fast)
`O + O_(3) overset(k)rarr 2O_(2)` (slow)
What should be the rate law expresison ?

Options

A. `r=k[O_3]^2`
B. `r=k[O_3]^2[O_2]^(-1)`
C. `r=k[O_3][O_2]`
D. unpredictable

Explanation

Rate depends upon slowest step.
Hence, from eq. (ii) , `r = k [O_3][O]. ….. (a)`
From eq. (i) , `K_(eq)=([O_2][O])/([O_3])`
or `[O]=(K_(eq)[O_3])/([O_2]) ….(b)`
Hence from (a) and (b)
`r =k[O_3](K_(eq)[O_3])/([O_3])=k'[O_3]^2[O_2]^(-1)`.