Elemantary unimolecular reactions have first order rate laws, elementary bimolecular reactions have second order rate laws. A rate law is often derived from a proposed mechanism by imposing the state approximation or by assuming that there is a pre -equilibrium. A proposed mechanism must be consistent with the experiment rate law.
The decomposition of `O_(3)` obeys the mechanism give below
Step 1: `O_(3)hArrO_(2)+(O)` (both forward and backward reactions are fast)
Step 2: `O_(3)+(O)overset("slow")(to)O_(2)+O_(2)` (ignore) backward reaction), the rate of reaction is given by

Options

A. `k[O_(3)]^(2)[O_(2)]`
B. `k[O_(3)]^(2)[O_(2)]^(-1)`
C. `k[O_(3)]^(2)`
D. `k[O_(2)]^(2)`

Answer

B

Explanation

`K_(e)=[(O_(2)][O])/([O_(3)])implies[O]=(K_(e).[O_(3)])/([O_(2)]),r=K_(1)[O_(3)][O]=r=K_(1).[O_(3)].K_(C).([O_(3)])/([O_(2)]),r=K.[O_(3)]^(2)[O_(2)]^(-1)`