For a reaction, $\mathrm{A} \longrightarrow \mathrm{B}$, rate equation is $\mathrm{r}=\mathrm{k}[\mathrm{A}]^{\circ}$. If initial concentration of reactant is 'a'mol dm ${ }^{-3}$ find half life time of reaction.

What is the order and molecularity respectively for the elementary reaction given below?

$$ \mathrm{O}_{3(\mathrm{~g})}+\mathrm{O}_{(\mathrm{g})} \longrightarrow 2 \mathrm{O}_{2(\mathrm{~g})} \text { if } \mathrm{r}=\mathrm{k}\left[\mathrm{O}_3\right][\mathrm{O}] $$

Calculate the time in seconds required to reduce the concentration of reactant to half of initial concentration for first order reaction if rate constant is $1.386 \times 10^{-3} \mathrm{~s}^{-1}$.

If concentration of reactant ' $A$ ' is increased by 10 times, rate of reaction increases 100 times. What is order of reaction if rate law is $r=k[A]^r$ ?