A first order reaction takes 40 minute for $20 \%$ decomposition. Calculate its rate constant.

If instantaneous rate of reaction is given as $$ -\frac{1}{\mathrm{a}} \frac{\mathrm{~d}[\mathrm{~A}]}{\mathrm{dt}}=-\frac{1}{\mathrm{~b}} \frac{\mathrm{~d}[\mathrm{~B}]}{\mathrm{dt}}=\frac{1 \mathrm{~d}[\mathrm{C}]}{\mathrm{c}]}=\frac{1 \mathrm{~d}[\mathrm{D}]}{\mathrm{d}]}$$

the reaction is represented as

Rate law for a reaction is $r=k[A]^2[B]$. If rate constant is $6.25 \mathrm{~mol}^{-2} \mathrm{dm}^6 \mathrm{~s}^{-1}$, what is the rate of reaction when $[\mathrm{A}]=1 \mathrm{~mol} \mathrm{dm}^{-3}$ and $[\mathrm{B}]=0.2 \mathrm{~mol} \mathrm{dm}^{-3}$ ?

What is the time needed to reduce the initial concentration of reactant to $10 \%$ in a first order reaction if its half life time is 10 minutes?