A first order reaction takes 23.03 minutes for $$20 \%$$ decomposition. Calculate its rate constant.

The rate law for the reaction $$\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}$$ at $$25^{\circ} \mathrm{C}$$ is given by rate $$=k[A][B]^2$$. Calculate the rate of reaction if rate constant at same temperature is $$6.25 \mathrm{~mol}^{-2} \mathrm{~dm}^6 \mathrm{~s}^{-1}[[\mathrm{~A}]=1 \mathrm{M},[\mathrm{B}]=0.2 \mathrm{M}]$$

Calculate the time needed for reactant to decompose $$99.9 \%$$ if rate constant of first order reaction is 0.576 minute$$^{-1}$$.

Calculate the rate constant of first order reaction if half life of reaction is 40 minutes.