Calculate the rate constant for the first order reaction, $$\mathrm{A} \rightarrow \mathrm{B}$$ if the rate of reaction is $$5.4 \times 10^{-6} \mathrm{~mol} \mathrm{~dm}^{-3} \mathrm{~s}^{-1}$$ and $$[\mathrm{A}]=0.3 \mathrm{M}$$.

Time required for $$90 \%$$ completion of a first order reaction is '$$x$$' minute. Calculate the time required to complete $$99.9 \%$$ of the reaction at same temperature.

For the reaction, $$3 \mathrm{~I}+\mathrm{S}_2 \mathrm{O}_8^{2-} \rightarrow \mathrm{I}_3^{-}+2 \mathrm{SO}_4^{2-}$$, at a particular time $$\mathrm{t}, \frac{\mathrm{d}\left[\mathrm{SO}_4^{2-}\right]}{\mathrm{dt}}$$ is $$2.2 \times 10^{-2} \mathrm{~mol} \mathrm{~dm}^{-3} \mathrm{~s}^{-1}$$. What is the value of $$-\frac{\mathrm{d}\left[\mathrm{I}^{-}\right]}{\mathrm{dt}}$$ ?

What is the half life of a first order reaction if rate constant is $$4.2 \times 10^{-2}$$ per day?