The rate constant for a first-order reaction is $0.02232 \ min^{-1}$. Calculate the time required for $75 \%$ completion of the reaction. (in $min$)

$10 \ g$ mixture of two gases $A_2$ (mol. wt. $= 20$) and $B_2$ (mol. wt. $= 30$),which decompose by first order kinetics,was taken in a vessel. The half-life of decomposition of $A_2$ and $B_2$ are $2 \ hours$ and $3 \ hours$ respectively. After $6 \ hours$,the weight of the mixture of $A_2$ and $B_2$ is found to be $2 \ g$. Find the weight of $A_2$ in the initial mixture in $g$.

For a first-order reaction at $100\,^oC$,the rate constant is $K = 1.5 \times 10^{-2} \, s^{-1}$. If the initial concentration of the reactant is $100 \, mol \, L^{-1}$,what will be the concentration of the reactant after $10 \, min$?

Half life of a first order reaction is $3 \ minute$. What is the time required to reduce the concentration of reactant by $90 \%$ of its initial concentration?

$A$ first order reaction is half completed in $45 \ min$. How long does it need $99.9 \%$ of the reaction to be completed (in $Hours$)?

The half-life of a first-order reaction is $10 \ minutes$. If the initial concentration is $0.08 \ mol/L$ and at some instant the concentration is $0.01 \ mol/L$,then the time elapsed is ...... minutes.