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

$A_{(g)} \rightarrow 2B_{(g)}$. Initially,$2 \ mol$ of $A$ are taken in a $5 \ L$ vessel. After $20 \ min$,$[A]_t = \frac{[B]_t}{2}$. Find the half-life time of $A$ in the first-order reaction in $\min$.

The half-life period for a first-order reaction is . . . . . . .

The time taken for $10 \%$ completion of a first order reaction is $20$ minutes. The time required for the completion of $19 \%$ of the same reaction in minutes is

The half-life for the reaction $N_2O_5 \rightleftharpoons 2NO_2 + \frac{1}{2}O_2$ is $24 \ hr$ at $30 \ ^\circ C$. Starting with $10 \ g$ of $N_2O_5$,how many grams of $N_2O_5$ will remain after a period of $96 \ hr$?

The half-life of a first-order reaction is $2000$ years. If the concentration after $8000$ years is $0.02 \, M$,then the initial concentration was $........... \, M$.