For a first order reaction,the half-life period is

Calculate the rate constant of the first order reaction if $20 \%$ of the reactant decomposes in $15 \ minutes$.

$A$ and $B$ decompose via first order kinetics with half-lives $54.0 \, min$ and $18.0 \, min$ respectively. Starting from an equimolar non-reactive mixture of $A$ and $B$,the time taken for the concentration of $A$ to become $16$ times that of $B$ is ...... $min.$ (Round off to the Nearest Integer).

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 the same temperature.

In a first-order reaction,the concentration of the reactant decreases from $1.0 \, M$ to $0.25 \, M$ in $20 \, \text{minutes}$. What will be the rate constant of the reaction?

Time required for completion of $90 \%$ of a first order reaction is '$t$'. What is the time required for completion of $99.9 \%$ of the reaction?