If the rate constant for a first order reaction is $k$,the time $(t)$ required for the completion of $99 \%$ of the reaction is given by

The reaction $2N_2O_5 \,(g) \to 4NO_2 \,(g) + O_2 \,(g)$ follows first order kinetics. The pressure of a vessel containing only $N_2O_5$ was found to increase from $50 \, mmHg$ to $87.5 \, mmHg$ in $30 \, min$. The pressure exerted by the gases after $60 \, min$ will be .......... $mmHg$ (assume temperature remains constant).

The half-life period of a first order reaction is $100 \, \text{sec}$. The rate constant of the reaction is

Calculate the rate constant of a first order reaction if the half-life of the reaction is $40 \ minute$.

For a first-order reaction,if $75\%$ of the reaction is completed in $15 \ min$,then the time required for $90\%$ completion of the reaction will be ........... $min$.

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 $........... \, M$.