If the half-life $(t_{1/2})$ of a first-order reaction is $20 \ minutes$,what fraction of the reactant remains after $40 \ minutes$?

$99 \%$ of a first order reaction was completed in $64 \text{ min}$. In how many minutes will $99.9 \%$ of the reaction be complete?

Following data was obtained for the first order decomposition of $SO_2Cl_{2(g)}$ at constant volume:
$SO_2Cl_{2(g)} \to SO_{2(g)} + Cl_{2(g)}$

$S. No.$	$Time$ $(s)$	$Total$ $pressure$ $(atm)$
$1$	$0$	$0.5$
$2$	$100$	$0.6$

Calculate the rate constant.

$N_2O_{(g)} \to N_{2(g)} + \frac{1}{2}O_{2(g)}$
In a closed vessel,the reaction follows first-order kinetics. If starting with pure $N_2O_{(g)}$,the total pressure after time $t$ is $P_t$ and after a very long time is $P_{\infty}$,then which of the following expressions is correct?

In a first order reaction,the concentration of reactant decreases from $800 \ mol/dm^3$ to $50 \ mol/dm^3$ in $2 \times 10^2 \ s$. The rate constant of the reaction in $s^{-1}$ is:

For a first-order reaction,it takes $20 \, \text{min}$ for the concentration to decrease from $1 \, M$ to $0.6 \, M$. How much time is required for the concentration to decrease from $0.6 \, M$ to $0.36 \, M$?