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

The half-life period of a first-order reaction is given by:

$A_{(g)} \xrightarrow{\Delta} P_{(g)} + Q_{(g)} + R_{(g)}$ follows first-order kinetics with a half-life of $69.3 \ s$ at $500^{\circ}C$. Starting from the gas '$A$' enclosed in a container at $500^{\circ}C$ and at a pressure of $0.4 \ atm$,the total pressure of the system after $230 \ s$ will be (in $atm$)

What is the slope of the graph plotted between half-life $(t_{1/2})$ and initial concentration $(a)$ for a $1^{st}$ order reaction?

$A$ first order reaction requires $30 \ min$ for $50\%$ completion. The time required to complete the reaction by $75\%$ will be .......... $\min.$

The rate for a first order reaction is $0.6932 \times 10^{-2} \, mol \, L^{-1} \, min^{-1}$ and the initial concentration of the reactants is $1 \, M$. The half-life $T_{1/2}$ is equal to ........ $min$.