For a first-order reaction at $25\,^oC$,the half-life period is $248\,s$. What is the value of the rate constant at this temperature?

Identify True $(T)$ and False $(F)$ statements for the first order reaction $R \rightarrow P$ given below:
$I. \ k = \frac{1}{t} \ln \frac{[R]_0}{[R]}$
$II. \ k = \frac{1}{t} \ln \frac{[R]}{[R]_0}$

$A$ first-order reaction is $50\%$ complete in $45 \text{ minutes}$. How many hours will it take for the reaction to be $99.9\%$ complete?

$A$ reaction which is of first order with respect to reactant $A$,has a rate constant $6 \, min^{-1}$. If we start with $[A] = 0.5 \, mol \, L^{-1}$,when would $[A]$ reach the value of $0.05 \, mol \, L^{-1}$?

In a first order reaction,the concentration of the reactant decreases from $20 \ mmol$ to $10 \ mmol$ in $1.151 \ min$. What is the rate constant (in $min^{-1}$)?

The decomposition reaction $2N_2O_{5(g)} \xrightarrow{\Delta} 2N_2O_{4(g)} + O_{2(g)}$ is started in a closed cylinder under isothermal isochoric conditions at an initial pressure of $1 \ atm$. After $Y \times 10^3 \ s$,the pressure inside the cylinder is found to be $1.45 \ atm$. If the rate constant of the reaction is $5 \times 10^{-4} \ s^{-1}$,assuming ideal gas behavior,the value of $Y$ is. . . . . . . .