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

For a first order reaction,the intercept of the graph between $\log \left(\frac{[A]_0}{[A]_t}\right)$ ($Y$-axis) and time ($X$-axis) is equal to

$A \rightarrow P$ is a first order reaction. At $300 \ K$,this reaction was started with $[A] = 0.5 \ mol \ L^{-1}$. The rate constant of the reaction was $0.125 \ min^{-1}$. The same reaction was started separately with $[A] = 1 \ mol \ L^{-1}$ at $300 \ K$. The rate constant (in $min^{-1}$) now is:

Identify $True$ $(T)$ and $False$ $(F)$ statements of the following for a first order reaction $R \rightarrow P$.
$I. \log \frac{[R]}{[R]_0} = -\frac{kt}{2.303}$
$II. \log \frac{[R]}{[R]_0} = \frac{kt}{2.303}$

For the gaseous reaction $A(g) \longrightarrow B(g) + C(g) + D(g)$,starting with an initial pressure of $400 \ atm$. If the total pressure after $2 \ hr$ is $800 \ atm$,the value of the rate constant is: (consider the reaction to be $1^{st}$ order): (in $hr^{-1}$)

If a $99\%$ first-order reaction is completed in $32$ minutes,how many minutes will it take for $99.9\%$ of the reaction to be completed?