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

If the half-life of a first-order reaction is $4 \ min$,then after how many minutes will the reaction be $99.9 \%$ complete?

For a first-order reaction,which of the following statements is correct?

Consider the following two first order reactions occurring at $298 \ K$ with same initial concentration of $A$: $(1)$ $A \rightarrow B$; rate constant,$k=0.693 \ min^{-1}$ $(2)$ $A \rightarrow C$; half-life,$t_{1/2}=0.693 \ min$. Choose the correct option.

$N_{2}O_{5(g)} \rightarrow 2NO_{2(g)} + \frac{1}{2}O_{2(g)}$
In the above first order reaction,the initial concentration of $N_{2}O_{5}$ is $2.40 \times 10^{-2} \ mol \ L^{-1}$ at $318 \ K$. The concentration of $N_{2}O_{5}$ after $1 \ hour$ was $1.60 \times 10^{-2} \ mol \ L^{-1}$. The rate constant of the reaction at $318 \ K$ is $..... \times 10^{-3} \ min^{-1}$. (Nearest integer)
[Given: $\log 3 = 0.477, \log 5 = 0.699$]

In a first-order reaction,the rate constant $k = 70 \, s^{-1}$. How much time is required for the concentration to become $\frac{1}{18}$ of the initial concentration (in $, s$)?