The half-life period of a reaction is $1386 \ s$. What is the value of the specific rate constant for the reaction?

$N_{2}O_{5(g)} \rightarrow 2NO_{2(g)} + \frac{1}{2}O_{2(g)}$
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: $\log 3 = 0.477, \log 5 = 0.699$]

What is the value of the rate constant for a first-order reaction if the slope for the graph of rate versus concentration is $2.5 \times 10^{-3}$?

Which one of the following plots is correct for a first order reaction?

The half-life of a first order reaction is $30 \, min$. The time required for $75 \, \%$ completion of the same reaction will be $..... \, min$

Show that in a first order reaction,the time required for completion of $99.9 \%$ is $10$ times the half-life $(t_{1/2})$ of the reaction.