Identify $True$ $(T)$ and $False$ $(F)$ statements for the following equations related to a first-order reaction $R \rightarrow P$:
$(i) \ln [R] = -kt + \ln [R]_{0}$
$(ii) \ln [R] = +kt + \ln [R]_{0}$

It takes $1 \, h$ for a first order reaction to go to $50 \, \%$ completion. The total time required for the same reaction to reach $87.5 \, \%$ completion will be $..... \, h$.

For a first order reaction $A_{(g)} \rightarrow 2B_{(g)} + C_{(g)}$ at constant volume and $300 \ K$,the total pressure at the beginning $(t=0)$ and at time $t$ are $P_0$ and $P_t$,respectively. Initially,only $A$ is present with concentration $[A]_0$,and $t_{1/3}$ is the time required for the partial pressure of $A$ to reach $1/3^{rd}$ of its initial value. The correct option$(s)$ is (are) (Assume that all these gases behave as ideal gases)

The rate constant of a first order reaction is $1.15 \times 10^{-3} \ s^{-1}$. How long will $5 \ g$ of reactant take to reduce to $3 \ g$ (in $s$)?

$75\%$ of the first order reaction was completed in $32$ minutes. When was $50\%$ of the reaction completed? (in $\text{minutes}$)

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