The units of rate constant for a first-order reaction are:

For a homogeneous gaseous reaction $A_{(g)} \to 3B_{(g)}$,if the pressure after time $t$ is $P_t$ and after completion of the reaction the pressure is $P_\infty$,select the correct relation for the rate constant $K$.

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.

$A$ first order reaction undergoes $50\,\%$ completion in $50\, min$,then it undergoes $80\, \%$ completion in ........... $min$

Identify True $(T)$ and False $(F)$ statements for the following expressions regarding a first-order reaction $R \rightarrow P$:
Statement $I$: $\text{Rate} = -\frac{d[R]}{dt} = k[R]$
Statement $II$: $\text{Rate} = -\frac{d[R]}{dt} = -k[R]$

The rate constant of a reaction is $0.693 \times 10^{-2} \ min^{-1}$. What is the half-life period (in $s$)?