For a first-order reaction,the time taken for the initial concentration to decrease to $1/4$ of its value is $20 \ min$. The time taken for the initial concentration to decrease to $1/16$ of its value will be $......... \ min$.

The decomposition of substance $A$ in a solution follows first-order kinetics. Vessel-$I$ contains $1 \ L$ of $1 \ M$ solution of $A$. Vessel-$II$ contains $100 \ mL$ of $0.6 \ M$ solution of $A$. If the concentration of $A$ in Vessel-$I$ becomes $0.25 \ M$ in $8 \ hr$,then the time required for the concentration of $A$ in Vessel-$II$ to become $0.3 \ M$ is ......... $hr$.

Half-life for a first order reaction is $6.93 \ hour$. What is the time required for $80 \%$ completion of the reaction (in $hours$)?

The unit of the specific reaction rate constant for a first-order reaction (if the concentration is expressed in molarity) is:

Given below are two statements:
Statement $I$: The graph of $t_{1/2}$ versus initial concentration $[R]_0$ for a first-order reaction is a horizontal line.
Statement $II$: The graph of $\log \frac{[R]_0}{[R]}$ versus time $t$ for a first-order reaction is a straight line passing through the origin with a slope equal to $\frac{k}{2.303}$.
In the light of the above statements,choose the correct answer from the options given below:

For a first order reaction,to obtain a positive slope,we need to plot $...$ where $[A]$ is the concentration of reactant $A$.