Calculate the time in seconds required to reduce the concentration of reactant to half of initial concentration for a first order reaction if the rate constant is $1.386 \times 10^{-3} \ s^{-1}$. (in $s$)

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 $......... \ min$.

Which one of the following formulas represents a first-order reaction?

Hydrolysis of methyl acetate in aqueous solution has been studied by titrating the liberated acetic acid against sodium hydroxide. The concentration of the ester at different times is given below:

Time $(t)$ $\text{min}$	$0$	$30$	$60$	$90$
Conc. of ester $(C)$ $\text{mol L}^{-1}$	$0.850$	$0.800$	$0.754$	$0.710$

Show that it follows a pseudo first-order reaction as the concentration of $H_2O$ remains nearly constant $(54.2 \text{ mol L}^{-1})$ during the course of the reaction. What is the value of $k'$ in this reaction?

Which of the following plots is(are) correct for the given reaction? $( [P]_0$ is the initial concentration of $P$ $)$

$A$ reaction which is of first order with respect to reactant $A$,has a rate constant $6 \, min^{-1}$. If we start with $[A] = 0.5 \, mol \, L^{-1}$,when would $[A]$ reach the value of $0.05 \, mol \, L^{-1}$?