If a $99\%$ first-order reaction is completed in $32$ minutes,how many minutes will it take for $99.9\%$ of the reaction to be completed?

At $500\,^oC$,cyclopropane isomerizes to propene. This reaction is first order with a rate constant of $6.7 \times 10^{-4}\,s^{-1}$. If the initial concentration of cyclopropane is $0.05\, M$,what will be the molarity of cyclopropane after $30\, min$ (in $, M$)?

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?

In a first-order reaction,the rate constant $k = 70 \, s^{-1}$. How much time is required for the concentration to become $\frac{1}{18}$ of the initial concentration (in $, s$)?

Consider the two different first order reactions given below:
$A + B \rightarrow C$ (Reaction $1$)
$P \rightarrow Q$ (Reaction $2$)
The ratio of the half-life of Reaction $1$ : Reaction $2$ is $5 : 2$. If $t_1$ and $t_2$ represent the time taken to complete $2/3$ and $4/5$ of Reaction $1$ and Reaction $2$,respectively,then the value of the ratio $t_1 : t_2$ is $. . . . \times 10^{-1}$ (nearest integer).
[Given: $\log_{10}(3) = 0.477$ and $\log_{10}(5) = 0.699$]

Half-life and rate constant for a first-order reaction are related by the equation: