The half-life for the reaction $N_2O_5 \rightleftharpoons 2NO_2 + \frac{1}{2}O_2$ is $24 \ hr$ at $30 \ ^\circ C$. Starting with $10 \ g$ of $N_2O_5$,how many grams of $N_2O_5$ will remain after a period of $96 \ hr$?

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?

Calculate the rate constant of a first-order reaction having a half-life of $1 \text{ minute } 40 \text{ seconds}$.

What is the rate constant of a first-order reaction if $60 \%$ of the reactant decomposes in $45 \ minutes$?

Calculate the half-life of a first-order reaction in minutes if the rate constant is $1 \times 10^{-3} \ sec^{-1}$.

In a first order reaction,if the concentration of reactant drops from $0.8 \ mol \ L^{-1}$ to $0.4 \ mol \ L^{-1}$ in $15$ minutes,what is the time required to drop the concentration from $0.1 \ mol \ L^{-1}$ to $0.025 \ mol \ L^{-1}$?