The reaction $2A \rightarrow \text{Product}$ follows first-order kinetics. If the initial concentration $[A]_0 = 0.2 \ mol \ L^{-1}$ and the half-life period $t_{1/2} = 20 \ min$,calculate the rate constant $k$.

Decomposition of nitrogen pentoxide is known to be a first order reaction. $75\%$ of the oxide had decomposed in the first $24 \ minutes$. At the end of an hour,after the start of the reaction,the amount of oxide left will be

$A$ first order reaction is $50 \%$ completed in $16 \ minutes$. Find the percentage of reactant reacting in $32 \ minutes$. (in $\%$)

The decay constant of a first-order reaction is $1.1 \times 10^{-9} \ s^{-1}$. Calculate the half-life of the 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 $(t)$ $(\min)$	$0$	$30$	$60$	$90$
Conc. of ester $(C)$ $(M)$	$0.850$	$0.800$	$0.754$	$0.710$

Show that it follows a pseudo first order reaction as the concentration of $H_{2}O$ remains nearly constant $(55 \ mol \ L^{-1})$ during the course of the reaction. What is the value of $k^{\prime}$ in this reaction?

The slope of a graph $\log [A]_t$ versus '$t$' for a first-order reaction is $-2.5 \times 10^{-3} \,s^{-1}$. Find the rate constant of the reaction.