For a first order reaction,the rate constant is $0.6932 \ hr^{-1}$,then the half-life for the reaction is ......... $hr$.

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

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?

The reaction $A \to B$ follows first order kinetics. The time taken for $0.8 \ mol$ of $A$ to produce $0.6 \ mol$ of $B$ is $1 \ hr$. What is the time taken for the conversion of $0.9 \ mol$ of $A$ to produce $0.675 \ mol$ of $B$?

For a first-order reaction at $25\,^oC$,the half-life period is $248\,s$. What is the value of the rate constant at this temperature?

For the reaction ${N_2}{O_{5(g)}} \to 2N{O_{2(g)}} + \frac{1}{2}{O_{2(g)}}$,the rate constant is $2.3 \times 10^{-2} \ s^{-1}$. Which of the following equations represents the variation of $[{N_2}{O_5}]$ with time?