$A$ flask contains a mixture of compounds $A$ and $B.$ Both compounds decompose by first-order kinetics. The half-lives for $A$ and $B$ are $300 \ s$ and $180 \ s,$ respectively. If the concentrations of $A$ and $B$ are equal initially,the time required for the concentration of $A$ to be four times that of $B$ (in $s$): (Use $\ln 2 = 0.693$)

Dissociation of $N_2O_5$ dissolved in $CCl_4$ at constant temperature: $N_2O_{5(soln)} \to 2NO_{2(soln)} + \frac{1}{2}O_{2(g)}$. This is a first order reaction. The velocity constant is $5.0 \times 10^{-4} \ s^{-1}$. The initial concentration of $N_2O_5$ is $0.25 \ mol \ L^{-1}$. How much time is required to produce $0.20 \ mol \ L^{-1}$ concentration of $NO_2$ (in $s$)?

In a first order reaction,the concentration of the reactant decreases from $0.6 \ M$ to $0.3 \ M$ in $15 \ min$. The time taken for the concentration to change from $0.1 \ M$ to $0.025 \ M$ in minutes is

For the first order reaction with rate constant $k$,which expression gives the half-life period? (Initial concentration $= a$)

The value of rate constant for a first order reaction is $2.303 \times 10^{-2} \text{ s}^{-1}$. What will be the time required to reduce the concentration to $\frac{1}{10}$th of its initial concentration (in $\text{ s}$)?

$A$ first order reaction is half completed in $45 \, \text{minutes}$. How long does it need for $99.9 \%$ of the reaction to be completed? (in $hr$)