For a first-order reaction,the ratio of the time required for $99.9\%$ completion to the time required for $50\%$ completion is:

$N_2O_5 \rightarrow 2NO_{2(g)} + \frac{1}{2}O_{2(g)}$ is a first order reaction. $k = 5 \times 10^{-4} \ s^{-1}$. The initial concentration of $N_2O_5 = 0.2 \ mol \ L^{-1}$. After how much time will its concentration be $25 \%$ of the initial concentration (in $s$)?

For the decomposition of azomethane,$CH_3N_2CH_{3(g)} \rightarrow CH_3CH_{3(g)} + N_{2(g)}$,a first order reaction,the variation in partial pressure with time at $600 \ K$ is given as shown in the graph. The value of the rate constant $k$ in $s^{-1}$ is $x \times 10^4$. Find the value of $x$.

For the first order reaction,half life is $14 \, sec$. The time required for the initial concentration to reduce to $\frac{1}{8}$ of its value is .......... $sec$.

$A$ first order reaction takes $40 \ min$ for $30 \%$ decomposition. Calculate $t_{1/2}$.

The decomposition of $O_{3(g)}$ follows first order kinetics and is given by $O_{3(g)} \longrightarrow O_{2(g)} + O_{(g)}$. The rate constant for this reaction is $1.0 \times 10^{-3} \ s^{-1}$. The initial pressure of $O_{3(g)}$ is $100 \ atm$. What will be the partial pressure (in $atm$) of $O_3, O_2, O$ respectively after $38.38 \ minutes$?