The decomposition of $N_2O_5$ is a first order reaction represented by $N_2O_5 \to N_2O_4 + \frac{1}{2} O_2$. After $15 \ min$,the volume of $O_2$ produced is $9 \ mL$ and at the end of the reaction,it is $35 \ mL$. The rate constant is equal to:

For a first-order reaction,if $75\%$ of the reaction is completed in $15 \ min$,then the time required for $90\%$ completion of the reaction will be ........... $min$.

$A$ particular reaction has a rate constant $1.15 \times 10^{-3} \,s^{-1}$. How long does it take for $6 \,g$ of the reactant to reduce to $3 \,g$ (in $\,s$)? $(\log 2 = 0.301)$

For the first order reaction $2 N_2O_{5(g)} \rightarrow 4 NO_{2(g)} + O_{2(g)}$,which of the following statements are correct?
$A.$ The concentration of the reactant decreases exponentially with time.
$B.$ The half-life of the reaction decreases with increasing temperature.
$C.$ The half-life of the reaction depends on the initial concentration of the reactant.
$D.$ The reaction proceeds to $99.6 \%$ completion in eight half-life durations.

In a first-order reaction,the concentration of reactant $X$ decreases from $0.1 \, M$ to $0.005 \, M$ in $40 \, min$. What will be the rate of reaction when the concentration of $X$ is $0.01 \, M$?

Calculate the time in seconds required to reduce the concentration of reactant to half of initial concentration for a first order reaction if the rate constant is $1.386 \times 10^{-3} \ s^{-1}$. (in $s$)