$N_2O_5$ decomposes to $NO_2$ and $O_2$ and follows first order kinetics. After $50 \, min$,the pressure inside the vessel increases from $50 \, mm \, Hg$ to $87.5 \, mm \, Hg$. The pressure of the gaseous mixture after $100 \, min$ at constant temperature will be ........... $mm \, Hg$

For a first order reaction,the velocity constant is $K = 10^{-3} \ s^{-1}$. The two-third life for it would be ........... $s$.

Which among the following represents the expression for the $\left(\frac{3}{4}\right)^{\text{th}}$ life of a $1^{\text{st}}$ order reaction?

For a first order reaction,the half-life period is

Consider the following first order gas phase reaction at constant temperature:
$A_{(g)} \rightarrow 2B_{(g)} + C_{(g)}$
If the total pressure of the gases is found to be $200 \ torr$ after $23 \ s$ and $300 \ torr$ upon the complete decomposition of $A$ after a very long time,then the rate constant of the given reaction is . . . . . . $\times 10^{-2} \ s^{-1}$ (nearest integer).
[Given: $\log_{10}(2) = 0.301$]

For a first-order reaction,the time required for $93.75\%$ completion is $4$ times the half-life of the reaction. What is the relationship between the time required for $93.75\%$ completion and the half-life $(t_{0.5})$?