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 $(t_{0.5})$?

The rate constant for a first order reaction is $4.606 \times 10^{-3} \ s^{-1}$. The time required to reduce $2.0 \ g$ of the reactant to $0.2 \ g$ is......... $s$

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

The decomposition reaction $2N_2O_{5(g)} \xrightarrow{\Delta} 2N_2O_{4(g)} + O_{2(g)}$ is started in a closed cylinder under isothermal isochoric conditions at an initial pressure of $1 \ atm$. After $Y \times 10^3 \ s$,the pressure inside the cylinder is found to be $1.45 \ atm$. If the rate constant of the reaction is $5 \times 10^{-4} \ s^{-1}$,assuming ideal gas behavior,the value of $Y$ is. . . . . . . .

$N_2O_5$ 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 ........... $mm \, Hg$

$A$ first-order reaction takes $16 \text{ minutes}$ for its $50\%$ completion. What fraction of the reactant would react in $32 \text{ minutes}$ from the beginning?