For a first order reaction,$A \to P$,$t_{1/2}$ (half-life) is $10 \ days$. The time required for $\frac{1}{4}$ conversion of $A$ (in days) is: $(\ln 2 = 0.693, \ln 3 = 1.1)$.

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

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

$t_{87.5}$ is the time required for the reaction to undergo $87.5 \%$ completion and $t_{50}$ is the time required for the reaction to undergo $50 \%$ completion. The relation between $t_{87.5}$ and $t_{50}$ for a first order reaction is $t_{87.5} = x \times t_{50}$. The value of $x$ is $......$. (Nearest integer)

Time required for $99.9 \%$ completion of a first order reaction is . . . . . . . times the time required for completion of $90 \%$ reaction. (nearest integer).

$A$ $20 \%$ first-order reaction is completed in $32 \ \text{min}$. How much time (in $\text{min}$) will it take for $60 \%$ of the reaction to be completed (in $.00$)?