Calculate the half-life of the first-order reaction $C_2H_4O_{(g)} \to CH_{4(g)} + CO_{(g)}$ if the initial pressure of $C_2H_4O_{(g)}$ is $80 \ mm$ and the total pressure at the end of $20 \ minutes$ is $120 \ mm$. (in $min$)

$75\%$ of a first-order reaction was completed in $32 \text{ minutes}$. When was $50\%$ of the reaction completed? (in $\text{minutes}$)

Mathematical representation for $t_{1/4}$ life for a first-order reaction is given by:

The following data is obtained during the first-order thermal decomposition of $2A_{(g)} \longrightarrow B_{(g)} + C_{(s)}$ at constant volume and temperature. The rate constant in $min^{-1}$ is:

$S$.No.	Time	Total pressure in $Pa$
$1$.	At $t = 10 \ min$	$300$
$2$.	At $t = \infty$	$200$

The rate constant of a first-order reaction is $1.20 \times 10^{-3} \, s^{-1}$. How much time will it take for $5 \, g$ of the reactant to reduce to $3 \, g$ (in $, s$)?

$A$ flask contains a mixture of compounds $A$ and $B.$ Both compounds decompose by first-order kinetics. The half-lives for $A$ and $B$ are $300 \ s$ and $180 \ s,$ respectively. If the concentrations of $A$ and $B$ are equal initially,the time required for the concentration of $A$ to be four times that of $B$ (in $s$): (Use $\ln 2 = 0.693$)