The rate of a first-order reaction is $0.04 \ mol \ L^{-1} \ s^{-1}$ at $10 \ s$ and $0.03 \ mol \ L^{-1} \ s^{-1}$ at $20 \ s$ after the initiation of the reaction. The half-life period of the reaction is ......... $s$. (in $.1$)

What is the time needed to reduce the initial concentration of reactant to $10 \%$ in a first order reaction if its half life time is $10 \ minute$?

Reaction $A_{(g)} \rightarrow 2B_{(g)} + C_{(g)}$ is a first order reaction. It was started with pure $A$.

$t/min$	Pressure of system at time $t/mm \ Hg$
$10$	$160$
$\infty$	$240$

Which of the following option is incorrect?

For the thermal decomposition of $N_2O_{5(g)}$ at constant volume,the following table can be formed for the reaction mentioned below:
$2N_2O_{5(g)} \rightarrow 2N_2O_{4(g)} + O_{2(g)}$

$S.NO$	$Time/s$	Total pressure $(atm)$
$1.$	$0$	$0.6$
$2.$	$100$	$X$

$X = . . . . . . \times 10^{-3} \ atm$ [nearest integer]
Given: Rate constant for the reaction is $4.606 \times 10^{-2} \ s^{-1}$.

$A$ first-order reaction starts with a decimolar solution of the reactant. After $8$ minutes,its concentration becomes $M/100$. Calculate the rate constant of the reaction.

The half-life period of a first-order reaction is given by: