What is the half-life of a first-order reaction if the time required to decrease the concentration of the reactant from $0.4 \ M$ to $0.1 \ M$ is $x \ \text{hours}$?

The experimental data for decomposition of $N_2O_5$ in the gas phase at $318 \, K$ are given below:

$t/s$	$0$	$400$	$800$	$1200$	$1600$	$2000$	$2400$	$2800$	$3200$
$10^2 \times [N_2O_5] / mol \, L^{-1}$	$1.63$	$1.36$	$1.14$	$0.93$	$0.78$	$0.64$	$0.53$	$0.43$	$0.35$

$(i)$ Plot $[N_2O_5]$ against $t$.
$(ii)$ Find the half-life period for the reaction.
$(iii)$ Draw a graph between $\log[N_2O_5]$ and $t$.
$(iv)$ What is the rate law?
$(v)$ Calculate the rate constant.
$(vi)$ Calculate the half-life period from $k$ and compare it with $(ii)$.

The ratio of $t_{0.75}$ and $t_{0.5}$ for a first-order reaction is:

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 $.1$)

The half-life period for a first-order reaction is . . . . . . .

For the first order reaction with rate constant $k$,which expression gives the half-life period? (Initial concentration $= a$)