In a first order reaction,$60 \%$ of the reactant decomposes in $4.606 \ min$. What is the half-life of the reaction (in $min$)? (Given: $k = 0.1989 \ min^{-1}$)

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 $(ii)$.

For a first-order reaction,the half-life period is $69.3 \ s$. If the concentration of the reactant is $0.10 \ mol \ L^{-1}$,what will be the rate of the reaction?

For the first order reaction,half life is $14 \, sec$. The time required for the initial concentration to reduce to $\frac{1}{8}$ of its value is .......... $sec$.

The half-life period of a first order reaction is $100 \, \text{sec}$. The rate constant of the reaction is

The first order rate constant for the decomposition of $N_2O_5$ is $6.2 \times 10^{-4} \ s^{-1}$. The half-life period for this decomposition in seconds is: