The decomposition of dinitrogen pentoxide $(N_2O_5)$ follows first order rate law. What will be the rate constant from the given data?
At $t = 800 \ s$,$[N_2O_5] = 1.45 \ mol \ L^{-1}$
At $t = 1600 \ s$,$[N_2O_5] = 0.88 \ mol \ L^{-1}$

For a first order reaction at $27^{\circ} C$,the ratio of time required for $75 \%$ completion to $25 \%$ completion of reaction is

If the rate constant of a first-order reaction is $0.6932 \ hr^{-1}$,then its half-life period is .......... $hr$.

What is the rate constant of a first-order reaction if the time required to decrease the concentration of the reactant from $1.6 \ M$ to $0.4 \ M$ is $12 \ hours$?

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 slope of a graph $\log [A]_t$ versus '$t$' for a first-order reaction is $-2.5 \times 10^{-3} \,s^{-1}$. Find the rate constant of the reaction.