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

$A$ first order reaction has a rate constant of $5.78 \times 10^{-5} \ s^{-1}$. What fraction of the reactant will remain after $10 \ hours$?

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 $(ii)$.

For a first order reaction,to obtain a positive slope,we need to plot $...$ where $[A]$ is the concentration of reactant $A$.

The rate of a first-order reaction is $0.04 \ mol \ L^{-1} \ s^{-1}$ at $10 \ minutes$ and $0.03 \ mol \ L^{-1} \ s^{-1}$ at $20 \ minutes$ after initiation. The half-life of the reaction is . . . . . . minutes. (Given $\log 2 = 0.3010, \log 3 = 0.4771$)

The reaction $2A \rightarrow \text{Product}$ follows first-order kinetics. If the initial concentration $[A]_0 = 0.2 \ mol \ L^{-1}$ and the half-life period $t_{1/2} = 20 \ min$,calculate the rate constant $k$.