For a first order reaction $A \to \text{products}$,the concentration of $[A]$ is reduced from $2 \ M$ to $0.125 \ M$ in one hour. The $t_{1/2}$ of this reaction (in $\text{min}$) is:

The rate constant of the reaction $2H_2O_{2(aq)} \to 2H_2O_{(l)} + O_{2(g)}$ is $3 \times 10^{-3} \ min^{-1}$. At what concentration of $H_2O_2$,the rate of reaction will be $2 \times 10^{-4} \ M \ s^{-1}$? ............ $M$

For a reaction,$r = k[A]$. If $50 \%$ of $A$ is decomposed in $120 \ \text{minutes}$,the time taken for $90 \%$ decomposition of $A$ is $............ \ \text{minutes}$.

The reaction $N_{2}O_{5} \longrightarrow 2NO_{2} + \frac{1}{2}O_{2}$ is first order in $N_{2}O_{5}$ having rate constant $6.2 \times 10^{-4} \ s^{-1}$. What is the value of rate of reaction when concentration of $N_{2}O_{5}$ is $1.25 \ mol \ L^{-1}$?

Which of the following is the slope of the graph of rate versus concentration of the reactant for a first-order reaction?

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 $(ii)$.