The rate constant for the oxidation of hydrogen peroxide by $KMnO_4$ is $6.93 \times 10^{-5} \ s^{-1}$. How much time will it take for the volume of a standard $KMnO_4$ solution to decrease from $20 \ mL$ to $8 \ mL$?

The rate constant for the decomposition of $H_2O_2$ is $3.66 \times 10^{-3} \ s^{-1}$. If the initial concentration of $H_2O_2$ is $0.882 \ M$,then in how many seconds will its concentration become $0.600 \ M$?

For the first order reaction $A \rightarrow B$,the half-life is $30 \ min$. The time taken for $75 \%$ completion of the reaction is $..... \ min$. (Nearest integer)
Given: $\log 2 = 0.3010, \log 3 = 0.4771, \log 5 = 0.6989$

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 $(ii)$.

$75\%$ of a first order reaction was completed in $32$ minutes. When was $50\%$ of the reaction completed? ......... $\min$

The rate constant of a reaction is $k = 3.28 \times 10^{-4} \text{ s}^{-1}$. Find the order of the reaction.