In a first order reaction,the concentration of the reactant decreased from $0.4 \, M$ to $0.1 \, M$ in $20 \, \min$. The rate constant of the reaction will be:

If a $75\%$ first-order reaction is completed in $32 \text{ minutes}$,how many minutes will it take for the same reaction to be $50\%$ completed?

$75\%$ of a first-order reaction was completed in $32 \text{ minutes}$. When was $50\%$ of the reaction completed? (in $\text{minutes}$)

Identify True $(T)$ and False $(F)$ statements of the following for a first-order reaction $R \rightarrow P$.
Statement $I$: $k = \frac{1}{(t_1 - t_2)} \ln \frac{[R]_1}{[R]_2}$
Statement $II$: $k = -\frac{1}{(t_1 - t_2)} \ln \frac{[R]_2}{[R]_1}$

Catalytic decomposition of hydrogen peroxide is a ........ order reaction.

The rate constant of a first-order reaction is $6 \ min^{-1}$. If the initial concentration of the reactant is $0.5 \ mol \ L^{-1}$,after how many minutes will the concentration of the reactant become $0.05 \ mol \ L^{-1}$?