For a first-order reaction,the concentration decreases from $800 \ mol/dm^3$ to $50 \ mol/dm^3$ in $2 \times 10^4 \ s$. What is the rate constant of the reaction?

The initial concentration of $N_2O_5$ in the following first order reaction $N_2O_{5(g)} \rightarrow 2NO_{2(g)} + 1/2O_{2(g)}$ was $1.24 \times 10^{-2} \, mol \, L^{-1}$ at $318 \, K$. The concentration of $N_2O_5$ after $60 \, minutes$ was $0.20 \times 10^{-2} \, mol \, L^{-1}$. Calculate the rate constant of the reaction at $318 \, K$.

What is the half-life of a first-order reaction if the time required to decrease the concentration of the reactant from $0.8 \ mol \ dm^{-3}$ to $0.2 \ mol \ dm^{-3}$ is $12 \ hour$ (in $hour$)?

For the first-order reaction $2N_2O_{5(g)} \rightarrow 4NO_{2(g)} + O_{2(g)}$,which of the following statements is incorrect?

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

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?