The half-life of a first-order reaction is $2000$ years. If the concentration after $8000$ years is $0.02 \, M$,then the initial concentration was $........... \, M$.

The half-life of a first-order reaction is $900 \text{ s}$. If the initial concentration of the reactant is $0.08 \text{ mol dm}^{-3}$, find the concentration that remains after $35 \text{ minutes}$?

$A$ first order reaction is half completed in $45 \, \text{minutes}$. How long does it need for $99.9 \%$ of the reaction to be completed? (in $hr$)

For the first order reaction $2 N_2O_{5(g)} \rightarrow 4 NO_{2(g)} + O_{2(g)}$,which of the following statements are correct?
$A.$ The concentration of the reactant decreases exponentially with time.
$B.$ The half-life of the reaction decreases with increasing temperature.
$C.$ The half-life of the reaction depends on the initial concentration of the reactant.
$D.$ The reaction proceeds to $99.6 \%$ completion in eight half-life durations.

In a first order reaction,the concentration of the reactant is reduced from $0.6 \ mol \ L^{-1}$ to $0.2 \ mol \ L^{-1}$ in $5 \ min$. What is the rate constant of the reaction (in $min^{-1}$)? $(\log 3 = 0.4771)$

If a $99\%$ first-order reaction is completed in $32$ minutes,how many minutes will it take for $99.9\%$ of the reaction to be completed?