For a first-order reaction $A \to B$,the rate of reaction at a reactant concentration of $0.01 \, M$ is $2.0 \times 10^{-5} \, mol \, L^{-1} \, s^{-1}$. The half-life period of the reaction is .... $s$.

$A$ first order reaction has the rate constant,$k = 4.6 \times 10^{-3} \ s^{-1}$. The number of correct statement/s from the following is/are
Given : $\log 3 = 0.48$
$A.$ Reaction completes in $1000 \ s$.
$B.$ The reaction has a half-life of $500 \ s$.
$C.$ The time required for $10 \ \%$ completion is $25$ times the time required for $90 \ \%$ completion.
$D.$ The degree of dissociation is equal to $(1 - e^{-kt})$.
$E.$ The rate and the rate constant have the same unit.

For a first-order reaction,the concentration of the reactant decreases from $0.8 \, M$ to $0.4 \, M$ in $15 \, \text{minutes}$. The time required for the concentration to change from $0.1 \, M$ to $0.025 \, M$ is ....... $\text{min}$.

The first order reaction takes $20 \ min$ to complete $15\%$. How much time is required to complete $75\%$ of the reaction (in $min$)?

If the concentration unit decreases by a factor of $n$,what will be the value of the rate constant for a first-order reaction?

Calculate the half-life of the first-order reaction $C_2H_4O_{(g)} \to CH_{4(g)} + CO_{(g)}$ if the initial pressure of $C_2H_4O_{(g)}$ is $80 \ mm$ and the total pressure at the end of $20 \ minutes$ is $120 \ mm$. (in $min$)