For a first-order reaction, if the initial concentration $[A]_0 = 1.0 \text{ M}$ and the concentration after time $t = 276 \text{ s}$ is $[A]_t = 0.25 \text{ M}$, find the value of the rate constant $(k)$. (in $\text{ s}^{-1}$)

In a first-order reaction,the concentration of the reactant decreases from $1.0 \, M$ to $0.25 \, M$ in $20 \, \text{minutes}$. What will be the rate constant of the reaction?

Calculate the time in seconds required to reduce the concentration of reactant to half of initial concentration for a first order reaction if the rate constant is $1.386 \times 10^{-3} \ s^{-1}$. (in $s$)

$A$ first-order reaction takes $10 \ hours$ to complete $90\%$ of the reaction. How much time will it take to complete $99.9\%$ of the reaction (in $hours$)?

What is the rate constant of a first-order reaction if $60 \%$ of the reactant decomposes in $45 \ minutes$?

$A$ molecule undergoes two independent first order reactions whose respective half-lives are $12 \ min$ and $3 \ min$. If both the reactions are occurring simultaneously,the time taken for the $50 \%$ consumption of the reactant is $.......... \ min$ (Nearest integer).