In a first order reaction,$60 \%$ of the reactant decomposes in $4.606 \ min$. What is the half-life of the reaction (in $min$)? (Given: $k = 0.1989 \ min^{-1}$)

Calculate the rate constant of the first order reaction if $20 \%$ of the reactant decomposes in $15 \ minutes$.

What is the half-life of a first-order reaction if the time required to decrease the concentration of the reactant from $0.8 \text{ M}$ to $0.2 \text{ M}$ is $12 \text{ hours}$ (in $\text{ hours}$)?

Calculate the rate constant of a first-order reaction $A \rightarrow B$ having a rate of $5.4 \times 10^{-6} \text{ mol dm}^{-3} \text{ s}^{-1}$ and concentration $[A] = 0.3 \text{ M}$.

The following is a first-order reaction:
$N_2O_5 \text{ (solution)} \rightarrow 2 NO_2 \text{ (solution)} + \frac{1}{2} O_2 \text{ (g)}$
In this reaction,$CCl_4$ is the solvent. The rate constant is $k = 5.0 \times 10^{-4} \ s^{-1}$. The initial concentration of $N_2O_5$ is $0.25 \ mol \ L^{-1}$.
$(i)$ What will be the initial rate of reaction?
$(ii)$ Calculate the half-life $(t_{1/2})$.
$(iii)$ How much time is required to complete $75\%$ of the reaction?
$(iv)$ Calculate the concentration of $N_2O_5$ and $NO_2$ after $30 \ min$.

Half life of a first order reaction is $3 \ minute$. What is the time required to reduce the concentration of reactant by $90 \%$ of its initial concentration?