The rate constant of a first order reaction whose half-life is $480 \ s$,is

$A$ reaction has a half-life of $1 \, \text{min}$. The time required for $99.9 \, \%$ completion of the reaction is ......... $\text{min}$. (Round off to the nearest integer)
[Use: $\ln 2 = 0.69, \ln 10 = 2.3$]

In a first order reaction, $20 \text{ mmol}$ of reactant is reduced to $10 \text{ mmol}$ in $0.3010 \text{ min}$. Find the rate constant of the reaction. (in $\text{ min}^{-1}$)

What is the value of the rate constant for a first-order reaction,if it takes $15 \ min$ for the consumption of $20 \%$ of the reactants?

The decomposition reaction $2N_2O_{5(g)} \xrightarrow{\Delta} 2N_2O_{4(g)} + O_{2(g)}$ is started in a closed cylinder under isothermal isochoric conditions at an initial pressure of $1 \ atm$. After $Y \times 10^3 \ s$,the pressure inside the cylinder is found to be $1.45 \ atm$. If the rate constant of the reaction is $5 \times 10^{-4} \ s^{-1}$,assuming ideal gas behavior,the value of $Y$ is. . . . . . . .

What is the rate constant of a first-order reaction if the time required to decrease the concentration of the reactant from $1.6 \ M$ to $0.4 \ M$ is $12 \ hours$?