The decay constant of a first-order reaction is $1.1 \times 10^{-9} \ s^{-1}$. Calculate the half-life of the reaction.

In a first order reaction,the concentration of the reactant decreases from $20 \ mmol \ dm^{-3}$ to $8 \ mmol \ dm^{-3}$ in $40 \ minute$. Find the rate constant of the reaction.

The rate of a first-order reaction is $1.5 \times 10^{-2} \, mol \, L^{-1} \, min^{-1}$ when the concentration of the reactant is $0.5 \, M$. Find the half-life $(t_{1/2})$ of the reaction in $min$.

The rate constant for a first order reaction is $60 \ s^{-1}$. How much time will it take to reduce the initial concentration of the reactant to its $1/16^{th}$ value?

For a homogeneous gaseous reaction $A_{(g)} \to 3B_{(g)}$,if the pressure after time $t$ is $P_t$ and after completion of the reaction the pressure is $P_\infty$,select the correct relation for the rate constant $K$.

The half-life of a first-order reaction $X \longrightarrow Y + Z$ is $3 \ minutes$. What is the time required to reduce the concentration of $X$ by $90 \%$ of its initial concentration?