What is the half-life of a first-order reaction if the time required to decrease the concentration of the reactant from $0.8 \ mol \ dm^{-3}$ to $0.2 \ mol \ dm^{-3}$ is $12 \ hour$ (in $hour$)?

Two first order reactions have half-lives in the ratio $3 : 2$. Calculate the ratio of time intervals $t_1 : t_2$ if $t_1$ is the time period for $25\%$ completion of the first reaction and $t_2$ for $75\%$ completion of the second reaction. (in $: 1$)

For a first order reaction,the concentration of reactant was reduced from $0.03 \ mol \ L^{-1}$ to $0.02 \ mol \ L^{-1}$ in $25 \ min$. What is its rate (in $mol \ L^{-1} \ s^{-1}$)?

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.

$A$ reactant undergoes $90\%$ decomposition in $366 \text{ minutes}$. What is the half-life of this first-order reaction?

The rate constant $k = 2.303 \ min^{-1}$ for a particular reaction,and the initial concentration of the reactant is $1 \ mol/L$. What is the rate of reaction after $1 \ minute$?