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.

At $30^{\circ}C$,the half-life for the decomposition of $AB_{2}$ is $200\,s$ and is independent of the initial concentration of $AB_{2}$. The time required for $80\%$ of the $AB_{2}$ to decompose is $....s$ (Given: $\log 2 = 0.30; \log 5 = 0.70$)

$A$ flask is filled with equal moles of $A$ and $B$. The half-lives of $A$ and $B$ are $100 \, s$ and $50 \, s$ respectively and are independent of the initial concentration. The time required for the concentration of $A$ to be four times that of $B$ is $.... \, s.$
(Given : $\ln 2 = 0.693$ )

$A$ first order reaction has a specific reaction rate of $10^{-2} \ sec^{-1}.$ How much time will it take for $20 \ g$ of the reactant to reduce to $5 \ g?$ ........ $sec$

What is the time needed to reduce the initial concentration of reactant to $10 \%$ in a first order reaction if its half life time is $10 \ minute$?

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