The half-life of a first-order reaction is $10 \ min$. If the initial concentration is $0.08 \ mol \ L^{-1}$ and the concentration at some instant is $0.01 \ mol \ L^{-1}$,then $t =$ ........... $\min$.

$A$ first-order reaction takes $30$ minutes for $75\%$ decomposition. Calculate its rate constant. (in $\text{ min}^{-1}$)

In a first order reaction,the concentration of the reactant is reduced to $1/8$ of the initial concentration in $75 \ minutes$. The $t_{1/2}$ of the reaction (in minutes) is $(\log 2 = 0.30, \log 3 = 0.47, \log 4 = 0.60)$.

Drug $X$ becomes ineffective after $50 \%$ decomposition. The original concentration of drug in a bottle was $16 \ mg/mL$ which becomes $4 \ mg/mL$ in $12 \ months$. The expiry time of the drug in months is $..........$ Assume that the decomposition of the drug follows first order kinetics.

$75\%$ of a first order reaction is completed in $30 \ min$. What is the time required for $93.75\%$ of the reaction (in minutes)?

Time required to decompose $SO_{2}Cl_{2}$ to half of its initial amount is $60 \ minutes$. If the decomposition is a first order reaction,calculate the rate constant of the reaction.