$A$ first order reaction is half completed in $45 \, \text{minutes}$. How long does it need for $99.9 \%$ of the reaction to be completed? (in $hr$)

At $500\,^oC$,cyclopropane isomerizes to propene. This reaction is first order with a rate constant of $6.7 \times 10^{-4}\,s^{-1}$. If the initial concentration of cyclopropane is $0.05\, M$,what will be the molarity of cyclopropane after $30\, min$ (in $, M$)?

The reaction $A \to B$ follows first-order kinetics. It takes $1 \ hr$ for $0.60 \ mole$ of $B$ to be formed from $0.80 \ mole$ of $A$. How much time (in $hr$) will it take for $0.675 \ mole$ of $B$ to be formed from $0.90 \ mole$ of $A$?

For the first-order isomerization reaction $A \rightarrow B$,the rate constant is $4.5 \times 10^{-3} \ min^{-1}$. If the initial concentration of $A$ is $1 \ M$,find the rate of the reaction after $1 \ hour$.

After how many seconds will the concentration of the reactant in a first order reaction be halved if the rate constant is $1.155 \times 10^{-3} \ s^{-1}$?

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 $10 \ minute$?