The rate constant for a first-order reaction is $0.02232 \ min^{-1}$. Calculate the time required for $75 \%$ completion of the reaction. (in $min$)

For the reaction $2A + B \to \text{product}$,the rate law is given by $\frac{-d[A]}{dt} = k[A]$. At a time $t = \frac{t_{1/2}}{\ln 2}$,what is the concentration of the reactant $A$?

In a first order reaction,$60 \%$ of the reactant converts into product in $45 \ minutes$. Calculate the rate constant of the reaction.

$A$ first order reaction has a rate constant of $5.78 \times 10^{-5} \ s^{-1}$. What fraction of the reactant will remain after $10 \ hours$?

$A$ first-order reaction takes $16 \text{ minutes}$ for its $50\%$ completion. What fraction of the reactant would react in $32 \text{ minutes}$ from the beginning?

In a reaction $A + B \rightarrow C$,initial concentrations of $A$ and $B$ are related as $[A]_0 = 8[B]_0$. The half-lives of $A$ and $B$ are $10 \ min$ and $40 \ min$,respectively. If they start to disappear at the same time,both following first-order kinetics,after how much time will the concentration of both the reactants be the same (in $min$)?