Find the time period of a $1^{st}$ order reaction when the reaction is $\frac{2}{3} ^{rd}$ complete. If the value of the rate constant is $4.3 \times 10^{-4} \, s^{-1}$.

For which of the following graphs is the intersection (y-intercept) zero?

$A \rightarrow P$ is a first order reaction. At $300 \ K$,this reaction was started with $[A] = 0.5 \ mol \ L^{-1}$. The rate constant of the reaction was $0.125 \ min^{-1}$. The same reaction was started separately with $[A] = 1 \ mol \ L^{-1}$ at $300 \ K$. The rate constant (in $min^{-1}$) now is:

The rate constant for a first order reaction is $20 \, min^{-1}$. The time required for the initial concentration of the reactant to reduce to its $\frac{1}{32}$ level is $........ \times 10^{-2} \, min$. (Nearest integer) (Given: $\ln 10 = 2.303, \log 2 = 0.3010$)

For a first order reaction, the half-life is $5 \text{ hour}$. What time is required to reduce $10 \text{ g}$ of reactant to $2.5 \text{ g}$ (in $\text{ hour}$)?

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 $10 \ minute$?