The half-life of a first-order reaction $X \longrightarrow Y + Z$ is $3 \ minutes$. What is the time required to reduce the concentration of $X$ by $90 \%$ of its initial concentration?

$A$ first-order reaction takes $10 \ hours$ to complete $90\%$ of the reaction. How much time will it take to complete $99.9\%$ of the reaction (in $hours$)?

Calculate the rate constant for the first order reaction,$A \rightarrow B$ if the rate of reaction is $5.4 \times 10^{-6} \ mol \ dm^{-3} \ s^{-1}$ and $[A]=0.3 \ M$.

$A$ reaction that is of the first order with respect to reactant $A$ has a rate constant $6 \ min^{-1}$. If we start with $[A] = 0.5 \ mol \ L^{-1}$,when would $[A]$ reach the value $0.05 \ mol \ L^{-1}$? (in $min$)

For a first-order reaction $A \rightarrow \text{product}$, the rate constant is $k = 2 \times 10^{-2} \text{ s}^{-1}$. If the initial concentration of $A$ is $[A]_0 = 1.0 \text{ mol dm}^{-3}$, find the value of $\log \frac{1}{[A]_t}$ after $t = 100 \text{ s}$.

$75\%$ of a first order reaction was completed in $32$ minutes. When was $50\%$ of the reaction completed? ......... $\min$