The rate constant of a first-order reaction is $6 \ min^{-1}$. If the initial concentration of the reactant is $0.5 \ mol \ L^{-1}$,after how many minutes will the concentration of the reactant become $0.05 \ mol \ L^{-1}$?

For an elementary reaction,$X_{(g)} \rightarrow Y_{(g)} + Z_{(g)}$,the $t_{1/2}$ is $10 \text{ minutes}$. In what period of time would the concentration of $X$ be reduced to $10 \%$ of its original concentration?

For a first-order reaction,it takes $20 \, \text{min}$ for the concentration to decrease from $1 \, M$ to $0.6 \, M$. How much time is required for the concentration to decrease from $0.6 \, M$ to $0.36 \, M$?

For a first-order reaction,the concentration of the reactant decreases from $0.8 \, M$ to $0.4 \, M$ in $15 \, \text{minutes}$. The time required for the concentration to change from $0.1 \, M$ to $0.025 \, M$ is ....... $\text{min}$.

The first order reaction $A_{(g)} \rightarrow B_{(g)} + 2C_{(g)}$ occurs at $25^{\circ} C$. After $24 \ min$,the ratio of the concentration of products to the concentration of the reactant is $1:3$. What is the half-life of the reaction (in $min$)? $(\log 1.11 = 0.046)$

The half-life of a first-order reaction is