Which one of the following formulas represents a first-order reaction?

The decomposition of substance $A$ in a solution follows first-order kinetics. Vessel-$I$ contains $1 \ L$ of $1 \ M$ solution of $A$. Vessel-$II$ contains $100 \ mL$ of $0.6 \ M$ solution of $A$. If the concentration of $A$ in Vessel-$I$ becomes $0.25 \ M$ in $8 \ hr$,then the time required for the concentration of $A$ in Vessel-$II$ to become $0.3 \ M$ is ......... $hr$.

Calculate the half-life of the first-order reaction $C_2H_4O_{(g)} \to CH_{4(g)} + CO_{(g)}$. If the initial pressure of $C_2H_4O_{(g)}$ is $80 \ mm$ and the total pressure at the end of $20 \ minutes$ is $120 \ mm$,find the half-life in $\text{min}$.

In a first order reaction, $20 \text{ mmol}$ of reactant is reduced to $10 \text{ mmol}$ in $0.3010 \text{ min}$. Find the rate constant of the reaction. (in $\text{ min}^{-1}$)

The value of rate constant for a first order reaction is $2.303 \times 10^{-2} \text{ s}^{-1}$. What will be the time required to reduce the concentration to $\frac{1}{10}$th of its initial concentration (in $\text{ s}$)?

In a first order reaction,the concentration of the reactant is reduced to $25\%$ in one hour. The half-life period of the reaction is: (in $hr$)