Water in a container at $290 \mathrm{~K}$ is exposed to air containing $3 \% ~ \mathrm{CO}_2$ by volume. Air behaves like an ideal gas and is maintained at $100 ~ \mathrm{kPa}$ pressure. The liquid phase comprising of dissolved $\mathrm{CO}_2$ in water behaves like an ideal solution. Use Henry's constant of $\mathrm{CO}_2$ dissolved in water at $290 \mathrm{~K}$ as $12 ~\mathrm{MPa}$. Under equilibrium conditions, which one of the following is the $\text{CORRECT}$ value of the mole fraction of $\mathrm{CO}_2$ dissolved in water?
- $2.9 \times 10^{-4}$
- $0.9 \times 10^{-4}$
- $2.5 \times 10^{-4}$
- $0.5 \times 10^{-4}$