Question #44712

A closed vessel of total volume $2.0\text{ L}$ contains $1.0\text{ L}$ of an aqueous solution of a reactive substrate \ce{S} at an initial concentration of $10.0\text{ M}$. The remaining $1.0\text{ L}$ is filled with a reactive gas \ce{G} at an initial partial pressure of $2.0\text{ atm}$. The gas \ce{G} dissolves in the aqueous phase and reacts with \ce{S} according to the elementary bimolecular reaction: $\ce{G(aq) + S(aq) -> Products}$ Given:

• Rate constant $k = 0.1\text{ L mol}^{-1}\text{ min}^{-1}$.
• Henry's law constant for \ce{G} in water is $K_H = 5.55 \times 10^3\text{ atm}$ (defined as $P_G = K_H \chi_G$, where $\chi_G$ is the mole fraction of \ce{G} in the solution).
• The dissolution of \ce{G} is rapid and maintains phase equilibrium at all times.
• The temperature is constant, and $RT = 25\text{ L atm mol}^{-1}$.
• The concentration of water is $55.5\text{ M}$ and remains constant.
• The volume of the solution remains exactly $1.0\text{ L}$.

Calculate the time required for the partial pressure of gas \ce{G} in the vessel to drop to $0.25\text{ atm}$. (Assume the concentration of \ce{S} remains effectively constant).