Question #44084

A $1.0\text{ L}$ aqueous solution of a weak acid salt $\ce{HACl}$ (initial concentration $= \sqrt{2} \times 10^{-7}\text{ M}$) is kept in a closed vessel of total volume $2.0\text{ L}$ at $300\text{ K}$. The cation $\ce{HA+}$ dissociates according to the following equilibrium: $\ce{HA+(aq) <=> H+(aq) + A(g)}$ At equilibrium, the pH of the solution is found to be $7 - \frac{1}{2} \log 2$. Assuming the gas $\ce{A}$ is completely insoluble in water and behaves ideally, calculate the thermodynamic equilibrium constant $K$ for the reaction. (Given: $K_w = 1.0 \times 10^{-14}$ at $300\text{ K}$, $R = 0.08\text{ L atm K}^{-1}\text{ mol}^{-1}$. Standard states: $1\text{ M}$ for aqueous species, $1\text{ atm}$ for gases.)