Question #44973

A $100 \text{ mL}$ aqueous buffer solution at $298 \text{ K}$ ($\text{pH} = 5.0$) contains $1.65 \text{ mmol}$ of a native globular protein non-covalently bound to its prosthetic group, Vitamin C (Ascorbic acid, a monoprotic weak acid with $\text{p}K_a = 4.0$). To study the prosthetic group, $50 \text{ mL}$ of an immiscible organic solvent (1-octanol) is added, and the mixture is vigorously shaken. The low dielectric constant of 1-octanol disrupts the hydrophobic core of the protein, causing complete denaturation and precipitation at the interface, quantitatively releasing the Vitamin C. The released Vitamin C partitions between the aqueous and organic phases. Only the unionized form of Vitamin C ($\ce{HA}$) is soluble in the organic phase, with a distribution coefficient $K_D = \frac{[\ce{HA}]_{org}}{[\ce{HA}]_{aq}} = 11.0$. Assuming the pH of the aqueous phase remains constant and the volumes are strictly additive, what is the total concentration of Vitamin C (in all its forms) remaining in the aqueous phase at equilibrium?