Question #44529

A multimeric globular protein ($M_w = 2.56 \times 10^5 \text{ g/mol}$) consists of 8 identical non-covalently linked subunits. At low concentrations, it exists entirely in its native folded octameric state. However, when $256 \text{ g}$ of this protein is dissolved in $900 \text{ g}$ of water at $298 \text{ K}$, the high concentration induces complete denaturation. The protein fully dissociates into its 8 unfolded monomeric peptide chains. Furthermore, due to the exposure of previously buried hydrophobic and hydrophilic residues, each unfolded monomeric chain strongly binds $250$ molecules of water in its primary hydration shell, effectively removing them from the bulk solvent (these bound water molecules do not contribute to the vapor pressure). Given that the vapor pressure of pure water at $298 \text{ K}$ is $24.00 \text{ Torr}$, calculate the vapor pressure lowering ($\Delta P$) of this solution. (Assume the unfolded chains act as ideal independent kinetic particles and the molar mass of water is $18.0 \text{ g/mol}$).