Question #44721

A $40 \text{ g L}^{-1}$ aqueous solution of a monomeric globular peptide ($M = 5,000 \text{ g mol}^{-1}$) is subjected to purification via Reverse Osmosis (RO) at $298 \text{ K}$. In its native state, the peptide behaves as an ideal solute. However, under the extreme hydraulic pressure at the RO membrane surface, the peptide undergoes localized denaturation. While the rigid planarity of the peptide bonds ($\omega \approx 180^\circ$) is preserved, the unfolding exposes hydrophobic residues, causing the peptide to quantitatively aggregate into stable pentamers. Furthermore, the extended conformation of the denatured chains interacts non-ideally with the solvent, characterized by a second virial coefficient $A_2 = 4.9 \times 10^{-5} \text{ L mol g}^{-2}$. Given $RT = 25 \text{ L atm mol}^{-1}$, calculate the effective osmotic pressure ($\pi$) exerted by the protein at the membrane surface.