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A solution of 250 mg of a protein in 50.0 mL of solution has an osmotic pressure of 0.430 kPa at…

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A solution of $250\ \text{mg}$ of a protein in $50.0\ \text{mL}$ of solution has an osmotic pressure of $0.430\ \text{kPa}$ at $298\ \text{K}$ . Find the molar mass of the protein. Then find the height of the column of water that this pressure holds up, in millimetres. Take $\rho = 1000\ \text{kg/m}^3$ and $g = 9.8\ \text{m/s}^2$ .

Need a reminder? The key ideaShow

The osmotic pressure of a dilute solution is $\pi = CRT$ , with $C$ in mol/L and $T$ in kelvin. $R = 0.0821\ \text{L atm K}^{-1}\text{mol}^{-1}$ gives atm, and $R = 8.314\ \text{J K}^{-1}\text{mol}^{-1}$ gives kPa. Isotonic solutions have equal $\pi$ . A column of height $h$ of a liquid of density $\rho$ gives a pressure $\rho g h$ .

The worked solution

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