Determining Molar Mass from a Colligative Property

Determining an unknown solute's molar mass from a colligative-property measurement means calculating the solute's molal or molar concentration from the observed freezing point change, boiling point change, or osmotic pressure, then dividing the solute's known mass by the moles that concentration implies.

A 10.0-g sample of hemoglobin dissolved in 0.500 L of water produces an osmotic pressure of 5.9 torr at 22 °C. Converting to atmospheres and solving for molarity from osmotic pressure gives a very small concentration, and dividing the 10.0-g sample by the resulting small number of moles yields a molar mass in the tens of thousands of grams per mole, consistent with hemoglobin's identity as a large protein.