Question

200 cm3 of an aqueous solution of a protein contains 1.26 g of the protein. The osmotic pressure of this solution at 300 K is found to be 2.57 × 10^-3 bar. Calculate the molar mass of the protein.

Given: R = 0.083 L bar mol^-1 K^-1

Hint:

Osmotic pressure is the preferred method for determining the molar mass of macromolecules like proteins because the pressure changes are measurable even at very low molar concentrations.

Answer 1

Concept:
Osmotic pressure (π) is a colligative property related to the molarity of the solution.

π = (w₂ × R × T) / (M₂ × V)

Where:
w₂ = mass of solute (1.26 g)
V = volume of solution in litres
M₂ = molar mass of solute
R = gas constant (0.083 L bar mol⁻¹ K⁻¹)
T = temperature (300 K)

Step 1: Convert units.
Volume V = 200 cm³ = 0.200 L
π = 2.57 × 10⁻³ bar

Step 2: Calculate molar mass (M₂).
M₂ = (w₂ × R × T) / (π × V)

M₂ = (1.26 × 0.083 × 300) / (2.57 × 10⁻³ × 0.200)

M₂ = 31.374 / 0.000514

M₂ ≈ 61,038.9 g/mol