Q.12 One gram of a protein is dissolved in one liter of water. The resulting solution exerts an osmotic
pressure of 1.4 Torr at 298 K. Assuming that the protein does not ionize in solution, the molecular weight
of the protein is ____ 𝐠𝐦𝐨𝐥−𝟏 . (𝐑 = 𝟎. 𝟎𝟖𝟐𝐋𝐚𝐭𝐦𝐦𝐨𝐥−𝟏 𝐊 −𝟏 )
Protein Molecular Weight from Osmotic Pressure: 1g in 1L Water, 1.4 Torr at 298K Calculation
Van’t Hoff Osmotic Pressure Formula Explained
The osmotic pressure formula is:
π = C·R·T
- π = osmotic pressure (atm)
- C = molarity of solute (mol/L)
- R = gas constant (0.0821 L·atm·mol⁻¹·K⁻¹)
- T = temperature in Kelvin (K)
For proteins, we can rearrange the formula to calculate molarity, then moles (n = C × V), and finally molecular weight (M = mass / n).
Key: Convert pressure from Torr to atm: 1 atm = 760 Torr.
Detailed Calculation Steps
- Convert osmotic pressure to atm: π = 1.4 / 760 ≈ 0.001842 atm
- Calculate RT: R × T = 0.0821 × 298 ≈ 24.4658 L·atm·mol⁻¹
- Calculate molarity: C = π / (R·T) = 0.001842 / 24.4658 ≈ 7.529 × 10⁻⁵ mol/L
- Moles of protein: n = C × V = 7.529 × 10⁻⁵ mol (V = 1 L)
- Molecular weight: M = mass / n = 1 g / 7.529 × 10⁻⁵ mol ≈ 13,281 g/mol
Applications in Protein Analysis
Osmotic pressure is particularly useful for measuring high molecular weight proteins at low concentrations, unlike colligative methods such as boiling point elevation. The calculated molecular weight (≈13,281 g/mol) is consistent with typical protein sizes (10,000–100,000 g/mol).
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