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

1. Convert osmotic pressure to atm: π = 1.4 / 760 ≈ 0.001842 atm
2. Calculate RT: R × T = 0.0821 × 298 ≈ 24.4658 L·atm·mol⁻¹
3. Calculate molarity: C = π / (R·T) = 0.001842 / 24.4658 ≈ 7.529 × 10⁻⁵ mol/L
4. Moles of protein: n = C × V = 7.529 × 10⁻⁵ mol (V = 1 L)
5. 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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