A solution of 0.635 g of a protein in 100 mL water has an osmotic pressure due to the protein of 2.35 cm H,0 at 27 °C. Then the molecular weight of the protein is: 

CONCEPT:

Osmotic Pressure and Molecular Weight

• Osmotic pressure (π) is a colligative property and is given by the formula:

  π = (n/V)RT = CRT

• Where:
  • π = osmotic pressure (in atm)
  • C = concentration in mol/L
  • R = gas constant = 0.0821 L·atm/mol·K
  • T = temperature in Kelvin (K = °C + 273)
• Molecular weight (M) can be calculated using:

  π = (w/MV)RT ⇒ M = (wRT)/(πV)

EXPLANATION:

• Given:
  • Weight of protein (w) = 0.635 g
  • Volume of solution (V) = 100 mL = 0.1 L
  • Osmotic pressure (π) = 2.35 cm H₂O = 2.35 / 76 = 0.03092 atm
  • Temperature (T) = 27 °C = 300 K
  • R = 0.0821 L·atm/mol·K
• Now apply the formula:

  M = (wRT) / (πV)

  = (0.635 × 0.0821 × 300) / (0.03092 × 0.1)

  = 15.638025 / 0.003092

  ≈ 69,000 g/mol

Therefore, the molecular weight of the protein is approximately 69,000 g/mol.