devarshi-dt-logo

Question:

200 mL of an aqueous solution of a protein contains 1.26 g of protein. The osmotic pressure of this solution at 300 K is found to be 2.57 × 10⁷ bar. The molar mass of protein will be: [R = 0.083 L bar mol⁻¹K⁻¹]

122044 g mol⁻¹

51022 g mol⁻¹

31011 g mol⁻¹

61038 g mol⁻¹

Solution:

The expression for the osmotic pressure of the solution is given below.
π = CRT
Substitute values in the above expression.
π = (w/M) × (1000/V) × RT
2.57 × 10⁷ = (1.26/M) × (1000/200) × 0.083 × 300
M = 61038 g
Thus, the molar mass of protein is 61038 g mol⁻¹
Hence, the correct option is D