Question

Osmotic pressure of a solution containing 7.0 g of a protein in 100 ml of solution is 20 mm Hg at 37°C. Calculate the molecular mass of the protein.

(R = 0.0821 L atm K⁻¹ mol⁻¹)

Answer 1

Given: Mass of solute (protein) = 7.0 g

Volume of solution = 100 mL = 0.1 L

Osmotic pressure, π = 20 mm Hg = 20/760 atm ≈ 0.02632 atm

Temperature T = 37°C = 310 KT 

R = 0.0821 L atm K⁻¹ mol⁻¹

`pi = n/V RT`

`n = (pi V)/(R T)`

`n = (0.02632 xx 0.1)/(0.0821 xx 310)`

= `0.002632/25.451`

= 1.034 × 10⁻⁴ mol

Molar mass = `"Mass of solute"/"moles"`

= `7.0/(1.034 xx 10^-4)`

= `7.0/0.001034`

= 6769 g/mol