Question

A solution of 7.50 mg of a small protein in 5.00 mL aqueous solution has an osmotic pressure of 6.15 torr at 23 1degree C. What is the molar mass of the protein? g/mol

Answer 1

Convert the unit of osmotic pressure using the relation 1 atm = 760 torr
The osmotic pressure

$\pi = 6.15 \: torr = 6.15 \: torr \times \dfrac {1 \: atm}{760 \: torr} = 0.008092 \: atm$

The molar mass of protein
$M = \dfrac {W}{\pi}\dfrac {RT}{V}$

$M = \dfrac {7.50 \: mg \times 10^{-6} \: kg/mg}{0.008092 \: atm} \times \dfrac {8.314 \: J/K/mol \times (23.1 + 273.15 ) \: K}{5.00 \: mL \times 10^{-3} \: L/mL}$

Hence, the molar mass of protein is 457 kg/mol.