A solution containing 29.60 mg of an unknown protein per 27.0 mL solution was found to have
an osmotic pressure of 3.65 torr at 35 ?C.
What is the molar mass of the protein?
Solution
by definition
osmotic pressure = C x R x T
given
osmotic pressure = 3.65 torr x ( 1 atm / 760 torr) = 0.0048 atm
R= gas constant = 0.0821 L atm / mol K
T = temperature = 35 C = 35 + 273 K = 308 K
plug in the values
0.0048 atm = C x 0.0821 (L-atm / mol K) x 308 K
C = 0.00019 mol/L
so
concentration of protein = 0.00019 mol / L
volume of solution = 27 ml = 0.027 L
now
moles of protein = 0.027 L x 0.00019 mol / L = 5.128 x 10-6 mol
now

molar mass of protein = 29.60 x 10-3 g / (5.128 x 10-6 mol)
molar mass of protein = 5772 g/mol
so
molar mass of the protein is 5772 g/mol