Question

What is the molar mass of a protein, if a solution of 0.12 g of the protein in 0.040 L of solution has an osmotic pressure of 0.76 torr at 35∘C?

Answer 1

Given : osmotic pressure = 0.76 torr

osmotic pressure = 0.76 torr * (1 atm / 760 torr)

osmotic pressure = (0.76 / 760) atm

osmotic pressure = 1 x 10^-3 atm

Concentration of protein in solution = (osmotic pressure) / [(R) * (T)]

where R = gas constant = 0.0821 L-atm/mol-K

T = temperature of solution = 35 ^oC = (35 + 273)K = 308 K

Substituting the values,

Concentration of protein in solution = (1 x 10^-3 atm) / [(0.0821 L-atm/mol-K) * (308 K)]

Concentration of protein in solution = 3.95 x 10^-5 mol/L

moles of protein in solution = (Concentration of protein in solution) * (volume of solution)

moles of protein in solution = (3.95 x 10^-5 mol/L) * (0.040 L)

moles of protein in solution = 1.6 x 10^-6 mol

Molar mass of protein = (mass of protein in solution) / (moles of protein in solution)

Molar mass of protein = (0.12 g) / (1.6 x 10^-6 mol)

Molar mass of protein = 75857.6 g/mol

Molar mass of protein = 7.6 x 10⁴ g/mol          (with correct significant figures)