Question 11.14: USING OSMOTIC PRESSURE TO CALCULATE THE MOLECULAR MASS OF A ...
USING OSMOTIC PRESSURE TO CALCULATE THE MOLECULAR MASS OF A SOLUTE
A solution prepared by dissolving 20.0 mg of insulin in water and diluting to a volume of 5.00 mL gives an osmotic pressure of 12.5 mm Hg at 300 K. What is the molecular mass of insulin?
STRATEGY
To determine molecular mass, we need to know the number of moles of insulin represented by the 20.0 mg sample. We can do this by first rearranging the equation for osmotic pressure to find the molar concentration of the insulin solution and then multiplying by the volume of the solution to obtain the number of moles of insulin.
Since \Pi = MRT, then M = \frac{\Pi}{RT}
M = \frac{12.5 mm Hg × \frac{1 atm}{760 mm Hg}}{0.082 06\frac{L · atm}{K · mol} × 300 K} = 6.68 × 10^{-4} M
Since the volume of the solution is 5.00 mL, the number of moles of insulin is
Moles insulin = 6.68 × 10^{-4} \frac{mol}{L} × \frac{1 L}{1000 mL} × 5.00 mL = 3.34 × 10^{-6} mol
Knowing both the mass and the number of moles of insulin, we can calculate the molar mass and thus the molecular mass:
Molar mass = \frac{mass insulin}{moles of insulin} = \frac{0.0200 g insulin}{3.34 × 10^{-6} mol insulin} = 5990 g/mol
The molecular mass of insulin is 5990 amu.