Question 13.9: Establishing a Molar Mass from a Measurement of Osmotic Pres...
Establishing a Molar Mass from a Measurement of Osmotic Pressure
A 50.00 mL sample of an aqueous solution contains 1.08 g of human serum albumin, a blood-plasma protein. The solution has an osmotic pressure of 5.85 mmHg at 298 K. What is the molar mass of the albumin?
Analyze
We need to use osmotic pressure to determine the molar mass of a protein, human serum albumin, in a solution.
Express osmotic pressure in atmospheres.
\pi = 5.85 mmHg \times \frac{1 atm }{760 mmHg } = 7.70 \times 10^{-3} atm
Modify the basic equation for osmotic pressure, by showing moles of solute (n) as the mass of solute (m) divided by its molar mass (M), and solve for M.
\pi V = n R T \quad \pi V = \frac{m}{M} R T \quad M = \frac{m R T}{\pi V}
Obtain the value of M by substituting the given data into the last equation above, ensuring that units cancel to yield g/mol as the unit for M.
M = \frac{1.08 \times 0.08206 atm L mol^{-1} K^{-1} \times 298 K}{7.70 \times 10^{-3} \times 0.0500 L} = 6.86 \times 10^4 g/mol
Assess
Even though the solution is relatively dilute, knowing the osmotic pressure helped us determine the molar mass of human serum albumin.