Question 13.4.3: Determine the molar mass of a solute from osmotic pressure.I......
Determine the molar mass of a solute from osmotic pressure.
In a laboratory experiment, a student found that a 229.5-mL aqueous solution containing 11.34 g of a compound had an osmotic pressure of 15.4 mm Hg at 298 K. The compound was also found to be nonvolatile and a nonelectrolyte. What is the molar mass of this compound?
You are asked to calculate the molar mass of a compound.
You are given the osmotic pressure, temperature, and volume of a solution containing the compound and the mass of compound in the solution.
Use the osmotic pressure, and temperature to calculate the concentration of solute in the solution.
15.4 mm Hg \times \frac{1\text{ atm}}{760\text{ mm Hg}} = 0.0203 atm
Π = cRTi
0.0203 atm = c(0.082057 L · atm/K · mol)(298 K)(1)
c = 8.30 × 10^{-4} mol/L
Use the concentration and the volume of the solution to calculate moles of solute.
\frac{8.30 \times 10^{-4}\text{ mol solute}}{1\text{ L}} × 0.2295 L = 1.90 × 10^{-4} mol solute
Use the mass of solute and the moles of solute calculated above to calculate molar mass.
molar mass = \frac{11.34 \text{ g}}{1.90 \times 10^{-4}\text{ mol}}=5.96 \times 10^{4} g/mol