Calculation of Molecular Weight from Freezing Point Depression Data
The freezing point of a solution that contains 1.00 g of an unknown compound, (A), dissolved in 10.0 g of benzene is found to be 2.07 oC. The freezing point of pure benzene is 5.48 oC. The molal freezing point depression constant of benzene is 5.12 oC/molal. What is the molecular weight of the unknown compound?
- Step 1: Calculate the freezing point depression of the solution.
Tf = (Freezing point of pure solvent) - (Freezing point of solution)
(5.48 oC) - (2.07 oC) = 3.41 oC
- Step 2 : Calculate the molal concentration of the solution using the freezing
Tf = (Kf) (m)
m = (3.41 oC) / (5.12 oC/molal)
m = 0.666 molal
- Step 3: Calculate the molecular weight of the unknown using the molal concentration.
m = 0.666 molal = 0.666 mol A / kg benzene
moles A = (0.66 mol A / kg benzene) (0.100 kg benzene) = 6.66 X 10-3 mol A
molecular weight of A = (1.00 g A) / (6.66 X 10-3 mol A)
molecular weigh of A = 150. g/mol