Colligative Properties

Using the formula for freezing point depression, we calculate the change in freezing point: Where Kf is the freezing point depression constant and m is the molality of the solution.

Using Raoult's Law and the formula for boiling point elevation, the change in vapor pressure can be used to calculate the molar mass of the solute.
The molecular mass is found to be 41.34.

Raoult’s Law states that the vapour pressure of a solvent in a solution is proportional to the mole fraction of the solvent. This law can be expressed as: where is the vapour pressure of the solvent in the solution, is the vapour pressure of the pure solvent, and is the mole fraction of the solvent. Since urea is a non-volatile solute, it does not contribute to the vapour pressure. The presence of the solute reduces the vapour pressure slightly. The change in vapour pressure can be calculated using: where is the mole fraction of the solute. However, because the solution is dilute, the mole fraction of the solute is small, and thus the change in vapour pressure is also small. Therefore, the vapour pressure of the solution is approximately equal to that of pure water, which is 23 mm Hg in this case.

Thus, the vapour pressure of the solution is close to 23 mm Hg.