Answer :
Final answer:
The molar mass of the unknown compound is calculated by determining the change in freezing point, using the freezing point depression constant of the solvent to find the molality, calculating the number of moles of solute, and then dividing the mass of solute by the number of moles. In the given example, the molar mass is found to be 298.7 g/mol.
Explanation:
To calculate the molar mass of the unknown compound using its freezing point depression, we apply the following steps:
- Determine the change in freezing point by subtracting the freezing point of the pure solvent (0 °C for water) from the observed freezing point of the solution.
- Use the freezing point depression constant (Kf) for water, which is 1.86 °C/m, alongside the change in freezing point to calculate the molality (m) of the solution.
- Calculate the number of moles of solute using the molality and the mass of the solvent in kilograms.
- Finally, the molar mass is determined by dividing the mass of solute by the calculated number of moles.
Example Calculation:
Let's calculate the molar mass for a solution that causes the freezing point to drop by 1.5 °C.
- Change in freezing point (ΔTf) = 1.5 °C
- Molality (m) = ΔTf / Kf = 1.5 °C / 1.86 °C/m = 0.806 m
- Mass of solvent (water) in kilograms = 153.4 g / 1000 = 0.1534 kg
- Number of moles of solute = molality x mass of solvent = 0.806 m x 0.1534 kg = 0.1237 moles
- Molar mass = mass of solute / number of moles of solute = 36.9 g / 0.1237 moles
The calculated molar mass of the solute would then be 298.7 g/mol