You can determine the molar mass of an unknown sample using freezing point depression, a colligative property that depends on the number of solute particles in a solution. Here's a detailed, step-by-step process:
Understanding Freezing Point Depression
Freezing point depression occurs when a non-volatile solute is added to a solvent, lowering the freezing point of the solution compared to the pure solvent. The extent of the freezing point depression (ΔTf) is directly proportional to the molality (m) of the solution, as described by the equation:
*ΔTf = Kf m**
Where:
- ΔTf is the freezing point depression (the change in freezing point)
- Kf is the cryoscopic constant (freezing point depression constant), specific to the solvent
- m is the molality of the solution (moles of solute per kilogram of solvent)
Step-by-Step Process for Determining Molar Mass
Here's how to determine the molar mass of an unknown sample using freezing point depression:
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Prepare a Solution: Dissolve a known mass of your unknown solute in a known mass of a suitable solvent. Choose a solvent for which the Kf value is known.
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Measure the Freezing Point: Carefully measure the freezing point of both the pure solvent and the solution. Accurate measurements are crucial.
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Calculate ΔTf: Subtract the freezing point of the solution from the freezing point of the pure solvent. This gives you the freezing point depression, ΔTf.
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Calculate Molality (m): Using the equation above (ΔTf = Kf * m), solve for the molality (m) of the solution. The equation will become m = ΔTf / Kf. You will need the Kf value, which will be specific to the solvent used in the solution.
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Calculate Moles of Solute: Molality is defined as moles of solute per kilogram of solvent. Using the calculated molality (m) and the mass of the solvent (in kilograms), you can calculate the moles of the unknown solute:
*Moles of solute = molality (m) kilograms of solvent**
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Calculate Molar Mass: Finally, divide the mass of the solute (in grams) by the moles of solute you just calculated. This will give you the molar mass of the unknown sample:
Molar mass = grams of solute / moles of solute
Example
Let's say you dissolved 1.5 grams of an unknown solute in 100 grams (0.1 kg) of water. The freezing point of pure water is 0°C. The solution’s freezing point was measured to be -0.45°C. The cryoscopic constant (Kf) for water is 1.86 °C·kg/mol.
- ΔTf = 0°C - (-0.45°C) = 0.45°C
- m = ΔTf / Kf = 0.45°C / 1.86 °C·kg/mol = 0.242 mol/kg
- Moles of solute = 0.242 mol/kg * 0.1 kg = 0.0242 moles
- Molar mass = 1.5 g / 0.0242 moles = 61.98 g/mol
Therefore, the molar mass of the unknown solute is approximately 61.98 g/mol.
Summary of Steps
| Step | Action |
|---|---|
| 1 | Prepare a solution with known amounts of solute and solvent. |
| 2 | Measure the freezing point of both the solvent and the solution. |
| 3 | Calculate the freezing point depression (ΔTf) |
| 4 | Calculate the molality (m) of the solution using the formula ΔTf = Kf * m. |
| 5 | Calculate the moles of solute using the molality and mass of the solvent. |
| 6 | Calculate the molar mass by dividing grams of solute by moles of solute. |
This method allows you to determine the molar mass of an unknown substance accurately using the principle of freezing point depression.
