Using Freezing Point Depression To Find Molecular Weight Lab Answers

Freezing point depression stands as a fascinating colligative property, offering a straightforward method to determine the molecular weight of an unknown solute. This technique, rooted in thermodynamics, finds practical applications in various fields, from chemistry labs to industrial settings.

Understanding Freezing Point Depression

Freezing point depression occurs when a solute is added to a solvent, causing the freezing point of the solution to be lower than that of the pure solvent. This phenomenon arises because the presence of solute particles disrupts the solvent's ability to form a crystalline lattice structure, requiring a lower temperature to initiate freezing.

The extent of freezing point depression is directly proportional to the molality of the solute in the solution. Molality (m) is defined as the number of moles of solute per kilogram of solvent. The relationship is expressed by the following equation:

ΔTf = Kf * m

Where:

• ΔTf is the freezing point depression, i.e., the difference between the freezing point of the pure solvent and the freezing point of the solution.
• Kf is the cryoscopic constant, a characteristic constant for each solvent that represents the freezing point depression caused by one mole of solute dissolved in one kilogram of the solvent.
• m is the molality of the solution.

Laboratory Procedure: Determining Molecular Weight

Materials Required

• A solvent with a known Kf value (e.g., cyclohexane, water, camphor)
• An unknown solute
• Test tubes or beakers
• Thermometer or temperature probe
• Stirring apparatus (magnetic stirrer or glass rod)
• Weighing balance

Step-by-Step Protocol

1. Determine the Freezing Point of the Pure Solvent:

   • Measure a known mass of the pure solvent into a test tube or beaker.
   • Place the container in a cooling bath (ice water or a suitable coolant).
   • Insert a thermometer or temperature probe into the solvent and stir continuously.
   • Record the temperature at which the solvent begins to freeze and remains constant for a period. This is the freezing point of the pure solvent (Tf°).

2. Prepare the Solution:

   • Accurately weigh a known mass of the unknown solute.
   • Add the solute to the solvent used in step 1, ensuring the mass of the solvent is precisely recorded.
   • Stir the mixture thoroughly until the solute is completely dissolved.

3. Determine the Freezing Point of the Solution:

   • Place the solution in the same cooling bath used in step 1.
   • Insert the thermometer or temperature probe into the solution and stir continuously.
   • Record the temperature at which the solution begins to freeze and remains constant. This is the freezing point of the solution (Tf).

4. Calculate the Freezing Point Depression:

   • Calculate the difference between the freezing point of the pure solvent and the freezing point of the solution: ΔTf = Tf° - Tf

5. Calculate the Molality of the Solution:

   • Using the freezing point depression equation, calculate the molality of the solution: m = ΔTf / Kf

6. Calculate the Moles of Solute:

   • Calculate the number of moles of solute using the molality and the mass of the solvent (in kilograms): Moles of solute = m * mass of solvent (kg)

7. Calculate the Molecular Weight of the Solute:

   • Calculate the molecular weight of the solute by dividing the mass of the solute by the number of moles of solute: Molecular weight = mass of solute / moles of solute

Example Calculation

Let's say we use cyclohexane as the solvent and an unknown organic compound as the solute.

• Kf of cyclohexane = 20.2 °C kg/mol
• Mass of cyclohexane = 50.0 g (0.050 kg)
• Mass of unknown solute = 1.60 g
• Freezing point of pure cyclohexane = 6.5 °C
• Freezing point of solution = 4.1 °C

1. Freezing Point Depression: ΔTf = 6.5 °C - 4.1 °C = 2.4 °C
2. Molality of the Solution: m = 2.4 °C / 20.2 °C kg/mol = 0.119 mol/kg
3. Moles of Solute: Moles of solute = 0.119 mol/kg * 0.050 kg = 0.00595 mol
4. Molecular Weight of the Solute: Molecular weight = 1.60 g / 0.00595 mol = 268.9 g/mol

Therefore, the estimated molecular weight of the unknown solute is approximately 268.9 g/mol.

Key Considerations and Potential Errors

Solvent Selection

The choice of solvent is crucial for accurate results. The solvent should:

• Have a large Kf value to produce a significant freezing point depression, making temperature measurements more accurate.
• Be readily available and relatively inexpensive.
• Be easy to handle and purify.
• Dissolve the solute adequately.
• Be chemically inert and not react with the solute.

Commonly used solvents include water, cyclohexane, camphor, and tert-butanol.

Temperature Measurement

Accurate temperature measurements are critical. Use a calibrated thermometer or temperature probe with appropriate precision. Ensure proper immersion of the thermometer in the solution and continuous stirring to maintain a uniform temperature.

Supercooling

Supercooling is a phenomenon where a liquid is cooled below its freezing point without solidifying. This can occur if the solution is cooled too rapidly or if there are insufficient nucleation sites for crystal formation. To minimize supercooling:

• Cool the solution slowly and steadily.
• Introduce a seed crystal of the solvent to initiate freezing.
• Ensure thorough stirring to promote uniform cooling and crystal formation.

Solute Dissolution

The solute must be completely dissolved in the solvent for the experiment to be valid. Incomplete dissolution will lead to an underestimation of the freezing point depression and an inaccurate molecular weight determination. Stir the solution thoroughly and allow sufficient time for dissolution.

Concentration Effects

The freezing point depression equation is most accurate for dilute solutions. At higher concentrations, solute-solute interactions can affect the freezing point depression, leading to deviations from the ideal behavior. Keep the solute concentration relatively low to minimize these effects.

Impurities

Impurities in the solvent or solute can affect the freezing point. Use high-purity solvents and solutes whenever possible. If necessary, purify the solvent and solute before use.

Colligative Properties Assumptions

Freezing point depression relies on colligative properties, which depend only on the number of solute particles, not their identity. This assumes the solute does not dissociate or associate in the solvent. If the solute is an electrolyte that dissociates into ions, the freezing point depression will be greater than expected. The van't Hoff factor (i) accounts for the dissociation of electrolytes:

ΔTf = i * Kf * m

For example, NaCl dissociates into two ions (Na+ and Cl-) in water, so i ≈ 2.

Applications of Freezing Point Depression

Molecular Weight Determination

The primary application of freezing point depression is determining the molecular weight of unknown substances. This is particularly useful for characterizing new compounds or polymers.

Determining the Degree of Dissociation

By measuring the freezing point depression of an electrolyte solution, the van't Hoff factor (i) can be determined. This allows for the calculation of the degree of dissociation of the electrolyte, providing insights into its behavior in solution.

Antifreeze Applications

Freezing point depression is utilized in antifreeze solutions for vehicles. Ethylene glycol is added to water to lower its freezing point, preventing the water from freezing and potentially damaging the engine in cold weather.

Food Science

In food science, freezing point depression is relevant in understanding the freezing behavior of foods and beverages. The addition of sugars or salts lowers the freezing point of water in the food, affecting its texture and preservation.

Pharmaceuticals

Freezing point depression can be used to determine the purity of pharmaceutical compounds. Impurities in a drug can lower its freezing point, providing a means to assess its quality.

Advantages and Limitations

Advantages:

• Simplicity: The experimental setup and calculations are relatively straightforward.
• Cost-Effectiveness: The equipment required is readily available and inexpensive.
• Versatility: The method can be applied to a wide range of solutes and solvents.

Limitations:

• Accuracy: The accuracy is limited by the precision of temperature measurements and the assumptions of colligative properties.
• Applicability: The method is not suitable for high concentrations or solutes that dissociate or associate in solution.
• Solvent Dependency: The choice of solvent is critical and can affect the results.

Frequently Asked Questions (FAQ)

Q: Why does adding a solute lower the freezing point of a solvent?

A: The addition of a solute disrupts the solvent's ability to form a crystalline lattice structure. This disruption requires a lower temperature to initiate freezing, resulting in a lower freezing point.

Q: What is the cryoscopic constant (Kf)?

A: The cryoscopic constant is a characteristic constant for each solvent that represents the freezing point depression caused by one mole of solute dissolved in one kilogram of the solvent.

Q: How does supercooling affect the experiment?

A: Supercooling can lead to an inaccurate determination of the freezing point. It's important to cool the solution slowly and steadily, and to ensure thorough stirring to minimize supercooling.

Q: What is the van't Hoff factor, and why is it important?

A: The van't Hoff factor (i) accounts for the dissociation of electrolytes in solution. It's important because electrolytes dissociate into ions, increasing the number of particles in the solution and affecting the freezing point depression.

Q: Can freezing point depression be used to determine the molecular weight of polymers?

A: Yes, freezing point depression can be used to determine the molecular weight of polymers, although the accuracy may be limited due to the complex behavior of polymers in solution.

Conclusion

Freezing point depression is a powerful and versatile technique for determining the molecular weight of unknown solutes. By carefully controlling experimental conditions and understanding the underlying principles, accurate and reliable results can be obtained. This method continues to be a valuable tool in chemistry laboratories and various industries for characterizing materials and understanding their properties. The key lies in selecting the appropriate solvent, maintaining accurate temperature measurements, and accounting for potential sources of error, such as supercooling and solute dissociation. With these considerations in mind, freezing point depression remains a fundamental and practical technique in the realm of physical chemistry.