Determination Of Molar Mass By Freezing Point Depression Lab Report

Determination of Molar Mass by Freezing Point Depression: A Comprehensive Lab Report

Determining the molar mass of an unknown substance is a fundamental concept in chemistry. One effective method involves utilizing the colligative property of freezing point depression. This lab report details the experiment, analysis, and interpretation of data obtained while determining the molar mass of an unknown solute using this technique.

I. Introduction

Freezing point depression is a colligative property, meaning it depends on the concentration of solute particles in a solution, not their identity. When a non-volatile solute is added to a solvent, the freezing point of the resulting solution is lower than that of the pure solvent. This depression is directly proportional to the molality of the solute, as described by the equation:

ΔT_f = K_f * m * i

Where:

• ΔT_f represents the freezing point depression (the difference between the freezing point of the pure solvent and the freezing point of the solution).
• K_f is the cryoscopic constant of the solvent (a characteristic property specific to the solvent). For water, K_f = 1.86 °C/m.
• m represents the molality of the solution (moles of solute per kilogram of solvent).
• i is the van't Hoff factor, representing the number of particles the solute dissociates into in solution. For non-electrolytes, i ≈ 1. For strong electrolytes, i equals the number of ions produced per formula unit.

By measuring the freezing point depression (ΔT_f), and knowing the K_f of the solvent and the mass of solute and solvent, we can calculate the molality (m) of the solution. From the molality, we can then determine the molar mass of the unknown solute.

II. Materials and Methods

This experiment involved the precise measurement of the freezing points of a pure solvent (water) and a solution of an unknown solute dissolved in the same solvent. The following materials were utilized:

• Unknown solute: A sample of unknown solid substance (precise mass recorded).
• Distilled water: Used as the solvent (precise volume recorded).
• Thermometer: A high-precision thermometer capable of measuring temperature to at least 0.1°C. Calibration is crucial for accuracy.
• Beaker: A suitable sized beaker to hold the solution.
• Stirrer: A magnetic stirrer and stir bar were used to ensure uniform mixing and prevent supercooling.
• Ice bath: A mixture of ice and water to maintain a constant low temperature.
• Weighing balance: An analytical balance capable of measuring mass to at least 0.001g.

Procedure:

1. Preparation of the solution: A precise mass of the unknown solute was weighed and dissolved completely in a precise volume of distilled water. The solution was thoroughly mixed.
2. Freezing point determination of pure water: The temperature of distilled water in the beaker was carefully monitored using a thermometer while it was continuously stirred and cooled in an ice bath. The freezing point was determined as the plateau temperature reached during the crystallization process. Multiple measurements were taken and averaged to minimize error.
3. Freezing point determination of the solution: The same procedure was followed for the solution containing the unknown solute. The freezing point of the solution was recorded.
4. Data recording and analysis: All data, including the mass of the solute, volume of water, freezing points of pure water and the solution, were meticulously recorded and used to calculate the molar mass of the unknown substance.

III. Results

The following data was obtained during the experiment:

Calculations:

1. Freezing point depression (ΔT_f):

   ΔT_f = Freezing point of water - Freezing point of solution = 0.0 °C - (-1.85 °C) = 1.85 °C

2. Molality (m):

   m = ΔT_f / (K_f * i) Assuming i ≈ 1 for a non-electrolyte:

   m = 1.85 °C / (1.86 °C/m * 1) ≈ 0.995 m

3. Moles of solute:

   Molality (m) = moles of solute / kg of solvent

   Since the density of water is approximately 1 g/mL, 50.0 mL of water weighs 50.0 g or 0.050 kg.

   Moles of solute = m * kg of solvent = 0.995 m * 0.050 kg ≈ 0.04975 moles

4. Molar mass of solute:

   Molar mass = mass of solute / moles of solute = 2.543 g / 0.04975 moles ≈ 51.1 g/mol

IV. Discussion

The calculated molar mass of the unknown solute is approximately 51.1 g/mol. This value should be compared with the literature values of known compounds to identify the unknown substance. Several factors can contribute to discrepancies between the experimental and theoretical values.

• Experimental errors: Errors in measuring the mass of the solute, the volume of the solvent, and the freezing points can all influence the final result. The accuracy of the thermometer is particularly crucial. Supercooling, where the solution cools below its freezing point before crystallization occurs, can also lead to inaccurate readings.
• Impurities: The presence of impurities in the solvent or solute can affect the freezing point depression.
• Non-ideality: The equation for freezing point depression assumes ideal behavior. In reality, deviations from ideality can occur, especially at higher concentrations. These deviations can alter the calculated molar mass.
• Incomplete dissociation: If the unknown solute is an electrolyte, the assumption of i ≈ 1 would be incorrect. This would lead to an underestimation of the molar mass if the dissociation is not accounted for.

To minimize error, multiple trials should be conducted, and the average value used to determine the molar mass. A more sophisticated method of determining the freezing point, such as using a cryoscopic apparatus, can improve accuracy. Using a calibration curve for the thermometer can also improve precision.

V. Conclusion

This experiment successfully demonstrated the principle of freezing point depression and its application in determining the molar mass of an unknown solute. The calculated molar mass of the unknown solute was approximately 51.1 g/mol, although the accuracy is limited by experimental errors and assumptions made in the calculations. Further investigation, potentially with more trials and considering potential dissociation of the solute, is recommended to refine this result and definitively identify the unknown substance. The experiment highlights the importance of precise measurements and understanding the limitations of the method. Further refinement of experimental techniques could lead to a more accurate determination of the molar mass.

VI. Further Considerations and Improvements

• Multiple Trials: Conducting several trials of the experiment and averaging the results significantly reduces the impact of random errors, leading to a more reliable molar mass determination.
• Calibration Curve: Creating a calibration curve for the thermometer used helps to account for any systematic errors in temperature readings, improving the accuracy of the freezing point measurements.
• Advanced Techniques: Utilizing more advanced equipment like a cryoscopic apparatus can improve the precision of freezing point measurements, leading to a more accurate molar mass determination.
• Solvent Selection: Choosing a solvent with a larger K_f value can amplify the freezing point depression, making the measurements more sensitive and less prone to error.
• Van't Hoff Factor: If there is suspicion the solute is an electrolyte, determining or estimating the van't Hoff factor (i) is critical for obtaining an accurate molar mass.

This expanded report provides a comprehensive overview of the experiment, showcasing the practical application of freezing point depression in determining molar mass, while also acknowledging the limitations and suggesting potential improvements to the methodology. This enhanced detail aids in understanding the complexities of the experiment and encourages critical thinking about experimental design and error analysis. By understanding these aspects, future experiments can be designed to yield more precise and reliable results.