Experiment 14 Molar Mass Of A Solid

The determination of molar mass stands as a cornerstone in chemistry, essential for identifying substances, understanding their properties, and quantifying their behavior in reactions. Experiment 14 delves into this fundamental concept, offering a hands-on approach to calculating the molar mass of an unknown solid through colligative properties. This experiment not only reinforces theoretical knowledge but also hones practical laboratory skills.

Introduction to Molar Mass Determination

Molar mass, defined as the mass of one mole of a substance, is a crucial property in chemistry. Determining the molar mass of a solid is vital for several reasons:

• Identification of Unknown Substances: By comparing the experimentally determined molar mass to known values, chemists can identify unknown compounds.
• Stoichiometry: Molar mass is essential for stoichiometric calculations, enabling accurate predictions of reactant and product quantities in chemical reactions.
• Characterization of New Materials: When synthesizing new compounds, determining the molar mass is a key step in characterizing the material.

Experiment 14 uses the colligative property of freezing point depression to experimentally determine the molar mass of a solid. Colligative properties are properties of solutions that depend on the number of solute particles present, rather than the nature of the solute. Freezing point depression refers to the lowering of the freezing point of a solvent upon the addition of a solute. This phenomenon is directly proportional to the molality of the solute, allowing for the calculation of the solute's molar mass.

Theoretical Background: Freezing Point Depression

Freezing point depression occurs because the introduction of a solute disrupts the solvent's crystal lattice formation. The solute particles interfere with the solvent molecules' ability to come together and form the ordered structure of the solid phase. As a result, a lower temperature is required to achieve freezing.

The relationship between freezing point depression and molality is given by the following equation:

ΔTf = Kf * m

Where:

• ΔTf is the freezing point depression, the difference between the freezing point of the pure solvent and the freezing point of the solution.
• Kf is the cryoscopic constant, a characteristic of the solvent, representing the freezing point depression caused by a 1 molal solution.
• m is the molality of the solution, defined as the number of moles of solute per kilogram of solvent.

By experimentally determining ΔTf and knowing Kf for the solvent, the molality of the solution can be calculated. From the molality and the mass of the solvent, the number of moles of solute can be found. Finally, using the mass of the solute, the molar mass can be calculated using the formula:

Molar mass = Mass of solute / Moles of solute

Materials and Equipment Required

To perform Experiment 14 successfully, you will need the following materials and equipment:

• Unknown solid sample
• Solvent (e.g., cyclohexane, tert-butanol)
• Test tubes or small beakers
• Thermometer or temperature probe
• Stirring rod or magnetic stirrer
• Analytical balance
• Ice bath or cooling bath
• Hot plate (optional, for dissolving solute)
• Pipettes or graduated cylinders
• Weighing paper or boats

Step-by-Step Procedure

1. Determining the Freezing Point of the Pure Solvent

1. Prepare the Solvent: Accurately weigh approximately 10-15 grams of the chosen solvent into a clean, dry test tube or small beaker. Record the exact mass of the solvent.
2. Set Up the Cooling Bath: Prepare an ice bath or cooling bath to lower the temperature of the solvent. Ensure the cooling bath is sufficiently cold to freeze the solvent.
3. Monitor Temperature: Insert a thermometer or temperature probe into the solvent. Ensure the thermometer does not touch the sides or bottom of the container.
4. Cool the Solvent: Place the test tube containing the solvent into the cooling bath. Stir the solvent gently and continuously.
5. Observe Freezing Point: Carefully monitor the temperature as the solvent cools. As the solvent approaches its freezing point, the temperature will plateau. Record the temperature at which the plateau occurs; this is the freezing point of the pure solvent. The freezing point can also be determined using temperature vs time graph; the freezing point will be the temperature where the graph plateaus.
6. Repeat: Repeat the measurement at least twice to ensure accuracy and consistency. Calculate the average freezing point of the pure solvent.

2. Preparing the Solution and Measuring its Freezing Point

1. Weigh the Solute: Accurately weigh a known mass of the unknown solid sample (e.g., 0.1-0.5 grams) into a separate weighing boat or paper. Record the exact mass of the solute.
2. Prepare the Solution: Add the weighed solute to the test tube containing the frozen solvent.
3. Dissolve the Solute: Gently heat the mixture using a hot plate or warm water bath, if necessary, to dissolve the solute completely. Stir the mixture continuously to ensure uniform dissolution. Allow the solution to cool back down to room temperature.
4. Cool the Solution: Place the test tube containing the solution into the cooling bath. Stir the solution gently and continuously.
5. Observe Freezing Point: Carefully monitor the temperature as the solution cools. As the solution approaches its freezing point, the temperature will plateau. Record the temperature at which the plateau occurs; this is the freezing point of the solution.
6. Repeat: Repeat the measurement at least twice with slightly different masses of the solute to obtain multiple data points and improve accuracy.

3. Data Analysis and Calculations

1. Calculate Freezing Point Depression (ΔTf): Subtract the freezing point of the solution from the freezing point of the pure solvent for each trial.

   ΔTf = Freezing point of pure solvent - Freezing point of solution

2. Calculate Molality (m): Use the freezing point depression equation to calculate the molality of the solution for each trial. The Kf value for your solvent must be known.

   m = ΔTf / Kf

3. Calculate Moles of Solute: Determine the number of moles of solute in each solution using the molality and the mass of the solvent. Remember to convert the mass of the solvent from grams to kilograms.

   Moles of solute = m * Mass of solvent (in kg)

4. Calculate Molar Mass: Calculate the molar mass of the unknown solid for each trial by dividing the mass of the solute by the number of moles of solute.

   Molar mass = Mass of solute / Moles of solute

5. Average Molar Mass: Calculate the average molar mass from the values obtained in each trial.

6. Statistical Analysis (Optional): Calculate the standard deviation and percent error of your results to assess the accuracy and precision of your measurements. If the actual molar mass of the unknown solid is known, compare the experimental and actual molar mass of the solute.

Factors Affecting Accuracy and Precision

Several factors can influence the accuracy and precision of the results in Experiment 14:

• Purity of Solvent and Solute: Impurities in the solvent or solute can affect the freezing point depression and lead to inaccurate results. Use high-purity chemicals and ensure they are free from contaminants.
• Accuracy of Mass Measurements: Precise mass measurements are crucial for accurate calculations. Use an analytical balance and ensure it is properly calibrated.
• Temperature Measurement: The accuracy of the thermometer or temperature probe is critical. Use a calibrated thermometer and ensure it is properly immersed in the solution.
• Supercooling: Supercooling occurs when a liquid is cooled below its freezing point without solidifying. This can lead to inaccurate freezing point measurements. Stirring the solution continuously can help minimize supercooling.
• Heat Loss: Heat loss from the test tube to the surroundings can affect the freezing point measurements. Insulate the test tube or use a well-insulated cooling bath.
• Solubility of Solute: If the solute is not completely soluble in the solvent, the measured freezing point depression will be inaccurate. Ensure the solute is fully dissolved before taking measurements.

Alternative Solvents

The choice of solvent is important in determining the molar mass of a solid through freezing point depression. Here's a brief look into some alternative solvents and their specific advantages and considerations:

• Cyclohexane (C6H12):
  • Advantages: Cyclohexane is a common solvent for freezing point depression experiments due to its relatively large Kf value (20.2 °C·kg/mol), which allows for more noticeable and measurable freezing point depressions.
  • Considerations: It has a relatively high freezing point (6.5 °C), which can be a drawback if very low temperatures are needed. Cyclohexane is also flammable, so care must be taken in the lab.
• tert-Butanol ((CH3)3COH):
  • Advantages: tert-Butanol has a moderate Kf value (8.37 °C·kg/mol) and is miscible with water and many organic solvents. Its freezing point (25.5 °C) is convenient for laboratory settings.
  • Considerations: It can be hygroscopic, meaning it absorbs moisture from the air, which can affect the freezing point and introduce errors. It also has a distinctive odor that some may find unpleasant.
• Camphor (C10H16O):
  • Advantages: Camphor has an exceptionally high Kf value (39.7 °C·kg/mol), making it very sensitive to small amounts of solute. This makes it useful for determining very small molar masses.
  • Considerations: It has a high melting point (176-177 °C), and its strong odor and potential for sublimation can be problematic.

Safety Precautions

• Wear appropriate personal protective equipment (PPE), including safety goggles, gloves, and a lab coat, at all times.
• Handle solvents with care. Many organic solvents are flammable or toxic. Work in a well-ventilated area and avoid contact with skin or eyes.
• Dispose of chemicals properly according to laboratory guidelines.
• Use caution when heating solutions. Use a hot plate or water bath to avoid overheating or splashing.
• Handle glassware carefully to avoid breakage.

Applications and Extensions

The principles and techniques learned in Experiment 14 have several real-world applications:

• Pharmaceutical Industry: Determining the molar mass of drug compounds is essential for formulation and dosage calculations.
• Polymer Chemistry: Molar mass determination is used to characterize polymers and determine their properties.
• Environmental Science: Freezing point depression can be used to measure the concentration of salts in water samples.

Extensions of this experiment could include:

• Investigating the effect of different solvents on the freezing point depression.
• Determining the molar mass of volatile compounds using vapor pressure depression.
• Using a more sophisticated temperature measurement system, such as a differential scanning calorimeter (DSC), to improve accuracy.

Example Calculation

Let's consider an example to illustrate the calculations involved in Experiment 14.

Suppose we have the following data:

• Solvent: Cyclohexane
• Kf (Cyclohexane): 20.2 °C·kg/mol
• Mass of cyclohexane: 15.00 g (0.015 kg)
• Freezing point of pure cyclohexane: 6.50 °C
• Mass of unknown solute: 0.250 g
• Freezing point of solution: 4.25 °C

1. Calculate Freezing Point Depression (ΔTf):

   ΔTf = 6.50 °C - 4.25 °C = 2.25 °C

2. Calculate Molality (m):

   m = ΔTf / Kf = 2.25 °C / 20.2 °C·kg/mol = 0.111 mol/kg

3. Calculate Moles of Solute:

   Moles of solute = m * Mass of solvent (in kg) = 0.111 mol/kg * 0.015 kg = 0.00167 mol

4. Calculate Molar Mass:

   Molar mass = Mass of solute / Moles of solute = 0.250 g / 0.00167 mol = 149.7 g/mol

Therefore, the experimentally determined molar mass of the unknown solid is approximately 149.7 g/mol.

Common Mistakes to Avoid

To ensure accurate results in Experiment 14, be mindful of these common pitfalls:

• Incorrect Mass Measurements: Double-check all mass measurements to ensure accuracy.
• Incomplete Dissolution of Solute: Ensure the solute is completely dissolved in the solvent before measuring the freezing point.
• Contamination of Solvent or Solute: Use pure chemicals and avoid contamination.
• Inaccurate Temperature Readings: Use a calibrated thermometer and ensure it is properly immersed in the solution.
• Failure to Account for Supercooling: Stir the solution continuously to minimize supercooling.
• Incorrect Units: Pay attention to units and convert them appropriately.
• Not Repeating Measurements: Performing multiple trials is important to obtain more accurate results and assess the precision of the measurements.
• Neglecting Safety Precautions: Always wear appropriate PPE and handle chemicals with care.

Conclusion

Experiment 14 provides a valuable hands-on experience in determining the molar mass of a solid using the colligative property of freezing point depression. By understanding the theoretical principles, following the experimental procedure carefully, and analyzing the data accurately, one can successfully determine the molar mass of an unknown solid. This experiment reinforces fundamental concepts in chemistry and develops essential laboratory skills that are applicable in various scientific fields. Remember to pay attention to potential sources of error and take appropriate safety precautions to ensure accurate and reliable results. Through this experiment, students gain a deeper appreciation for the importance of molar mass determination in chemistry and its diverse applications.