Question

Virtual Lab:

Freezing-Point Depression and Molecular Weight

(Cryoscopy)

Adapted from Advanced Chemistry with Vernier, Experiment 4

Using the Physical Chemistry Virtual Lab (vLabs) Cryoscopy Simulation

https://pcv-amrt.vlabs.ac.in/exp/cryoscopy/simulation.html

Introduction

When a solute is dissolved in a solvent, the freezing temperature of the resulting solution is lower than the freezing point of the pure solvent. This phenomenon is known as freezing-point

depression and is classified as a colligative property, meaning it depends on the number of

solute particles present in solution rather than their chemical identity.

The relationship between freezing-point depression and solution concentration is described by

the equation:

ΔTf = Kf × i × m

where ΔTf is the freezing-point depression, Kf is the cryoscopic constant (molal freezing-point

depression constant) of the solvent, i is the van’t Hoff factor, and m is the molality of the solution

(mol solute / kg solvent).

This equation can be rearranged to solve for the molecular weight of an unknown solute:

MB = (1000 × Kf × i × WB) / (ΔTf × WA)

where WB is the mass of solute (g), WA is the mass of solvent (g), and MB is the molar mass of

the solute (g/mol).

The van’t Hoff factor (i) accounts for dissociation or association of the solute. For non-

electrolytes (like sugar or benzoic acid), i = 1. For strong electrolytes like NaCl, i = 2 (dissociates

into Na⁺ and Cl⁻), and for CaCl2, i = 3.

In this virtual lab, you will use an online cryoscopy simulation to investigate freezing-point depression with multiple solvent-solute systems, determine unknown molecular weights, and

compare your results with accepted values.

Objectives

• Explore the theory of freezing-point depression (cryoscopy) using an online simulation.

• Use the cryoscopic equation to calculate freezing-point depression for known solutions.

• Determine the molecular weight of an unknown solute from simulated experimental data.

• Understand the role of the van’t Hoff factor for electrolytes vs. non-electrolytes.

• Calculate percent error between experimental and accepted molecular weights.

Reference Data: Cryoscopic Constants

The following table lists cryoscopic constants and freezing points for common solvents used in

this simulation. You will need these values for your calculations.

Solvent Freezing Point (°C) Kf (°C·kg/mol) Molar Mass (g/mol)

Water (H₂O) 0.00 −1.86 18.015

Benzene (C₆H₆) 5.50 −4.90 78.11

Carbon tetrachloride (CCl₄) −22.62 −29.8 153.82

Carbon disulfide (CS₂) −111.61 −3.83 76.14

Lauric acid 43.8 −3.9 200.32

Procedure

Part I: Explore the Virtual Lab

1. Open the virtual lab in your web browser by navigating to: https://pcv-amrt.vlabs.ac.in/exp/cryoscopy/index.html

2. Before using the simulation, read through the Theory tab on the virtual lab website to

review the equations and concepts.

3. Complete the Self Evaluation (pretest) questions on the virtual lab site. These will help

you check your understanding before proceeding.

4. Familiarize yourself with the simulation interface. Identify where you select the solvent, the solute, and where you enter the masses of each. Note how the simulation reports the

freezing-point depression and/or the depressed freezing point.

Part II: Freezing-Point Depression of a Known Solution

In this part, you will verify the cryoscopic equation by using the simulation with a known solute (one whose molar mass you can look up). Compare the simulation’s output with your hand-

calculated values.

1. In the simulation, select Water as the solvent.

2. Select a non-electrolyte solute available in the simulation (e.g., urea or sucrose).

3. Enter a mass of solvent (e.g., 100 g of water) and a mass of solute (e.g., 5 g). Record

your exact values.

4. Run the simulation and record the freezing point of the solution as reported.

5. Record all data in Data Table 1.

Part III: Determining an Unknown Molecular Weight

Now use a different solvent-solute combination to determine the molecular weight of the solute,

as if it were unknown.

1. Select a different solvent (e.g., Benzene or Carbon tetrachloride).

2. Select a solute available in the simulation. Record its name, but pretend you do not

know its molar mass.

1. Enter masses for solvent and solute. Record exact values.

2. Run the simulation. Record the freezing point of the solution.

3. Use the cryoscopic equation to calculate the experimental molecular weight of the

solute.

4. Record all data in Data Table 2.

Data Tables

Data Table 1: Known Solution (Part II)

Measurement Value

Solvent selected

Solute selected

Mass of solvent, W_A (g)

Mass of solute, W_B (g)

Freezing point of pure solvent (°C)

Freezing point of solution from simulation (°C)

Kf of solvent (°C·kg/mol)

Van’t Hoff factor (i)

Known molar mass of solute (g/mol)

Data Table 2: Unknown Molecular Weight (Part III)

Measurement Value

Solvent selected

Solute selected

Mass of solvent, W_A (g)

Mass of solute, W_B (g)

Freezing point of pure solvent (°C)

Freezing point of solution from simulation (°C)

Observed ΔTf (°C)

Kf of solvent (°C·kg/mol)

Van’t Hoff factor (i)

Data Analysis

Complete the following calculations. Show all work with proper units.

1. Using your Data Table 1, calculate the expected ΔTf using the cryoscopic equation: ΔTf = Kf × i × m. First calculate molality from the known molar mass of your solute and the

mass of solvent. Compare your calculated ΔTf with the simulation’s result.

2. Using your Data Table 2, calculate the molality (m) from the observed ΔTf and the

known Kf of your solvent. Use: m = ΔTf / (Kf × i).

3. From the molality calculated in #2, determine the moles of solute. Use: moles = m ×

(mass of solvent in kg).

4. Calculate the experimental molecular weight of the solute: MW = (mass of solute in g) /

(moles of solute).

5. Look up the accepted molecular weight of your Part III solute. Calculate the percent

error: % error = |experimental − accepted| / accepted × 100%.