Q1. What is the freezing point of a 1.00 molal Na₂SO₄ solution? (Kf for water = 1.86 °C/m)

Background

Topic: Freezing Point Depression (Colligative Properties)

This question tests your understanding of how solutes affect the freezing point of a solvent, specifically using the freezing point depression equation. You must identify the van 't Hoff factor (i), use the given molality, and apply the formula to find the new freezing point.

Key Terms and Formulas

• Molality (m): Moles of solute per kilogram of solvent.

• Freezing Point Depression Constant (Kf): A property of the solvent (for water, Kf = 1.86 °C/m).

• van 't Hoff factor (i): Number of particles the solute dissociates into.

Key Formula:

Where:

• = freezing point depression (°C)

• = van 't Hoff factor

• = freezing point depression constant (°C/m)

• = molality (mol/kg)

Step-by-Step Guidance

1. Determine the van 't Hoff factor () for Na₂SO₄. When Na₂SO₄ dissolves, it dissociates into 2 Na⁺ and 1 SO₄²⁻ ions, so .

2. Identify the given molality: m (mol/kg).

3. Plug the values into the freezing point depression formula:

4. Calculate the new freezing point by subtracting from the normal freezing point of water (0.00°C):

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Q2. What is the boiling point of a 0.222 m aqueous solution of sucrose (C₁₂H₂₂O₁₁)? (Kb = 0.512 °C/m)

Background

Topic: Boiling Point Elevation (Colligative Properties)

This question tests your ability to calculate the boiling point elevation for a solution using a non-electrolyte solute.

Key Terms and Formulas

• Boiling Point Elevation Constant (Kb): For water, Kb = 0.512 °C/m.

• van 't Hoff factor (i): For non-electrolytes like sucrose, .

Key Formula:

Where:

• = boiling point elevation (°C)

• = van 't Hoff factor

• = boiling point elevation constant (°C/m)

• = molality (mol/kg)

Step-by-Step Guidance

1. Identify the van 't Hoff factor for sucrose: (since it does not dissociate in water).

2. Molality is given: m.

3. Plug the values into the boiling point elevation formula:

4. Add to the normal boiling point of water (100.000°C):

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Q3. What is the normal boiling point of a 0.122 m aqueous solution of KI? (Kb = 0.512 °C/m)

Background

Topic: Boiling Point Elevation (Colligative Properties)

This question tests your ability to determine the boiling point elevation for an ionic solute that dissociates in water.

Key Terms and Formulas

• Boiling Point Elevation Constant (Kb): For water, Kb = 0.512 °C/m.

• van 't Hoff factor (i): For KI, (K⁺ and I⁻).

Key Formula:

Step-by-Step Guidance

1. Determine the van 't Hoff factor for KI: (since KI dissociates into K⁺ and I⁻).

2. Molality is given: m.

3. Plug the values into the formula:

4. Add to the normal boiling point of water (100.000°C):

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Q4. Calculate the boiling point and freezing point of a 25.0 mass percent solution of ethylene glycol (C₂H₆O₂) in water. (Kb = 0.512 °C/m, Kf = 1.86 °C/m, M = 62.07 g/mol)

Background

Topic: Boiling Point Elevation and Freezing Point Depression (Colligative Properties)

This question tests your ability to convert mass percent to molality, then use colligative property equations to find new boiling and freezing points.

Key Terms and Formulas

• Molality (m): Moles of solute per kg of solvent.

• Boiling Point Elevation and Freezing Point Depression:

Step-by-Step Guidance

1. Assume 1.00 kg of solution for convenience. Calculate mass of solute (25% of 1.00 kg = 250 g) and mass of solvent (1000 g - 250 g = 750 g = 0.750 kg).

2. Find moles of ethylene glycol:

3. Calculate molality:

4. Since ethylene glycol is a non-electrolyte, .

5. Calculate and using the formulas above.

6. Add to 100.00°C for boiling point, and subtract from 0.00°C for freezing point.

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Q5. Calculate the freezing point of a solution containing 0.600 kg of CHCl₃ and 42.0 g of eucalyptol (C₁₀H₁₈O). (Kf for CHCl₃ = 4.68 °C/m, normal FP = -63.5°C, M = 154.25 g/mol)

Background

Topic: Freezing Point Depression (Colligative Properties)

This question tests your ability to calculate the freezing point of a solution using a non-aqueous solvent and a non-electrolyte solute.

Key Terms and Formulas

• Freezing Point Depression Constant (Kf): For CHCl₃, Kf = 4.68 °C/m.

• van 't Hoff factor (i): For eucalyptol, .

Key Formula:

Step-by-Step Guidance

1. Calculate moles of eucalyptol:

2. Calculate molality:

3. Since eucalyptol is a non-electrolyte, .

4. Calculate using the formula above.

5. Subtract from the normal freezing point of CHCl₃ (-63.5°C):

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Q6. List the following aqueous solutions in order of their expected freezing points (from lowest to highest): 0.050 m CaCl₂; 0.15 m NaCl; 0.10 m HCl; 0.050 m HC₂H₃O₂; 0.10 m C₁₂H₂₂O₁₁

Background

Topic: Freezing Point Depression (Comparing Solutions)

This question tests your ability to compare the effects of different solutes and concentrations on freezing point depression, using the concept of effective molality ().

Key Terms and Formulas

• Effective Molality: (accounts for both concentration and dissociation)

• van 't Hoff factor (i): Number of particles produced per formula unit

Step-by-Step Guidance

1. For each solution, determine (number of particles):

   • CaCl₂:

   • NaCl:

   • HCl:

   • HC₂H₃O₂: (weak acid, partial dissociation)

   • C₁₂H₂₂O₁₁: (non-electrolyte)

2. Calculate effective molality for each:

   • CaCl₂:

   • NaCl:

   • HCl:

   • HC₂H₃O₂:

   • C₁₂H₂₂O₁₁:

3. Rank the solutions from highest to lowest effective molality. The lowest freezing point corresponds to the highest effective molality.

4. List the solutions in order from lowest to highest freezing point (most to least depressed).

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Q7. A solution of an unknown nonvolatile non-electrolyte was prepared by dissolving 0.250 g in 40.0 g CCl₄. The normal boiling point of the resultant solution increased by 0.357°C. Calculate the molar mass of the solute. (Kb = 5.02°C/molal)

Background

Topic: Determining Molar Mass from Boiling Point Elevation

This question tests your ability to work backwards from a measured boiling point elevation to determine the molar mass of an unknown solute.

Key Terms and Formulas

• Boiling Point Elevation:

• Molality (m):

• Molar Mass (M):

Step-by-Step Guidance

1. Boiling point elevation is given: °C.

2. Assume (non-electrolyte).

3. Calculate molality:

4. Find moles of solute:

5. Calculate molar mass:

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Q8. When 0.186 g of an organic substance is dissolved in 22.01 g of liquid camphor (Kf = 40.0°C/molal), the freezing point drops from 179.8°C to 176.7°C. What is the approximate molar mass of the solute?

Background

Topic: Determining Molar Mass from Freezing Point Depression

This question tests your ability to use freezing point depression data to calculate the molar mass of an unknown solute.

Key Terms and Formulas

• Freezing Point Depression:

• Molality (m):

• Molar Mass (M):

Step-by-Step Guidance

1. Calculate

2. Assume (organic substance, non-electrolyte).

3. Calculate molality:

4. Find moles of solute:

5. Calculate molar mass:

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Q9. When 4.04 g of pyrene (empirical formula C₈H₅) is dissolved in 10.00 g of benzene, the boiling point of the solution is 85.1°C. Calculate the molar mass of pyrene and determine its molecular formula. (Kb = 2.53°C/m, normal BP = 80.1°C)

Background

Topic: Determining Molar Mass and Molecular Formula from Boiling Point Elevation

This question tests your ability to use boiling point elevation to find the molar mass of a compound, then relate it to the empirical formula to find the molecular formula.

Key Terms and Formulas

• Boiling Point Elevation:

• Empirical Formula Mass: Sum of atomic masses in empirical formula

• Molecular Formula:

Step-by-Step Guidance

1. Calculate

2. Assume (pyrene is a non-electrolyte).

3. Calculate molality:

4. Find moles of solute: kg

5. Calculate molar mass:

6. Find empirical formula mass and determine the multiplier to get the molecular formula.

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Q10. A mass of CaCl₂, when dissolved in 100.00 g of water, gives an expected freezing point of -5.0°C. What mass of glucose (C₆H₁₂O₆) would give the same result? (Kf = 1.86°C/m, M(CaCl₂) = 110.98 g/mol, M(glucose) = 180.18 g/mol)

Background

Topic: Comparing Freezing Point Depression for Different Solutes

This question tests your ability to compare the effects of an electrolyte and a non-electrolyte on freezing point depression, and to calculate the mass of solute needed to achieve the same effect.

Key Terms and Formulas

• Freezing Point Depression:

• Molality (m):

• Mass:

Step-by-Step Guidance

Part A: CaCl₂ Solution

1. Calculate for the target freezing point:

2. Find for CaCl₂: (Ca²⁺ + 2Cl⁻)

3. Find molality:

4. Find moles of CaCl₂: kg

5. Calculate mass of CaCl₂:

Part B: Glucose Solution (same )

1. Use the same (5.0°C).

2. For glucose, (non-electrolyte).

3. Find molality:

4. Find moles of glucose: kg

5. Calculate mass of glucose:

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