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Solutions: Class 12 Chemistry Practice Questions

30 original exam-pattern questions with full answers, matched to the current CBSE Class 12 paper design, including case-based questions. Attempt each question before opening the answer — or start a free 14-day trial ↓ for the full bank.

Q1Case-based4 marks

A food technology student is developing a sports drink. She dissolves a non-volatile, non-electrolyte carbohydrate (molar mass = 180 g mol⁻¹) in water to study its colligative properties before finalising the formulation.

A food technology student is developing a sports drink. She dissolves a non-volatile, non-electrolyte carbohydrate (molar mass = 180 g mol⁻¹) in water. She prepares Solution P by dissolving 9.0 g of this carbohydrate in 500 g of water, and Solution Q by dissolving 9.0 g of the same carbohydrate in 250 g of water.

(a) Calculate the boiling point elevation (ΔT_b) of Solution P. (K_b for water = 0.52 K kg mol⁻¹) [2 marks]

(b) Without further calculation, predict how the boiling point elevation of Solution Q compares with that of Solution P. Give one reason for your answer. [1 mark]

(c) The student later adds a small amount of NaCl (van't Hoff factor i = 2) to Solution Q to improve conductivity. State with reason whether the osmotic pressure of the resulting solution would increase, decrease, or remain the same compared to Solution Q (before NaCl addition), assuming volume remains constant. [1 mark]

Show answer
(a) Calculation of ΔT_b for Solution P:

The governing formula for boiling point elevation is:
ΔT_b = K_b × m

where m = molality = (mass of solute / molar mass of solute) / (mass of solvent in kg)

Moles of carbohydrate = 9.0 / 180 = 0.05 mol

Mass of solvent (water) = 500 g = 0.500 kg

m = 0.05 / 0.500 = 0.1 mol kg⁻¹

ΔT_b = 0.52 × 0.1 = 0.052 K

∴ Boiling point elevation of Solution P = 0.052 K

(b) The boiling point elevation of Solution Q will be greater (double) than that of Solution P.

Reason: Solution Q contains the same mass of solute (9.0 g, same moles = 0.05 mol) dissolved in half the mass of solvent (250 g = 0.250 kg), giving double the molality (m = 0.2 mol kg⁻¹). Since ΔT_b = K_b × m, a higher molality produces a greater boiling point elevation. (ΔT_b of Q = 0.104 K)

(c) The osmotic pressure of the resulting solution would increase.

Reason: Osmotic pressure is given by π = i·C·R·T. Adding NaCl (i = 2) increases the total effective concentration of solute particles (ionic species Na⁺ and Cl⁻) in the solution. Since volume is constant and temperature is unchanged, the total particle concentration (C_effective) increases, and therefore π increases.
Q2Case-based4 marks

A school chemistry club is studying the effect of dissolving different solutes in water for a science project. They dissolve glucose (non-electrolyte, molar mass = 180 g mol⁻¹) in water and measure the boiling point elevation. In a second experiment, they dissolve NaCl (molar mass = 58.5 g mol⁻¹) in water and observe a greater boiling point elevation for the same mass of solute in the same mass of solvent.

A school chemistry club is studying the effect of dissolving different solutes in water for a science project. They dissolve glucose (non-electrolyte, molar mass = 180 g mol⁻¹) in water and measure the boiling point elevation. In a second experiment, they dissolve NaCl (molar mass = 58.5 g mol⁻¹) in water and observe a greater boiling point elevation for the same mass of solute in the same mass of solvent.

(a) The students dissolve 18 g of glucose in 500 g of water. Calculate the boiling point elevation produced. (K_b for water = 0.52 K kg mol⁻¹) [2 marks]

(b) Explain why the same mass of NaCl produces a greater boiling point elevation than glucose under identical conditions of solvent and solute mass. [1 mark]

(c) State the van't Hoff factor (i) for glucose and for NaCl (assuming complete dissociation), and identify which colligative property is used to determine molar mass of a polymer in the laboratory and why. [1 mark]

Show answer
(a) Calculating boiling point elevation for glucose:

Governing formula: ΔT_b = K_b × m, where m = (mass of solute / molar mass) × (1000 / mass of solvent in g)

Moles of glucose = 18 g ÷ 180 g mol⁻¹ = 0.1 mol

Molality, m = 0.1 mol × (1000 g / 500 g) = 0.2 mol kg⁻¹

ΔT_b = 0.52 K kg mol⁻¹ × 0.2 mol kg⁻¹

∴ ΔT_b = 0.104 K

(b) NaCl is a strong electrolyte that undergoes complete dissociation in water:

NaCl(aq) → Na⁺(aq) + Cl⁻(aq)

This gives i = 2 for NaCl, meaning each formula unit produces 2 particles in solution. Since ΔT_b = i × K_b × m, the effective number of solute particles for NaCl is double that of glucose (i = 1, non-electrolyte) for the same moles. Additionally, the molar mass of NaCl (58.5 g mol⁻¹) is much lower than that of glucose (180 g mol⁻¹), so the same mass of NaCl gives far more moles and hence far more particles in solution. Both factors together result in a significantly greater boiling point elevation for NaCl.

(c) Van't Hoff factor:
— For glucose (non-electrolyte, no dissociation): i = 1
— For NaCl (complete dissociation into Na⁺ and Cl⁻): i = 2

Osmotic pressure (π = iCRT) is the colligative property preferred for determining the molar mass of polymers in the laboratory, because even very dilute solutions of high-molar-mass polymers produce a measurable osmotic pressure, whereas the corresponding boiling point elevation or freezing point depression values are too small to measure accurately.
Q3Case-based4 marks

A pharmaceutical company is developing an oral rehydration solution (ORS). A chemist dissolves 9.0 g of glucose (M = 180 g mol⁻¹) and 1.17 g of NaCl (M = 58.5 g mol⁻¹) in 500 g of water. Assume NaCl dissociates completely into Na⁺ and Cl⁻ ions. Kb for water = 0.52 K kg mol⁻¹.

A pharmaceutical company is developing an oral rehydration solution (ORS). A chemist dissolves 9.0 g of glucose (M = 180 g mol⁻¹) and 1.17 g of NaCl (M = 58.5 g mol⁻¹) in 500 g of water to prepare the ORS. Assume NaCl dissociates completely and Kb for water = 0.52 K kg mol⁻¹.

(a) Calculate the molality of glucose in the solution. [1 mark]
(b) Calculate the elevation in boiling point (ΔTb) of the ORS due to both solutes. [2 marks]
(c) The chemist observes that the actual boiling point elevation is slightly less than the calculated value. Give ONE reason for this observation. [1 mark]

Show answer
Part (a): Molality of glucose [1 mark]

Formula: m = (mass of solute / molar mass of solute) × (1000 / mass of solvent in g)

Moles of glucose = 9.0 / 180 = 0.05 mol

Molality of glucose = 0.05 × (1000 / 500) = 0.10 mol kg⁻¹

∴ Molality of glucose = 0.10 mol kg⁻¹

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Part (b): Elevation in boiling point of ORS [2 marks]

Formula: ΔTb = i · Kb · m

For glucose (non-electrolyte): i = 1
Molality of glucose = 0.10 mol kg⁻¹
ΔTb (glucose) = 1 × 0.52 × 0.10 = 0.052 K

For NaCl (complete dissociation into Na⁺ + Cl⁻): i = 2
Moles of NaCl = 1.17 / 58.5 = 0.02 mol
Molality of NaCl = 0.02 × (1000 / 500) = 0.04 mol kg⁻¹
ΔTb (NaCl) = 2 × 0.52 × 0.04 = 0.0416 K

Total ΔTb = 0.052 + 0.0416 = 0.0936 K

∴ Elevation in boiling point of the ORS = 0.0936 K (≈ 0.094 K)

---

Part (c): Reason for lower actual boiling point elevation [1 mark]

Due to interionic attractions between Na⁺ and Cl⁻ ions in solution, NaCl does not dissociate completely into free independent ions in practice. The effective number of particles (van't Hoff factor i) is less than 2, making the actual ΔTb smaller than the theoretically calculated value.
Q4Case-based4 marks

A group of students dissolves 3.42 g of cane sugar (sucrose, molar mass = 342 g mol⁻¹) in 500 g of water during a food science project. They observe that the solution boils at a temperature slightly above 100°C.

A group of students is conducting a chemistry experiment in their school laboratory. They dissolve 3.42 g of cane sugar (sucrose, molar mass = 342 g mol⁻¹) in 500 g of water to prepare a sugar solution for a food science project. They notice that the solution boils at a temperature slightly higher than 100°C.

(a) Calculate the boiling point elevation (ΔTb) of the solution. (Kb for water = 0.52 K kg mol⁻¹) [2 marks]
(b) Why does the boiling point of the sugar solution increase compared to pure water? Give reason. [1 mark]
(c) If the students had used 3.42 g of NaCl (molar mass = 58.5 g mol⁻¹) instead of sucrose in the same amount of water, would the boiling point elevation be more or less than that obtained with sucrose? Give reason. [1 mark]

Show answer
MARKING SCHEME

(a) Calculation of ΔTb: [2 marks]

Governing formula:
ΔTb = Kb × m

where m = molality = (mass of solute / molar mass of solute) / (mass of solvent in kg)

Step 1 — Calculate molality:
m = (3.42 g / 342 g mol⁻¹) / (500 / 1000 kg)
m = 0.01 mol / 0.5 kg
m = 0.02 mol kg⁻¹

Step 2 — Calculate ΔTb:
ΔTb = Kb × m
ΔTb = 0.52 K kg mol⁻¹ × 0.02 mol kg⁻¹

∴ ΔTb = 0.0104 K

(Note: Sucrose is a non-electrolyte, so van't Hoff factor i = 1; no modification needed.)

(b) Reason for elevation of boiling point: [1 mark]

Due to the presence of dissolved sucrose (non-volatile solute), the vapour pressure of the solution decreases below that of pure water (Raoult's law). A higher temperature is therefore required for the vapour pressure of the solution to equal atmospheric pressure, causing the boiling point to increase.

(OR: Addition of a non-volatile solute lowers the vapour pressure of the solvent; the solution must be heated to a higher temperature to achieve vapour pressure equal to atmospheric pressure, thus the boiling point is elevated.)

(c) Comparison with NaCl solution: [1 mark]

Moles of NaCl = 3.42 / 58.5 = 0.0585 mol
Molality of NaCl solution = 0.0585 / 0.5 = 0.117 mol kg⁻¹

NaCl is a strong electrolyte that dissociates as:
NaCl → Na⁺ + Cl⁻ (i = 2)

Effective molality = i × m = 2 × 0.117 = 0.234 mol kg⁻¹

ΔTb (NaCl) = 0.52 × 0.234 = 0.1217 K

This is much greater than ΔTb (sucrose) = 0.0104 K.

∴ The boiling point elevation with NaCl would be MORE than that with sucrose, because NaCl dissociates into two ions (i = 2), greatly increasing the number of solute particles in solution and hence causing a larger elevation in boiling point.
Q5Case-based4 marks

A chemist working in a beverage quality-control laboratory prepares two solutions at 298 K — Solution P (glucose in water) and Solution Q (urea in water) — and also handles solvent mixtures in the laboratory.

A chemist working in a beverage quality-control laboratory prepares two solutions at 298 K:

Solution P: 5 g of glucose (M = 180 g mol⁻¹) dissolved in 100 g of water.
Solution Q: 5 g of urea (M = 60 g mol⁻¹) dissolved in 100 g of water.

(a) Which solution, P or Q, will have the higher boiling point? Calculate the boiling point elevation (ΔT_b) for BOTH solutions and verify your answer numerically. (K_b for water = 0.52 K kg mol⁻¹) [2 marks]

(b) The chemist then mixes chloroform (CHCl₃) with acetone (CH₃COCH₃) in the laboratory. What type of deviation from Raoult's law will this mixture show? Give one reason. [1 mark]

(c) Define 'molality' as a measure of concentration. Why is molality preferred over molarity when studying colligative properties at different temperatures? [1 mark]

Show answer
(a) The formula for elevation in boiling point is:

ΔT_b = K_b × m, where m = (mass of solute / molar mass of solute) × (1000 / mass of solvent in g)

For Solution P (glucose, M = 180 g mol⁻¹):

m_P = (5 / 180) × (1000 / 100) = 0.02778 × 10 = 0.2778 mol kg⁻¹

ΔT_b(P) = 0.52 × 0.2778 = 0.144 K

For Solution Q (urea, M = 60 g mol⁻¹):

m_Q = (5 / 60) × (1000 / 100) = 0.08333 × 10 = 0.8333 mol kg⁻¹

ΔT_b(Q) = 0.52 × 0.8333 = 0.433 K

∴ ΔT_b(Q) > ΔT_b(P), so Solution Q (urea) has the higher boiling point.

This is because urea has a smaller molar mass than glucose, so 5 g of urea produces more moles of solute and hence a greater molality, leading to a larger boiling point elevation.

(b) A mixture of chloroform (CHCl₃) and acetone (CH₃COCH₃) shows NEGATIVE deviation from Raoult's law.

Reason: Due to the formation of intermolecular hydrogen bonding (C–H···O=C) between chloroform and acetone, the A–B interactions are stronger than the A–A and B–B interactions present in the pure components. This reduces the tendency of molecules to escape into the vapour phase, causing the vapour pressure of the mixture to be lower than predicted by Raoult's law.

(c) Molality (m) is defined as the number of moles of solute dissolved per kilogram (1000 g) of solvent.

m = moles of solute / mass of solvent in kg

Unit: mol kg⁻¹

Molality is preferred over molarity for studying colligative properties because molality depends only on the masses of solute and solvent, which do not change with temperature. Molarity, on the other hand, is expressed in terms of volume of solution, which changes with temperature due to thermal expansion or contraction. Hence, molality remains independent of temperature, making it more reliable for colligative property calculations.
Q6Case-based4 marks

A sports drink manufacturer dissolves glucose (C₆H₁₂O₆, M = 180 g mol⁻¹) and sodium chloride (NaCl, M = 58.5 g mol⁻¹) separately in water to prepare two isotonic solutions at 37°C. The osmotic pressure of the glucose solution is found to be 8.21 atm. The NaCl solution is prepared to match this osmotic pressure exactly. (R = 0.0821 L atm K⁻¹ mol⁻¹, T = 310 K)

A sports drink manufacturer dissolves glucose (C₆H₁₂O₆, M = 180 g mol⁻¹) and sodium chloride (NaCl, M = 58.5 g mol⁻¹) separately in water to prepare two isotonic solutions at 37°C. The osmotic pressure of the glucose solution is found to be 8.21 atm. The NaCl solution is prepared to match this osmotic pressure exactly.

(a) Calculate the molar concentration of the glucose solution. (R = 0.0821 L atm K⁻¹ mol⁻¹, T = 310 K) [2 marks]

(b) If NaCl is assumed to dissociate completely in water, what is the molar concentration of the NaCl solution needed to produce the same osmotic pressure of 8.21 atm? [1 mark]

(c) The manufacturer claims that dissolving the same mass of NaCl produces a higher osmotic pressure than the same mass of glucose. Justify this claim. [1 mark]

Show answer
(a) The governing equation for osmotic pressure is:
π = i · C · R · T

For glucose (non-electrolyte), i = 1.

∴ C = π / (i · R · T)

Substituting:
C = 8.21 / (1 × 0.0821 × 310)
C = 8.21 / 25.451

∴ C(glucose) = 0.3226 mol L⁻¹ ≈ 0.323 mol L⁻¹

(b) For NaCl (complete dissociation: NaCl → Na⁺ + Cl⁻), the van't Hoff factor i = 2.

Using π = i · C · R · T for the same osmotic pressure:

C = π / (i · R · T)
C = 8.21 / (2 × 0.0821 × 310)
C = 8.21 / 50.902

∴ C(NaCl) = 0.1613 mol L⁻¹ ≈ 0.161 mol L⁻¹

(c) Justification:
Osmotic pressure depends on the total number of solute particles in solution (π = i · C · R · T).

For the same mass dissolved in the same volume of water:
— Molar mass of glucose = 180 g mol⁻¹ → fewer moles per gram.
— Molar mass of NaCl = 58.5 g mol⁻¹ → more moles per gram.

Additionally, NaCl dissociates completely into two ions (i = 2), while glucose does not dissociate (i = 1).

∴ The same mass of NaCl produces a far greater number of solute particles in solution than the same mass of glucose, and hence generates a higher osmotic pressure.
Q7Case-based4 marks

A nurse in a hospital needs to prepare an intravenous (IV) drip solution that is isotonic with human blood plasma. Human blood plasma has an osmotic pressure of 7.65 atm at 310 K (normal body temperature). The nurse uses glucose (molar mass = 180 g mol⁻¹) to prepare the drip solution. (R = 0.0821 L atm K⁻¹ mol⁻¹)

A nurse in a hospital needs to prepare an intravenous (IV) drip solution that is isotonic with human blood plasma. Human blood plasma has an osmotic pressure of 7.65 atm at 310 K (normal body temperature). The nurse prepares a glucose solution (molar mass of glucose = 180 g mol⁻¹) for this purpose.

(a) Write the formula used to calculate osmotic pressure of a solution. Using this formula, calculate the molarity of the glucose solution that would be isotonic with blood plasma at 310 K. (R = 0.0821 L atm K⁻¹ mol⁻¹) (2 marks)

(b) What mass of glucose must be dissolved to prepare 500 mL of this isotonic glucose solution? (1 mark)

(c) If a patient is accidentally given a solution more concentrated than isotonic (hypertonic solution) intravenously, what will happen to the red blood cells? Name this phenomenon. (1 mark)

Show answer
(a) The formula for osmotic pressure is:

π = C·R·T

where π = osmotic pressure (atm), C = molarity of the solution (mol L⁻¹), R = gas constant = 0.0821 L atm K⁻¹ mol⁻¹, T = temperature in Kelvin.

For the glucose solution to be isotonic with blood plasma, its osmotic pressure must equal 7.65 atm.

Substituting:

7.65 = C × 0.0821 × 310

7.65 = C × 25.451

C = 7.65 / 25.451

∴ C = 0.3006 mol L⁻¹ ≈ 0.30 mol L⁻¹

(b) Moles of glucose required for 500 mL (0.500 L) of 0.30 mol L⁻¹ solution:

Moles = C × V = 0.30 × 0.500 = 0.15 mol

Mass of glucose = moles × molar mass = 0.15 × 180

∴ Mass of glucose = 27 g

(c) When a hypertonic solution is given intravenously, water molecules move out of the red blood cells into the surrounding solution through the semi-permeable cell membrane (by osmosis), since the outside solution has a higher osmotic pressure (lower water concentration). As a result, the red blood cells shrink and become crenated.

This phenomenon is called Crenation (or Plasmolysis in plant cells).
Q8Case-based4 marks

A mountaineer carries a bottle of water to a high-altitude camp where atmospheric pressure is significantly lower than at sea level, causing water to boil at only 82°C. To cook rice properly, the mountaineer dissolves 17.1 g of sucrose (C₁₂H₂₂O₁₁) in 500 g of water before heating.

A mountaineer carries a bottle of water to a high-altitude camp. At that altitude, the atmospheric pressure is significantly lower than at sea level, so the water boils at only 82°C. To cook rice properly, the mountaineer dissolves 17.1 g of sucrose (C₁₂H₂₂O₁₁) in 500 g of water before heating.

(a) Calculate the elevation in boiling point of the sucrose solution prepared by the mountaineer. Will the solution boil above or below 100°C at sea level? (Given: Molar mass of sucrose = 342 g mol⁻¹; Kb for water = 0.52 K kg mol⁻¹)

(b) Sucrose is a non-electrolyte. What is the value of the van't Hoff factor (i) for sucrose in this solution? Give one reason for your answer.

(c) At high altitude, even the sucrose solution boils at a temperature lower than 100°C. State the colligative property responsible for the elevation in boiling point and explain in one sentence why a solute elevates the boiling point of a solvent.

Show answer
MARKING SCHEME (Total: 4 marks)

(a) [2 marks]

Formula: ΔTb = i · Kb · m

Since sucrose is a non-electrolyte, i = 1.

Molality (m):
Moles of sucrose = 17.1 / 342 = 0.05 mol
Mass of solvent = 500 g = 0.500 kg
m = 0.05 / 0.500 = 0.1 mol kg⁻¹

Substituting:
ΔTb = 1 × 0.52 × 0.1
ΔTb = 0.052 K

∴ Elevation in boiling point = 0.052 K (or 0.052°C)

Normal boiling point of pure water = 100°C.
∴ Boiling point of solution at sea level = 100 + 0.052 = 100.052°C

The solution will boil ABOVE 100°C at sea level.

(Award: ½ for correct formula; ½ for correct molality; ½ for correct substitution; ½ for correct answer with conclusion)

(b) [1 mark]

The van't Hoff factor i = 1 for sucrose.

Reason: Sucrose is a non-electrolyte — it does not ionise (dissociate) in water. The number of solute particles in solution equals the number of moles dissolved, so i = 1.

(Award: ½ for i = 1; ½ for correct reason)

(c) [1 mark]

Colligative property: Elevation of boiling point (ΔTb).

Explanation: The presence of a non-volatile solute lowers the vapour pressure of the solvent (Raoult's law), so a higher temperature is required for the vapour pressure of the solution to equal the external atmospheric pressure — hence the boiling point is elevated.

(Award: ½ for naming the correct colligative property; ½ for correct one-sentence explanation involving lowering of vapour pressure)
Q9MCQ1 mark

Which of the following correctly explains why acetic acid dissolved in benzene shows a van't Hoff factor (i) less than 1?

Show answer
(B)

Explanation: The van't Hoff factor i = (actual number of particles in solution) / (number of particles if no association or dissociation occurs). In benzene (a non-polar solvent), acetic acid molecules form dimers through intermolecular hydrogen bonding between two –COOH groups. Two molecules associate into one dimer, so the effective number of solute particles decreases. Since i = (observed colligative property) / (calculated colligative property for no association), i < 1 whenever association occurs. Ionisation (which would give i > 1) does not occur in a non-polar solvent like benzene.
Q10MCQ1 mark

Which one of the following aqueous solutions will show the highest boiling point elevation?

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(C) 0.1 m BaCl₂

Explanation: Boiling point elevation is a colligative property given by ΔTb = i·Kb·m. For the same molality (0.1 m), the solution with the highest van't Hoff factor (i) gives the greatest ΔTb. Glucose and urea are non-electrolytes (i = 1). NaCl dissociates into 2 ions (Na⁺ + Cl⁻), so i = 2. BaCl₂ dissociates into 3 ions (Ba²⁺ + 2Cl⁻), so i = 3. ∴ 0.1 m BaCl₂ has the highest effective particle concentration and shows the greatest boiling point elevation.
Q11MCQ1 mark

Which of the following aqueous solutions has the lowest freezing point?

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(C) 0.1 M MgCl₂

Explanation: The depression in freezing point is a colligative property given by ΔTf = i · Kf · m, where i is the van't Hoff factor. The solution with the greatest value of i produces the greatest ΔTf and hence the lowest freezing point. MgCl₂ dissociates as MgCl₂ → Mg²⁺ + 2Cl⁻, giving i = 3, which is the highest among the four options (glucose and urea are non-electrolytes with i = 1; NaCl gives i = 2). Therefore, 0.1 M MgCl₂ has the lowest freezing point.
Q12MCQ1 mark

The vapour pressure of a solution of two liquids P and Q is found to be lower than the vapour pressure of either pure component. What type of deviation from Raoult's law does this solution show?

Show answer
(B) Negative deviation

Explanation: According to Raoult's law, the vapour pressure of an ideal solution is the weighted sum of the vapour pressures of its pure components. When the observed vapour pressure of a solution is lower than that predicted by Raoult's law — and specifically lower than the vapour pressure of either pure component — the solution exhibits negative deviation. This occurs because the A–B intermolecular interactions in the mixture are stronger than the A–A and B–B interactions in the pure liquids, causing molecules to escape less readily into the vapour phase. A classic example is a mixture of chloroform and acetone, where hydrogen bonding between the two components is stronger than in either pure liquid.
Q13MCQ1 mark

Which of the following aqueous solutions will have the highest boiling point?

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(C) 0.1 M MgCl₂

Explanation: Elevation in boiling point is a colligative property given by ΔT_b = i · K_b · m. At the same molar concentration, the solution with the highest van't Hoff factor i produces the greatest ΔT_b. NaCl dissociates into 2 ions (i = 2); glucose and urea are non-electrolytes (i = 1); MgCl₂ dissociates as MgCl₂ → Mg²⁺ + 2Cl⁻, giving i = 3. Since i is highest for MgCl₂, its 0.1 M solution has the highest boiling point.
Q14MCQ1 mark

For a dilute aqueous solution of glucose, the van't Hoff factor (i) is:

Show answer
Option (B) — Equal to 1.

Explanation: Glucose (C₆H₁₂O₆) is a non-electrolyte and does not undergo either dissociation or association in aqueous solution. The van't Hoff factor i = (actual number of particles in solution) / (number of formula units dissolved). Since the number of solute particles in solution equals the number of formula units dissolved, i = 1.
Q15MCQ1 mark

Which of the following is a colligative property of a solution?

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(B) Elevation in boiling point

Explanation: Colligative properties depend solely on the number of solute particles in a solution, not on the nature or identity of those particles. Elevation in boiling point (ΔTb) is directly proportional to the molality of the solute and is therefore a colligative property. Boiling point of the pure solvent is a fixed physical property of the solvent, not a property of the solution. Viscosity and surface tension depend on the chemical nature of both solvent and solute, so they are not colligative properties.
Q16Short Answer2 marks

A 5% solution of urea (molar mass = 60 g mol⁻¹) is isotonic with a 3% solution of an unknown non-electrolyte. Calculate the molar mass of the unknown non-electrolyte.

Show answer
For two isotonic solutions, their osmotic pressures are equal, i.e., π₁ = π₂.

Using π = CRT, at the same temperature:

C₁ = C₂

i.e., (w₁ × 1000) / (M₁ × V) = (w₂ × 1000) / (M₂ × V)

For a given volume of solution (say 100 mL), concentrations (in g per 100 mL) may be compared directly:

w₁/M₁ = w₂/M₂

Substituting the values:

5/60 = 3/M₂

M₂ = (3 × 60) / 5

∴ M₂ = 36 g mol⁻¹
Q17Short Answer2 marks

The boiling point of a 0·500 molal aqueous solution of urea (a non-electrolyte) is found to be 100·256°C. Calculate the van't Hoff factor for urea. (Given: K<sub>b</sub> for water = 0·512 K kg mol⁻¹)

Show answer
Using the formula for elevation in boiling point:

ΔT<sub>b</sub> = i × K<sub>b</sub> × m

Observed ΔT<sub>b</sub> = 100·256 − 100·000 = 0·256 K

Substituting:

0·256 = i × 0·512 × 0·500

0·256 = i × 0·256

∴ i = 1

The van't Hoff factor for urea = 1, which confirms that urea does not undergo association or dissociation in aqueous solution.
Q18Short Answer2 marks

A solution of chloroform (CHCl₃) and acetone (CH₃COCH₃) shows negative deviation from Raoult's law. Give one reason for this deviation. What type of azeotrope does such a solution form?

Show answer
Due to the formation of intermolecular hydrogen bonds between CHCl₃ and CH₃COCH₃ (A–B interactions are stronger than A–A and B–B interactions), the vapour pressure of the solution is lower than expected — hence negative deviation from Raoult's law.

Such a solution forms a maximum boiling azeotrope.
Q19Short Answer2 marks

Calculate the depression in freezing point when 5 g of glucose (Molar mass = 180 g mol⁻¹) is dissolved in 250 g of water. (K_f for water = 1.86 K kg mol⁻¹)

Show answer
Formula: ΔT_f = K_f × m, where m = (mass of solute / molar mass of solute) / (mass of solvent in kg)

Calculating molality:
m = (5 / 180) / (250 / 1000)
m = 0.02778 / 0.250
m = 0.1111 mol kg⁻¹

Substituting:
ΔT_f = 1.86 × 0.1111

∴ ΔT_f = 0.207 K
Q20Short Answer3 marks

A solution is prepared by dissolving 5.85 g of sodium chloride (NaCl) in 200 g of water. The boiling point of pure water is 100°C and the molal elevation constant (Kᵇ) for water is 0.512 K kg mol⁻¹. Assuming complete dissociation of NaCl, calculate the boiling point of the solution. (Molar mass of NaCl = 58.5 g mol⁻¹)

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Step 1 — Formula (Value Point 1)

The elevation in boiling point for an electrolyte is given by:

ΔTᵇ = i × Kᵇ × m

where i = van’t Hoff factor, Kᵇ = molal elevation constant, m = molality of the solution.

Step 2 — Substitution and Calculation (Value Point 2)

Moles of NaCl = 5.85 / 58.5 = 0.1 mol

Mass of solvent = 200 g = 0.200 kg

Molality, m = 0.1 / 0.200 = 0.5 mol kg⁻¹

NaCl dissociates completely: NaCl → Na⁺ + Cl⁻

∴ van’t Hoff factor, i = 2

Substituting:

ΔTᵇ = 2 × 0.512 × 0.5

ΔTᵇ = 0.512 K

Step 3 — Final Answer with Unit (Value Point 3)

Boiling point of solution = 100 + 0.512

∴ Boiling point of solution = 100.512°C
Q21Short Answer3 marks

A solution is prepared by dissolving 1.85 g of a non-electrolyte solute in 90 g of water. The boiling point of this solution is 100.104°C. Calculate the molar mass of the solute. Additionally, state the effect on the boiling point elevation if the same mass of solute were dissolved in 45 g of water instead.

(Kb for water = 0.52 K kg mol⁻¹, B.P. of pure water = 100°C)

Show answer
Part (i): Calculation of Molar Mass [2 marks]

The governing equation for boiling point elevation is:

ΔTb = Kb × m

where m = molality = (mass of solute / molar mass of solute) × (1000 / mass of solvent in g)

Step 1 — Calculate ΔTb:

ΔTb = 100.104 − 100.000 = 0.104°C = 0.104 K

Step 2 — Substitute in the formula:

0.104 = 0.52 × [ (1.85 / M) × (1000 / 90) ]

0.104 = 0.52 × (1850 / 90M)

0.104 = (960.4) / (90M)

0.104 × 90M = 960.4

9.36 M = 960.4

∴ M = 960.4 / 9.36

∴ Molar mass of solute = 102.6 g mol⁻¹

Part (ii): Effect on ΔTb when solvent mass is halved [1 mark]

Since molality = moles of solute / mass of solvent (in kg), halving the mass of solvent (from 90 g to 45 g) doubles the molality.

Since ΔTb = Kb × m, the boiling point elevation will also double.

∴ The boiling point elevation becomes 2 × 0.104 = 0.208 K, and the new boiling point of the solution is 100.208°C.
Q22Short Answer3 marks

State Raoult's law for a solution containing a non-volatile solute. A solution is prepared by dissolving 1.8 g of glucose (molar mass = 180 g mol⁻¹) in 100 g of water. The vapour pressure of pure water at 298 K is 23.8 mm Hg. Calculate the vapour pressure of the solution and the lowering in vapour pressure.

Show answer
Raoult's Law: The relative lowering of vapour pressure of a solution containing a non-volatile solute is equal to the mole fraction of the solute in the solution.

Mathematically: (P° − Ps) / P° = x_solute

where P° = vapour pressure of pure solvent and Ps = vapour pressure of the solution.

[1 mark for stating Raoult's law correctly]

Step 1 — Calculate moles of solute and solvent:

Moles of glucose (solute) = 1.8 / 180 = 0.01 mol

Moles of water (solvent) = 100 / 18 = 5.556 mol

Step 2 — Calculate mole fraction of solute:

x_solute = n_solute / (n_solute + n_solvent)

x_solute = 0.01 / (0.01 + 5.556) = 0.01 / 5.566 = 1.797 × 10⁻³

Step 3 — Apply Raoult's law to find lowering in vapour pressure:

(P° − Ps) / P° = x_solute

P° − Ps = P° × x_solute = 23.8 × 1.797 × 10⁻³

∴ P° − Ps = 0.0428 mm Hg ≈ 0.043 mm Hg

Step 4 — Calculate vapour pressure of the solution:

Ps = P° − (P° − Ps) = 23.8 − 0.043

∴ Ps = 23.757 mm Hg ≈ 23.76 mm Hg

[1 mark for correct substitution and calculation of mole fraction]
[1 mark for correct values of Ps and (P° − Ps) with units]
Q23Short Answer3 marks

The vapour pressure of pure liquid A at 25°C is 80 mm Hg and that of pure liquid B at the same temperature is 120 mm Hg. A solution is prepared by mixing 3 mol of A with 2 mol of B. Assuming the solution behaves ideally:
(i) Calculate the vapour pressure of the solution.
(ii) Calculate the mole fraction of B in the vapour phase above the solution.
(iii) State whether the solution shows positive deviation, negative deviation, or no deviation from Raoult's law, giving one reason.

Show answer
Given:
P°A = 80 mm Hg, P°B = 120 mm Hg
Moles of A = 3, moles of B = 2
Total moles = 3 + 2 = 5

Mole fractions in the liquid phase:
xA = 3/5 = 0.6
xB = 2/5 = 0.4

(i) By Raoult's law, the vapour pressure of an ideal solution is:
P = xA · P°A + xB · P°B
P = (0.6 × 80) + (0.4 × 120)
P = 48 + 48
∴ Vapour pressure of the solution = 96 mm Hg

(i) [1 mark]

(ii) Partial pressures in the vapour phase:
pB = xB · P°B = 0.4 × 120 = 48 mm Hg

Mole fraction of B in the vapour phase (yB):
yB = pB / P = 48 / 96
∴ yB = 0.5

(ii) [1 mark]

(iii) The solution shows NO deviation (ideal behaviour) from Raoult's law.
Due to the assumption that intermolecular interactions between A–B molecules are equal in strength to those between A–A and B–B molecules, resulting in ΔH_mix = 0 and ΔV_mix = 0.

(iii) [1 mark]
Q24Short Answer3 marks

2.4 g of a non-volatile, non-electrolyte solute is dissolved in 60 g of water. The solution boils at 100.52°C. Calculate the molar mass of the solute. (Kᵇ for water = 0.52 K kg mol⁻¹; boiling point of pure water = 100°C)

Show answer
Given:
Mass of solute, wᵇ = 2.4 g
Mass of solvent, wᵀ = 60 g = 0.060 kg
Boiling point of solution, Tᵇ(solution) = 100.52°C
Boiling point of pure water, T°ᵇ = 100.00°C
Kᵇ = 0.52 K kg mol⁻¹

Step 1 — Apply the formula for elevation of boiling point:

ΔTᵇ = Kᵇ × m

where m = molality = (wᵇ / Mᵇ) / wᵀ (in kg)

ΔTᵇ = Tᵇ(solution) − T°ᵇ = 100.52 − 100.00 = 0.52 K

Step 2 — Substitute into the formula and solve for Mᵇ:

ΔTᵇ = Kᵇ × (wᵇ × 1000) / (Mᵇ × wᵀ in g)

0.52 = 0.52 × (2.4 × 1000) / (Mᵇ × 60)

Step 3 — Rearrange:

Mᵇ = (0.52 × 2.4 × 1000) / (0.52 × 60)

Mᵇ = (0.52 × 2400) / (0.52 × 60)

Mᵇ = 2400 / 60

∴ Mᵇ = 40 g mol⁻¹
Q25Short Answer3 marks

State Raoult's law for a solution of volatile liquids. The vapour pressures of pure liquids A and B at 298 K are 450 mmHg and 150 mmHg respectively. A solution is prepared by mixing 2 moles of A and 3 moles of B. Assuming ideal behaviour, calculate: (i) the mole fractions of A and B in the solution, (ii) the total vapour pressure of the solution.

Show answer
Raoult's Law: For a solution of volatile liquids, the partial vapour pressure of each component is directly proportional to its mole fraction in the solution.

Mathematically: p<sub>A</sub> = x<sub>A</sub> · p°<sub>A</sub> and p<sub>B</sub> = x<sub>B</sub> · p°<sub>B</sub>

where p°<sub>A</sub> and p°<sub>B</sub> are the vapour pressures of the pure components. [1 mark]

(i) Calculating mole fractions:

Total moles = n<sub>A</sub> + n<sub>B</sub> = 2 + 3 = 5 mol

x<sub>A</sub> = n<sub>A</sub> / (n<sub>A</sub> + n<sub>B</sub>) = 2/5 = 0.4

x<sub>B</sub> = n<sub>B</sub> / (n<sub>A</sub> + n<sub>B</sub>) = 3/5 = 0.6 [1 mark]

(ii) Calculating total vapour pressure:

p<sub>total</sub> = x<sub>A</sub> · p°<sub>A</sub> + x<sub>B</sub> · p°<sub>B</sub>

p<sub>total</sub> = (0.4 × 450) + (0.6 × 150)

p<sub>total</sub> = 180 + 90

∴ p<sub>total</sub> = 270 mmHg [1 mark]
Q26Case-based4 marks

A food technologist is studying the preservation properties of sugar solutions used in jam-making. She prepares two solutions — one of sucrose and one of glucose — and investigates their colligative properties.

A food technologist is studying the preservation properties of a sugar solution used in jam-making. She dissolves 171 g of sucrose (C₁₂H₂₂O₁₁, molar mass = 342 g mol⁻¹) in 1000 g of water and measures its boiling point elevation. She then compares this with a glucose solution prepared by dissolving 90 g of glucose (C₆H₁₂O₆, molar mass = 180 g mol⁻¹) in 500 g of water.

(a) Calculate the boiling point of the sucrose solution. [Given: Kb for water = 0.52 K kg mol⁻¹; boiling point of pure water = 100°C] (2 marks)

(b) The technologist claims that both solutions will show the same elevation in boiling point. Is her claim correct? Justify your answer with a calculation. (1 mark)

(c) She further notes that neither sucrose nor glucose solution deviates from Raoult's law ideally when concentrated. State the type of deviation these solutions are expected to show and give ONE reason. (1 mark)

Show answer
(a) Calculating the boiling point of the sucrose solution:

The governing formula is:

ΔTb = Kb × m

where m = molality = moles of solute / mass of solvent in kg.

Moles of sucrose = 171 / 342 = 0.5 mol

Mass of solvent = 1000 g = 1.0 kg

∴ m = 0.5 / 1.0 = 0.5 mol kg⁻¹

ΔTb = 0.52 × 0.5 = 0.26 K

∴ Boiling point of sucrose solution = 100 + 0.26 = 100.26°C

(b) Checking the technologist's claim:

For the glucose solution:

Moles of glucose = 90 / 180 = 0.5 mol

Mass of solvent = 500 g = 0.5 kg

m = 0.5 / 0.5 = 1.0 mol kg⁻¹

ΔTb = 0.52 × 1.0 = 0.52 K

Since ΔTb (sucrose) = 0.26 K and ΔTb (glucose) = 0.52 K, the two values are NOT equal.

∴ The technologist's claim is INCORRECT. Although both solutions contain 0.5 mol of solute, the glucose solution has only 500 g of solvent (half that of the sucrose solution), giving it twice the molality and hence twice the boiling point elevation.

(c) Both sucrose and glucose are non-electrolytes that can form hydrogen bonds with water (solute–solvent interactions are stronger than solute–solute or solvent–solvent interactions in dilute solutions). However, when concentrated, these solutions show NEGATIVE deviation from Raoult's law, because the solute–solvent (sugar–water) hydrogen bonding interactions are stronger than the solvent–solvent (water–water) interactions, reducing the vapour pressure below the ideal value predicted by Raoult's law.
Q27Case-based4 marks

A sports drink manufacturer claims that their new electrolyte drink has an osmotic pressure equal to that of human blood plasma (approximately 7.65 atm at 37°C). A quality-control chemist dissolves 2.85 g of a non-electrolyte organic solute in enough water to make 100 mL of solution at 37°C and measures its osmotic pressure as 7.65 atm. The drink, when mixed with a small amount of a volatile organic solvent, also shows a boiling point lower than that of pure water.

A sports drink manufacturer claims that their new electrolyte drink has an osmotic pressure equal to that of human blood plasma (approximately 7.65 atm at 37°C). To verify this, a quality-control chemist dissolves 2.85 g of the active organic solute (a non-electrolyte) in enough water to make 100 mL of solution at 37°C.

(a) Write the formula used to calculate osmotic pressure of a solution and identify each term. (1 mark)

(b) Calculate the molar mass of the organic solute, given that the osmotic pressure of the prepared solution is 7.65 atm. (R = 0.0821 L atm K⁻¹ mol⁻¹) (2 marks)

(c) The chemist also notices that the drink, when mixed with a small amount of a volatile organic solvent, shows a boiling point LOWER than that of pure water. Identify the type of deviation from Raoult's law shown and give ONE reason for it. (1 mark)

Show answer
CBSE MARKING SCHEME — SOLUTIONS (4 marks)

──────────────────────────────────────
Part (a) — 1 mark
──────────────────────────────────────

The formula for osmotic pressure is:

π = C R T

where:
π = osmotic pressure of the solution (atm)
C = molar concentration of the solute (mol L⁻¹)
R = gas constant (0.0821 L atm K⁻¹ mol⁻¹)
T = absolute temperature in Kelvin (K)

[Award 1 mark for correct formula with identification of at least π, C, R and T.]

──────────────────────────────────────
Part (b) — 2 marks
──────────────────────────────────────

Given:
π = 7.65 atm
Mass of solute (w) = 2.85 g
Volume of solution (V) = 100 mL = 0.1 L
T = 37°C = 37 + 273 = 310 K
R = 0.0821 L atm K⁻¹ mol⁻¹

Step 1 — Write the working formula:

π = (w / M) × (1 / V) × R × T

∴ M = (w × R × T) / (π × V) [1 mark — correct substitution]

Step 2 — Substitute values:

M = (2.85 × 0.0821 × 310) / (7.65 × 0.1)

M = (2.85 × 25.451) / (0.765)

M = 72.535 / 0.765

∴ M = 94.8 g mol⁻¹ ≈ 95 g mol⁻¹ [1 mark — correct answer with unit]

[ECF: If a student uses T = 37 K (error), carry the incorrect T through; penalise only at the substitution step, not again at the final answer.]

──────────────────────────────────────
Part (c) — 1 mark
──────────────────────────────────────

The solution shows POSITIVE deviation from Raoult's law.

Reason: Due to the solute–solvent (A–B) interactions being weaker than the solute–solute (A–A) and solvent–solvent (B–B) interactions, molecules escape more easily into the vapour phase, increasing the vapour pressure above the ideal value — hence the boiling point is LOWER than expected.

[Award 1 mark for: naming positive deviation (½) + one correct reason (½).]
[Accept equivalent reasoning such as: 'intermolecular forces between the mixed components are weaker than in the pure components, so vapour pressure increases, lowering the boiling point.']
Q28Case-based4 marks

A nurse in a hospital pharmacy is preparing intravenous (IV) fluids. She has four saline solutions at 25°C:

Solution P: 0.9% (w/v) NaCl in water (normal saline)
Solution Q: 1.8% (w/v) NaCl in water
Solution R: 0.45% (w/v) NaCl in water
Solution S: 5.0% (w/v) glucose (M = 180 g mol⁻¹) in water

Assume NaCl is completely dissociated (i = 2) and glucose does not dissociate (i = 1). The osmotic pressure of blood plasma is approximately 7.7 atm at 25°C. (R = 0.082 L atm K⁻¹ mol⁻¹, Molar mass of NaCl = 58.5 g mol⁻¹)

A nurse in a hospital pharmacy is preparing intravenous (IV) fluids. She has four saline solutions at 25°C:

Solution P: 0.9% (w/v) NaCl in water (normal saline)
Solution Q: 1.8% (w/v) NaCl in water
Solution R: 0.45% (w/v) NaCl in water
Solution S: 5.0% (w/v) glucose (M = 180 g mol⁻¹) in water

Assume NaCl is completely dissociated (i = 2) and glucose does not dissociate (i = 1). The osmotic pressure of blood plasma is approximately 7.7 atm at 25°C. (R = 0.082 L atm K⁻¹ mol⁻¹, Molar mass of NaCl = 58.5 g mol⁻¹)

(a) Calculate the osmotic pressure of Solution Q (1.8% w/v NaCl). Show your working. (2 marks)
(b) The nurse must choose an isotonic solution — one whose osmotic pressure matches that of blood plasma (≈ 7.7 atm). Based on your answer to (a) and the data given, identify which solution (P, Q, R or S) is isotonic and justify your choice. (1 mark)
(c) What will happen to red blood cells (RBCs) if Solution Q is administered intravenously? Name the phenomenon. (1 mark)

Show answer
(a) Calculation of osmotic pressure of Solution Q (1.8% w/v NaCl): [2 marks]

The formula for osmotic pressure is:
π = i · C · R · T

where C is the molar concentration (mol L⁻¹), R = 0.082 L atm K⁻¹ mol⁻¹, T = 298 K, i = 2 (complete dissociation of NaCl).

1.8% (w/v) means 1.8 g of NaCl per 100 mL = 18 g per 1000 mL = 18 g per litre.

Molar concentration of NaCl:
C = 18 / 58.5 = 0.3077 mol L⁻¹

Substituting in the formula:
π = 2 × 0.3077 × 0.082 × 298
π = 2 × 0.3077 × 24.436
π = 2 × 7.52
π ≈ 15.0 atm

∴ Osmotic pressure of Solution Q ≈ 15.0 atm

(b) Identification of the isotonic solution: [1 mark]

Solution P (0.9% w/v NaCl) is isotonic.

Justification: Solution Q (1.8% w/v NaCl) has π ≈ 15.0 atm, which is approximately twice the osmotic pressure of blood plasma (7.7 atm). Since Solution P has exactly half the NaCl concentration of Solution Q, its osmotic pressure ≈ 15.0 / 2 = 7.5 atm ≈ 7.7 atm, which matches blood plasma. Hence Solution P (normal saline, 0.9% NaCl) is isotonic with blood.

(c) Effect of Solution Q on RBCs — phenomenon: [1 mark]

Solution Q is hypertonic (π ≈ 15.0 atm > 7.7 atm of blood plasma). When administered intravenously, water will move out of the RBCs into the surrounding solution by osmosis (from lower solute concentration inside the cell to higher outside). As a result, the RBCs will shrink and become crenated.

The phenomenon is called Crenation (or Plasmolysis in plant cells / Exosmosis).
Q29Case-based4 marks

A food technologist is developing a sports drink that must remain liquid even when stored at −3.72°C. She dissolves glucose or NaCl in water and studies the effect on freezing point.

A food technologist is developing a sports drink that must remain liquid even when stored at −3.72°C. She dissolves a calculated mass of glucose (C₆H₁₂O₆, molar mass = 180 g mol⁻¹) in 500 g of water. She also considers replacing glucose with NaCl (molar mass = 58.5 g mol⁻¹), assuming complete dissociation of NaCl into two ions.

(a) Calculate the mass of glucose that must be dissolved in 500 g of water so that the solution does not freeze at −3.72°C.
(Given: Kf for water = 1.86 K kg mol⁻¹)

(b) What mass of NaCl would produce the same freezing point depression (ΔTf = 3.72 K) in 500 g of water? (Assume complete dissociation; i = 2)

(c) In terms of colligative properties, explain why NaCl is more effective than glucose at lowering the freezing point, even when equal masses of each are dissolved.

Show answer
Part (a): Mass of glucose required [2 marks]

The governing formula for freezing point depression is:
ΔTf = Kf × m
where m = molality = moles of solute / mass of solvent in kg.

Given: ΔTf = 3.72 K, Kf = 1.86 K kg mol⁻¹, mass of solvent = 500 g = 0.500 kg.

Step 1 — Calculate required molality:
m = ΔTf / Kf = 3.72 / 1.86 = 2.0 mol kg⁻¹

Step 2 — Calculate moles of glucose needed:
moles of glucose = m × mass of solvent (kg) = 2.0 × 0.500 = 1.0 mol

Step 3 — Calculate mass of glucose:
mass = moles × molar mass = 1.0 × 180 = 180 g

∴ Mass of glucose required = 180 g

---

Part (b): Mass of NaCl required [1 mark]

For an electrolyte, the modified formula is:
ΔTf = i × Kf × m

Given: ΔTf = 3.72 K, Kf = 1.86 K kg mol⁻¹, i = 2 (complete dissociation into Na⁺ and Cl⁻), mass of solvent = 0.500 kg.

Step 1 — Calculate required molality:
m = ΔTf / (i × Kf) = 3.72 / (2 × 1.86) = 3.72 / 3.72 = 1.0 mol kg⁻¹

Step 2 — Calculate moles of NaCl needed:
moles of NaCl = 1.0 × 0.500 = 0.5 mol

Step 3 — Calculate mass of NaCl:
mass = 0.5 × 58.5 = 29.25 g

∴ Mass of NaCl required = 29.25 g

---

Part (c): Why NaCl is more effective than glucose [1 mark]

Freezing point depression is a colligative property — it depends on the number of solute particles in solution, not on the nature or identity of the solute.

NaCl is a strong electrolyte that dissociates completely: NaCl(aq) → Na⁺(aq) + Cl⁻(aq), giving a van't Hoff factor i = 2. Thus, each mole of NaCl produces 2 moles of particles in solution.

Glucose is a non-electrolyte and does not dissociate (i = 1). Each mole of glucose produces only 1 mole of particles.

∴ For the same mass dissolved, NaCl generates a greater number of solute particles in solution and hence produces a larger freezing point depression than glucose. Equivalently, NaCl requires far less mass (29.25 g versus 180 g) to achieve the same ΔTf.
Q30Case-based4 marks

Four aqueous solutions, each 0.1 mol kg⁻¹, are prepared in a school laboratory for a freezing point depression experiment: glucose (non-electrolyte), NaCl (strong electrolyte, complete ionisation), CaCl₂ (strong electrolyte, complete ionisation), and acetic acid (weak electrolyte, α = 0.02).

A school laboratory has four aqueous solutions prepared for a freezing point depression experiment. Each solution is 0.1 mol kg⁻¹. The solutions are:
(i) Glucose (C₆H₁₂O₆) — a non-electrolyte
(ii) Sodium chloride (NaCl) — strong electrolyte, assume complete ionisation
(iii) Calcium chloride (CaCl₂) — strong electrolyte, assume complete ionisation
(iv) Acetic acid (CH₃COOH) — weak electrolyte, partial ionisation (degree of ionisation α = 0.02)

(a) Calculate the van't Hoff factor (i) for each solution and arrange the four solutions in increasing order of their freezing point depression. (2 marks)
(b) Which solution will have the HIGHEST freezing point? Justify your answer in one sentence. (1 mark)
(c) The teacher notices that the experimentally observed freezing point depression for acetic acid is slightly higher than that calculated for a pure non-electrolyte at the same molality, but much lower than for NaCl. Explain why. (1 mark)

Show answer
PART (a) — 2 marks

The governing relation for freezing point depression is:

ΔT_f = i · K_f · m

Since K_f and m are identical for all four solutions, the magnitude of ΔT_f depends only on the van't Hoff factor i.

Calculating i for each solution:

(i) Glucose — non-electrolyte, no ionisation:
i = 1

(ii) NaCl → Na⁺ + Cl⁻ (2 ions, complete ionisation):
i = 2

(iii) CaCl₂ → Ca²⁺ + 2Cl⁻ (3 ions, complete ionisation):
i = 3

(iv) CH₃COOH ⇌ CH₃COO⁻ + H⁺ (weak electrolyte, partial ionisation)
For a binary weak electrolyte: i = 1 + α = 1 + 0.02 = 1.02

Summary of i values:

Solution | i
---------------|------
Glucose | 1.00
CH₃COOH | 1.02
NaCl | 2.00
CaCl₂ | 3.00

Since ΔT_f ∝ i, the increasing order of freezing point depression is:

Glucose < CH₃COOH < NaCl < CaCl₂

∴ Increasing order of ΔT_f: Glucose < Acetic acid < NaCl < CaCl₂

(1 mark for all four correct i values; 1 mark for the correct increasing order)

---

PART (b) — 1 mark

The solution with the LOWEST ΔT_f will have the HIGHEST freezing point.

∴ Glucose solution (i = 1, least freezing point depression) will have the highest freezing point.

Justification: Glucose is a non-electrolyte (i = 1) and produces the fewest solute particles, resulting in the smallest depression of freezing point and hence the highest freezing point among the four solutions.

---

PART (c) — 1 mark

Acetic acid is a weak electrolyte that partially ionises in aqueous solution (α = 0.02), producing a small number of additional ions (CH₃COO⁻ and H⁺). Due to this partial ionisation, the total number of solute particles is slightly greater than that of a non-electrolyte at the same molality (i = 1.02 > 1), so the freezing point depression is slightly higher than for glucose. However, since ionisation is only 2%, far fewer ions are produced compared to strong electrolytes like NaCl (i = 2), so the depression is much smaller than that of NaCl.

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