Depression Freezing Point

8 MCQs3 revision cards9-step worked example

Source: NCERT SolutionsPYQ coverage: NEET 2021, 2022, 2023, 2024, 2025Official key: NTA-verifiedLast reviewed: May 2026

Lesson

Depression of Freezing Point

Here is the trap that costs marks on this topic: you see NaCl or CaCl₂ in the stem, calculate ΔT_f using the plain formula, and forget to multiply by the Van't Hoff factor i. That single omission produces a distractor that NTA places among the options every time this topic appears.

The core idea. A non-volatile solute dissolved in a solvent lowers the solvent's freezing point. The depression is a colligative property — it depends on the number of solute particles, not their identity. NCERT Class 12 Chemistry Chapter 1 (page 20) gives the relationship:

ΔT_f = K_f × m

where K_f is the cryoscopic constant of the solvent (water: 1.86 K·kg/mol) and m is molality (moles of solute per kg of solvent — not per kg of solution).

For electrolytes, each formula unit dissociates into ions, increasing the effective particle count. The corrected form is:

ΔT_f = i × K_f × m

where i is the Van't Hoff factor. NaCl → Na⁺ + Cl⁻ gives i ≈ 2. CaCl₂ → Ca²⁺ + 2 Cl⁻ gives i ≈ 3. Forgetting i gives you exactly half (or one-third) of the correct answer — and that value will be sitting in the options waiting for you.

Molar mass from ΔT_f. A common NEET pattern: you observe a freezing-point depression, know K_f and the mass of solute, and back-calculate molar mass. Rearrange: M₂ = (K_f × w₂ × 1000) / (ΔT_f × w₁), where w₂ is mass of solute in grams and w₁ is mass of solvent in grams. For electrolytes, replace K_f with i × K_f (or equivalently divide the calculated M₂ by i).

Watch-out: molality uses mass of solvent, not mass of solution. If the problem gives total solution mass, subtract the solute mass first.

Practice MCQs

Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.

MCQ 1Easy RecallPractice

The freezing-point depression of a solution is a colligative property because it depends on:

MCQ 2Easy RecallPractice

The SI unit of the cryoscopic constant K_f is:

MCQ 3Easy RecallPractice

Which of the following aqueous solutions will show the greatest depression in freezing point? (Assume complete dissociation and equal molality for all.)

MCQ 4Direct ApplicationPractice

5.85 g of NaCl (molar mass = 58.5 g/mol) is dissolved in 500 g of water. If K_f for water is 1.86 K·kg/mol and NaCl dissociates completely, the depression in freezing point is:

MCQ 5Direct ApplicationPractice

3.0 g of a non-electrolyte solute is dissolved in 100 g of water. The freezing point of the solution is found to be −0.93 °C. If K_f for water is 1.86 K·kg/mol, the molar mass of the solute is:

MCQ 6Direct ApplicationPractice

The freezing point of a 0.05 m aqueous solution of K₂SO₄ is (assume complete dissociation, K_f = 1.86 K·kg/mol):

MCQ 7CalculationPractice

0.6 g of urea (molar mass 60 g/mol) and 0.585 g of NaCl (molar mass 58.5 g/mol) are dissolved together in 200 g of water. If K_f = 1.86 K·kg/mol and NaCl dissociates completely, the freezing-point depression is:

MCQ 8CalculationPractice

An aqueous solution of a substance X freezes at −0.558 °C. When 1.0 g of X is dissolved in 100 g of water, K_f = 1.86 K·kg/mol. The solution is found to have Van't Hoff factor i = 2. The molar mass of X (as an undissociated formula unit) is:

Quick recall before you leave

Worked Example

1
Given
- 11.1 g of CaCl₂ (molar mass = 111 g/mol) dissolved in 500 g of water - K_f for water = 1.86 K·kg/mol - CaCl₂ dissociates completely
2
Required
Depression of freezing point, ΔT_f
3
Concept
Freezing-point depression is a colligative property. For an electrolyte, the effective particle count is higher than the formula-unit count, so we must include the Van't Hoff factor *i*. CaCl₂ → Ca²⁺ + 2 Cl⁻ produces 3 ions per formula unit, so i = 3 (NCERT Class 12 Chemistry Chapter 1, page 20).
4
Formula
ΔT_f = i × K_f × m, where m = (moles of solute) / (kg of solvent)
5
Substitution
- Moles of CaCl₂ = 11.1 g / 111 g/mol = 0.1 mol - Mass of solvent = 500 g = 0.500 kg - m = 0.1 / 0.500 = 0.2 mol/kg - ΔT_f = 3 × 1.86 × 0.2
6
Calculation
ΔT_f = 3 × 1.86 × 0.2 = 3 × 0.372 = 1.116 K Note on exact values: the integer 3 (ion count) and the division 11.1/111 = 0.1 (exact by construction of the problem) are counting/exact quantities and do not limit significant figures. K_f = 1.86 (3 sig figs) governs precision.
7
Final answer
ΔT_f = 1.12 K (3 significant figures, governed by K_f = 1.86) Freezing point of solution = 0 − 1.12 = −1.12 °C
8
Common trap
Without the Van't Hoff factor: ΔT_f = 1.86 × 0.2 = 0.372 K — exactly one-third of the correct answer. This is the value NTA places as a distractor. If your answer is suspiciously small for an ionic compound, check whether you included *i*.
9
Similar NEET-style question
*What is the freezing point of a solution containing 5.85 g of NaCl (M = 58.5 g/mol) in 250 g of water? (K_f = 1.86 K·kg/mol, complete dissociation)* Approach: moles = 0.1, m = 0.1/0.250 = 0.4 mol/kg, i = 2 for NaCl. ΔT_f = 2 × 1.86 × 0.4 = 1.488 K. Freezing point = −1.49 °C. ---

Before solving, remember these

Formula

Freezing point depression

ΔT_f = K_f × m, where K_f is cryoscopic constant (water: 1.86 K·kg/mol). Used to determine molar mass of solute.

-- NCERT Class 12 Chemistry, Ch. 1, p. 20

Formulas

Molality

m = n / m_{solv}

Molal concentration: moles of solute per kg of solvent. Temperature-independent.

Symbol	Quantity	SI Unit
m	molality	mol/kg
n	moles solute	mol

Valid when

Mass of SOLVENT (not solution)

Molarity

M = n / V

Molar concentration: moles of solute per litre of solution.

Symbol	Quantity	SI Unit
M	molarity	mol/L
n	moles solute	mol
V	solution volume	L

Valid when

Volume of SOLUTION not solvent
Temperature dependent (volume changes with T)

Boiling-point elevation

Δ T_{b} = K_{b} m

Solute raises boiling point. K_b is ebullioscopic constant of solvent (water: 0.52 K kg/mol).

Symbol	Quantity	SI Unit
ΔT_b	BP elevation	K
K_b	ebullioscopic constant	K kg/mol
m	molality	mol/kg

Valid when

Dilute solution
Non-electrolyte

Freezing-point depression

Δ T_{f} = K_{f} m

Solute lowers freezing point. K_f is cryoscopic constant of solvent (water: 1.86 K kg/mol). Used for molar mass determination.

Symbol	Quantity	SI Unit
ΔT_f	FP depression	K
K_f	cryoscopic constant	K kg/mol
m	molality	mol/kg

Valid when

Dilute solution
Non-electrolyte (else multiply by i)

Osmotic pressure

π = C R T

Pressure required to prevent osmosis. C in mol/L; T in K. Used for high-molar-mass biomolecules.

Symbol	Quantity	SI Unit
π	osmotic pressure	Pa
C	molarity	mol/L
R	gas constant	J/mol/K
T	temp	K

Valid when

Dilute solution
Semipermeable membrane separating pure solvent from solution

Raoult's law

p = p_{1}^{\circ} x_{1} + p_{2}^{\circ} x_{2}

Total vapor pressure of ideal solution = sum of mole-fraction-weighted vapor pressures of components.

Symbol	Quantity	SI Unit
p	total vapor pressure	Pa
p_i°	pure component vp	Pa
x_i	mole fraction	-

Valid when

Ideal solution
Both volatile

Relative lowering of VP

\frac{p ^{\circ} - p}{p ^{\circ}} = x_{solute}

For non-volatile solute: relative lowering of VP equals mole fraction of solute.

Symbol	Quantity	SI Unit
p	solution vp	Pa
p°	pure solvent vp	Pa
x_solute	mole fraction	-

Valid when

Non-volatile solute
Dilute solution
Non-electrolyte (else use i)

Van't Hoff factor

i = \frac{observed}{theoretical}

Correction factor for electrolytes. NaCl: i≈2; CaCl₂: i≈3. Multiply colligative formula by i.

Symbol	Quantity	SI Unit
i	Van't Hoff factor	-

Valid when

Electrolyte solution
Account for ion-pair association/dissociation

Exam Traps & Common Mistakes

These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.

Trap

Mole vs mass fraction

Category: Similar Terms

Student uses mass fraction (w₁/total mass) where mole fraction (n₁/total moles) is required.

When it triggers

Question gives masses or molar masses and asks about Raoult's law or vapor pressure.

How to avoid

Raoult's law uses MOLE fractions, not mass fractions. Convert mass to moles first using molar mass.

Trap

Forgetting Van't Hoff factor

Category: Similar Terms

Student uses non-electrolyte colligative formula for ionic compound. NaCl: i ≈ 2; CaCl₂: i ≈ 3.

When it triggers

Question gives an ionic compound (NaCl, CaCl₂, K₂SO₄) and asks for colligative property.

How to avoid

For electrolytes, multiply colligative formula by Van't Hoff factor i. NaCl → Na⁺ + Cl⁻ (i=2). CaCl₂ → Ca²⁺ + 2Cl⁻ (i=3). K₂SO₄ → 2K⁺ + SO₄²⁻ (i=3).

Mistake

Substitutes mass fraction for mole fraction in Raoult's law.

Root cause: formula misuse

Correction

Convert mass to moles first using molar mass. Raoult uses MOLE fractions.

Mistake

Forgets Van't Hoff factor i for ionic compounds in colligative formulas.

Root cause: formula misuse

Correction

For NaCl i ≈ 2, CaCl₂ i ≈ 3, K₂SO₄ i ≈ 3. Multiply colligative formulas by i.

Past Year Questions

9 questions from NEET 2021, 2022, 2023, 2024, 2025. Answers verified against NTA official keys.

NEET 2025

Which of the following aqueous solution will exhibit highest boiling point?

10.015M C H O

20.01M Urea 6 12 6

30.01M KNO

40.01M Na SO 3 2 4

NTA Answer: Option 4(final)

NEET 2024Revised key

The Henry’s law constant (K ) values of three gases (A, B, C) in water are 145, 2 × 10–5 and 35 kbar, H respectively. The solubility of these gases in water follow the order:

1B > A > C

2B > C > A

3A > C > B

4A > B > C

NTA Answer: Option 2(revised_final)

NEET 2024Revised key

Given below are two statements: Statement I: The boiling point of hydrides of Group 16 elements follow the order H O > H Te > H Se > H S. 2 2 2 2 Statement II: On the basis of molecular mass, H O is expected to have lower boiling point than the other 2 members of the group but due to the presence of extensive H-bonding in H O, it has higher boiling point. 2 In the light of the above statements, choose the correct answer from the options given below:

1Both Statement I and Statement II are true

2Both Statement I and Statement II are false

3Statement I is true but Statement II is false

4Statement I is false but Statement II is true

NTA Answer: Option 1(revised_final)

NEET 2024Revised key

The plot of osmotic pressure () vs concentration (mol L–1) for a solution gives a straight line with slope 25.73 L bar mol–1. The temperature at which the osmotic pressure measurement is done is (Use R = 0.083 L bar mol–1 K–1)

137°C

2310°C

325.73°C

412.05°C

NTA Answer: Option 1(revised_final)

NEET 2023

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Helium is used to dilute oxygen in diving apparatus. Reason R : Helium has high solubility in O . 2 In the light of the above statements, choose the correct answer from the options given below

1Both A and R are true and R is NOT the correct explanation of A

2A is true but R is false

3A is false but R is true

4Both A and R are true and R is the correct explanation of A

NTA Answer: Option 2(final)

NEET 2022

The IUPAC name of an element with atomic number 119 is

1ununoctium

2ununennium

3unnilennium

4unununnium

NTA Answer: Option 2(final)

NEET 2021

The structures of beryllium chloride in solid state and vapour phase, are :

1Chain in both

2Chain and dimer, respectively

3Linear in both

4Dimer and Linear, respectively

NTA Answer: Option 2(final)

NEET 2021

A particular station of All India Radio, New Delhi broadcasts on a frequency of 1,368 kHz (kilohertz). The wavelength of the electromagnetic radiation emitted by the transmitter is : [speed of light 108 ms–1] c = 3.0 ×

121.92 cm

2219.3 m

3219.2 m

42192 m

NTA Answer: Option 2(final)

NEET 2021

The following solutions were prepared by dissolving 10 g of glucose (C H O ) in 250 ml of water (P ), 6 12 6 1 10 g of urea (CH N O) in 250 ml of water (P ) and 4 2 2 10 g of sucrose (C H O ) in 250 ml of water (P ). 12 22 11 3 The right option for the decreasing order of osmotic pressure of these solutions is :

1P > P > P 3 1 2

2P > P > P 2 1 3

3P > P > P 1 2 3

4P > P > P 2 3 1

NTA Answer: Option 2(final)

How NEET usually asks this

Recurring question shapes from past papers. Each pattern shows why wrong options look tempting.

Calculate ΔT_f or ΔT_b given molality. Or determine molar mass from observed colligative property.

Multi StepMedium

Common distractors

forgets i factor electrolytes

Uses non-electrolyte formula for ionic solute

π = CRT. Find molar mass of solute from observed osmotic pressure.

Direct ApplicationEasy

Common distractors

forgets conversion of units

Mixes Pa with atm; L with m^3

Find total VP of ideal solution from mole fractions and pure-component VPs.

Direct ApplicationEasy

Common distractors

uses mass fractions not mole

Substitutes mass fraction for x

Sources

Test yourself on this topic with real past-paper questions:

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Depression Freezing Point

Lesson

Depression of Freezing Point

Practice MCQs

Quick recall before you leave

ΔT_f = K_f × m

ΔT_f = i × K_f × m

m = moles solute / kg solvent

Worked Example

Before solving, remember these

Formulas

Valid when

Valid when

Valid when

Valid when

Valid when

Valid when

Valid when

Valid when

Exam Traps & Common Mistakes

When it triggers

How to avoid

When it triggers

How to avoid

Correction

Correction

Past Year Questions

How NEET usually asks this

Common distractors

Common distractors

Common distractors

Sources

Free NEET study resources