Here is the trap that costs marks on this topic: you see "NaCl solution" in the stem, calculate ΔT_f or ΔT_b using the standard colligative formula, get a clean number — and pick the wrong option because you forgot to multiply by the Van't Hoff factor i.
The Van't Hoff factor corrects colligative property formulas for solutes that dissociate (electrolytes) or associate in solution. NCERT Class 12 Chemistry Chapter 1, page 24 defines it as:
i = (observed colligative property) / (calculated colligative property for non-electrolyte)
For complete dissociation: NaCl → Na⁺ + Cl⁻ gives i = 2. CaCl₂ → Ca²⁺ + 2 Cl⁻ gives i = 3. K₂SO₄ → 2 K⁺ + SO₄²⁻ gives i = 3. Acetic acid dimerising in benzene gives i < 1 (association).
Every colligative formula gets multiplied by i when the solute is not a non-electrolyte:
Abnormal molar mass is the direct consequence. If you measure a colligative property and back-calculate molar mass without accounting for i, you get a molar mass that is too low (for dissociating solutes) or too high (for associating solutes). The relationship is:
i = (normal molar mass) / (abnormal molar mass)
The connection between i and degree of dissociation α for a solute producing n ions:
i = 1 + (n − 1)α
This lets NEET frame questions in both directions: given α, find i; or given observed vs. expected colligative property, find α.
Watch-out: When a question says "assuming complete dissociation," i equals the total number of ions per formula unit — no partial α needed.
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
The Van't Hoff factor *i* for a non-electrolyte dissolved in water is:
For a solute that associates in solution, the Van't Hoff factor *i* is:
Assuming complete dissociation, the Van't Hoff factor for K₂SO₄ is:
0.1 m aqueous NaCl solution (assume complete dissociation, K_f for water = 1.86 K kg/mol). The freezing-point depression ΔT_f is:
A 0.05 m aqueous solution of CaCl₂ (assume complete dissociation, K_b for water = 0.52 K kg/mol). The boiling-point elevation ΔT_b is:
The degree of dissociation of an electrolyte that produces 3 ions per formula unit is 0.8. Its Van't Hoff factor *i* is:
A solute has a normal molar mass of 120 g/mol. When dissolved in water, its observed molar mass (from freezing-point depression) is 40 g/mol. How many ions does each formula unit produce on complete dissociation?
An electrolyte AB₂ has a degree of dissociation α = 0.6 in water. Its Van't Hoff factor is *i*. If 0.2 m of this solute is dissolved in water (K_f = 1.86 K kg/mol), the freezing-point depression ΔT_f is:
Pattern: Calculate ΔT_f for an ionic solute using the Van't Hoff factor (aligned with P.CHE.U05.COLLIGATIVE_PROPERTIES_CALC).
Given
- Mass of NaCl = 5.85 g - Molar mass of NaCl = 58.5 g/mol (exact, problem-defined) - Mass of solvent (water) = 500 g = 0.500 kg - K_f = 1.86 K kg/mol - Complete dissociation assumed
Required
ΔT_f = ?
Concept
Freezing-point depression for an electrolyte uses the Van't Hoff-corrected formula: ΔT_f = i · K_f · m. NaCl dissociates completely into Na⁺ and Cl⁻, giving i = 2.
Formula
ΔT_f = i · K_f · m, where m = (moles of solute) / (mass of solvent in kg)
Substitution
Moles of NaCl = 5.85 / 58.5 = 0.1 mol Molality m = 0.1 / 0.500 = 0.2 mol/kg ΔT_f = 2 × 1.86 × 0.2
Calculation
ΔT_f = 2 × 1.86 × 0.2 = 2 × 0.372 = 0.744 K **Note on exact values:** The molar mass 58.5 g/mol, solvent mass 500 g, and the integer 2 (Van't Hoff factor for complete dissociation) are problem-defined exact values and do not limit significant figures in the final answer.
Final answer
**ΔT_f = 0.744 K**
Common trap
Without the Van't Hoff factor: ΔT_f = K_f · m = 1.86 × 0.2 = 0.372 K — exactly half the correct answer. This is the classic trap for ionic solutes: forgetting to multiply by *i*. NEET distractors routinely include this half-value as an option.
Similar NEET-style question
"0.1 m aqueous CaCl₂ (complete dissociation). K_f = 1.86 K kg/mol. Find ΔT_f." Answer: i = 3, ΔT_f = 3 × 1.86 × 0.1 = 0.558 K. The non-electrolyte trap answer would be 0.186 K. ---
i = (observed colligative property) / (calculated value as if non-electrolyte). For ionic compounds dissociating into n ions: i ≈ n. Modify colligative formulas: ΔT_b = i K_b m, etc.
-- NCERT Class 12 Chemistry, Ch. 1, p. 24Molal concentration: moles of solute per kg of solvent. Temperature-independent.
| Symbol | Quantity | SI Unit |
|---|---|---|
| m | molality | mol/kg |
| n | moles solute | mol |
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 |
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 |
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 |
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 |
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 | - |
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 | - |
Correction factor for electrolytes. NaCl: i≈2; CaCl₂: i≈3. Multiply colligative formula by i.
| Symbol | Quantity | SI Unit |
|---|---|---|
| i | Van't Hoff factor | - |
These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.
Category: Similar Terms
Student uses mass fraction (w₁/total mass) where mole fraction (n₁/total moles) is required.
Question gives masses or molar masses and asks about Raoult's law or vapor pressure.
Raoult's law uses MOLE fractions, not mass fractions. Convert mass to moles first using molar mass.
Category: Similar Terms
Student uses non-electrolyte colligative formula for ionic compound. NaCl: i ≈ 2; CaCl₂: i ≈ 3.
Question gives an ionic compound (NaCl, CaCl₂, K₂SO₄) and asks for colligative property.
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).
Root cause: formula misuse
Convert mass to moles first using molar mass. Raoult uses MOLE fractions.
Root cause: formula misuse
For NaCl i ≈ 2, CaCl₂ i ≈ 3, K₂SO₄ i ≈ 3. Multiply colligative formulas by i.
9 questions from NEET 2021, 2022, 2023, 2024, 2025. Answers verified against NTA official keys.
Which of the following aqueous solution will exhibit highest boiling point?
The IUPAC name of an element with atomic number 119 is
The structures of beryllium chloride in solid state and vapour phase, are :
Recurring question shapes from past papers. Each pattern shows why wrong options look tempting.
forgets i factor electrolytes
Uses non-electrolyte formula for ionic solute
forgets conversion of units
Mixes Pa with atm; L with m^3
uses mass fractions not mole
Substitutes mass fraction for x
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