Canvas Classes - Free JEE & NEET Chemistry Preparation

Quantitative ReasoningLevel 3 · Analysis

0.1 molal NaCl in water shows a freezing point depression of 0.348°C. But if you calculate using ΔTf = Kf × m = 1.86 × 0.1 = 0.186°C, you get a very different answer. The observed ΔTf is almost exactly double the predicted value. What does this tell you about NaCl in water — without needing to know any chemistry?

✦Real Life Hook

In 1884, Jacobus van't Hoff noticed something strange: colligative properties of salt solutions were always much larger than calculated, while acetic acid in benzene was always smaller. He introduced the factor $i$ to account for this. It was chemistry's first glimpse of the reality of ions in solution — before Arrhenius's ionic theory was published. Van't Hoff factor $i$ was the experimental proof of ionic dissociation, years before anyone had directly observed ions. The numbers in solutions were telling the truth about molecular structure.

Van't Hoff Factor (i)

The van't Hoff factor $i$ accounts for the actual number of particles produced per formula unit of solute:

$i = \frac{\text{observed colligative property}}{\text{calculated colligative property (for non-electrolyte)}}$

Or equivalently:
$i = \frac{\text{actual moles of particles in solution}}{\text{moles of formula units dissolved}}$

Three cases:

$i = 1$ : Non-electrolyte, no dissociation (glucose, urea, sugar)
$i > 1$ : Electrolyte that dissociates (NaCl $\to$ 2 ions, CaCl₂ $\to$ 3 ions, AlCl₃ $\to$ 4 ions)
$i < 1$ : Association in solution (acetic acid in benzene dimerises: $2\ce{CH3COOH} \to (\ce{CH3COOH})_2$ )

Modified Colligative Property Equations

All four colligative property equations are modified by inserting $i$ :

$\text{RLVP: } \frac{p^\circ - p_s}{p^\circ} = i \cdot x_2$

$\Delta T_b = i \cdot K_b \cdot m$

$\Delta T_f = i \cdot K_f \cdot m$

$\pi = i \cdot M \cdot R \cdot T$

Abnormal molar mass: When colligative properties are measured experimentally and molar mass calculated assuming $i = 1$ , the result is the apparent (abnormal) molar mass — lower than true for electrolytes (more particles), higher than true for associating solutes.

Degree of dissociation ( $\alpha$ ) and van't Hoff factor:

For an electrolyte $\ce{AB} \to \ce{A+} + \ce{B-}$ (splits into $n$ ions):
$i = 1 + (n-1)\alpha$

where $\alpha$ = degree of dissociation (fraction dissociated), $n$ = number of ions formed.

For association (dimerisation: $2A \to A_2$ ):
$i = 1 - \frac{\alpha}{2}$

These allow you to calculate the degree of dissociation from experimental colligative property data.

📖NCERT 2.13NCERT Intext

Problem

2 g of benzoic acid ( $\ce{C6H5COOH}$ , $M = 122$ g/mol) dissolved in 25 g of benzene shows a depression in freezing point equal to 1.62 K. The molar enthalpy of fusion of benzene is 10.0 kJ/mol at its freezing point. Calculate the van't Hoff factor and explain the result. ( $K_f$ for benzene = 5.12 K·kg/mol)

📖NCERT 2.14NCERT Intext

Problem

0.6 mL of acetic acid ( $\rho = 1.06$ g/mL) is dissolved in 1 litre of water. The depression in freezing point observed is 0.0205°C. Calculate the van't Hoff factor and degree of dissociation. ( $K_f = 1.86$ , $M_{\text{acetic acid}} = 60$ g/mol)

Dissociation (i > 1) vs Association (i < 1)

Dissociation (Electrolytes)

i > 1
More particles than formula units
Colligative effect larger than predicted
Apparent molar mass < true molar mass
Examples: NaCl (i≈2), CaCl₂ (i≈3), AlCl₃ (i≈4)
α = (i−1)/(n−1)

Association (Non-polar solvents)

i < 1
Fewer particles than formula units (dimers)
Colligative effect smaller than predicted
Apparent molar mass > true molar mass
Example: acetic acid in benzene (i≈0.5)
α = 2(1−i) for dimerisation

Dissociation (Electrolytes)

i > 1
More particles than formula units
Colligative effect larger than predicted
Apparent molar mass < true molar mass
Examples: NaCl (i≈2), CaCl₂ (i≈3), AlCl₃ (i≈4)
α = (i−1)/(n−1)

Association (Non-polar solvents)

i < 1
Fewer particles than formula units (dimers)
Colligative effect smaller than predicted
Apparent molar mass > true molar mass
Example: acetic acid in benzene (i≈0.5)
α = 2(1−i) for dimerisation

✦JEE / NEET Exam InsightJEE / NEET

◆Abnormal molar mass summary:

◆Electrolytes in water → apparent

M

< true

M

(measured colligative property too large → overestimates solute particles → underestimates

M

)

◆Acetic acid in benzene → apparent

M

> true

M

(measured colligative property too small → underestimates solute particles → overestimates

M

)

◆Degree of dissociation formula:

i = 1 + (n-1)\alpha

(dissociation). Rearranged:

\alpha = \frac{i-1}{n-1}

◆JEE pattern: 'Calculate the degree of dissociation from observed ΔTf' — always use

i = \text{observed}/\text{expected}

first, then the

\alpha

formula.

Quick Check

Q1.The van't Hoff factor (i) for a 0.1 m solution of K₂SO₄ (which dissociates into 3 ions: 2K⁺ + SO₄²⁻) is approximately:

Quantitative ReasoningLevel 3 · Analysis

✦Real Life Hook

Van't Hoff Factor (i)

The van't Hoff factor $i$ accounts for the actual number of particles produced per formula unit of solute:

$i = \frac{\text{observed colligative property}}{\text{calculated colligative property (for non-electrolyte)}}$

Or equivalently:
$i = \frac{\text{actual moles of particles in solution}}{\text{moles of formula units dissolved}}$

Three cases:

$i = 1$ : Non-electrolyte, no dissociation (glucose, urea, sugar)
$i > 1$ : Electrolyte that dissociates (NaCl $\to$ 2 ions, CaCl₂ $\to$ 3 ions, AlCl₃ $\to$ 4 ions)
$i < 1$ : Association in solution (acetic acid in benzene dimerises: $2\ce{CH3COOH} \to (\ce{CH3COOH})_2$ )

Modified Colligative Property Equations

All four colligative property equations are modified by inserting $i$ :

$\text{RLVP: } \frac{p^\circ - p_s}{p^\circ} = i \cdot x_2$

$\Delta T_b = i \cdot K_b \cdot m$

$\Delta T_f = i \cdot K_f \cdot m$

$\pi = i \cdot M \cdot R \cdot T$

Degree of dissociation ( $\alpha$ ) and van't Hoff factor:

For an electrolyte $\ce{AB} \to \ce{A+} + \ce{B-}$ (splits into $n$ ions):
$i = 1 + (n-1)\alpha$

where $\alpha$ = degree of dissociation (fraction dissociated), $n$ = number of ions formed.

For association (dimerisation: $2A \to A_2$ ):
$i = 1 - \frac{\alpha}{2}$

These allow you to calculate the degree of dissociation from experimental colligative property data.

📖NCERT 2.13NCERT Intext

Problem

📖NCERT 2.14NCERT Intext

Problem

Dissociation (i > 1) vs Association (i < 1)

Dissociation (Electrolytes)

i > 1
More particles than formula units
Colligative effect larger than predicted
Apparent molar mass < true molar mass
Examples: NaCl (i≈2), CaCl₂ (i≈3), AlCl₃ (i≈4)
α = (i−1)/(n−1)

Association (Non-polar solvents)

i < 1
Fewer particles than formula units (dimers)
Colligative effect smaller than predicted
Apparent molar mass > true molar mass
Example: acetic acid in benzene (i≈0.5)
α = 2(1−i) for dimerisation

Dissociation (Electrolytes)

i > 1
More particles than formula units
Colligative effect larger than predicted
Apparent molar mass < true molar mass
Examples: NaCl (i≈2), CaCl₂ (i≈3), AlCl₃ (i≈4)
α = (i−1)/(n−1)

Association (Non-polar solvents)

i < 1
Fewer particles than formula units (dimers)
Colligative effect smaller than predicted
Apparent molar mass > true molar mass
Example: acetic acid in benzene (i≈0.5)
α = 2(1−i) for dimerisation

Quick Check

Q1.The van't Hoff factor (i) for a 0.1 m solution of K₂SO₄ (which dissociates into 3 ions: 2K⁺ + SO₄²⁻) is approximately: