Abnormal Molar Mass 

Abnormal molar mass is the molar mass obtained experimentally that differs from the actual molar mass due to association or dissociation of solute particles in solution.

Meaning

Sometimes, the molar mass calculated experimentally is different 

from the actual molar mass of a substance.
This is called abnormal molar mass.

It happens because solute particles in solution may:

1. Break into smaller particles → Dissociation

2. Join together to form bigger particles → Association

Since colligative properties depend on the number of particles,

 the molar mass becomes abnormal.

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1. Dissociation

When one solute particle breaks into many particles.

Example

NaCl ----------->  Na+     +      Cl-

1 particle becomes 2 particles.

Effect

• Number of particles increases

• Colligative properties increase

• Calculated molar mass becomes smaller than actual

Examples

• NaCl

• KCl

• CaCl₂

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2. Association

When small molecules combine together.

Example

In benzene:

2CH_3COOH ----------------------> (CH_3COOH)_2

Two acetic acid molecules join to form one particle.

Effect

• Number of particles decreases

• Colligative properties decrease

• Calculated molar mass becomes greater than actual

Examples

• Acetic acid in benzene

• Benzoic acid in benzene

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Reason for Abnormal Molar Mass

Colligative properties depend on:

• number of solute particles, not their nature.

If particles increase or decrease, observed values change, giving abnormal molar mass.

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Van’t Hoff Factor (i)

To explain abnormal molar mass, we use Van’t Hoff factor.

i = {Observed colligative property}/{Calculated colligative property}}

OR

i = {Normal molar mass}\{Abnormal molar mass}}

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Values of (i)

For Dissociation

i > 1

because particles increase.

For Association

i < 1

because particles decrease.

For Normal Solute

i = 1

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Quick Summary Table

Situation	Number of Particles	Value of (i)	Molar Mass
Dissociation	Increases	(i > 1)	Smaller
Association	Decreases	(i < 1)	Greater
Normal case	Same	(i = 1)	Normal

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Simple One-Line Definition

Abnormal molar mass is the molar mass obtained experimentally that differs from the actual molar mass due to association or dissociation of solute particles in solution.

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Relation Between $n$ and $i$

Here,

• $n$ = number of particles formed after dissociation or association
• $i$ = Van’t Hoff factor

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For Dissociation

If 1 molecule gives $n$ particles:

$$A\to nB$$

then,

$$i=1+(n-1)\alpha$$

where:

• $\alpha$ = degree of dissociation

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Complete Dissociation

If dissociation is complete $(\alpha = 1)$,

$$i=n$$

Example

$$CaCl_2 \rightarrow Ca^{2+} + 2Cl^-$$

Total particles:

$$n=3$$

So,

$$i = 3$$

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For Association

If $n$ molecules combine to form 1 particle:

$$nA \rightarrow A_n$$

then,

$$i = 1 - \frac{(n-1)\alpha}{n}$$

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Complete Association

If association is complete $(\alpha = 1)$,

$$i = \frac{1}{n}$$

Example

$$2CH_3COOH \rightarrow (CH_3COOH)_2$$

Here,

$$n=2$$

So,

$$i = \frac{1}{2}$$

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Summary

Process	Relation
Dissociation	$i = 1 + (n-1)\alpha$
Complete Dissociation	$i = n$
Association	$i = 1 - \frac{(n-1)\alpha}{n}$
Complete Association	$i = \frac{1}{n}$

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