# Abnormal molecular mass and Van’t Hoff factor

##### Abnormal Molecular Mass

When the molecular mass of a substance determined by studying any of the colligative properties comes out to be different than the theoretically expected value, then the substance is said to show abnormal molecular mass**. **

**The abnormal molecular masses are observed in any one of the following cases : **

- When the solute undergoes
**dissociation**in the solution. - When the solute undergoes
**association**in the solution. - When the solution is
**non-ideal**.

##### Van’t Hoff factor

To calculate the extent of association or dissociation, Van’t Hoff introduced a factor **‘i’ **called **Van’t Hoff factor.** It is defined as the **ratio** of the **observed or experimental value** of the colligative property to the **calculated or normal value** of the colligative property.

\( i=\frac{Observed~Colligative~Property}{Calculated~Colligative~property}=\frac{C_{o}}{C_{c}} \)

As we know that, colligative property is inversely proportional to the molecular mass of the solute, we can also write:

\( i=\frac{Calculated~Molecular~Mass}{Observed~Molecular~Mass}=\frac{M_{c}}{M_{o}} \)

Note:

- i > 1 :: Dissociation
- i < 1 :: Association
- i = 1 :: No association nor dissociation

###### Modified Expressions of Colligative Properties

**Relative Lowering in Vapour pressure:**

\( \frac{\Delta P_{A}}{P_{A}^{o}}=i.\chi _{B}~~~OR~~~\frac{\Delta P_{A}}{P_{A}^{o}}=~\frac{i~\times W_{B}\times M_{A}}{M_{B}\times W_{A}} \)

**Elevation in Boiling point:**

\( \Delta T_{b}=i.K_{b}.m \)

Or

\( \Delta T_{b}=\frac{i~\times K_{b}\times W_{B}\times ~1000}{M_{B}\times W_{A}} \)

**Depression in Freezing point:**

\( \Delta T_{f}=i.K_{f}.m \)

Or

\( \Delta T_{f}=\frac{i~\times K_{f}\times W_{B}\times ~1000}{M_{B}\times W_{A}} \)

**Osmotic pressure:**

\( \pi =\frac{i~\times W_{B}\times RT\times ~1000}{M_{B}\times V_{sol~in~ml}} \)

##### Calculation of the degree of Dissociation

When an electrolyte is dissolved in a solvent, it dissociates into ions. The fraction of the total number of electrolyte molecules that undergoes dissociation is called **degree of dissociation (α)**.

\( \alpha =\frac{Number~of~moles~dissociated}{Total~number~of~moles~taken} \)

Observed colligative property **= (1-α)+nα = 1+(n-1)α**

Calculated colligative property **= 1**

\( i=\frac{C_{o}}{C_{c}}=\frac{1+(n-1)\alpha }{1}~~OR~~\alpha =\frac{i-1}{n-1} \)

As we know that, \( i=\frac{M_{c}}{M_{o}} \)

\( \therefore~~ \alpha =\frac{\frac{M_{c}}{M_{o}}-1}{n-1}=\frac{M_{c}-M_{o}}{M_{o}(n-1)} \)

##### Calculation of the degree of Association

In some cases, ‘n’ molecules of the solute ‘A’ associate to form large associated molecule ‘A_{n}’. The fraction of the total number of solute molecules which exist in the form of associated molecule is called **degree of association (α)**.

\( \alpha =\frac{Number~of~moles~associated}{Total~number~of~moles~taken} \)

Observed colligative property** = \( (1-\alpha )+\frac{\alpha }{n} \)**

Calculated colligative property **= 1**

\( i=\frac{C_{o}}{C_{c}}=\frac{(1-\alpha )+\frac{\alpha }{n}}{1} \)

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

As we know that, \( i=\frac{M_{c}}{M_{o}} \)

\( \therefore ~~~\alpha = \left ( 1-\frac{M_{c}}{M_{o}} \right )\frac{n}{n-1}= \left ( \frac{M_{o}-M_{c}}{M_{o}} \right )\frac{n}{n-1} \)

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