# Abnormal molecular mass and Van’t Hoff factor

### 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 ‘An’. 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,  $$i=\frac{M_{c}}{M_{o}}$$

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