Van't Hoff Factor and Abnormal Molecular Masses

When the solute associates or dissociates in solution, abnormal results (for all colligative properties and molar masses) are obtained. i.e., experimental value for colligative properties and molar mass deviates from calculated or normal value. The deviation depends on extent of dissociation or association of solute.

To calculate the extent of association or dissociation, Van't Hoff in 1886 introduced a factor 'i' called Van't Hoff factor.

Van't Hoff factor 'i' is defined as ratio of the experimental value of colligative property to the calculated value (normal value) of colligative property.

i.e., i = 

or i = 

or i = 

Using Van't Hoff factor, the colligative properties are modified as follows:
Relative lowering of vapour pressure,

Elevation of boiling point,
ΔT_b = i K_bm
Depression in freezing point,
ΔT_f = i K_{f .}m
Osmotic pressure,
 = i CRT

Association of Solute

Many organic solutes when dissolved in non-aqueous (non polar) solvent associate to form a bigger molecule. Thus the no. of molecules decreases and hence colligative properties decrease.
Examples:
Acetic acid in benzene, chloro acetic acid in naphthalene

Association of two molecules (dimerisation) of acetic acid in benzene.
Consider the following reaction for association

nA 1	-->	(A)n0	moles before association
(1 - α)			moles after association

i = 

i =

obviously, i < 1 i.e., colligative properties decrease on association.

Dissociation of Solute

Some solutes (organic acids, bases and salts) in aqueous solution undergo dissociation. In such case no. of particles increases and hence colligative properties increase.
Examples:
Dissociation of NaCl in aqueous solution.
Consider the following dissociation reaction,

NaCl (1 - α)

Na+(aq) + α

Cl- (aq) α

moles after dissociation

i =

obviously, i > 1 i.e., colligative properties increases.