Since the colligative properties of solutions, viz. lowering of vapour pressure, elevation in boiling point, depression in freezing point and osmotic pressure, depends solely on the number of solute particles present in solution and not on their nature. Colligative properties of the solutes which undergo dissociation (electrolytes) in solution would be higher than expected for the normal substances (non-electrolytes).
To account for the above anomalies, Van’t Hoff introduced a factor ‘i’ in the Van’t Hoff equation
(p V = RT) of osmotic pressure. The modified equation may thus be written as pV = iRT
The factor ‘i’ was defined by the expression
Because colligative properties directly µ n
As we know, colligative properties µ
Hence ‘i' can also be defined as
When the Van’t Hoff factor is included then the colligative properties get modified as follows:
(a) Relative Lowering in Vapour Pressure
= i ´ Xsolute
Where i = van’t Hoff factor
(b) Elevation in Boiling point
DTb = iKb m
(c) Depression in Freezing Point
DTf = iKf m.
(d) Osmotic Pressure
p = i CRT
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