Question

What is the van't Hoff factor? Write the equation for colligative properties including the van't Hoff factor.

Hint:

\( i \) = observed colligative property divided by calculated value; insert \( i \) as a multiplier in \( \Delta T_b, \Delta T_f, \pi \) and vapour-pressure lowering.

Answer 1

Step 1: Definition.
The van't Hoff factor \( (i) \) accounts for the association or dissociation of a solute in solution. It is defined as:
\( i = \dfrac{\text{observed (experimental) colligative property}}{\text{calculated (normal) colligative property}} \)
Equivalently, \( i = \dfrac{\text{normal molar mass}}{\text{observed molar mass}} = \dfrac{\text{number of particles after dissociation/association}}{\text{number of particles before}} \).

Step 2: Meaning of its value.
\( i = 1 \): no association or dissociation (e.g. glucose).
\( i > 1 \): solute dissociates (e.g. NaCl gives \( i \approx 2 \)).
\( i < 1 \): solute associates (e.g. benzoic acid in benzene forms dimers).

Step 3: Modified colligative property equations (multiply each by \( i \)).
Relative lowering of vapour pressure: \( \dfrac{p^{\circ}-p_s}{p^{\circ}} = i \cdot x_{solute} \)
Elevation of boiling point: \( \Delta T_b = i\,K_b\,m \)
Depression of freezing point: \( \Delta T_f = i\,K_f\,m \)
Osmotic pressure: \( \pi = i\,CRT \)

Conclusion: The van't Hoff factor corrects colligative property formulae for solutes that split into or combine into a different number of particles.
\[\boxed{i = \dfrac{\text{observed colligative property}}{\text{calculated colligative property}}}\]