Question

1.00 molal aqueous solution of trichloroacetic acid is heated to its boiling point. The boiling point of this solution was found to be 100.18\(^\circ\)C. Calculate the Van’t Hoff factor for trichloroacetic acid. (Given: \( K_b \) for water = 0.512 K kg mol\(^{-1}\))

Hint:

If \( i<1 \) → Association of molecules If \( i>1 \) → Dissociation into ions

Answer 1

Concept: Elevation in boiling point is a colligative property and is given by: \[ \Delta T_b = i \, K_b \, m \] where:

• \( i \) = Van’t Hoff factor
• \( K_b \) = ebullioscopic constant
• \( m \) = molality

Step 1: Calculate elevation in boiling point. \[ \Delta T_b = 100.18 - 100 = 0.18 \, \text{K} \]
Step 2: Substitute values into formula. \[ 0.18 = i \times 0.512 \times 1 \]
Step 3: Solve for Van’t Hoff factor. \[ i = \frac{0.18}{0.512} \approx 0.35 \]
Step 4: Interpretation. A value less than 1 indicates association of solute molecules in solution (dimerization or higher aggregation). \[ \therefore i \approx 0.35 \]