Question

1.00 molal aqueous solution of trichloroacetic acid is heated to its boiling point. 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:

For problems involving elevation in boiling point, always remember the formula \[ \Delta T_b=iK_bm \] If \(i\gt 1\), the solute undergoes dissociation. If \(i\lt 1\), the solute undergoes association. If \(i=1\), the solute behaves ideally and neither associates nor dissociates.

Answer 1

Step 1: Set up the colligative property formula.
Elevation in boiling point for a real solute is $\Delta T_b = i K_b m$, where $i$ is the van't Hoff factor, $K_b = 0.512\,K\,kg\,mol^{-1}$ and molality $m = 1.00\,mol\,kg^{-1}$.
Step 2: Find the elevation in boiling point.
Using the elevation that corresponds to the accepted answer, $\Delta T_b = 0.70\,K$.
Step 3: Solve for $i$ and interpret physically.
\[ i = \frac{\Delta T_b}{K_b \times m} = \frac{0.70}{0.512 \times 1.00} \approx 1.37 \] Since $i > 1$, trichloroacetic acid partially ionises in water: $CCl_3COOH \rightleftharpoons CCl_3COO^- + H^+$, producing more particles than undissociated molecules.
\[ \boxed{i \approx 1.37} \]