Question

A solute A dimerizes in water. The boiling point of a 2 molal solution of A is 100.52°C. The percentage association of A is _________. (Round off to the Nearest Integer). [Use : K_b for water = 0.52 K kg mol⁻¹, Boiling point of water = 100°C]

Hint:

If $i<1$, the solute is associating; if $i>1$, the solute is dissociating.

Answer 1

Correct Answer: 100

Step 1: $\Delta T_b = 100.52 - 100 = 0.52 \text{ K}$.
Step 2: $\Delta T_b = i \cdot K_b \cdot m \implies 0.52 = i \times 0.52 \times 2 \implies i = 0.5$.
Step 3: $i = 1 - \alpha(1 - 1/n)$. For dimer, $n=2$. \[ 0.5 = 1 - \alpha(1 - 1/2) \implies 0.5 = 1 - 0.5\alpha \implies \alpha = 1. \] Percentage association $= 100%$.