Question:
A solute a dimerizes in water. The boiling point of a 2 molar solution of $\mathrm{A}$ is $100.52^{\circ} \mathrm{C}$. The percentage association of $A$ is_______.
(Round off to the Nearest integer)
[Use: $\mathrm{K}_{\mathrm{b}}$ for water $=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
Boiling point of water $=100^{\circ} \mathrm{C}$ ]
Solution:
$\Delta \mathrm{T}_{\mathrm{b}}=\mathrm{T}_{\mathrm{b}}-\mathrm{T}_{\mathrm{b}}{ }^{0}$
$100.52-100$
$=0.52^{\circ} \mathrm{C}$
$i=\left(1-\frac{\alpha}{2}\right)$
$\because \Delta \mathrm{T}_{\mathrm{b}}=\mathrm{i} \mathrm{K}_{\mathrm{b}} \times \mathrm{m}$
$0.52=\left(1-\frac{\alpha}{2}\right) \times 0.52 \times 2$
$\alpha=1$
So, percentage association $=100 \%$.