A solute A dimerizes in water. The boiling point of a 2 molal solution of A is $100.52°\mathrm{C}$. The percentage association of A is______
(Round off to the Nearest Integer) [Use: ${\mathrm{K}}_{\mathrm{b}}$ for water =0.52 K kg ${ \mathrm{mol}}^{-1}$
Boiling point of water $=100°\mathrm{C}]$

In water, a solute A dimerizes. A 2 molal solution of A has a boiling point of $100.52°\mathrm{C}$. A has the following percentage association:

$\Delta {\mathrm{T}}_{\mathrm{b}}={\mathrm{T}}_{\mathrm{b}}-{\mathrm{T}}_{\mathrm{b}}^0$
100.52 - 100
$=0.52°\mathrm{C}$
$\mathrm{i}=\left(1-\frac{\alpha }{2}\right)$
$\because \Delta {\mathrm{T}}_{\mathrm{b}}={\mathrm{iK}}_{\mathrm{b}}\times \mathrm{m}$
$0.52=\left(1-\frac{\alpha }{2}\right)\times 0.52\times 2$
$\alpha =1$
Hence, 100% is the percentage association.