A solute A dimerizes in water. The boiling point of a 2 molal...

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 $= 0 . 52Kkg{mol}^{- 1}$

Boiling point of water $= 100 ° C$

Correct answer

Step-by-step solution

$\Delta{T}_{b} = {T}_{b} - {T}_{b}^{0}$

$100 . 52 - 100$

$= 0 . 52 ° C$

$i = \left(1 - \dfrac{\alpha}{2}\right)$

$∵ \Delta{T}_{b} = {iK}_{b} \times m$

$0 . 52 = \left(1 - \dfrac{\alpha}{2}\right) \times 0 . 52 \times 2$

$\alpha = 1$

So, percentage association $= 100 %$ .

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