The freezing point of benzene decreases by $0.45 ° C$ when 0.2 g of acetic acid is added to 20g of benzene. If acetic acid associated to form a dimer in benzene, percentage association of acetic acid in benzene will be _________ $(K_{f}$ for benzene $= 5.12 K {kgmol}^{- 1})$

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answer is 94.5.

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Detailed Solution

In benzene,
$2 {CH}_{3} COOH ⇌ {({CH}_{3} COOH)}_{2}$
$i = 1 + (\frac{1}{2} - 1)$
$i - 1 - \frac{α}{2}$

Here $α$ is degree of association

$Δ T_{f} = i K_{f} m$

$0.45 = (1 - \frac{α}{2}) (5.12) \frac{(\frac{0.2}{60})}{\frac{20}{1000}}$
$1 - \frac{α}{2} = 0.527$
$α = 0.945$
94.5% of associations are strong.

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