1.22 g of benzoic acid (molar mass 122 g mol^-1) is dissolved in 50 g of benzene (K_f = 5.12 K kg mol^-1). The freezing point falls by 0.614 K. The acid dimerises, 2A leftharpoons A_2 with i = 1 - beta/2. Find the percentage of benzoic acid molecules that are associated (nearest integer).

JEE Advanced levelNumerical answerDifficulty 3 of 3so106

$1.22 g$ of benzoic acid (molar mass $122 g mo l^{- 1}$ ) is dissolved in $50 g$ of benzene ( $K_{f} = 5.12 K kg mo l^{- 1}$ ). The freezing point falls by $0.614 K$ . The acid dimerises, $2 A ⇌ A_{2}$ with $i = 1 - β /2$ . Find the percentage of benzoic acid molecules that are associated (nearest integer).

Numerical answer type, answer in %, tolerance 1.

Calculated

m = (1.22/122) /0.050 = 0.200 mol k g^{- 1}

, so

Δ T_{f} (calc) = 5.12 \times 0.200 = 1.024 K

i = 0.614/1.024 = 0.5996

β = 2 (1 - i) = 0.8008

, i.e. about

80%