JEE Main 2020 · Chemistry · Solutions, Solid State and Surface Chemistry · medium

22 g of benzoic acid (M=122) is dissolved in 25 g of benzene (Kf=5.12 K kg mol^-1), where it partly dimerises, 2C6H5COOHrightleftharpoons(C6H5COOH)2.…

Single correct option

1.22\ \mathrm{g}

of benzoic acid (

M=122

) is dissolved in

25\ \mathrm{g}

of benzene (

K_f=5.12\ \mathrm{K\,kg\,mol^{-1}}

), where it partly dimerises,

2\mathrm{C_6H_5COOH}\rightleftharpoons(\mathrm{C_6H_5COOH})_2

. The observed depression in freezing point is

1.23\ \mathrm{K}

. The fraction of benzoic acid that exists as dimer is closest to

Show answer and solution

Answer: (C) $0.80$

Molality

=\dfrac{0.01}{0.025}=0.40

mol kg

^{-1}

; expected

\Delta T_f=5.12\times0.40=2.048

i=\dfrac{1.23}{2.048}=0.60

. For association into dimers

i=1-\dfrac{\alpha}{2}

, so

\alpha=2(1-0.60)=0.80

. (Taking

i=1-\alpha

gives the wrong value

0.40

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