JEE Main 2022 · Chemistry · Solutions, Solid State and Surface Chemistry · medium

44 g of benzoic acid (M=122) dissolved in 50 g of benzene (Kf=5.1 K kg mol^-1) lowers the freezing point by 1.53 K. Assuming that the acid only…

Single correct option

2.44\ \mathrm g

of benzoic acid (

M=122

) dissolved in

50\ \mathrm g

of benzene (

K_f=5.1\ \mathrm{K\,kg\,mol^{-1}}

) lowers the freezing point by

1.53\ \mathrm K

. Assuming that the acid only dimerises in benzene, the percentage association is

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Answer: (B) $25\%$

Molality

m=\dfrac{2.44/122}{0.050}=0.40

, so the expected depression for no association is

K_fm=2.04

K. Van't Hoff factor

i=1.53/2.04=0.75

. For

2\mathrm A\rightleftharpoons \mathrm A_2

i=1-\alpha/2

, so

\alpha/2=0.25

and

\alpha=0.50

, i.e.

50\%

association. (Using

i=1-\alpha

would wrongly give

25\%

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