JEE Main 2023 · Chemistry · Solutions, Solid State and Surface Chemistry · hard

10 g of benzoic acid (M=122 g mol^-1) is dissolved in 100 g benzene (Kf=5.12 K kg mol^-1). The acid dimerises to the extent of 80%. The depression in…

Numerical answer

6.10\ \mathrm g

of benzoic acid (

M=122\ \mathrm{g\,mol^{-1}}

) is dissolved in

100\ \mathrm g

benzene (

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

). The acid dimerises to the extent of

80\%

. The depression in freezing point is

x\times10^{-2}\ \mathrm K

. The value of

x

to the nearest integer is

Show answer and solution

Answer: 154

Molality of the undissociated formula

=\frac{6.10/122}{0.100}=0.500\ \mathrm{mol\,kg^{-1}}

. For dimerisation

2\mathrm{A}\rightleftharpoons\mathrm{A_2}

with degree of association

\beta=0.8

: total particles

=1-\beta/2=0.6

per mole, so

i=0.6

\Delta T_f=iK_fm=0.6\times5.12\times0.500=1.536\ \mathrm K=153.6\times10^{-2}

, i.e.

x\approx154

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