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44 g of benzoic acid (M=122) is dissolved in 50 g of benzene (Kf=5.12 K kg mol^-1) and the observed depression of freezing point is 1.19 K. If the…

Single correct option

2.44\ \mathrm{g}

of benzoic acid (

M=122

) is dissolved in

50\ \mathrm{g}

of benzene (

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

) and the observed depression of freezing point is

1.19\ \mathrm{K}

. If the acid only associates to dimers, the percentage association is nearly

Show answer and solution

Answer: (A) $84\%$

Molality

=\dfrac{2.44/122}{0.050}=0.40\ \mathrm{mol\,kg^{-1}}

, so the calculated

\Delta T_f=5.12\times0.40=2.048\ \mathrm{K}

. Van't Hoff factor

i=1.19/2.048=0.581

. For

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

with degree of association

\alpha

i=1-\alpha/2

, so

\alpha=2(1-0.581)=0.838\approx84\%

58\%

is simply

i

and

42\%

1-i

(forgetting the factor

2

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