1.22 g of $C_{6} H_{5} C O O H$ is added in two different solvents:
i) In 100 g $C H_{3} C O C H_{3};$ $Δ T_{b} = 0.17, K_{b} = 1.7 K g - K / m o l$
ii) In 100 g $C_{6} H_{6}; Δ T_{b} = 0.13, K_{b} = 2.6 K g - K / m o l$
which of the following is/are correct?

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Apparent molecular weight of $C_{6} H_{5} C O O H$ in both the solvents is equal.

Apparent molecular weight of $C_{6} H_{5} C O O H$ in both the solvents is not equal

$C_{6} H_{5} C O O H$ dimerizes in benzene

$C_{6} H_{5} C O O H$ remains in monomeric form in acetone.

answer is B, C, D.

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Detailed Solution

Molecular weight of $C_{6} H_{5} C O O H i n C H_{3} C O C H_{3} = \frac{K_{b} \times W_{s o l u t e} \times 1000}{^{Δ T_{b} \times W_{s o l v e n t}}} = \frac{1.70 \times 1.22 \times 1000}{0.17 \times 1000} = 122$
Molecular weight of $C_{6} H_{5} C O O H i n C_{6} H_{6} = \frac{2.6 \times 1.22 \times 1000}{0.13 \times 1000} = 244$
Hence, molecular weight of $C_{6} H_{5} C O O H$ in both the solvent is not equal. $C_{6} H_{5} C O O H$ dimerise in $C_{6} H_{6}$ and remains in monomeric form in acetone.