Pure benzene freezes t `5.3^(@)C`. A solution of 0.223 g of phenylacetic acid `(C_(6)H_(5)CH_(2)COOH)` in 4.4 g of benzene ` (K_(f) = 5.12 Kkg mol^(-1))` freezes at `4.47^(@)C`. From the observation one can conclude that :

Options

A. Phenylacetic acid exists as such in benzene
B. Phenylacetic acid undergoes partial ionization in benzene
C. Phenylacetic acid undergoes complete ionization in benzene
D. Phenylacetic acid dimerizes in benzene

Answer

D

Explanation

`DeltaT_(f)=T_(0)-T_(f)=5.3-4.47=0.83`
Molality of solvent `m=(0.223)/(136)xx(1000)/(4.4)=0.373`
(Molecular weight of phenylacetic acid = 136)
`K_(f)=5.12`
`DeltaT_(f)=i.K_(f)m`
`i=(DeltaT_(f))/(K_(f)m)=(0.83)/(5.12xx0.373)=0.45`
i is nearly equal to 0.5 it means phenylacetic acid undergoes dimerization in benzene.