Pure benzene freezes at `5.3^@C`. A solution of 0.223 g of phenylacetic acid `(C_H_5CH_2COOH)` in 4.4 g of benzene `(K_f = 5.12 K kg mol^(-1))` freezes at `4.47^@C`. From this observation, one can conclude that

Options

A. phenyl acetic acid exists as such in benzene
B. phenyl acetic acid undergoes partial ionisation in benzene
C. phenyl acetic acid undergoes complete ionisation in benzene
D. phenyl acetic acid dimerises in benzene.

Answer

D

Explanation

`DeltaT_f=T_f^@ 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_fm) = (0.83)/(5.12 xx0.373)=0.435`
It means phenylacetic acid undergoes dimerization in benzene.