Question

Pure benzene freezes at $5.3^{\circ }C$. A solution of $0.223g$ of phenylacetic acid $(C_6{H}_{5}C{H}_{2}COOH)$ in $4.4g$ of benzene $(k_f=5.12kgmo{l}^{-1})$ freezes at $4.47^{\circ }C$. From this observation, one can conclude that

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

Answer 1

Answer: (D)

Depression in freezing point, $\Delta T_f=k_{f}m$
(where $m=$ molality)
$=5.12\times \frac{0.223\times 1000}{4.4\times 136}$
$=5.12\times 0.372$
$=1.91^{\circ }C$
$\therefore$ Theoretical $\Delta T_f=1.91$
Actual $\Delta T_f=5.3^{\circ }C-4.47^{\circ }C$
$=0.83^{\circ }C$
$\therefore i=\frac{0.83}{1.91}=0.43$
$\because i<1$
$\therefore$ Association will take place.
Thus, it can be said that phenylacetic acid dimerises in benzene.