Question

$75.2g$ of $C_6{H}_{5}OH$ (phenol) is dissolved in a solvent of $K_f=14$. If the depression in freezing point is $7K$ then find the percentage of phenol that dimerises.

Answer 1

Answer: 75

The dimerization reaction of phenol is
$2C_6{H}_{5}OH\rightleftharpoons {\left(C_6{H}_{5}OH\right)}_2$

Here, $C$ is the concentration of phenol:
$C=\frac{75.2}{Mol.wt}=\frac{75.2}{94}=0.8$
and $\alpha$ is the degree of dissociation.
Then $i=C-Ca+Ca/2=\frac{C(2-\alpha )}{2}$
Freezing point depression is given by
$\Delta T_f=K_f\times i$
$7=14\times 0.8\times \left(2-\frac{\alpha }{2}\right)$
$\alpha =0.75=75\%$