Question

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

Answer 1

The equilibrium for the association of phenol is as shown.
$2C_6{H}_{5}OH\leftrightharpoons (C_6{H}_{5}OH{)}_2$
The molar mass of phenol is 94.11 g/mol
75.2 g of phenol corresponds to $\frac{75.2}{94.11}=0.8$ moles
Let $\alpha$ be the degree of association
The vant Hoff's factor i is $\left(\frac{2-\alpha }{2}\right)$
The depression in the freezing point $=7=14\times 0.8\left(\frac{2-\alpha }{2}\right)$
$\alpha =0.75=75$%