Question

$75.2\text{g}$ of $C_6{H}_{5}OH\text{(Phenol)}$ is dissolved in a solvent of $K_f=14$. If the depression in freezing point is $7\text{K}$. Then find the percentage of phenol that dimerizes.
(Given, $\text{molar mass of phenol}=94{\text{g mol}}^{-1}$, mass of solvent $=1\text{kg}$)

Answer 1

$$\begin{array}{ccc}2\left(C_6{H}_{5}OH\right)& \rightleftharpoons & (C_6{H}_{5}OH{)}_2\\ 1& & 0\\ 1-\alpha & & \frac{\alpha }{2}\end{array}$$
By using the formula,
$\Delta T_f=K_f\times {\text{(molarity)}}_{obs}$
$\Rightarrow 7=14\times \frac{75.2}{94}\times (1-\frac{\alpha }{2})$
$\therefore \alpha =0.75$
So, percentage of phenol that dimerizes $=75\%$.