Question

$$75.2g$$ of $${\text{C}}_{\text{6}}{\text{H}}_{\text{5}}\text{OH}$$ (Phenol) is dissolved in a solvent of $${\text{K}}_{\text{f}}\text{ = 14}$$, If the depression in freezing point is $$\text{7K}$$ then find the $$\text{\% }$$ of phenol that dimerises.

Answer 1

Hint: Dimerise means combining with similar molecules to form a dimer. In this question a phenol dimer is being formed and to calculate the percentage of phenol which formed a dimer, find the degree of dissociation.

Complete step by step answer:
Let’s start with discussing a little about the freezing point depression. According to the concept of freezing point depression whenever a solute is added to a pure solvent, the freezing point of the solvent (which is now a solution) decreases. For example, when $$\text{NaCl}$$ is dissolved in pure water, the freezing point of water is reduced from $${\text{0}}^{\text{o}}\text{C}$$ to - $${21.1}^{o}C$$ (Max).
Coming back to the question we are given an unknown solvent in which we are adding $$75.2g$$ of Phenol. The $${\text{K}}_{\text{f}}$$ of the solvent is $$\text{14}$$. The depression given to us is $$\text{7K}$$ and we have to find the $$\text{\% }$$ of phenol that dimerises.
The equilibrium that must have establish between different phenol molecules is given:
$$\text{2}{\text{C}}_{\text{6}}{\text{H}}_{\text{5}}\text{OH}\underset{}{\leftrightarrows }\text{(}{\text{C}}_{\text{6}}{\text{H}}_{\text{5}}{\text{OH)}}_{\text{2}}$$
The molecular mass of phenol is $$94.11\text{g/mol}$$. So, the amount of Phenol added in solvent in moles will be
${\displaystyle \frac{\text{Given Mass}}{\text{Molecular Mass}}}\text{ = }{\displaystyle \frac{75.2}{94.11}}=0.8\text{ moles}$
If $\alpha$ is the degree of dissociation, then the van't hoff factor I will be $\left({\displaystyle \frac{2-\alpha }{2}}\right)$
Also, the depression in freezing point is given by $${\text{K}}_{\text{f}}$$ $$\text{X}$$ moles $$\text{X i}$$
Which will be, Depression in freezing point $=7=14\times 0.8\left({\displaystyle \frac{2-\alpha }{2}}\right)$
Solving this we will get $\alpha =0.75$, which means $$75\mathrm{\%}$$ of phenol is dimerises.

Note:
Since we know that, Phenol is an alcoholic ring compound with the molecular formula of C6H5OH. This molecule is being used as a disinfectant, slimicide and antiseptic. Slimicides are the chemicals which are used to kill slime forming organisms like bacteria and fungi. Phenol is also used in the preparation of mouthwash.