Question

$75.2{\text{ }}g$ 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

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 $75.2{\text{ }}g$ 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
$\dfrac{{{\text{Given Mass}}}}{{{\text{Molecular Mass}}}}{\text{ = }}\dfrac{{75.2}}{{94.11}} = 0.8{\text{ moles}}$
If $\alpha$ is the degree of dissociation, then the van't hoff factor I will be $\left( {\dfrac{{2 - \alpha }}{2}} \right)$
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 $= 7 = 14 \times 0.8\left( {\dfrac{{2 - \alpha }}{2}} \right)$
Solving this we will get $\alpha = 0.75$, which means $75\%$ 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.