Question

$75.2g$ of phenol is dissolved in a solvent of $K_f=14$. If the depression in freezing point is $7K$ then find the $\cdot$ of phenol that dimerises.

• A. $75\%$
• B. $80\%$
• C. $70\%$
• D. $100\%$

Answer 1

Answer: (A)

$\begin{array}{cccc}& 2C_6{H}_{5}OH& \rightleftharpoons & {\left(C_6{H}_{5}OH\right)}_2\\ \text{initially}& C& & 0\\ \text{at equil}& C\left(1-\alpha \right)& & C\alpha /2\end{array}$
Total number of moles $=C-C\alpha +\left(C\alpha /2\right)$
$=C-\frac{C\alpha }{2}=\frac{2C-C\alpha }{2}$
$=\frac{C\left(2-\alpha \right)}{2}$
$C=\frac{\text{Weight}}{\text{Molecular weight}}$
$=\frac{75.2}{94}=0.8$
$\Delta T_f=K_f\times m$
$\Rightarrow 7=14\times 0.8\left(\frac{2-\alpha }{2}\right)$ or,
$1=0.8\left(2-\alpha \right)$
$\alpha =0.75=75\%$