Question

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

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

Answer 1

Answer: (A)

$\begin{matrix}&2C_{6}H_{5}OH&\rightleftharpoons&\left(C_{6}H_{5}OH\right)_{2}\\ \text{initially}&C&&0\\ \text{at equil}&C\left(1-\alpha\right)&&C\alpha /2\end{matrix}$
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,
$1= 0.8\left(2-\alpha\right)$
$\alpha = 0.75 = 75\%$