Question

Phenol associates in benzene to form dimer. A solution of $2.0g$ of phenol in $100g$ benzene lowers its freezing point by ${0.72}^{o}C$ $K_f$ of benzene is $5.12$ k/molal. Calculate the degree of association of phenol in benzene.

Answer 1

Let, degree of association be $\alpha$

$\underset{1-\alpha }{B_2{C}_6{H}_{5}OH}\rightleftharpoons \underset{\alpha /2}{(C_6{H}_{5}OH{)}_2}$

$\therefore i=1-\frac{\alpha }{2}$

We know, $\Delta T_f=i{K}_{f}m$

$\Rightarrow i=\frac{0.72}{5.12}\times \frac{\frac{2}{94}}{100}\times 1000$

$\Rightarrow i$

$\Rightarrow i=\frac{\Delta T_f}{K_{f}m}=0.66$

$\Rightarrow 1-\frac{\alpha }{2}=0.66$

$\Rightarrow \alpha =0.68$