When $1.5 \ g$ of phenol $(C_6H_5OH)$ is dissolved in $100 \ g$ of toluene,a decrease in freezing point of $0.56 \ K$ is observed. If the association is dimeric in nature,find the percentage of association. Given: $K_f = 4 \ K \ kg \ mol^{-1}$.

(25 %) $1$. Molar mass of phenol $(C_6H_5OH)$ = $94 \ g \ mol^{-1}$.
$2$. Molality $(m)$ = $\frac{1.5 \ g / 94 \ g \ mol^{-1}}{0.1 \ kg} = 0.1596 \ mol \ kg^{-1}$.
$3$. Observed depression in freezing point: $\Delta T_f = K_f \times m \times i$.
$4$. $0.56 = 4 \times 0.1596 \times i \implies i = \frac{0.56}{0.6384} \approx 0.877$.
$5$. For dimerization,$i = 1 + (\frac{1}{n} - 1)\alpha$,where $n = 2$.
$6$. $0.877 = 1 + (\frac{1}{2} - 1)\alpha \implies 0.877 = 1 - 0.5\alpha$.
$7$. $0.5\alpha = 0.123 \implies \alpha = 0.246 \approx 25 \%$.