where, $\Delta T_{f}=$ depression in freezing point

$\mathrm{i}=\mathrm{vant}$ hoff factor

$k_{f}=$ freezing point constant

$\mathrm{m}=$ molality

$\mathrm{i}=\frac{\text { Total no on moles at equilibrium }}{\text { Init inl moles }}$

$\quad \quad H X \rightarrow H^{+}+X^{-}$

$\mathrm{l}: \quad 0.5\quad \quad 0 \quad \quad 0$

$\mathrm{C}: \mathrm{c}-\mathrm{c\alpha} \quad \mathrm{c\alpha} \quad \mathrm{c\alpha}$

$\alpha=\frac{20}{100}=0.2, c=0.5 \mathrm{M}$

$\mathrm{c}-\mathrm{c} \alpha=0.4 \mathrm{M}, \mathrm{c\alpha}=0.1 \mathrm{M}, \mathrm{c\alpha} = 0.1 \mathrm{M}$

Total moles at equilibrium $=0.4 \mathrm{M}+0.1 \mathrm{M}+0.1 \mathrm{M}=0.6 \mathrm{M}$

$i=\frac{0.6 M}{0.5 M}=1.2$

Depression in freezing point: $\Delta T_{f}=1.2 \times 1.86 \;K / kg\;mol$ $\times 0.5 M=1.12\; K$