b
Depression in freezing point: \(\Delta T_{f}=i \times k_{f} \times m\)

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: \(\Delta T_{f}=1.2 \times 1.86 \;K / kg\;mol\) \(\times 0.5 M=1.12\; K\)