a
\(\Delta \mathrm{T}_{\mathrm{f}}\) is maximum when \(\mathrm{i} \times \mathrm{m}\) is maximum.

1) \(\mathrm{m}_1=\frac{180}{60}=3, \mathrm{i}=1+\alpha\)

Hence

\(\Delta \mathrm{T}_{\mathrm{f}}=(1+\alpha) \cdot \mathrm{k}_{\mathrm{f}}=3 \times 1.86=5.58^{\circ} \mathrm{C}(\alpha<<1)\)

\(2)\) \(\mathrm{m}_2=\frac{180}{60}=3, \mathrm{i}=0.5, \Delta \mathrm{T}_{\mathrm{f}}=\frac{3}{2} \times \mathrm{k}_{\mathrm{f}}{ }^{\prime}=7.68^{\circ} \mathrm{C}\)

3) \(\mathrm{m}_3=\frac{180}{122}=1.48, \mathrm{i}=0.5, \Delta \mathrm{T}_{\mathrm{f}}=\frac{1.48}{2} \times \mathrm{k}_{\mathrm{f}}^{\prime}=3.8^{\circ} \mathrm{C}\)

4) \(\mathrm{m}_4=\frac{180}{180}=1, \mathrm{i}=1, \Delta \mathrm{T}_{\mathrm{f}}=1 \cdot \mathrm{k}_{\mathrm{f}}^{\prime}=1.86^{\circ} \mathrm{C}\)

As per NCERT, \(\mathrm{k}_{\mathrm{f}}{ }^{\prime}\left(\mathrm{H}_2 \mathrm{O}\right)=1.86 \mathrm{k} \cdot \mathrm{kg} \mathrm{mol}^{-1}\)

\(\mathrm{k}_{\mathrm{f}}{ }^{\prime}(\) Benzene \()=5.12 \mathrm{k} \cdot \mathrm{kg} \mathrm{mol}^{-1}\)