Of the following $$0.10$$ $$m$$  aqueous solutions, which one will exhibit the largest freezing point depression?

Solution :
$$\Delta {T_f}$$  ( freezing point depression ) is a colligative property and depends upon the van't Hoff factor $$(i),$$ i.e. number of ions given by the electrolyte in aqueous solution.
$$\Delta {T_f} = i \times {k_f} \times m$$
where, $${k_f} = $$  molal freezing point depression constant
              $$m=$$  molality of the solution
$$\eqalign{ & \therefore {k_f}\,\,{\text{and }}m{\text{ are constant,}} \cr & \therefore \,\,{T_f} \propto i \cr} $$
$${\text{van't Hoff factor for ionic solution}}{\text{.}}$$
$$\left( {\text{A}} \right)KCl\left( {aq} \right) \rightleftharpoons {K^ + }\left( {aq} \right) + C{l^ - }\left( {aq} \right),$$       $$\left( {{\text{Total ions}} = 2\,{\text{thus,}}\,i = 2} \right)$$
$$\left( {\text{B}} \right){C_6}{H_{12}}{O_6} \rightleftharpoons {\text{no ions}}\left[ {i = 0} \right]$$
$${\text{because glucose does not gives ions}}{\text{.}}$$
$$\left( {\text{C}} \right)A{l_2}{\left( {S{O_4}} \right)_3}\left( {aq} \right) \rightleftharpoons 2A{l^{3 + }} + 3SO_4^{2 - }$$        $$\left[ {{\text{Total ions}}\, = 5{\text{,}}\,{\text{thus,}}\,i = 5} \right]$$
$$\left( {\text{D}} \right){K_2}S{O_4}\left( {aq} \right) \rightleftharpoons 2{K^ + } + SO_4^{2 - }$$       $$\left[ {{\text{Total ions}}\, = 3{\text{,}}\,{\text{thus,}}\,i = 3} \right]$$
Hence, $$A{l_2}{\left( {S{O_4}} \right)_3}$$   will exhibit largest freezing point depression due to the highest value of $$i.$$