Which of the following solutions shows maximum depression in freezing point?

Hint: Depression in freezing point is a colligative property. We know that colligative properties depend on the number of particles i.e. the quantity and not the type of particle in solution. So the solution having more number of solute particles , that solution will show maximum depression in freezing point. When the solute dissociates in solvent, consider the Van't Hoff factor to determine particles after dissociation.

Complete step-by-step answer:
Colligative properties are the properties of solutions that depend on the ratio of the number of solute particles to the number of solvent molecules in a solution, and not on the nature of the chemical species present.
The number ratio can be related to the various units for concentration of a solution, for example, molarity, molality, normality etc.
The colligative properties are:
Relative lowering of vapor pressure
Elevation of boiling point
Depression of freezing point
Osmotic pressure
When a non-volatile solute is dissolved in a liquid solvent, the freezing point temperature of the solution becomes lower than the freezing point of the pure liquid solvent.
The formula to find depression in freezing point is :
$\Delta {{T}_{f}}\text{ = i }\text{. }{{\text{K}}_{f}}\text{ }\text{. m}$
Where,
$\Delta {{T}_{f}}$ is the difference in freezing point
i is the Van't Hoff factor
${{K}_{f}}$ is the cryoscopic constant
m is the molality of solution
Since the cryoscopic constant is the same for all compounds, the compound with higher i x C value will have maximum depression in freezing point.
The Van't Hoff factor for:
$L{{i}_{2}}S{{O}_{4}}$ = 3
$NaCl$ = 2
$A{{l}_{2}}{{(S{{O}_{4}})}_{3}}$ = 5
$BaC{{l}_{2}}$ = 3
The concentration of :
$L{{i}_{2}}S{{O}_{4}}$ = 0.5
$NaCl$ = 1
$A{{l}_{2}}{{(S{{O}_{4}})}_{3}}$ = 0.5
$BaC{{l}_{2}}$ = 0.5
The solution having maximum i x C value and that shows maximum depression in freezing point is $A{{l}_{2}}{{(S{{O}_{4}})}_{3}}$ .


Therefore, the correct answer is option (C).


Note: Van't Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved and the concentration of a substance as per its mass. The value of the Van't Hoff factor is greater than 1 for dissociation of ionic compounds. The factor is used when the solute undergoes dissociation or association in the solvent.