Here's how to calculate the freezing point depression of an aqueous solution containing 25.0 grams of magnesium chloride (MgCl₂):

1. Calculate the molality of the solution.

* Molar mass of MgCl₂: 24.31 g/mol (Mg) + 2 * 35.45 g/mol (Cl) = 95.21 g/mol

* Moles of MgCl₂: 25.0 g / 95.21 g/mol = 0.263 mol

* Mass of water (solvent): Assume you're making a 1 kg (1000 g) solution. Therefore, the mass of water is 1000 g - 25.0 g = 975 g = 0.975 kg

* Molality (m): moles of solute / kg of solvent = 0.263 mol / 0.975 kg = 0.270 mol/kg

2. Calculate the van't Hoff factor (i).

* MgCl₂ dissociates into 3 ions in solution: Mg²⁺ + 2Cl⁻. Therefore, i = 3.

3. Calculate the freezing point depression (ΔT_f).

* Freezing point depression constant (K_f) for water: 1.86 °C/m

* ΔT_f = i * K_f * m

* ΔT_f = 3 * 1.86 °C/m * 0.270 m = 1.50 °C

Therefore, the freezing point depression of the aqueous solution containing 25.0 grams of magnesium chloride is 1.50 °C.

Important Note: This calculation assumes ideal behavior, meaning that the solute completely dissociates into ions. In reality, some ion pairing might occur, which would slightly reduce the actual freezing point depression.