Understanding the Concepts

* Freezing Point Depression: The freezing point of a solvent is lowered when a solute is dissolved in it. This is a colligative property, meaning it depends on the concentration of solute particles, not their identity.

* Van't Hoff Factor (i): This factor accounts for the number of ions a solute dissociates into when dissolved in a solvent. Aluminum chloride (AlCl₃) dissociates into four ions: one aluminum ion (Al³⁺) and three chloride ions (Cl⁻). So, its van't Hoff factor (i) is 4.

* Freezing Point Depression Equation: ΔT_f = i * K_f * m

* ΔT_f is the change in freezing point

* i is the van't Hoff factor

* K_f is the freezing point depression constant of the solvent (for water, K_f = 1.86 °C/m)

* m is the molality of the solution (moles of solute per kilogram of solvent)

Calculations

1. Molality (m):

* You have 1 mole of AlCl₃ dissolved in 1000 g (1 kg) of water.

* Therefore, molality (m) = 1 mol / 1 kg = 1 mol/kg

2. Freezing Point Change (ΔT_f):

* ΔT_f = i * K_f * m

* ΔT_f = 4 * 1.86 °C/m * 1 mol/kg

* ΔT_f = 7.44 °C

Conclusion

The freezing point of the solution will decrease by 7.44 °C compared to the freezing point of pure water (0 °C). This means the solution will freeze at approximately -7.44 °C.