The freezing point of ideal solutions lower respect the freezing point of the pure solvent following the freezing depression formula:
ΔT = i * Kf * m
Where:
- i is the vant'Hoff, which is the number of partilces (ions in this case) that are the solute forms when dissociate.
- kf is cryoscopic constant of the pure solvent (water because we assume it is an aqueous solution).
Then kf = - 1.86 °C / mol
- and m is the molality, m = 0.030 m
i = 2 + 3 = 5, given the one molecule of Al2 (SO4)3 produces 2 ions of Al(+) and 3 ions of SO4 (2-).
Then, ΔT = 5 * 1.86°C/m * 0.030 m = 0.279 °C.
That is the depression of the freezing point which you have to subtract from the freezing point of the pure water => 0°C - 0.279°C = - 0.279 °C.
Answer: - 0.279°C
