How can I estimate the freezing point of a solution?

Calculate the freezing point of .100 molality solution of K₂SO₄.

You can crudely estimate the freezing point using the approximate relation

T_f(water) - T_f(soln) = k_f m

where T_f(water) is the freezing point of water, T_f(soln) is the freezing point of the solution, k_f is the apparent molal freezing point constant (1.86 °C kg/mol, for water), and m is the total molality of particles in solution. If you assume that the potassium sulfate dissociates completely in solution, m = 3· 0.1 = 0.3 mol/kg for your problem. That makes the freezing point depression equal to about (0.3 mol/kg)×(1.86 °C kg/mol) = 0.5₆°C, so the freezing point of the solution is roughly -0.6°C.

Why is this only a crude estimate? The relationship was derived by assuming a dilute, ideal solution. Your solution doesn't meet either of those requirements. The ions (being charged) interact rather strongly in solution, producing deviations from ideal behavior that are difficult to ignore. Also polyvalent ions like sulfate tend to form ion pairs (e. g. KSO₄^-(aq)) at concentrations this high, so the assumption of complete dissociation isn't correct.

Author: Fred Senese senese@antoine.frostburg.edu

General Chemistry Online! How can I estimate the freezing point of a solution?