Freezing Point Depression for an Electrolyte Solution

Calculating an electrolyte solution's freezing point depression means multiplying the ordinary freezing-point-depression formula by the solute's van't Hoff factor, to account for the extra dissolved particles ionization produces.

A 1.0 m aqueous NaCl solution has molality b = 1.0 m, freezing-point-depression constant Kf = 1.86 °C/m for water, and a predicted van't Hoff factor i = 2. Substituting these named quantities into ΔTf = i·Kf·b gives ΔTf = (2)(1.86 °C/m)(1.0 m); the "per molal" unit in Kf cancels against the solution's molality, leaving a temperature change in °C, about 3.7 °C. Subtracting that change from water's normal freezing point places the predicted freezing point near -3.7 °C, close to the measured value of -3.4 °C — a modest, sub-zero shift of the size expected for a dilute electrolyte, with the small remaining gap reflecting NaCl's actual measured van't Hoff factor of about 1.9 rather than the idealized value of 2.