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Cryoscopic Constant of Water

Kf=1.86 K⋅kg/molK_{\mathrm{f}} = 1.86\ \text{K}{\cdot}\text{kg/mol}
Value1.86 K·kg/mol
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StatusMeasured: ± 0.01 K·kg/mol (0.54 % relative)
SourceComputed, K_f = R·T_f²/Δh_fus, from the IAPWS melting point (273.15 K) and the IAPWS heat of fusion (333.43 kJ/kg): 1.8605 K·kg/mol
CategoriesChemistry
Cryoscopic Constant of Water in every molal constant unit
UnitValue
kelvin kilogram per mole1.86 K·kg/mol
Celsius kilogram per mole1.86 °C·kg/mol
kelvin kilogram per kilomole1,860 K·kg/kmol
kelvin per molal1.86 K/molal
Celsius degree per molal1.86 °C/molal

Learning zone

Dissolve anything in water and the freezing point drops in proportion to the number of dissolved particles, not their identity: ΔTf = i·Kf·m, with Kf = 1.86 K·kg/mol. Sodium chloride splits into two ions, so its van 't Hoff factor is close to 2 and a 1 molal solution freezes near −3.7 °C, which is exactly why road salt works and why it stops working below about −10 °C, where the practical limit of saturated brine is reached.

François-Marie Raoult established the proportionality in the 1880s, and it became the standard way of measuring molar masses for the next forty years: dissolve a known mass, measure the freezing point drop, and the molar mass falls out. The technique still survives as osmometry in clinical laboratories, where freezing-point depression measures the osmolality of blood and urine to a few milliosmoles. It is a colligative property in the strict sense: 1 mole of sugar and 1 mole of urea depress the freezing point identically.

Used by 2 solvers

Freezing-Point Depression

ΔTf=Kf b\Delta T_f = K_f \, b

Molality (b = n/m)

b=nmsolventb = \frac{n}{m_{\text{solvent}}}
Revised 1 November 2026
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formula.expert. (2026, November 1). Cryoscopic Constant of Water. https://formula.expert/constants/cryoscopic-constant-water