Last updated: July 3, 2026
Freezing Point Depression Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
This freezing point depression calculator uses ΔTf = i × Kf × m to find the freezing point lowering, new freezing point, molality, or van 't Hoff factor for dilute solutions.
Freezing point depression equals the van 't Hoff factor times the cryoscopic constant times molality. For water, a 1 molal nonelectrolyte lowers freezing by 1.86 degrees Celsius.
Key Takeaways
- Freezing point depression is calculated as ΔTf = i × Kf × m.
- The new freezing point equals the pure solvent freezing point minus ΔTf.
- Water commonly uses Kf = 1.86 °C·kg/mol and Tf° = 0 °C.
- Molality, not molarity, is the concentration unit in the colligative equation.
- Ideal van 't Hoff factors are approximations for real electrolyte solutions.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
ΔTf = i × Kf × m; Tf(solution) = Tf° − ΔTf
Where:
- ΔTf=Freezing point depression(°C)
- i=van 't Hoff factor(dimensionless)
- Kf=Cryoscopic constant(°C·kg/mol)
- m=Molality(mol/kg)
- Tf°=Normal freezing point of pure solvent(°C)
Worked Examples
1 molal nonelectrolyte in water
A molecular solute with i = 1 is dissolved at 1 mol/kg in water.
- 1Use ΔTf = i × Kf × m.
- 2Substitute i = 1, Kf = 1.86 °C·kg/mol, and m = 1 mol/kg.
- 3ΔTf = 1 × 1.86 × 1 = 1.86 °C, so Tf = 0 − 1.86 = −1.86 °C.
Ideal sodium chloride solution
NaCl is approximated as i = 2 at 0.5 mol/kg in water.
- 1Use ΔTf = iKf m.
- 2Substitute i = 2, Kf = 1.86, and m = 0.5.
- 3ΔTf = 2 × 1.86 × 0.5 = 1.86 °C, giving Tf = −1.86 °C.
2 molal nonelectrolyte
A more concentrated nonelectrolyte in water lowers the freezing point more strongly.
- 1Multiply the particle factor, solvent constant, and molality.
- 2ΔTf = 1 × 1.86 × 2 = 3.72 °C.
- 3The new freezing point is 0 − 3.72 = −3.72 °C.
Introduction
Freezing point depression is a colligative property: it depends mainly on how many dissolved particles are present, not on their chemical identity. This calculator applies ΔTf = i × Kf × m to estimate how far a solution freezes below the pure solvent.
Freezing point depression formula
The working equation is ΔTf = i × Kf × m. Here i is the van 't Hoff factor, Kf is the solvent's cryoscopic constant, and m is molality. For water, Kf is commonly 1.86 °C·kg/mol and the normal freezing point is 0 °C.
How to find the new freezing point
After calculating the positive depression ΔTf, subtract it from the pure-solvent freezing point: Tf(solution) = Tf° − ΔTf. This sign convention is the opposite of boiling point elevation, where the temperature is raised.
Solving for molality, i, or ΔTf
If ΔTf is unknown, multiply i, Kf, and molality. If molality is unknown, rearrange to m = ΔTf / (iKf). If the van 't Hoff factor is unknown, use i = ΔTf / (Kf m). These rearrangements are most reliable for dilute solutions.
Choosing a van 't Hoff factor
Use i = 1 for nonelectrolytes such as glucose or sucrose. Ideal NaCl is often approximated as i = 2, CaCl2 as i = 3, and AlCl3 as i = 4, but real electrolytes show ion pairing and activity effects. For rigorous terminology, see the IUPAC Gold Book.
Assumptions and limitations
The equation assumes a nonvolatile solute, a solvent constant appropriate to the solvent, and near-ideal dilute behavior. Concentrated brines, antifreeze mixtures, and associating solutes can deviate from simple particle counting. LibreTexts provides a useful overview of colligative properties.
Quick Reference Card
Freezing Point Depression — Quick Reference
Quick reference • Freezing Point Depression Calculator
ΔTf = i × Kf × m; Tf = Tf° − ΔTfValid range: Best for dilute, ideal solutions of nonvolatile solutes below solubility and eutectic limits.
Common Values
⚠ Watch Out
- •Do not enter molarity where molality is required.
- •Do not use water's Kf for a different solvent.
- •Ideal i values can overestimate concentrated electrolyte solutions.
- •Subtract ΔTf from Tf°; do not add it to the freezing point.
- •The formula assumes a nonvolatile solute and a nearly ideal dilute solution.
Pro Tips
- →Use i = 1 for glucose, sucrose, urea, and other nonelectrolytes.
- →For quick aqueous estimates, multiply 1.86 by i and molality.
- →Calculate molality from weighed solute and solvent before using the colligative equation.
- →Keep extra digits through intermediate steps and round the final displayed temperature.
- →Use measured effective i values when modeling real electrolyte brines.
FAQs
What is freezing point depression?
It is the lowering of a solvent's freezing point when solute particles are dissolved in it. The calculated ΔTf is positive, while the new freezing temperature is lower than the pure solvent value.
Why does the calculator use molality instead of molarity?
Colligative freezing point depression is based on moles of solute per kilogram of solvent. Molality does not change with temperature as solution volume can.
What Kf should I use for water?
Use 1.86 °C·kg/mol for water in standard general-chemistry calculations unless your source specifies a different value or temperature convention.
What van 't Hoff factor should I use for NaCl?
For an ideal dilute NaCl solution, use i = 2 because one formula unit gives two ions. Real NaCl solutions often have an effective i below 2 due to nonideal behavior.
Can this calculator solve for molality?
Yes. Enter ΔTf, Kf, and i, then leave molality blank or zero. The calculator rearranges the formula to m = ΔTf / (iKf).
Why is my new freezing point negative?
For water-based solutions, normal Tf° is 0 °C. Any positive depression is subtracted, so an aqueous solution commonly freezes below 0 °C.