Freezing Point Depression Calculator
Find the freezing point drop from Kf, molality, and particle count, in C and F.
What it does
Dissolved particles get in the way of freezing. A liquid can only build a crystal when enough solvent molecules meet in the right arrangement, and solute particles lower the chance of that meeting. The result is a freezing point below the pure solvent, with the size of the drop set by how many particles are present, not by what they are.
The tool above turns that rule into numbers. Enter the solvent constant Kf, the molality, the van t Hoff factor, and the pure freezing point. It returns the depression plus the new freezing point in both Celsius and Fahrenheit. Defaults describe a half molal sugar solution in water, so the page opens on the worked example.
Two choices decide accuracy. Molality must use kilograms of solvent, and i must reflect real dissociation: sugar counts once, table salt near twice, calcium chloride near three times in dilute use. At high concentration ion pairing pulls measured i below the ideal integer, so treat strong brine results as estimates and confirm with a table.
The example stays with water because its constants are familiar: Kf = 1.86 C/m and a pure point of 0 C. A 0.5 m sugar mix drops freezing by 0.93 C. Swap in benzene values (Kf = 5.12, pure point 5.5 C) to see the same formula serve a lab solvent, or raise i to model deicing salt.
Read the reference table for common Kf values, then test your own mix. The page assumes dilute ideal behavior, so very salty or syrupy mixes need measured data. Within its range it answers fast practical questions: will this coolant survive the night, or how much salt does this sidewalk need.
How to use
- Enter Kf for your solvent. Water defaults to 1.86 C/m.
- Enter molality in mol/kg of solvent.
- Enter i: 1 for nonelectrolytes, near 2 for NaCl, near 3 for CaCl2.
- Set the pure solvent freezing point (0 C for water, 5.5 C for benzene).
- Read the depression plus the new freezing point in C and F.
- For road salt math, raise i and m together and watch the drop scale.
Formula
- Kf
- Cryoscopic constant of the solvent, in C/m. Water is 1.86.
- m
- Moles of solute per kilogram of solvent.
- i
- Particles per formula unit after dissolving. Sugar is 1, NaCl near 2.
- Pure point
- Freezing point of the pure solvent in C.
- Depression
- Drop in freezing point in C.
Kf belongs to the solvent, m counts moles of solute per kilogram of solvent, and i corrects for dissociation. The page assumes a dilute ideal solution with no solid solution formation. For water the pure point defaults to 0 C; change it for other solvents such as benzene at 5.5 C.
Worked example
Example: 0.5 m sugar in water
Water has Kf = 1.86 C/m. A 0.5 mol/kg sugar solution (i = 1) freezes below 0 C. Find the drop and the new freezing point.
- Depression = i x Kf x m = 1 x 1.86 x 0.5 = 0.93 C.
- Pure water freezes at 0 C, so the solution freezes at 0 - 0.93 = -0.93 C.
- Convert to Fahrenheit: -0.93 x 9/5 + 32 = -1.674 + 32 = 30.33 F.
- Read the tool: depression 0.93 C, freezing point -0.93 C, which is 30.33 F.
- Salt with i = 2 would double the drop to 1.86 C at the same molality.
- Small molality errors scale directly, so weigh the solvent with care.
Reference table
| Solvent | Kf (C/m) | Pure point (C) |
|---|---|---|
| Water | 1.86 | 0 |
| Acetic acid | 3.9 | 16.6 |
| Benzene | 5.12 | 5.5 |
| Chloroform | 4.68 | -63.5 |
| Nitrobenzene | 8.1 | 5.7 |
Limits
- Dilute solutions only; concentrated mixes deviate.
- Assumes no solid solution and no supercooling tricks.
- i varies with concentration for electrolytes.
- Impurities and mixed solvents shift Kf in practice.
Common mistakes
- Using molarity instead of molality.
- Setting i = 1 for table salt or calcium chloride.
- Forgetting to change the pure point for non water solvents.
- Reading the depression as the final freezing point.
- Expecting road salt to work far below its eutectic point.
Try it yourself
Quick checks. Answers sit tucked under each question.
Same water mix but with NaCl (i = 2) at 0.5 m?
Depression = 1.86 C. New point is -1.86 C, which is 28.65 F.
Benzene mix: Kf 5.12, 0.33 m, i = 1, pure point 5.5 C?
Depression = 1.69 C. New point is 3.81 C, which is 38.86 F.
What if the sugar molality falls to 0.2 m?
Depression = 0.37 C. New point is -0.37 C, which is 31.33 F.
Questions
What is freezing point depression?
The drop in freezing point of a solvent when solute is added. For dilute solutions it equals i x Kf x m, where m is molality.
What is Kf?
Kf is the cryoscopic constant of the solvent. Water is 1.86 C/m, benzene is 5.12 C/m, and each solvent in the table has its own value.
Molality or molarity?
Use molality (moles per kilogram of solvent), not molarity. Molality does not change with temperature, so the result stays valid across the cooling range.
What is the van t Hoff factor?
i counts particles after dissolving. Sugar stays near 1, table salt approaches 2, and calcium chloride approaches 3 in dilute solutions.
Does it work for solvents other than water?
Yes. Set the pure freezing point to 5.5 C and Kf to 5.12 C/m for benzene, or enter the constants of your solvent, and the same formula applies.
Is the formula exact at any concentration?
No. The linear form fits dilute solutions. Concentrated brines, ion pairing, and supercooling all break the simple proportion.