Freezing Point Calculator
Freezing Point Depression1.8600 °C
New Freezing Point-1.8600 °C
Freezing point depression is a colligative property: dissolving a solute in a solvent lowers the temperature at which the solvent freezes. This calculator computes how far the freezing point drops using the cryoscopic constant, the molality of the solution, and the van't Hoff factor that accounts for how many particles each dissolved unit produces. It explains why salt melts icy roads and why antifreeze protects an engine in winter.
Formula
delta Tf = i * Kf * m; new freezing point = 0 - delta Tf
- delta Tf
- Freezing point depression in degrees Celsius
- i
- van't Hoff factor (number of particles per formula unit, e.g. 2 for NaCl)
- Kf
- Cryoscopic (freezing point depression) constant of the solvent, in C/molal
- m
- Molality of the solution in mol solute per kg solvent
How it works
- Enter the cryoscopic constant Kf for the solvent (water is 1.86 degrees Celsius per molal), the molality of the solution in mol of solute per kg of solvent, and the van't Hoff factor i.
- The calculator multiplies these three values to get the freezing point depression, the number of degrees by which the freezing point falls below that of the pure solvent.
- It then subtracts the depression from 0 degrees Celsius (the freezing point of pure water) to report the new freezing point of the solution, rounded to four decimal places.
Worked example
A 0.5 molal solution of table salt (NaCl) in water, with i = 2 and Kf = 1.86.
- Multiply the factors: delta Tf = 2 x 1.86 x 0.5.
- 2 x 1.86 = 3.72, then 3.72 x 0.5 = 1.86 degrees Celsius of depression.
- Subtract from the pure water freezing point: 0 - 1.86 = -1.86 degrees Celsius.
The freezing point drops by 1.86 C, so the solution freezes at about -1.86 C.
Frequently asked questions
- What is the van't Hoff factor and why does it matter?
- It is the number of dissolved particles produced by each formula unit of solute. Sugar stays as one particle (i = 1), while NaCl splits into two ions (i = 2), doubling its freezing point effect at the same molality.
- Why does the calculator use 0 degrees as the starting freezing point?
- The engine assumes water as the solvent, whose pure freezing point is 0 degrees Celsius, and reports the new freezing point relative to that. The depression itself depends only on Kf, molality, and the van't Hoff factor.
- What is molality and how is it different from molarity?
- Molality is moles of solute per kilogram of solvent, while molarity is moles per liter of solution. Colligative property formulas use molality because it does not change with temperature the way volume-based molarity does.
- Is this why salt is spread on icy roads?
- Yes. Dissolving salt in the thin layer of water on ice lowers its freezing point, so the ice melts at temperatures below the normal 0 degrees Celsius, helping clear roads in winter.