Colligative Properties Calculator (boiling, freezing, osmotic pressure)

Understanding the colligative properties calculator — concept and principle

Colligative properties depend only on how many solute particles are dissolved, not on what they are. This calculator gives the three most used ones for a water solution: how much the boiling point rises, how much the freezing point falls, and the osmotic pressure. It is used in general chemistry and to estimate brine freezing points or membrane pressures.

Every dissolved particle counts: NaCl splits into 2, so it raises boiling by 1.024 K and lowers freezing by 3.72 K.

How it is calculated

Boiling point elevation: ΔT_b = i × K_b × m
Freezing point depression: ΔT_f = i × K_f × m
Osmotic pressure: Π = i × M × R × T, with R = 0.082057 L·atm/(mol·K) and T in kelvin (°C + 273.15)

m is the molality in mol of solute per kg of solvent. i is the van 't Hoff factor, the number of particles each formula unit produces (1 for sugar or urea, 2 for NaCl, 3 for CaCl₂ in the ideal case). K_b and K_f are solvent constants in K·kg/mol; for water they are 0.512 and 1.86. For the osmotic pressure the calculator uses the molality as if it were the molarity M in mol/L, which is a reasonable approximation for dilute water solutions because 1 kg of water occupies about 1 L.

The principle

Solute particles lower the solvent's chemical potential and vapour pressure (Raoult's law), so the liquid must be heated more to boil and cooled further before solid solvent forms. Water molecules also tend to move through a semipermeable membrane toward the side with more particles; the osmotic pressure is the pressure needed to stop that flow. In dilute ideal solutions all three effects are proportional to the particle concentration, which is why the formulas are simple products.

Worked example

Inputs: m = 1 mol/kg, i = 2, K_b = 0.512, K_f = 1.86, T = 25 °C.
ΔT_b = 2 × 0.512 × 1 = 1.024 K, so the solution would boil near 101.0 °C at 1 atm.
ΔT_f = 2 × 1.86 × 1 = 3.72 K, so it would freeze near −3.72 °C.
T = 25 + 273.15 = 298.15 K; Π = 2 × 1 × 0.082057 × 298.15 = 48.93 atm.

Each point is the calculator re-run with only “Molality (mol/kg)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Molality (mol/kg)	Boiling point rise (K)
0.25	0.256
0.5	0.512
0.75	0.768
1	1.024
1.25	1.28
1.5	1.536
2	2.048

How to read the result

A change of 1 K in boiling or freezing temperature equals a change of 1 °C. Osmotic pressure is large even for modest concentrations: 48.9 atm is about 4.96 MPa, which is why reverse-osmosis desalination needs high pumps.

Common mistakes

Using molarity where molality is required for ΔT_b and ΔT_f.
Forgetting the van 't Hoff factor for salts, or using it for non-electrolytes.
Using water constants for a different solvent such as benzene or camphor.

Keep in mind: The formulas are ideal and work best below about 0.1 mol/kg. At 1 mol/kg ion pairing and non-ideal behaviour make the real i for NaCl noticeably lower than 2, so measured values are smaller than shown.

Frequently asked questions

Why does salt melt ice on roads?

Dissolved ions lower the freezing point of the thin water film on the ice, so it stays liquid below 0 °C.

How can freezing point depression find a molar mass?

Measure ΔT_f for a known mass of solute in a known mass of solvent, compute m = ΔT_f/(iK_f), then molar mass = grams of solute ÷ (m × kg of solvent).

Sources: P. Atkins and J. de Paula, Physical Chemistry, Oxford University Press (colligative properties) · IUPAC Compendium of Chemical Terminology (Gold Book), "colligative properties"

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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