Chemistry

Colligative Properties Calculator | Boiling Point Elevation & Freezing Point Depression

Compute the four colligative properties of solutions: boiling point elevation (ΔTb), freezing point depression (ΔTf), osmotic pressure (π), and vapor pressure lowering (ΔP). Supports electrolyte solutions via the van't Hoff i-factor for common solvents.

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PRESETS

Solvent

Solute mass (g)

Solute molar mass (g/mol)

Solvent mass (g)

van't Hoff factor i (1 = non-electrolyte)

Temperature for osmotic pressure (K)

Moles of solute (mol)

0.01711

Molality m (mol/kg)

0.1711

BOILING POINT ELEVATION (ΔTb = Kb·m·i)

ΔTb

+0.0876 °C

New boiling point

100.088 °C

Normal bp: 100 °C

FREEZING POINT DEPRESSION (ΔTf = Kf·m·i)

ΔTf

−0.3183 °C

New freezing point

-0.318 °C

Normal fp: 0 °C

OSMOTIC PRESSURE (π = iMRT, R=0.08206 L·atm/mol·K)

Osmotic pressure π (atm)

4.1844

Osmotic pressure π (kPa)

423.989

VAPOR PRESSURE LOWERING (ΔP = P°·x_solute·i)

ΔP (mmHg)

0.0731

P° solvent = 23.8 mmHg

New vapor pressure (mmHg)

23.727

Solvent	Kb (°C·kg/mol)	Kf (°C·kg/mol)	bp (°C)	fp (°C)
Water	0.512	1.86	100	0
Benzene	2.53	5.12	80.1	5.5
Cyclohexane	2.79	20.2	80.7	6.5
Acetic acid	3.07	3.9	117.9	16.6
Camphor	5.95	37.7	209	176

What Is the Colligative Properties Calculator | Boiling Point Elevation & Freezing Point Depression?

Colligative properties are solution properties that depend only on the number of dissolved particles, not their chemical identity. The four classical colligative properties are boiling point elevation, freezing point depression, osmotic pressure, and vapor pressure lowering.

The van't Hoff factor i accounts for electrolytes that dissociate in solution: NaCl (i ≈ 2), CaCl₂ (i ≈ 3), and AlCl₃ (i ≈ 4) for complete dissociation. For weak electrolytes i lies between 1 and the full-dissociation value; for covalent molecules i = 1.

These properties have wide practical applications: antifreeze lowers the freezing point of engine coolant, osmosis drives water across semipermeable membranes in cells, boiling point elevation explains why salted pasta water boils at a slightly higher temperature, and vapor pressure lowering is the thermodynamic basis of Raoult's Law.

Formula

Boiling Point Elevation:    ΔTb = Kb · m · i
Freezing Point Depression:  ΔTf = Kf · m · i
Osmotic Pressure:           π = i · M · R · T   (R = 0.08206 L·atm/mol·K)
Vapor Pressure Lowering:    ΔP = P°_solvent · x_solute · i  (Raoult's Law)

where:
  m = molality (mol solute / kg solvent)
  M = molarity (mol solute / L solution)
  i = van't Hoff factor (1 for non-electrolytes; 2 for NaCl, etc.)
  x_solute = mole fraction of solute

How to Use

1
Select the solvent from the dropdown (Water, Benzene, Cyclohexane, Acetic acid, or Camphor).
2
Enter the mass of solute in grams.
3
Enter the molar mass of the solute in g/mol (look it up or use the Molar Mass Calculator).
4
Enter the mass of solvent in grams (not total solution mass).
5
Enter the van't Hoff factor i: 1 for sugars/urea, 2 for NaCl/KCl, 3 for CaCl₂, etc.
6
Enter temperature T in Kelvin for the osmotic pressure calculation (default 298 K = 25°C).
7
Read ΔTb, new boiling point, ΔTf, new freezing point, osmotic pressure, and vapor pressure lowering.

Select a solvent, enter the solute mass, molar mass, solvent mass, van't Hoff factor, and temperature. All four colligative properties are shown simultaneously.

Example Calculation

Problem: 5.85 g of NaCl (MM = 58.44 g/mol, i = 2) dissolved in 100 g of water. Find all colligative properties at 25°C.

Solution:

Moles NaCl = 5.85 / 58.44 = 0.1001 mol

Molality m = 0.1001 / 0.100 = 1.001 mol/kg

ΔTb = 0.512 × 1.001 × 2 = 1.025 °C → new bp = 101.025 °C

ΔTf = 1.86 × 1.001 × 2 = 3.724 °C → new fp = −3.724 °C

π = 2 × (0.1001/0.1) × 0.08206 × 298 = 49.0 atm

ΔP = 23.8 × (0.1001/(0.1001 + 5.55)) × 2 = 0.853 mmHg

Understanding Colligative Properties | Boiling Point Elevation & Freezing Point Depression

van't Hoff Factors for Common Solutes

Solute	Formula	Ideal i	Typical measured i
Glucose	C₆H₁₂O₆	1	1.0
Sucrose	C₁₂H₂₂O₁₁	1	1.0
Urea	CO(NH₂)₂	1	1.0
Sodium chloride	NaCl	2	1.9
Potassium chloride	KCl	2	1.9
Magnesium chloride	MgCl₂	3	2.7
Calcium chloride	CaCl₂	3	2.8
Aluminium sulfate	Al₂(SO₄)₃	5	4.2

Real-World Applications

›Antifreeze (ethylene glycol, i=1): 50% solution lowers freezing point of water to −37°C.
›Osmotic pressure of seawater (~0.6 mol/L NaCl) ≈ 30 atm — must be overcome in reverse osmosis desalination.
›Red blood cells lyse below ~0.15 M NaCl (hypotonic) and crenate above ~0.3 M NaCl (hypertonic).
›Molar mass determination by cryoscopy: dissolve unknown in camphor (Kf=37.7) and measure ΔTf.
›De-icing roads: NaCl and CaCl₂ lower freezing point; CaCl₂ is preferred at very low temperatures.
›Boiling point elevation is used in sugar-making to monitor concentration (Brix scale correlates to bp elevation).

Frequently Asked Questions

Why do colligative properties depend on particle count, not identity?

Colligative effects arise from the statistical interaction between solute particles and solvent at interfaces or in the bulk. Whether the solute is sugar or salt, each dissolved particle equally disrupts solvent-solvent interactions (vapor pressure lowering), blocks crystal lattice formation (freezing point depression), or raises the chemical potential of the solvent needed for boiling.

What is the van't Hoff factor and how do I determine it?

The van't Hoff factor i is the ratio of effective particles to formula units after dissolution. For non-electrolytes (glucose, urea) i = 1. For strong electrolytes, i equals the number of ions in the formula (NaCl → 2, CaCl₂ → 3). Measured i values are slightly less than ideal due to ion pairing at realistic concentrations.

How is osmotic pressure used in medicine?

Intravenous saline must be isotonic (same osmotic pressure as blood, ~310 mOsm/kg) to prevent cell lysis or crenation. Hypertonic solutions draw water from cells (used in brain edema treatment). Dialysis uses osmosis to remove waste solutes from blood. Mannitol creates osmotic diuresis to reduce intracranial pressure.

Why is camphor used for molar mass determination?

Camphor has an exceptionally large cryoscopic constant (Kf = 37.7 °C·kg/mol), roughly 20× that of water. Even a small molality produces a measurable freezing point depression. This makes it suitable for determining molar masses of large organic molecules where water would produce too small a ΔTf to measure accurately.

What is the difference between molality and molarity, and which is used for colligative properties?

Molality (mol/kg solvent) is temperature-independent because it is based on mass. Molarity (mol/L solution) changes with temperature as liquid volume expands. Colligative property equations use molality because the physical effect depends on the mole ratio of solute to solvent, which is a mass-based quantity unaffected by thermal expansion.

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