Colligative Properties Calculator

Colligative properties are properties of solutions that depend only on the number of solute particles dissolved, not on what those particles are. Add the same molal amount of sugar or sodium chloride to water and the freezing point drops by similar amounts (corrected for the van’t Hoff factor below). The identity of the solute does not matter, just the count.

There are four colligative properties:

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

Vapor pressure lowering (Raoult’s law):

ΔP = x_solute × P°_solvent

The variables:

• i = van’t Hoff factor (number of particles released per formula unit)
• K_b = ebullioscopic constant (°C/m), solvent specific
• K_f = cryoscopic constant (°C/m), solvent specific
• m = molality (mol solute / kg solvent)
• M = molarity (mol/L), used for osmotic pressure
• R = gas constant (0.0821 L·atm/(mol·K))
• T = temperature in Kelvin
• x = mole fraction
• P° = pure solvent vapor pressure

The van’t Hoff factor i (count of particles):

• Non-electrolytes (sugar, alcohol, urea): i = 1, each molecule stays intact
• NaCl: i = 2 (Na⁺ + Cl⁻)
• CaCl₂: i = 3 (Ca²⁺ + 2 Cl⁻)
• MgCl₂: i = 3
• Na₂SO₄: i = 3 (2 Na⁺ + SO₄²⁻)
• Al(NO₃)₃: i = 4 (Al³⁺ + 3 NO₃⁻)

In real solutions, ion pairing reduces i slightly below the theoretical value at higher concentrations. For most practical work the integer count is close enough; for high-precision physical chemistry use the experimentally measured i.

Solvent constants you will encounter:

Camphor’s enormous K_f is the reason it shows up in introductory chemistry experiments to determine molar masses: a small amount of an unknown solute produces a large, easy-to-measure freezing point change.

Worked example, salting roads: You spread NaCl on an icy road. What molality do you need to lower the freezing point to −10 °C (so the ice melts above road temperatures of −10 °C)?

ΔT_f = 10 °C, i = 2 for NaCl, K_f = 1.86

10 = 2 × 1.86 × m m = 10 / 3.72 = 2.69 mol/kg

In mass terms with NaCl molar mass = 58.4 g/mol, that’s 2.69 × 58.4 = 157 g of salt per kg of water. Or about 14% salt by mass, close to ocean salinity. That is why ocean water freezes at about −2 °C rather than 0 °C, and why deicing salt loses effectiveness below −10 to −15 °C (you cannot keep up with the salt requirement).

Worked example, antifreeze: Ethylene glycol (i = 1, M_w = 62.07 g/mol) is added at 50% by mass in water (a typical car cooling system mix). Find the freezing point.

Mass of EG per kg water = 1 kg / (1 kg pure water with 1 kg EG dissolved) → m = 1000 g / 62.07 g/mol ÷ 1 kg = 16.1 mol/kg (very concentrated)

ΔT_f = 1 × 1.86 × 16.1 = 30 °C

So 50/50 EG/water freezes near −30 °C. Real commercial coolants achieve −37 °C at 50/50 because additional non-colligative effects (ion pairing, glass-transition behavior) take over at high concentrations. The pure colligative formula gives a useful estimate up to about 50% mass.

Worked example, IV fluid osmotic pressure: Normal saline is 0.9% NaCl by mass. At body temperature (37 °C = 310 K), what is its osmotic pressure?

0.9 g NaCl per 100 mL → 9 g/L → 9 / 58.4 = 0.154 mol/L

π = 2 × 0.154 × 0.0821 × 310 = 7.84 atm

This matches human blood plasma osmotic pressure, which is why normal saline is isotonic and safe to infuse intravenously. Hypertonic saline (3% or 7%) is used briefly for severe hyponatremia but pulls water out of cells, so it requires careful monitoring.

Why colligative properties matter even outside chemistry class:

• Antifreeze formulation (cars, aircraft de-icing, refrigerators)
• Road salt and brine formulation (deicing, dust suppression)
• Cryopreservation of biological samples (sperm, embryos, organs use DMSO + glycerol)
• Pharmaceutical formulation (IV fluids, eye drops must be isotonic)
• Food preservation (high salt or sugar concentrations stop microbial growth via osmotic stress)
• Determining molar mass of unknown compounds in physical chemistry labs