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Calculate boiling point elevation (ΔTb = Kb × m × i) and freezing point depression (ΔTf = Kf × m × i) for any solvent and solute. Includes built-in constants for water, benzene, and ethanol.
Colligative properties depend only on particle count. Dissolving solute raises boiling point and lowers freezing point — the basis for antifreeze, road salt, and cooking chemistry.
| Solvent | Kb (°C·kg/mol) | Kf (°C·kg/mol) | b.p. / f.p. |
|---|---|---|---|
| Water | 0.512 | 1.86 | 100°C / 0°C |
| Benzene | 2.53 | 5.12 | 80.1°C / 5.5°C |
| Ethanol | 1.22 | 1.99 | 78.4°C / -114.6°C |
| Acetic acid | 3.07 | 3.90 | 117.9°C / 16.6°C |
Road salt (NaCl, i=2): 1 molal → ΔTf=1.86×1×2=3.72°C. CaCl₂ (i=3) more effective below -10°C. Antifreeze (ethylene glycol): 50/50 water → ΔTf≈-34°C, ΔTb≈+129°C.
Non-electrolytes: i=1. NaCl: i=2. CaCl₂: i=3. AlCl₃: i=4. Actual i slightly less than theoretical at high concentration due to ion pairing.
Colligative properties are unique in chemistry because they depend only on the number of dissolved particles, not their chemical identity. This means 1 mole of NaCl (which dissociates into 2 moles of ions) has exactly twice the colligative effect of 1 mole of glucose (which stays as one particle). Boiling point elevation and freezing point depression have enormous practical applications from cooking to industrial refrigeration to biological cryopreservation.
Ice cream making exploits freezing point depression. Adding salt to ice creates a eutectic mixture that can reach -21°C — cold enough to freeze ice cream. The 18th-century discovery that salt-ice mixtures could freeze cream changed culinary history. Modern ice cream makers use this same principle. In the food industry, sugar concentration in frozen desserts affects freezing point — higher sugar content = softer texture at freezer temperatures (-18°C) because more remains unfrozen.
Cryopreservation (freezing biological samples) requires cryoprotectants that lower the freezing point and reduce ice crystal formation. Dimethyl sulfoxide (DMSO): 10% v/v is standard for cell lines. Glycerol: used for bacteria (15%) and sperm cryopreservation. These cryoprotectants act by two mechanisms: colligative (lowering freezing point) and kinetic (reducing ice crystal nucleation and growth). Without cryoprotection, ice crystals puncture cell membranes causing irreversible damage. Liquid nitrogen (-196°C) is used for long-term storage — at this temperature, molecular motion nearly stops and degradation is negligible for centuries.
At higher altitude, atmospheric pressure decreases, so water boils at lower temperature. At sea level (1 atm): water boils at 100°C. At 1500m (Denver): ~95°C. At 3500m (La Paz, Bolivia): ~87°C. At Everest base camp (~5400m): ~83°C. This lower boiling temperature affects cooking — pasta takes longer because water is cooler. Pressure cookers raise pressure above atmospheric, raising the boiling point (e.g., 1.5 atm → ~127°C), significantly reducing cooking time and energy use.
Colligative properties depend only on the number of dissolved solute particles per unit mass of solvent — not on the chemical identity of the particles. Adding any solute to a solvent always: raises its boiling point (boiling point elevation), lowers its freezing point (freezing point depression), lowers its vapor pressure (Raoult's Law), and raises its osmotic pressure. These four colligative properties are mathematically predictable and have enormous practical applications from antifreeze to food preservation to cryopreservation.
The magnitude of colligative effects depends on the molality (moles of solute per kilogram of solvent, not molarity) and the van't Hoff factor (i), which accounts for electrolyte dissociation: ΔTb = Kb × m × i and ΔTf = Kf × m × i. Molality rather than molarity is used because colligative properties are measured at the boiling or freezing point — temperatures at which volume changes make molarity less accurate.
Before mass spectrometry, molar masses of organic compounds were determined from freezing point depression. Dissolve a known mass of unknown compound in a known mass of solvent, measure ΔTf, calculate molality: m = ΔTf/Kf. Moles = m × kg solvent. MM = mass of compound/moles. Example: dissolve 1.500 g of unknown in 100.0 g benzene (Kf = 5.12°C·kg/mol), ΔTf = 1.02°C. m = 1.02/5.12 = 0.1992 mol/kg. Moles = 0.1992 × 0.1000 = 0.01992 mol. MM = 1.500/0.01992 = 75.3 g/mol. This classic technique (cryoscopy) confirmed the molecular formulas of sugars, amino acids, and many organic molecules in the 19th and early 20th centuries.
Sodium chloride (NaCl, i = 2): ΔTf = Kf × m × i = 1.86 × m × 2. At the eutectic composition (~23% NaCl by mass, ~6.1 molal): ΔTf = 1.86 × 6.1 × 2 = 22.7°C, effective down to -21°C. Calcium chloride (CaCl₂, i = 3): more effective at lower temperatures. At 30% CaCl₂: ΔTf reaches -49°C (effective de-icer at much lower temperatures). Magnesium chloride (MgCl₂, i = 3): similar to CaCl₂ but less corrosive to metals and infrastructure. Potassium acetate (CH₃COOK, i = 2): used at airports (less corrosive than chloride salts to aircraft aluminum). The ~$2.3 billion annual US road salt market represents the direct application of freezing point depression chemistry.
Ethylene glycol (HOCH₂CH₂OH, MM = 62.07 g/mol, i = 1 — does not ionize): dissolved in water at 50% by volume (approximately 12.3 molal). ΔTf = 1.86 × 12.3 × 1 = 22.9°C (theoretical) — actual −34°C due to non-ideal behavior at high concentration. ΔTb = 0.512 × 12.3 × 1 = 6.3°C (theoretical, boiling point raised to ~106.3°C — actual ~129°C under pressure). This protects car radiators from both winter freezing (down to −34°C) and summer boil-over (up to 129°C under the pressurized cooling system). The engine coolant must be changed periodically as ethylene glycol degrades to glycolic and oxalic acids over time, which become corrosive to the aluminum and other metals in the cooling system.
Cryopreservation (storing biological samples at very low temperatures) relies on cryoprotectants that lower the freezing point and reduce ice crystal formation. DMSO (dimethyl sulfoxide, 10% v/v standard for cell lines): enters cells, lowers intracellular freezing point, reduces ice crystal nucleation. Glycerol (15%): used for bacteria, red blood cells, and sperm cryopreservation. Sucrose and trehalose: protect proteins and membranes through preferential exclusion mechanism. Without cryoprotection: ice crystals puncture cell membranes causing irreversible damage (intracellular ice formation is lethal). Slow controlled-rate cooling (−1°C/minute) allows cellular dehydration before membrane-damaging ice forms. Storage in liquid nitrogen (−196°C) essentially stops all molecular motion — biological samples stored properly are stable for decades or longer.