Colligative Properties Calculators

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Colligative properties are solution properties that depend on the number of dissolved solute particles, not on their chemical identity. The four colligative properties are: vapor pressure lowering (Raoult's law), boiling point elevation, freezing point depression, and osmotic pressure. They are affected by the van't Hoff factor (i) for electrolytes, which accounts for dissociation. These properties are used in antifreeze formulation, food preservation, cryoprotection, determination of molecular weight by osmometry, and in physiology to understand osmolarity and cell volume regulation.

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Four Colligative Properties

Vapor pressure lowering: ΔP = P° × χ_solute (Raoult's law). Solute reduces the fraction of surface molecules that can evaporate.

Boiling point elevation: ΔT_b = K_b × m × i. K_b (water) = 0.512°C/m. m = molality; i = van't Hoff factor.

Freezing point depression: ΔT_f = K_f × m × i. K_f (water) = 1.86°C/m. Example: 0.5 m NaCl: ΔT_f = 1.86 × 0.5 × 2 = 1.86°C (freezes at −1.86°C).

Osmotic pressure: π = iMRT. M = molarity; R = 0.08206 L·atm/mol/K; T = Kelvin.

Van't Hoff Factor (i)

For nonelectrolytes: i = 1. For NaCl: i ≈ 2 (dissociates into Na⁺ + Cl⁻). For MgCl₂: i ≈ 3. For CaCl₂: i ≈ 3. For glucose: i = 1. At higher concentrations, ion pairing reduces i below the ideal value.

Osmolarity in Biology

Blood plasma osmolarity ≈ 285–295 mOsm/L (mainly from NaCl, glucose, proteins). IV fluids must be isotonic (~280–310 mOsm/L). Hypotonic → cells swell and lyse; hypertonic → cells shrink (crenation). π = iMRT = 0.285 × 0.08206 × 310 = 7.26 atm = 553 mmHg for blood plasma.

Glossary

Colligative Properties
Solution properties depending on particle number, not identity: vapor pressure lowering, boiling point elevation (ΔT_b = K_b×m×i), freezing point depression (ΔT_f = K_f×m×i), and osmotic pressure (π = iMRT).
Van't Hoff Factor (i)
Number of particles produced per formula unit in solution: NaCl i=2; MgCl₂ i=3; glucose i=1; multiplies into all colligative property formulas to account for electrolyte dissociation.
Osmotic Pressure (π)
π = iMRT; the pressure required to prevent osmotic water flow across a semipermeable membrane; blood plasma π ≈ 7.4 atm; drives water movement from low to high osmolarity.

Frequently Asked Questions

Colligative properties depend on the number (not identity) of dissolved particles. The four properties: (1) Vapor pressure lowering — solute reduces vapor pressure by diluting solvent molecules at the surface (Raoult's law). (2) Boiling point elevation — ΔT_b = K_b × m × i. (3) Freezing point depression — ΔT_f = K_f × m × i. (4) Osmotic pressure — π = iMRT. All increase proportionally with solute concentration (×i for electrolytes). Applications: antifreeze (ethylene glycol), salt ice roads, osmometry for molecular weight determination, IV fluid formulation.

The van't Hoff factor i accounts for the dissociation of electrolytes into multiple particles. Non-electrolytes: i = 1. NaCl (→Na⁺ + Cl⁻): i = 2. MgCl₂ (→Mg²⁺ + 2Cl⁻): i = 3. Each property is multiplied by i. Example: 0.1 m glucose vs. 0.1 m NaCl: ΔT_f = 1.86 × 0.1 × 1 = 0.186°C for glucose; 1.86 × 0.1 × 2 = 0.372°C for NaCl. In concentrated solutions, ion pairing reduces effective i below the theoretical value.

π = iMRT. M = molar concentration; R = 0.08206 L·atm/mol/K; T = absolute temperature (K). Example: 0.15 M NaCl at 37°C: π = 2 × 0.15 × 0.08206 × 310 = 7.63 atm ≈ 5,800 mmHg. Blood plasma (~0.285 osmol/L): π ≈ 7.4 atm. Osmotic pressure drives water movement across semipermeable membranes from low osmolarity to high osmolarity — critical for kidney function, cell volume regulation, and IV fluid therapy.

ΔT_f = K_f × m × i. Ethylene glycol (C₂H₆O₂, MW = 62 g/mol), a non-electrolyte (i = 1) is mixed with water in antifreeze. A 50:50 by volume mixture is ~8.7 m in water: ΔT_f = 1.86 × 8.7 × 1 = −16.2°C protection. The boiling point is also raised: ΔT_b = 0.512 × 8.7 = +4.5°C. Propylene glycol (less toxic) is used in food-grade antifreeze and aircraft de-icing. Road salt (NaCl, CaCl₂) depresses freezing point via the i × molality multiplication: CaCl₂ (i=3) is ~3× more effective per mole than NaCl (i=2).