10.1 Colligative Properties & Factors Affecting Solubility

Colligative Properties & Factors Affecting Solubility

Quick Answer: Colligative properties depend on the number of dissolved solute particles, not on what the solute is. The PA-CAT Bulletin of Information (rev. 20240815) groups vapor pressure, boiling point, freezing point, and osmotic pressure under its Liquids/Solids/Gases chemistry cluster (Table 5). Master the equations, the van't Hoff factor, and the solubility rules and you cover most of this objective.

The Four Colligative Properties

A colligative property changes when a nonvolatile solute is dissolved in a solvent. The magnitude scales with molality (moles solute per kg solvent) or molarity (moles per L), and with the van't Hoff factor i — the number of particles a formula unit yields in solution. For nonelectrolytes like glucose, i = 1. For NaCl, i ≈ 2 (Na⁺ and Cl⁻). For CaCl₂, i ≈ 3. Real i values are slightly below the ideal integer because of ion pairing.

For water, K_b = 0.512 °C·kg/mol and K_f = 1.86 °C·kg/mol. These constants appear on PA-CAT reference material when provided; otherwise memorize the water values.

Raoult's Law and Vapor-Pressure Lowering

Adding a nonvolatile solute lowers the solvent's vapor pressure because solute particles occupy surface sites that would otherwise evaporate. Raoult's law: P_solution = X_solvent · P°_solvent, where X_solvent is the mole fraction of solvent. The lowering ΔP = X_solute · P°_solvent. Positive deviations (vapor pressure higher than predicted) arise when solute-solvent attractions are weaker than solvent-solvent attractions (e.g., ethanol + water shows non-ideal behavior but is negative overall due to H-bonding).

Boiling-Point Elevation and Freezing-Point Depression

Because the solute lowers vapor pressure, a higher temperature is needed to boil (ΔT_b = i·K_b·m). It also disrupts crystal formation, so a lower temperature freezes the solution (ΔT_f = i·K_f·m). These effects are the basis of road salt (NaCl or CaCl₂) and antifreeze (ethylene glycol).

Worked example — freezing-point depression: What is the freezing point of a solution made by dissolving 58.5 g NaCl (molar mass 58.5 g/mol) in 1.00 kg water? Assume i = 2.

1. Moles NaCl = 58.5 g ÷ 58.5 g/mol = 1.00 mol.
2. Molality m = 1.00 mol ÷ 1.00 kg = 1.00 m.
3. ΔT_f = i · K_f · m = 2 × 1.86 × 1.00 = 3.72 °C.
4. New freezing point = 0.00 − 3.72 = −3.72 °C.

If you forgot the van't Hoff factor, you'd get −1.86 °C — half the real depression. On the PA-CAT, always check whether the solute is an electrolyte.

Osmotic Pressure

Osmotic pressure π = iMRT is the pressure required to stop net solvent flow across a semipermeable membrane. It is the most sensitive colligative property: a 0.001 M solution gives π ≈ 0.024 atm at 25 °C, easily measured, which is why osmometry is used to determine molar masses of proteins and polymers.

Factors Affecting Solubility

Temperature: For most ionic solids, solubility rises with temperature because dissolution is endothermic (Le Chatelier). A few exceptions (Ce₂(SO₄)₃, NaOH) become less soluble when heated.

Pressure (gases): Henry's law C = k_H · P states gas solubility is proportional to partial pressure above the liquid. That is why carbonated beverages fizz when opened — pressure drops, solubility drops, CO₂ escapes. Gas solubility usually decreases with temperature (exothermic dissolution), which is why warm soda goes flat faster and warm lakes hold less dissolved O₂ for fish.

Like dissolves like: Polar solvents dissolve polar/ionic solutes; nonpolar solvents dissolve nonpolar solutes. Hydrogen-bond donor solvents (water, methanol) dissolve H-bond acceptor solutes.

flowchart LR
    A[Solute added] --> B{Particles in solution?}
    B -->|Nonvolatile, i=1| C[Vapor pressure ↓ per Raoult]
    B -->|Electrolyte, i>1| D[Effect multiplied by i]
    C --> E[BP ↑ ΔT_b = i K_b m]
    C --> F[FP ↓ ΔT_f = i K_f m]
    D --> E
    D --> F
    D --> G[Osmotic pressure π = iMRT]

Common PA-CAT Pitfalls

• Using molarity instead of molality for ΔT_b and ΔT_f (molality is temperature-independent).
• Ignoring i for electrolytes — the single most common error.
• Forgetting that colligative properties ignore identity, so 1 m glucose ≈ 1 m sucrose in ΔT_f, but 1 m NaCl gives twice the effect.