The Van 't Hoff Factor
Every colligative property formula has the factor “i” in it - the van ‘t Hoff factor. This single number is what makes the difference between a 1 m NaCl solution (i = 2, producing 2 mol particles) and a 1 m glucose solution (i = 1, producing 1 mol particles). Getting “i” right is essential for any colligative property calculation.
Determining i
The van ‘t Hoff factor equals the number of particles produced per formula unit of solute when dissolved:
| Solute Type | Example | Dissociation | Expected i |
|---|---|---|---|
| Strong electrolyte | NaCl | Na⁺ + Cl⁻ | 2 |
| Strong electrolyte | CaCl₂ | Ca²⁺ + 2 Cl⁻ | 3 |
| Strong electrolyte | FeCl₃ | Fe³⁺ + 3 Cl⁻ | 4 |
| Strong electrolyte | Na₂SO₄ | 2 Na⁺ + SO₄²⁻ | 3 |
| Strong electrolyte | Al₂(SO₄)₃ | 2 Al³⁺ + 3 SO₄²⁻ | 5 |
| Weak electrolyte | CH₃COOH | Partial dissociation | 1 < i < 2 |
| Nonelectrolyte | Glucose (C₆H₁₂O₆) | No dissociation | 1 |
| Nonelectrolyte | Sucrose | No dissociation | 1 |
| Nonelectrolyte | Urea | No dissociation | 1 |
Weak Electrolytes - Partial Dissociation
Weak electrolytes like acetic acid (CH₃COOH) partially dissociate in water. If the degree of dissociation is α (where 0 < α < 1):
i = 1 + α(n - 1)
where n = the number of ions the compound would produce if it fully dissociated.
For acetic acid (n = 2) with α = 0.05 (5% dissociation):
i = 1 + 0.05(2 - 1) = 1 + 0.05 = 1.05
The van ‘t Hoff factor is just barely above 1, because very few molecules actually dissociate.
Expected vs. Measured i Values
Here is one of the most commonly tested subtleties in this chapter:
| Electrolyte | Expected i | Measured i (0.10 m) | Reason for Difference |
|---|---|---|---|
| NaCl | 2.00 | ~1.87 | Ion pairing between Na⁺ and Cl⁻ |
| MgSO₄ | 2.00 | ~1.21 | Strong ion pairing (both ions are doubly charged) |
| CaCl₂ | 3.00 | ~2.70 | Some Ca²⁺-Cl⁻ pairs form |
| Glucose | 1.00 | ~1.00 | No dissociation, no ion pairing |
Notice that MgSO₄ has an especially low measured i (1.21 vs. expected 2.00). This is because Mg²⁺ and SO₄²⁻ are both doubly charged - the electrostatic attraction between them is very strong, leading to extensive ion pairing.
Ion Pairing and Concentration
Ion pairing increases at higher concentrations because ions are closer together and more likely to encounter each other. This means:
- At low concentrations: measured i is close to expected i
- At high concentrations: measured i is significantly below expected i
Putting It All Together
To solve any colligative property problem:
- Identify the solute - strong electrolyte, weak electrolyte, or nonelectrolyte?
- Determine i - count the ions (strong electrolyte), use 1 (nonelectrolyte), or calculate from α (weak electrolyte)
- Plug into the formula - ΔTb = iKbm, ΔTf = iKfm, or π = iMRT
- Check for reasonableness - more particles always means a bigger effect