Oxidation Numbers
High-Yield Summary
- An oxidation number is a bookkeeping value that treats every bond as fully ionic, assigning shared electrons to the more electronegative atom.
- Free element = 0 (N₂, P₄, S₈); monatomic ion = its charge (Na⁺ = +1, Fe³⁺ = +3).
- Group IA always +1, Group IIA always +2, Group VIIA (halogens) -1 — except when bonded to a more electronegative element (Cl is +1 in HOCl).
- Hydrogen: +1 with nonmetals, -1 in metal hydrides (NaH). Oxygen: -2 usually, -1 in peroxides (H₂O₂), +2 in OF₂.
- Sum rule: oxidation numbers sum to 0 in a neutral compound, or to the overall charge in a polyatomic ion.
- Oxidation = increase in oxidation state; reduction = decrease in oxidation state.
Key Terms
- Oxidation number (oxidation state)
- A bookkeeping value assigned to an atom tracking electron distribution, treating each bond as if fully ionic.
- Free element rule
- An atom in its elemental form (single or elemental molecule, e.g. N₂, P₄, S₈) has oxidation number 0.
- Monatomic ion rule
- A monatomic ion's oxidation number equals its charge (e.g. Cu²⁺ = +2, N³⁻ = -3).
- Sum rule
- All atoms' oxidation numbers sum to the species' overall charge — 0 for a neutral compound, the ion's charge for a polyatomic ion.
Fixed Oxidation Numbers by Group / Element
| Species | Oxidation number |
|---|---|
| Group IA (alkali metals) | Always +1 in a compound (e.g. Na in NaCl) |
| Group IIA (alkaline earth metals) | Always +2 in a compound (e.g. Ca in CaCl₂) |
| Group VIIA (halogens) | -1, except +1 (or positive) when bonded to a more electronegative element (Cl in HOCl = +1) |
| Hydrogen | +1 with nonmetals (HCl); -1 in metal hydrides (NaH) |
| Oxygen | -2 usually (H₂O); -1 in peroxides (H₂O₂); +2 in OF₂ (only compound more electronegative than O) |
Solving for an Unknown Oxidation Number (Sum Rule)
- 1Assign oxidation numbers to every atom whose value is fixed by a rule (free element, monatomic ion, group, H, O).
- 2Set the sum of all oxidation numbers equal to the species' overall charge (0 for neutral, ion charge for a polyatomic ion).
- 3Solve algebraically for the remaining unknown atom.
- 4Example — sulfate SO₄²⁻: 4 O × (-2) = -8; charge is -2, so S = -2 - (-8) = +6. Check: 4(-2) + (+6) = -2 ✓
- 5Example — nitrate NO₃⁻: 3 O × (-2) = -6; charge is -1, so N = -1 - (-6) = +5. Check: (+5) + 3(-2) = -1 ✓
Must-Know Points
- Oxidation numbers directly define redox direction: oxidation = increase in oxidation state, reduction = decrease — the same electron-loss/gain relationship, now expressed numerically.
- The sum rule is the go-to tool whenever an atom's oxidation number isn't fixed by one of the standard rules — assign the known atoms first, then solve for the unknown.
Common MCAT Trap
- Group VIIA halogens are only -1 by default — when bonded to a MORE electronegative element (only oxygen and fluorine qualify for Cl/Br/I), the halogen flips positive (Cl = +1 in HOCl).
- OF₂ is the one compound where oxygen is positive (+2), since fluorine is the only element more electronegative than oxygen — don't default to -2 here.
Quick Recall
What is the oxidation number of sulfur in SO₄²⁻?
What is hydrogen's oxidation number in NaH?
Is oxidation an increase or decrease in oxidation state?
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