Lesson 5: Oxidation numbers

5.1 Concept

• Before the nature of chemical bonding was understood, valency expressed an atom's ability to combine with a number of other atoms.
• Today the concept of oxidation number is used instead.

Oxidation number is a number that expresses the electric charge (positive or negative) that the atom or ion carries (or appears to carry) in the compound, whether ionic or covalent.

5.2 Ionic compounds

The oxidation number of an ion or group equals its charge, with its sign: K⁺Br⁻ (K +1, Br −1), Na⁺Cl⁻, Mg²⁺O²⁻, Ca²⁺CO₃²⁻, Cu²⁺SO₄²⁻.

5.3 Covalent compounds

The atoms do not form ions, but the shared electrons are displaced towards the more electronegative atom; this atom is assigned a negative number and the less electronegative one a positive number.

• In molecules of an element (S₈, P₄, O₃, Cl₂, H₂, N₂, O₂) the electronegativities are equal, so there is no displacement and each atom has oxidation number zero.
• In molecules of two different atoms the bonding electrons are counted with the more electronegative atom. HCl: H +1, Cl −1. H₂O: H +1, O −2. CO₂: C +4, O −2.

5.4 Rules

1. The sum of oxidation numbers of all atoms in a neutral compound is zero; in an ion it equals the charge of the ion.
2. Group 1A elements are always +1; group 2A always +2; group 3A (Al) +3; fluorine is always −1. Start with these.
3. Oxygen is −2 in most compounds, except: peroxides (H₂O₂, Na₂O₂) −1; superoxides (KO₂) −½; oxygen difluoride (OF₂) +2.
4. Hydrogen is +1 in most compounds, except metal hydrides (NaH, CaH₂, AlH₃) where it is −1.
5. The oxidation number is calculated for one atom (or ion) at a time; some compounds contain atoms of the same element with different oxidation numbers (NH₄NO₂: N is −3 in NH₄⁺ and +3 in NO₂⁻).
6. The highest oxidation state of a representative element does not exceed its group number (A groups).
7. For a polyatomic group the oxidation number is the charge of the group: NO₃⁻ (−1), CO₃²⁻ (−2), SO₄²⁻ (−2), NH₄⁺ (+1).

Illustrations: Na₂O: Na +1, O −2. Na₂O₂: O −1. KO₂: K +1, O −½. CaH₂: Ca +2, H −1. AlH₃: Al +3, H −1.

5.5 Worked examples

Worked example 5.1. Oxidation number of Cr in K₂Cr₂O₇: 2(+1) + 2x + 7(−2) = 0 → 2x = 12 → x = +6.

Worked example 5.2. Mn in KMnO₄: +1 + x + 4(−2) = 0 → x = +7. Mn in MnO₂: x − 4 = 0 → +4. Mn in MnCl₂: x − 2 = 0 → +2.

Worked example 5.3. S in H₂SO₄: 2 + x − 8 = 0 → +6. S in Na₂S₂O₃: 2 + 2x − 6 = 0 → x = +2. S in SO₃²⁻: x − 6 = −2 → +4. S in H₂S: 2 + x = 0 → −2.

Worked example 5.4. N in NH₄⁺: x + 4 = +1 → −3. N in NO₃⁻: x − 6 = −1 → +5. N in HNO₂: 1 + x − 4 = 0 → +3. N in N₂O: 2x − 2 = 0 → +1. N in NO₂: x − 4 = 0 → +4. N in N₂H₄: 2x + 4 = 0 → −2.

Worked example 5.5. Cl in NaClO: +1 + x − 2 = 0 → +1; in KClO₃: +1 + x − 6 = 0 → +5; in HClO₄: 1 + x − 8 = 0 → +7.

Worked example 5.6. C in CH₄: x + 4 = 0 → −4; in CH₃OH: x + 3 + (−2) + 1 = 0 → −2; in HCOOH: 2 + x − 4 = 0 → +2; in CO: +2; in CO₂: +4.

Worked example 5.7. O in H₂O₂: 2(+1) + 2x = 0 → −1; in OF₂: x + 2(−1) = 0 → +2; in KO₂: +1 + 2x = 0 → −½.

Worked example 5.8 — average number. Fe in Fe₃O₄: 3x − 8 = 0 → x = +8/3 (average of 2 Fe³⁺ and 1 Fe²⁺).