Oxidation States

What an oxidation state actually is

An oxidation state is a thought experiment, not a physical measurement. Take a molecule, imagine breaking every bond ionically — give both bonding electrons to the more electronegative partner — and count the electrons each atom now "owns." Compare to the number of valence electrons that atom had as a free element. The difference is its oxidation state.

Two atoms in the same molecule can have wildly different oxidation states. In sulfuric acid (H₂SO₄), sulfur is +6 and each oxygen is -2 — they sum to zero for a neutral molecule. The fiction is consistent once you internalize the rules.

Assignment rules

The complete rule set, in priority order. Higher-priority rules override lower-priority ones when they conflict.

Priority	Rule	Example
1	Free element (any allotrope) is 0	O₂, Na(s), Hg(l), C (graphite) all = 0
2	Sum of oxidation states equals overall charge	Neutral molecule = 0; SO₄²⁻ = -2
3	Group 1 metals (Li, Na, K…) are +1 in compounds	NaCl: Na is +1
4	Group 2 metals (Be, Mg, Ca…) are +2	CaCO₃: Ca is +2
5	Fluorine is -1 (always, no exceptions)	HF, OF₂, ClF₃ — F is -1 in all
6	Hydrogen is +1, except in metal hydrides where it is -1	NaH, LiAlH₄: H is -1
7	Oxygen is -2, except in peroxides (-1), superoxides (-½), or with F (+2 in OF₂)	H₂O₂: O is -1; OF₂: O is +2
8	Other halogens (Cl, Br, I) default to -1, unless bonded to O or F	NaCl: Cl is -1; NaClO₄: Cl is +7
9	Bonds between identical atoms split electrons evenly (no contribution)	O-O in peroxide: each O at -1, not -2

For organics, C-H bonds give both electrons to C (slightly more electronegative than H); C-C bonds split evenly. This is why methane has C at -4 while CO₂ has C at +4 — both extremes of carbon's range.

Worked examples

Example 1: KMnO₄ (potassium permanganate)

1. Compound is neutral, so total = 0.
2. K is Group 1, so K = +1. Subtotal: +1.
3. Each O is -2. Four oxygens contribute -8. Subtotal: +1 + (-8) = -7.
4. Mn is the unknown. To bring the sum to zero, Mn = +7.

So in KMnO₄, manganese is in the +7 oxidation state — its highest accessible value, and the reason permanganate is such a powerful oxidant. Reducing MnO₄⁻ to Mn²⁺ shuffles five electrons per manganese atom; that is a huge charge change and a correspondingly large reduction potential (E° = +1.51 V in acidic solution).

Example 2: H₂SO₄ (sulfuric acid)

Two H at +1 give +2; four O at -2 give -8; total must equal 0; therefore S is +6.

Example 3: methanol CH₃OH

Three C-H bonds give C three "extra" electrons; one C-O bond gives the O the electrons. Net: C is -2 in methanol. The carbon ladder — methane (-4) → methanol (-2) → formaldehyde (0) → formic acid (+2) → CO₂ (+4) — gives two electrons of oxidation per rung.

Example 4: dichromate ion Cr₂O₇²⁻

Seven O at -2 = -14; total = -2; the two Cr share the remaining +12, so each Cr is +6.

Oxidation state assignment: special-case ladder

Element	Common state(s)	Notable exceptions / outliers
Hydrogen	+1 in most compounds	-1 in metal hydrides (NaH, LiAlH₄, CaH₂)
Oxygen	-2 in most compounds	-1 in peroxides; -½ in superoxides; +2 in OF₂
Fluorine	-1 always	None — F never has positive oxidation state
Other halogens (Cl, Br, I)	-1 in halides	+1 to +7 in oxoacids and interhalogens (HClO, KClO₃, KIO₄)
Group 1 metals	+1 always in compounds	Negative in alkalides — bizarre coordination chemistry only (Cs⁻ in cryptands)
Carbon	-4 (CH₄) to +4 (CO₂)	Mixed in molecules with multiple C; assign each C separately
Nitrogen	-3 (NH₃) to +5 (HNO₃)	Many intermediate states: -2 (N₂H₄), -1 (NH₂OH), 0 (N₂), +1 (N₂O), +2 (NO), +3 (NO₂⁻), +4 (NO₂)
Sulfur	-2 (H₂S) to +6 (SO₃, H₂SO₄)	Polysulfides (Sₙ²⁻) have fractional states; thiosulfate S₂O₃²⁻ has two different S oxidation states
Transition metals	Multiple stable states	Mn: +2, +3, +4, +6, +7; Cr: +2, +3, +6; Fe: +2, +3, +6 (rare)

Why oxidation states matter

• Identify oxidation and reduction. Oxidation = increase in oxidation state (loss of electrons); reduction = decrease (gain). The OIL RIG mnemonic is anchored by the oxidation-state change.
• Balance redox equations. The half-reaction method requires explicit oxidation states to count electrons transferred per atom.
• Predict reactivity. An element in an unusually high oxidation state (Mn(VII), Cr(VI), Os(VIII)) is hungry for electrons — likely a strong oxidant. An element in an unusually low one (S(-2), C(-4)) is often a strong reductant.
• Name compounds. Stock nomenclature uses oxidation state in the name: iron(II) chloride vs iron(III) chloride; chromium(VI) oxide.
• Spectroscopy detects it directly. XPS and XANES show characteristic energy shifts; Mn²⁺ vs Mn⁷⁺ differ by ~13 eV at the K-edge — the bookkeeping fiction has a measurable signature.

Real-world relevance

• Lithium-ion battery cathodes. In LiCoO₂ (Sony's 1991 commercial cathode), cobalt cycles between Co(III) when fully charged and Co(IV) when discharged. The voltage (~3.9 V vs Li/Li⁺) is set by the redox-couple energy. Modern NMC cathodes (Ni-Mn-Co) cycle multiple metals through their own oxidation states.
• Iron in hemoglobin. Fe(II) binds O₂ reversibly; oxidation to Fe(III) (methemoglobin) destroys oxygen binding. Methemoglobinemia is treated with reducing agents (methylene blue) that push iron back to +2.
• Permanganate titration. MnO₄⁻ (Mn = +7) titrated against Fe²⁺ (Fe = +2) gives Mn²⁺ + Fe³⁺ in acidic solution, with KMnO₄ acting as its own indicator. Five electrons per Mn, one per Fe.
• Combustion. Burning hydrocarbons takes carbon from -4 (CH₄) up to +4 (CO₂). Each carbon releases roughly 100 kcal/mol per oxidation step — this is what powers internal-combustion engines.
• Photosynthesis. Plants reverse the combustion ladder: CO₂ (C at +4) is reduced to glucose (C at 0 on average). 24 electrons must move per glucose; sunlight supplies the 2.8 MJ/mol.

Edge cases and ambiguity

• Mixed-valence compounds. Magnetite Fe₃O₄ has one Fe(II) and two Fe(III) per formula unit, but the simple bookkeeping assigns an average +8/3.
• Non-innocent ligands. Dithiolenes, NO, and porphyrin systems have ambiguous electron counts on the metal — the ligand can carry electrons that look "metal-localized" by formal rules. Oxidation-state notation is honestly approximate here.
• Organometallics. Different conventions coexist in inorganic textbooks for whether M-(η²-alkene) bonds give Pt(0) or Pt(II); both have defenders.
• Metal-metal bonds. [Re₂Cl₈]²⁻ has a quadruple Re-Re bond; each Re is formally +3, with metal-metal electrons split evenly — same convention as O-O in peroxides.

Common pitfalls

• Confusing oxidation state with formal charge. Formal charge splits bond pairs evenly; oxidation state gives them all to the more electronegative atom. Use oxidation state for redox bookkeeping, formal charge for choosing between Lewis-structure resonance forms.
• Forgetting hydride exception. H is +1 in most compounds, but -1 in metal hydrides (NaH, LiAlH₄, CaH₂) — exactly why they are reducing agents.
• Treating peroxides as oxide. H₂O₂ has oxygen at -1, not -2. Forgetting this throws every paired oxidation state off by one electron.
• Misidentifying organic carbons. Each carbon has its own oxidation state. In ethanol CH₃CH₂OH the methyl carbon is -3 and the alcohol carbon is -1; resolved values reveal which carbon gets oxidized.
• Treating oxidation state as physical charge. Mn in KMnO₄ is +7 by bookkeeping but real electron density is closer to +1 to +2. Oxidation states track formal electron flow, not coulombic charge.