Oxidation states
Oxidation state is a formal electron-counting device. It assigns bonding electrons to the more electronegative atom and asks what charge each atom would have under that ionic approximation. It is invaluable for redox accounting, but it is not the same as measured atomic charge.
Core rules and their order
Free elements have oxidation state 0. A monatomic ion has an oxidation state equal to its charge. Fluorine is −1 in compounds. Oxygen is usually −2; hydrogen is usually +1 with nonmetals and −1 in metal hydrides.
The sum of oxidation states equals the total charge of the molecule or ion. This final condition closes the calculation when one value is unknown.
Worked examples
KMnO₄
K is +1 and each O is −2. Let Mn = x: +1 + x − 8 = 0, so Mn = +7.
SO₄²⁻
4 O atoms contribute −8. x − 8 = −2, so S = +6.
NH₄⁺
Four H at +1 give +4. x + 4 = +1, so N = −3.
Fe₃O₄
Average Fe oxidation state is +8/3, reflecting mixed Fe²⁺/Fe³⁺ character rather than a literal fractional ion on every site.
Formal charge, oxidation state and partial charge differ
Formal charge splits covalent bonding electrons equally between bonded atoms. Oxidation state assigns them to the more electronegative partner. Partial charge comes from the actual quantum-mechanical electron density and is generally noninteger.
Carbon in CO₂ has oxidation state +4, yet it does not carry a physical +4e charge. The formalism is designed for electron bookkeeping and reaction classification.
Fractional and mixed oxidation states
Average oxidation states can be fractional when a material contains inequivalent sites or delocalized charge. Magnetite, Fe₃O₄, is conventionally described as containing Fe²⁺ and Fe³⁺, giving an average of +8/3.
Modern solid-state compounds can blur simple integer assignments further. Oxidation state remains useful, but the microscopic electron distribution may be more covalent or delocalized than the formal labels suggest.
Oxidation-state change identifies redox
An increase in oxidation state is oxidation; a decrease is reduction. In Zn + Cu²⁺ → Zn²⁺ + Cu, Zn changes 0 → +2 and Cu changes +2 → 0.
The oxidizing agent is the species that is reduced; the reducing agent is the species that is oxidized. Tracking oxidation states prevents the common mistake of naming the agents backwards.
Important exceptions to the usual assignment rules
Rule order matters. Fluorine is always −1 in ordinary compounds, so oxygen becomes positive in OF₂: O + 2(−1) = 0 gives O = +2. Oxygen is −1 in peroxides such as H₂O₂ and has an average −1/2 in superoxides such as KO₂.
Hydrogen is usually +1 with nonmetals but −1 in ionic metal hydrides such as NaH and CaH₂. These exceptions are not arbitrary; they reflect which partner is more electronegative under the formal ionic assignment.
Average oxidation state versus local sites
When an empirical formula gives a fractional average oxidation state, it may hide several chemically distinct sites. Fe₃O₄ gives an average Fe state +8/3, but a useful ionic description contains one Fe²⁺ and two Fe³⁺ per formula unit.
Other materials contain genuinely delocalized electrons, so assigning one integer oxidation state to each crystallographic atom becomes less literal. Spectroscopy, magnetism and electronic-structure calculations are needed to determine the real charge distribution.
Oxidation states in coordination and covalent chemistry
For metal complexes, oxidation state is assigned after treating ligands by formal charges. In [Fe(CN)₆]⁴⁻, six CN⁻ ligands contribute −6; the complex has charge −4, so Fe is +2.
Some ligands are redox non-innocent: electron density can be distributed between metal and ligand in ways that make a single oxidation-state picture incomplete. The formalism remains useful for bookkeeping, but spectroscopy may reveal a more nuanced electronic structure.
A repeatable assignment algorithm
- Set every free element to 0 and every monatomic ion to its charge.
- Assign F = −1; then apply O and H rules with their known exceptions.
- Use common group values when appropriate, such as +1 for alkali metals and +2 for alkaline-earth metals.
- Let the unknown oxidation state be x.
- Set the sum of all oxidation states equal to the species charge and solve.
Writing the algebra is safer than guessing. In ClO₃⁻, for example, x + 3(−2) = −1 gives Cl = +5.
Oxidation state and bond polarity can point in the same direction without being equal
In HCl, the formal oxidation states are H +1 and Cl −1 because Cl is more electronegative. The actual partial charges are much smaller than ±1e because the bond remains covalent.
Oxidation state deliberately exaggerates electron ownership to create an integer bookkeeping scheme. That is precisely what makes it useful for detecting redox changes across complicated reactions.
The value of oxidation state is consistency. It deliberately simplifies covalent electron sharing into formal ownership so that electron loss and gain can be tracked across reactions. It should be judged by that bookkeeping purpose, not by whether it equals a quantum-mechanical atomic charge.
When oxidation-state assignments become ambiguous in strongly delocalized systems, the ambiguity itself is a signal that the simple ionic partition is no longer a complete microscopic description.
Exercises
Chromate
Find Cr in CrO₄²⁻.
Solution
x + 4(−2) = −2, so Cr = +6.
Hydride
Find H in NaH.
Solution
Na is +1, so H is −1. Metal hydrides are an exception to the usual +1 rule for H.
Redox direction
Mn changes from +7 to +2. Oxidation or reduction?
Solution
Reduction, because the oxidation state decreases.