Oxidation Numbers
Oxidation numbers (also called oxidation states) are a bookkeeping tool chemists use to track the transfer of electrons in chemical reactions. Assigned to each atom in a compound or ion, an oxidation number represents the hypothetical charge that atom would carry if all bonds were perfectly ionic — that is, if the more electronegative atom in every bond took both electrons entirely. Although oxidation numbers are a simplification, they are extraordinarily powerful: they let us instantly identify which species gains electrons (is reduced) and which loses electrons (is oxidised) in any reaction. Redox reactions — short for reduction–oxidation reactions — are among the most important in all of chemistry and biology. Combustion, respiration, photosynthesis, corrosion of metals, and the operation of batteries all involve the transfer of electrons between species. Without a systematic way to track those electrons, analysing such reactions would be extremely difficult. Oxidation numbers give us exactly that system, providing a clear numerical record of electron gain and loss even when the electrons are not explicitly written in the equation. In this article you will learn the seven standard rules for assigning oxidation numbers to any atom in any chemical species, how to use those numbers to identify the oxidising agent (oxidant) and the reducing agent (reductant) in a reaction, and how to recognise the special class of reactions called disproportionation, in which a single element simultaneously increases and decreases its oxidation state.
- Rule 1 — Pure Elements
- Rule 2 — Monatomic Ions
- Rule 3 — Fluorine
- Rule 4 — Oxygen
- Rule 5 — Hydrogen
- Rule 6 — Neutral Compounds Sum to Zero
- Rule 7 — Polyatomic Ions Sum to Charge
- Identifying Oxidant and Reductant
- Disproportionation Reactions
Rule 1 — Pure Elements
Any atom in its elemental form has an oxidation number of 0, regardless of its allotrope or bonding. Examples: each Fe atom in Fe(s) is 0; each O atom in O₂(g) is 0; each S atom in S₈ is 0; each C atom in diamond is 0.
Rule 2 — Monatomic Ions
A monatomic ion has an oxidation number equal to its ionic charge. Examples: Na⁺ is +1; Ca²⁺ is +2; Cl⁻ is −1; Fe³⁺ is +3. This rule is exact, not hypothetical.
Rule 3 — Fluorine
Fluorine, the most electronegative element, is always −1 in all its compounds. It has no exceptions because it never forms bonds to a more electronegative element.
Rule 4 — Oxygen
Oxygen is almost always −2. The main exceptions are: (a) peroxides (e.g. H₂O₂, Na₂O₂), where oxygen is −1; (b) superoxides (e.g. KO₂), where oxygen is −½; (c) compounds with fluorine (e.g. OF₂), where oxygen is +2 because F is more electronegative and must be −1.
Rule 5 — Hydrogen
Hydrogen is +1 when bonded to a nonmetal (as in HCl, H₂O, NH₃) and −1 when bonded to a metal in binary metal hydrides (as in NaH, CaH₂). The +1 assignment reflects hydrogen's lower electronegativity compared to typical nonmetals.
Rule 6 — Neutral Compounds Sum to Zero
The sum of all oxidation numbers in a neutral molecule or formula unit equals zero. This constraint, combined with known values from Rules 1–5, lets you solve algebraically for the unknown oxidation number. Example: in SO₄²⁻, if O = −2, then S + 4(−2) = −2, giving S = +6.
Rule 7 — Polyatomic Ions Sum to Charge
The sum of all oxidation numbers in a polyatomic ion equals the charge of that ion. Example: in Cr₂O₇²⁻, 2(Cr) + 7(−2) = −2, so 2(Cr) = +12, giving Cr = +6 in dichromate.
Identifying Oxidant and Reductant
Once you assign oxidation numbers to every atom before and after the reaction, compare them. The species containing the atom whose oxidation number increases has been oxidised — it is the reducing agent (reductant) because it supplies electrons to the other species. The species containing the atom whose oxidation number decreases has been reduced — it is the oxidising agent (oxidant) because it accepts electrons. Memory aid: OIL RIG — Oxidation Is Loss (of electrons), Reduction Is Gain (of electrons). The oxidant is reduced; the reductant is oxidised.
Disproportionation Reactions
A disproportionation reaction is one in which the same element in a single reactant simultaneously undergoes both oxidation and reduction, producing two different products with different oxidation states of that element. A classic example is the decomposition of hydrogen peroxide: 2 H₂O₂ → 2 H₂O + O₂. In H₂O₂ oxygen is −1; in H₂O it becomes −2 (reduced) and in O₂ it becomes 0 (oxidised). Disproportionation reactions are identified by finding one starting oxidation state that 'splits' into a lower and a higher value in the products. The reverse process — two different oxidation states of the same element combining to form an intermediate state — is called comproportionation (or synproportionation).
The Key Equation
- n_i — Number of atoms of element i (dimensionless): The subscript count for element i in the chemical formula, e.g. n = 4 for O in SO₄²⁻.
- \text{ox}_i — Oxidation number of element i (dimensionless (reported as signed integer)): The hypothetical charge assigned to atom i according to the assignment rules. May be fractional in some species such as Fe₃O₄.
- \text{charge of species} — Net ionic charge (dimensionless): Zero for a neutral compound; equal to the ion charge for a polyatomic ion (e.g. −2 for SO₄²⁻, +1 for NH₄⁺).
Worked Example
Problem. Determine the oxidation number of manganese in KMnO₄ (potassium permanganate). Then, given the reaction: 2 KMnO₄ + 5 H₂C₂O₄ + 3 H₂SO₄ → 2 MnSO₄ + 10 CO₂ + K₂SO₄ + 8 H₂O, identify the oxidising agent and the reducing agent.
Answer. Mn in KMnO₄ is +7. KMnO₄ is the oxidising agent (Mn is reduced from +7 to +2); H₂C₂O₄ is the reducing agent (C is oxidised from +3 to +4).
Origins · 1 minAntoine Lavoisier and how this was discovered
Lavoisier established the modern concept of chemical elements and chemical compounds, and was the first to give a systematic, quantitative account of oxidation. He showed that combustion involves combination with oxygen — not the release of a mythical 'phlogiston' — and he coined the term 'oxygen' (from Greek, meaning 'acid-former'). His careful mass-balance experiments laid the foundation for the law of conservation of mass, without which the concept of electron bookkeeping in redox chemistry would be impossible. Despite his towering scientific legacy, Lavoisier was executed by guillotine during the French Revolution in 1794 at the age of 50. The mathematician Joseph-Louis Lagrange reportedly said: 'It took them only an instant to cut off his head, but France may not produce another such head in a century.'
Related Concepts
- Balancing Redox Equations — Oxidation numbers are the foundation for the half-reaction and oxidation-number-change methods of balancing redox equations; you cannot balance a redox equation without first assigning oxidation states correctly.
- Redox Titrations — In a redox titration (e.g. permanganate vs oxalic acid), the stoichiometry is derived from the change in oxidation numbers of the oxidant and reductant, making oxidation number assignment an essential first step.
- Electrochemical Cell Structure — In galvanic and electrolytic cells, oxidation occurs at the anode and reduction at the cathode — concepts defined by changes in oxidation number of the electroactive species.
- Electrode Potential — Standard electrode potentials rank species by their tendency to be oxidised or reduced, which directly corresponds to the direction and magnitude of oxidation number change in a half-reaction.
- Faraday's Laws of Electrolysis — Faraday's laws connect the moles of electrons transferred to the mass of product deposited; the number of electrons transferred per atom equals the change in oxidation number, linking oxidation states directly to quantitative electrolysis calculations.