Rules for Assigning Oxidation Numbers

An oxidation number (oxidation state) is the charge that an atom would have if all of its bonding electrons were assigned to the more electronegative atom in each bond, and it is found by following a set of rules that are applied in order. In brief: the oxidation number of an element is 0, of a monatomic ion equals its charge, of oxygen is usually −2, of hydrogen is usually +1, and the sum for a neutral compound is 0 (for an ion it equals the ion’s charge); for example, Mn in KMnO₄ is +7.

Oxidation numbers are a bookkeeping device that helps to name compounds, balance redox equations and follow electron transfer. They are not always real charges, as in covalent compounds the electrons are shared. This article lists the rules and their order of priority, shows how to apply them to compounds and ions, includes a table of common oxidation numbers, works through challenging examples, discusses fractional and exceptional cases and gives a short history.

What are the rules?

1. An atom in its elemental form has an oxidation number of 0. Examples: Na, O₂, P₄, S₈.
2. A monatomic ion has an oxidation number equal to its charge. Na⁺ is +1, Cl⁻ is −1, Fe³⁺ is +3.
3. The sum of the oxidation numbers in a neutral compound is 0, and in a polyatomic ion it equals the charge of the ion.
4. Group 1 metals are +1, and group 2 metals are +2 in their compounds. Aluminum is +3 and zinc is usually +2.
5. Fluorine is −1 in all compounds.
6. Hydrogen is +1 when bonded to nonmetals, and −1 when bonded to metals (hydrides such as NaH and CaH₂).
7. Oxygen is −2 in most compounds. Exceptions: −1 in peroxides (H₂O₂, Na₂O₂), −½ in superoxides (KO₂), and +2 in OF₂.
8. The other halogens (Cl, Br, I) are −1 in binary compounds with metals and with hydrogen, but positive when combined with oxygen or with a more electronegative halogen.

If two rules conflict, the rule that comes earlier in the list takes priority. The oxidation numbers of all remaining atoms are then found from rule 3.

Common oxidation numbers

How do you find an unknown oxidation number?

1. Write the formula and the overall charge (0 for a neutral compound).
2. Assign known numbers using the rules, starting with the highest priority.
3. Multiply each known oxidation number by the number of atoms in the formula.
4. Let x be the unknown and set the sum equal to the overall charge.
5. Solve for x. If the unknown atom appears more than once, divide by the number of atoms.
6. Check that the result is reasonable for the element.

Worked examples

1. Sulfur in H₂SO₄. H is +1 (×2 = +2), O is −2 (×4 = −8). 2 + x − 8 = 0, so x = +6.
2. Manganese in KMnO₄. K is +1, O is −2 (×4 = −8). 1 + x − 8 = 0, so x = +7.
3. Chromium in Cr₂O₇²⁻. 2x + 7(−2) = −2, so 2x = +12 and x = +6.
4. Nitrogen in NH₄⁺ and in NO₃⁻. In NH₄⁺: x + 4(+1) = +1, so x = −3. In NO₃⁻: x + 3(−2) = −1, so x = +5.
5. Oxygen in H₂O₂. H is +1 (rule 6), so 2(+1) + 2y = 0 and y = −1. Hydrogen peroxide is a peroxide, so the usual −2 for oxygen does not apply.
6. Carbon in different compounds. CH₄: x + 4(+1) = 0, so x = −4. CH₃OH: x + 3(+1) + (−2) + (+1) = 0, so x = −2. HCHO: x + 2(+1) + (−2) = 0, so x = 0. HCOOH: x + 2(+1) + 2(−2) = 0, so x = +2. CO₂: x + 2(−2) = 0, so x = +4. The oxidation number of carbon increases from methane to carbon dioxide, which shows the stages of oxidation.
7. Iron in Fe₃O₄. 3x + 4(−2) = 0, so x = +8/3, or about +2.67. This average oxidation number is fractional because the compound contains both Fe²⁺ and Fe³⁺ ions (one Fe²⁺ and two Fe³⁺: 2 + 6 = 8).

What are the exceptions?

Oxidation numbers can be fractional, as in Fe₃O₄ or in the tetrathionate ion S₄O₆²⁻ (average +2.5 for sulfur), because they are averages. Atoms of the same element in different environments may have different numbers: in the thiosulfate ion S₂O₃²⁻ the average oxidation number of sulfur is +2, but the two sulfur atoms are in different environments (+6 and −2). In compounds of two nonmetals, the rules assign the more electronegative element the negative number, which may not agree with the real distribution of charge. For these reasons, oxidation numbers are a formal tool.

Where are oxidation numbers used?

• Naming: Roman numerals in the names of compounds, such as iron(III) chloride, show the oxidation number.
• Redox reactions: an increase in oxidation number means oxidation, and a decrease means reduction. They allow you to identify oxidizing and reducing agents and to balance equations.
• Predicting formulas: the highest oxidation number of a main-group element usually equals its group number (for example, +7 for chlorine in group 17).
• Electrochemistry and corrosion: tracking of electron flow in cells and batteries.

How did the concept develop?

The idea of the oxidation state came from the early electronic theories of valence in the early 20th century and from the study of redox reactions. Alfred Stock introduced the Roman-numeral system of naming in 1919, which uses oxidation numbers in names. Wendell Latimer’s book on the oxidation states of the elements and their potentials, published in 1938, made oxidation states a standard tool for organizing inorganic chemistry. IUPAC has given a formal definition based on the assignment of bonding electrons to the more electronegative atom.

Which mistakes are common?

Mistake 1: Treating oxidation numbers as real charges

In covalent compounds the electrons are shared, and the oxidation number is a formal count.

Mistake 2: Forgetting that the sum must equal the charge of the ion

For ions the sum is not zero, but equal to the overall charge.

Mistake 3: Assuming that oxygen is always −2

In peroxides it is −1, and in OF₂ it is positive.

Mistake 4: Writing the sign in the wrong place

Oxidation numbers are written with the sign first (+3), while ionic charges are written with the sign after the number (3+).