Assigning Oxidation Numbers

Ionic compounds like NaCl make oxidation numbers obvious: sodium really does lose an electron to become Na⁺ (oxidation number +1), and chlorine really does gain one to become Cl⁻ (oxidation number −1). The trouble starts with covalent compounds. In water, H₂O, no electron is fully transferred — the O–H bonds are polar covalent, with electrons shared unequally. Yet chemists still assign oxygen an oxidation number of −2 and hydrogen +1. The trick is to imagine "un-sharing" every bond. Because oxygen is more electronegative than hydrogen, we pretend both electrons of each O–H bond end up on oxygen. Oxygen "gains" two electrons overall (one from each of its two bonds), giving it an oxidation number of −2. Each hydrogen "loses" its one shared electron, giving +1. Nothing physically transferred — but the bookkeeping mimics what would happen in the ionic extreme, using electronegativity as the tiebreaker. This convention becomes a powerful diagnostic. If you track oxidation numbers across a reaction and find that some atom's number went up while another's went down, you have found a genuine transfer of electron density — a redox process — even if the compounds involved are entirely covalent, like in the combustion of methane.

where: X is any atom in its uncombined elemental form (Na(s), O₂(g), P₄(s), etc.).

where: e.g. ON(Mg²⁺) = +2, ON(S²⁻) = −2.

where: the sum runs over all atoms in the formula unit, and $q$ is the overall charge (0 for a neutral compound, the ionic charge for a polyatomic ion).

where: fluorine is the most electronegative element and never gives up its −1 assignment, even bonded to oxygen.

where: peroxides contain the O₂²⁻ unit (e.g. H₂O₂, Na₂O₂); OF₂ is the sole common case where oxygen bonds to something more electronegative than itself.

where: metal hydrides such as NaH or CaH₂ pair hydrogen with a less electronegative metal, flipping the sign.

Example 1 — Chromium in the dichromate ion, Cr₂O₇²⁻ Oxygen is not in a peroxide or OF₂ context here, so it keeps its standard value.

The ion's total charge is $q = -2$. Let $x$ = ON(Cr), with 2 chromium atoms.

Each chromium atom in Cr₂O₇²⁻ has oxidation number +6 — consistent with chromium's common high oxidation states in oxo-anions. Limiting-case check: if the two chromium atoms instead carried a total charge as if the ion were neutral overall ($q=0$), the same algebra would give $2x = 14$, so $x = +7$, above chromium's accessible range — confirming that ignoring the actual ionic charge would produce a chemically impossible answer, a useful sanity check on the method itself.

Example 2 — Sulfur in sodium thiosulfate, Na₂S₂O₃ This is a neutral compound, so $q = 0$. Sodium is an alkali metal forming Na⁺ exclusively in compounds:

Oxygen takes its standard value:

Let $x$ = ON(S), with 2 sulfur atoms. The summation rule gives:

The average oxidation number of sulfur in thiosulfate is +2, even though the two sulfur atoms are not chemically identical (one is a central S, the other a terminal S bonded only to the central atom) — the simple summation method gives an average, not necessarily an actual per-atom value, a subtlety worth flagging for structures with nonequivalent atoms of the same element. Limiting-case check: replacing thiosulfate with plain sulfate, SO₄²⁻, and redoing the algebra with $q=-2$, $n(\text{O})=4$ gives $x - 8 = -2$, so $x = +6$ for sulfur — the well-known, verifiable oxidation state of sulfur in sulfate, confirming the method reproduces a textbook-standard result when applied to a simpler, single-sulfur ion.

The oxidation-number convention grew out of nineteenth- and twentieth-century efforts to unify the language of combustion, corrosion, and electrochemistry — processes that all seemed to involve "oxidation" in the original sense of combining with oxygen, long before electrons were understood. Once the electronic theory of valence matured in the 1910s–1920s, chemists reinterpreted oxidation and reduction in terms of electron transfer, and the oxidation-number system was formalized as the bookkeeping tool that lets this electron-transfer view apply even to covalent, non-ionic compounds. This reinterpretation is what makes it possible to recognize Oxidation-Reduction Reactions in organic and covalent chemistry, not just in classic ionic salts, and it underlies the ranking of metal reactivities captured later in The Activity Series.

Ask the tutor: How do I decide, just from oxidation-number changes, which reactant in an equation is the oxidizing agent and which is the reducing agent?