Oxidation Numbers
Assign an oxidation number to every element in a formula, with the rule that fixed each one.
| Element | Atoms | Oxidation | Why |
|---|---|---|---|
| H | 2 | +1 | Hydrogen is +1 with non-metals |
| S | 1 | +6 | Solved so the numbers sum to the overall charge of 0 |
| O | 4 | −2 | Oxygen is −2 in almost every compound |
Check: 2 × +1 + 1 × +6 + 4 × −2 = 0 — the overall charge.
An oxidation number is the charge an atom would carry if every bond were fully ionic. You fix the elements that follow a rule, then solve for the one left over so the numbers sum to the overall charge. In H₂SO₄, sulfur is +6.
A bookkeeping device, not a real charge
The sulfur in sulfuric acid does not carry six units of positive charge. Oxidation numbers pretend that every shared pair of electrons belongs entirely to the more electronegative atom, which is a deliberate fiction — but a useful one, because it makes electron transfer visible. If an element’s number rises between reactant and product it lost electrons and was oxidised; if it falls, it gained them and was reduced.
That is the whole reason the concept exists. Without it, deciding what is oxidised in MnO₄⁻ + Fe²⁺ → Mn²⁺ + Fe³⁺ means tracking electrons through bonds. With it, manganese goes from +7 to +2 and iron from +2 to +3, and the balancing follows from those two numbers.
The rules are a priority list
They conflict, so order matters. Fluorine outranks everything because nothing is more electronegative. Group 1 and group 2 metals come next, then hydrogen, then oxygen — which is why hydrogen is −1 in NaH, where sodium’s +1 has already been fixed, and why oxygen is +2 in OF₂, where fluorine has been. The last element takes whatever value makes the sum come out right.
0 for a neutral compound; the ion’s charge for a polyatomic ion
- 1 Check for a free element. An element bonded only to itself — O₂, Fe, S₈ — is 0 by definition, and there is nothing left to do.
- 2 Fix the elements that never vary. Fluorine is −1 always; group 1 metals are +1; group 2 metals are +2.
- 3 Apply hydrogen and oxygen next. Hydrogen is +1 with non-metals and −1 in a metal hydride. Oxygen is −2, except −1 in a peroxide and positive with fluorine.
- 4 Solve for what is left. In H₂SO₄: 2(+1) + 4(−2) = −6, so sulfur must be +6 to bring the total to zero.
- 5 Check the sum. 2(+1) + 1(+6) + 4(−2) = 2 + 6 − 8 = 0 — a neutral compound, as required.
The rules, in the order they apply
Each rule wins over the ones below it. The final element is solved from the sum.
| Rule | Value | Exception |
|---|---|---|
| A free element | 0 | None — this one is a definition |
| Monatomic ion | Its charge | None |
| Fluorine | −1 | None — nothing outranks it |
| Group 1 metal | +1 | None in a compound |
| Group 2 metal | +2 | None in a compound |
| Hydrogen | +1 | −1 in a metal hydride such as NaH |
| Oxygen | −2 | −1 in a peroxide; positive with fluorine |
| Cl, Br, I | −1 | Positive when bonded to oxygen or fluorine |
Where a single number stops being honest
Two cases break the arithmetic. The first is a compound where one element sits at two different states at once. Fe₃O₄ averages out to +8/3 for iron, but no iron atom carries eight thirds of a charge — the solid is really one Fe²⁺ and two Fe³⁺ per formula unit. Anything that produces a fraction is a signal of this, and the tool says so rather than reporting the fraction as an answer.
The second is organic chemistry, where carbon’s oxidation number differs atom by atom. In ethanol, CH₃CH₂OH, the average across both carbons is −2, but the methyl carbon is −3 and the one bearing the hydroxyl is −1. That distinction is exactly what matters when you are asking which carbon gets oxidised, so an average would hide the point.
A third limit is structural: the rules fix elements one at a time and solve for what remains, so they need every element but one to be covered. A salt such as FeSO₄ leaves both iron and sulfur unknown, and the honest way through is to split it into Fe²⁺ and SO₄²⁻ and do each ion separately.