Worked example 1
What is the oxidation number of sulfur in H₂SO₄?
Try it first: Assign hydrogen and oxygen first, then let sulfur absorb the remainder.
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Oxidation NumbersCourse level: High School / HonorsCourse level: AP Chemistry
Assigning Oxidation Numbers
What you'll be able to do: Assign oxidation numbers to every atom in a compound or ion using a fixed order of rules.
Introduction
Oxidation numbers are a bookkeeping device, a way of pretending that every bond is fully ionic so electrons can be counted. They are not real charges, but they provide a systematic way to identify redox changes.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- Apply the oxidation number rules in the correct priority order
- Determine the oxidation state of an unknown atom by algebra
- Recognise the standard exceptions for oxygen and hydrogen
- Use oxidation numbers to name compounds of variable-charge metals
A deliberate fiction
An oxidation number is the charge an atom would carry if every shared pair of electrons were handed entirely to the more electronegative partner. In CH₄ the carbon is not really at -4, but treating it that way lets us track electron flow consistently across any reaction.
Oxidation number assigns both bonding electrons to the more electronegative atom; formal charge instead divides a bonding pair equally. In H₂O, oxygen's oxidation number is −2 but its ordinary Lewis formal charge is zero. Neither number is a measurement of the partial atomic charge. Oxidation-state changes still provide consistent electron accounting even when the bonds are covalent.
Oxidation numbers are per atom, written with the sign first, as in +2. Ionic charges are written with the sign last, as in 2+.
The priority list
Apply the rules in order and stop when the atom is assigned. First, any atom in its free element form is 0. Second, a monatomic ion equals its charge. Third, bonded fluorine is −1. Fourth, group 1 metals are +1 and group 2 metals are +2.
Fifth, hydrogen is +1 with nonmetals. Sixth, oxygen is -2. Whatever is left is found by making the total come out right.
Order matters. In H₂O₂ oxygen cannot be -2, because hydrogen is assigned first and the total must be zero.
The exceptions worth knowing
Oxygen is -1 in peroxides such as H₂O₂ and Na₂O₂, and +2 when bonded to fluorine in OF₂. Hydrogen is -1 in metal hydrides such as NaH and CaH₂, because the metal is less electronegative. Also recognize superoxide O₂⁻, whose equivalent oxygens have average oxidation number −1/2.
Keep the uncombined-element rule ahead of the bonded-atom defaults: O₂ and F₂ both have oxidation number zero. In OF₂, assign each bonded fluorine −1 first, so oxygen must be +2. In peroxide O₂²⁻ the two equivalent oxygens average −1; in superoxide O₂⁻, as in KO₂, they average −1/2. Recognizing an O–O ion prevents forcing oxygen to its usual −2 value. In CaH₂, Ca is +2 so each hydride H is −1.
| Species | Charge-sum equation | Unknown oxidation number |
|---|---|---|
| SO₄²⁻ | x + 4(−2) = −2 | S = +6 |
| NH₄⁺ | x + 4(+1) = +1 | N = −3 |
| K₂Cr₂O₇ | 2(+1) + 2x + 7(−2) = 0 | Cr = +6 |
The unknown is the value per atom. The factor 2 in 2x counts two chromium atoms, not a different definition of oxidation state.
H₂O₂: H = +1, O = -1
Solving for the unknown
Set up a small equation. Multiply each known oxidation number by how many of that atom appear, add an unknown for the remaining atom, and set the sum equal to the overall charge. This works identically for neutral compounds and for polyatomic ions.
sum of (oxidation number x count) = overall charge
Why chemists care
Variable-charge metals are named by their oxidation state, so iron(III) chloride is FeCl₃. More importantly, comparing oxidation numbers before and after a reaction is the definitive test for whether electrons moved at all.
For FeCl₂, two Cl atoms contribute −2, so Fe is +2 and the name is iron(II) chloride. FeCl₃ contains Fe(+3), giving iron(III) chloride. Reverse the process when given a name: copper(II) oxide combines Cu²⁺ and O²⁻ as CuO, whereas copper(I) oxide is Cu₂O. Do not copy the Roman numeral directly as a subscript.
In polyatomic compounds, an oxidation state of a central atom is not the overall ion charge. Sulfur(+6) in sulfate does not turn sulfate into a 6+ ion; oxygen contributions make the whole ion 2−. Use the whole ion charge to build salts, then oxidation numbers to examine electron transfer.
An average oxidation state can hide distinct sites
The charge-sum rule sometimes gives a fractional average oxidation number in a mixed-valence compound. That does not require any individual atom to carry a fractional ionic charge.
Magnetite Fe₃O₄ is a familiar example: the formal total from oxygen is -8, so three iron atoms average +8/3, consistent with one Fe²⁺ and two Fe³⁺ in a simple ionic accounting.
Distinguish a formula-average value from oxidation states at individual sites.
Key ideas
Definition
Oxidation number
The hypothetical charge on an atom if all bonds were treated as fully ionic.
Rule
Free elements are zero
Any element in its uncombined form, including O₂, P₄ and Na(s), has an oxidation number of 0.
Rule
Sums are fixed
Oxidation numbers total zero in a neutral compound and equal the charge in a polyatomic ion.
Assumption
Oxygen defaults to -2
Oxygen is usually −2; recognize elemental O₂, peroxide, superoxide and oxygen–fluorine compounds before applying that default.
Assumption
Hydrogen defaults to +1
Hydrogen is +1 with nonmetals but -1 in metal hydrides.
Equation
Oxidation number sum rule
sum(n x oxidation number) = total charge
- n = number of atoms of that element in the formula
- total charge = zero for a compound, the ion charge for a polyatomic ion
Worked examples
Worked example 2
What is the oxidation number of chromium in Cr₂O₇²⁻?
Try it first: Remember that the total here is not zero.
0 of 4 steps revealed.
Worked example 3
Assign oxidation numbers to every atom in NaH and in H₂O₂.
0 of 4 steps revealed.
Worked example 4
Find the average Fe oxidation number in Fe₃O₄ and give one integer-state breakdown.
Try it first: Assign oxygen its usual -2.
0 of 3 steps revealed.
Common mistakes
| Mistake | Why it's wrong | Check instead |
|---|---|---|
| Assuming oxygen is always -2. | In peroxides oxygen is -1 and with fluorine it is positive. | Assign higher-priority atoms first and let the sum rule reveal the exception. |
| Multiplying the oxidation number by the subscript when reporting it. | Oxidation number is a per-atom quantity, the subscript is only used inside the sum. | Report the value for one atom, such as O = -2 in H₂O, not -4. |
| Confusing oxidation number with formal charge or actual charge. | Oxidation numbers assume bonds are fully ionic, which real bonds are not. | Use oxidation numbers only for tracking electron transfer. |
| Setting the sum to zero for a polyatomic ion. | The sum must equal the ion charge, not zero. | Read the superscript charge before writing the equation. |
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After the lesson · Question bank
Independent practice
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What you should now know
Oxidation numbers are assigned by working through a fixed priority list: free elements are zero, monatomic ions equal their charge, bonded fluorine is −1, oxygen is usually -2 and hydrogen is usually +1. The sum must equal zero for a neutral compound or the charge for a polyatomic ion, which lets you solve for any remaining unknown atom algebraically.
- Oxidation numbers are bookkeeping, not real charges
- Work through the priority rules in order, then solve for the leftover atom
- Free elements are always zero
- Oxygen is -1 in peroxides and hydrogen is -1 in metal hydrides
- The sum equals zero for compounds and the charge for polyatomic ions
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