Assigning oxidation numbers follows a set of rules applied in a specific order. The core idea is simple: you imagine every bond in a compound as completely ionic, then ask what charge each atom would carry. This is a formalism, not a description of reality, since many compounds are covalent. But it works reliably for tracking electrons in chemical reactions, balancing redox equations, and naming compounds.
What Oxidation Numbers Actually Represent
An oxidation number (also called an oxidation state) is the hypothetical charge an atom would have if every bond in the molecule were split so that all shared electrons went to the more electronegative atom. Bonds between two identical atoms get split equally. The result is a bookkeeping number, not a real charge. In sodium chloride, sodium’s oxidation number of +1 reflects an actual ionic charge. In carbon dioxide, carbon’s +4 is purely a formalism, since the bonds are covalent. Both are assigned the same way.
The Rules, in Order of Priority
These rules have a hierarchy. When two rules conflict, the one listed earlier wins.
- Free elements are zero. Any atom not bonded to a different element has an oxidation number of 0. This applies to pure metals like Fe, diatomic molecules like O₂ and N₂, and allotropes like P₄.
- Monatomic ions equal their charge. Na⁺ is +1, Ca²⁺ is +2, Cl⁻ is −1. The oxidation number is simply the ion’s charge.
- Fluorine is always −1. Fluorine is the most electronegative element, so it always pulls the electrons toward itself in any bond.
- Hydrogen is +1 in most compounds. The exception is metal hydrides (like NaH or CaH₂), where hydrogen bonds to a less electronegative metal and takes the electrons, giving it an oxidation number of −1.
- Oxygen is −2 in most compounds. Three exceptions matter here. In peroxides like H₂O₂ and Na₂O₂, oxygen is −1 because each oxygen shares a bond with the other oxygen atom, and that bond gets split equally. In superoxides like KO₂, oxygen is −1/2. And in OF₂, oxygen is +2 because fluorine’s rule takes priority.
- Group 1 metals (Li, Na, K, etc.) are always +1 in compounds.
- Group 2 metals (Mg, Ca, Ba, etc.) are always +2 in compounds.
- Aluminum is +3 in compounds.
- Halogens other than fluorine are −1 in most compounds. They deviate from −1 when bonded to oxygen or to a more electronegative halogen. Chlorine in HCl is −1, but chlorine in ClO₃⁻ is +5.
- The sum of all oxidation numbers in a neutral compound equals zero.
- The sum of all oxidation numbers in a polyatomic ion equals the ion’s charge.
Those last two rules are what let you solve for any unknown oxidation number using basic algebra.
Working Through a Neutral Compound
Take sulfuric acid, H₂SO₄. Start by assigning what you know. Hydrogen is +1 (two atoms contribute +2 total). Oxygen is −2 (four atoms contribute −8 total). The compound is neutral, so all oxidation numbers must add to zero.
Set up the equation: (+2) + S + (−8) = 0. Solving gives S = +6. Sulfur’s oxidation number in sulfuric acid is +6.
This same approach works for any compound where only one element is unknown. Assign every atom you can using the fixed rules, multiply each oxidation number by the number of that atom in the formula, then solve for the missing value.
Working Through a Polyatomic Ion
The permanganate ion, MnO₄⁻, carries a charge of −1. Oxygen is −2, and four oxygen atoms contribute −8. The total must equal the ion’s charge of −1, not zero.
The equation: Mn + (−8) = −1. Solving gives Mn = +7. Manganese has an oxidation number of +7 in permanganate. This is one of the highest oxidation states you’ll encounter for a transition metal, and it’s why permanganate is such a powerful oxidizing agent.
Transition Metals and Variable States
Unlike alkali or alkaline earth metals, transition metals can have multiple oxidation states. Iron can be +2 or +3, copper can be +1 or +2, and manganese ranges from +2 all the way to +7. You can’t look these up from a fixed rule. Instead, you assign everything else in the compound first and use the sum rule to calculate what the metal must be.
For a straightforward example, take CoBr₂. Bromine is a halogen, so each bromine is −1, giving a total of −2. The compound is neutral, so cobalt must be +2.
For AgCl, chlorine is −1 and the compound is neutral, so silver is +1. The process is identical regardless of which transition metal you’re working with: assign the known atoms, then solve the algebra.
Handling Peroxides
Peroxides trip people up because they break the “oxygen is −2” rule. In sodium peroxide, Na₂O₂, sodium is +1 (Group 1 metal), so two sodium atoms contribute +2. If oxygen were −2, the two oxygens would give −4, and the sum would be −2 instead of zero. That doesn’t work for a neutral compound.
The fix: recognize the compound as a peroxide. Each oxygen is −1 in peroxides. Now the math checks out: +2 from sodium, −2 from oxygen, sum is zero. The clue is the O-O bond in the structure. Whenever two oxygen atoms are bonded directly to each other (and it’s not O₂ itself), suspect a peroxide or superoxide.
Fractional Oxidation Numbers
Sometimes the math produces a fraction. Iron in Fe₃O₄ is a classic example. Oxygen contributes (4 × −2) = −8. Three iron atoms must balance that to zero, so each iron averages +8/3, which is about +2.67.
This doesn’t mean iron exists in some exotic partial state. Fe₃O₄ actually contains two Fe³⁺ ions and one Fe²⁺ ion per formula unit, and +8/3 is just the average across all three. Fractional values show up when a compound contains the same element in two different oxidation states. The math still works for balancing equations, even if the number feels odd.
Why Oxidation Numbers Matter
The main practical use is identifying what gets oxidized and what gets reduced in a chemical reaction. When an atom’s oxidation number increases going from reactants to products, that atom has been oxidized (it lost electrons). When the number decreases, the atom has been reduced (it gained electrons). The substance containing the oxidized atom is the reducing agent, and the substance containing the reduced atom is the oxidizing agent.
Oxidation numbers also show up in chemical naming. Roman numerals in names like iron(III) chloride or copper(II) sulfate refer directly to the metal’s oxidation state. If you can assign oxidation numbers, you can name (and interpret the names of) transition metal compounds correctly.
A Quick Step-by-Step Summary
For any compound or ion, follow this sequence:
- Step 1: Check if any atom is in its elemental form. If so, its oxidation number is 0.
- Step 2: Assign fluorine as −1, then hydrogen as +1 (or −1 in metal hydrides), then oxygen as −2 (or −1 in peroxides).
- Step 3: Assign Group 1 metals as +1, Group 2 metals as +2, and aluminum as +3.
- Step 4: Assign remaining halogens as −1, unless they’re bonded to oxygen or a more electronegative halogen.
- Step 5: Multiply each oxidation number by the number of atoms of that element. Set the total equal to zero for a neutral compound or to the charge for a polyatomic ion. Solve for the unknown.
With practice, most of these steps become automatic, and you’ll find yourself jumping straight to the algebra for the one element you can’t assign from the rules.