Oxidation Numbers, Redox Agents, and Half-Reaction Balancing

What an oxidation number records

An oxidation number is the charge an atom would carry if every bond between different atoms were completely ionic, with the shared electrons assigned to the more electronegative atom; electrons shared between identical atoms are split equally. It is a formal count, not a measured charge. In water, oxygen is assigned −2 and each hydrogen +1, even though the real partial charges are much smaller.

Oxidation is an increase in oxidation number, which corresponds to a loss of electrons. Reduction is a decrease in oxidation number, a gain of electrons. The two always occur together, because electrons lost by one species must be gained by another. In any redox equation, the total increase in oxidation number equals the total decrease, and every balancing method rests on that equality.

Assigning oxidation numbers in priority order

Apply the rules from the top of the list down. When two rules conflict, the higher one wins, and the last unknown atom in a formula is found by difference.

For the dihydrogen phosphate ion, H₂PO₄⁻: 2(+1) + P + 4(−2) = −1, so P = +5. For the tetrathionate ion, S₄O₆²⁻: 4S + 6(−2) = −2, so the four sulfur atoms total +10 and the average is +2.5. A fractional result means atoms of the same element sit in different environments and the number reported is an average. Magnetite, Fe₃O₄, averages +8/3 because it contains one Fe²⁺ for every two Fe³⁺.

• An atom in a pure element is 0 (Fe, O₂, S₈).
• A monatomic ion equals its charge (Mg²⁺ is +2, Br⁻ is −1).
• The oxidation numbers in a formula add up to its overall charge.
• Fluorine is −1 in all its compounds.
• Group 1 metals are +1 and group 2 metals +2 in compounds.
• Hydrogen is +1 with nonmetals and −1 in metal hydrides such as NaH.
• Oxygen is usually −2, but −1 in peroxides (H₂O₂), −½ in superoxides (KO₂), and +2 in OF₂.
• Chlorine, bromine, and iodine are usually −1, except when bonded to oxygen or to a lighter halogen.

Naming the oxidizing agent and the reducing agent

The oxidizing agent accepts electrons and causes something else to be oxidized, so it is itself reduced. The reducing agent donates electrons and is itself oxidized. Name the whole species rather than a single atom.

Consider 2Fe²⁺(aq) + H₂O₂(aq) + 2H⁺(aq) → 2Fe³⁺(aq) + 2H₂O(l). Iron rises from +2 to +3, so Fe²⁺ is oxidized and is the reducing agent. Oxygen falls from −1 in the peroxide to −2 in water, so H₂O₂ is reduced and is the oxidizing agent. Hydrogen stays +1 throughout. Two iron ions each lose one electron and two peroxide oxygen atoms each gain one, so two electrons are lost and two are gained.

One species can play both roles. In Cl₂ + 2OH⁻ → Cl⁻ + ClO⁻ + H₂O, one chlorine atom goes from 0 to −1 and the other from 0 to +1. This is disproportionation, and Cl₂ is both the oxidizing and the reducing agent.

Half-reaction balancing in acidic solution

Separating oxidation from reduction lets you balance each electron transfer on its own, then combine the halves so the electrons cancel. Water supplies oxygen atoms and H⁺ supplies hydrogen atoms because those are the species actually present in acidic water.

Worked example 1. In acid, dichromate oxidizes nitrite: Cr₂O₇²⁻ + NO₂⁻ → Cr³⁺ + NO₃⁻. Chromium goes from +6 to +3 and nitrogen from +3 to +5. Oxidation half: NO₂⁻ + H₂O → NO₃⁻ + 2H⁺ + 2e⁻, with charge −1 on each side. Reduction half: Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O, with charge +6 on each side. The six electrons match two chromium atoms changing by three units each.

Multiply the oxidation half by 3 so both halves involve 6e⁻, then add: Cr₂O₇²⁻ + 14H⁺ + 3NO₂⁻ + 3H₂O → 2Cr³⁺ + 7H₂O + 3NO₃⁻ + 6H⁺. Cancel 6H⁺ and 3H₂O from each side: Cr₂O₇²⁻ + 8H⁺ + 3NO₂⁻ → 2Cr³⁺ + 3NO₃⁻ + 4H₂O. Check: Cr 2 and 2; N 3 and 3; O 7 + 6 = 13 and 9 + 4 = 13; H 8 and 8; charge −2 + 8 − 3 = +3 and +6 − 3 = +3.

• Split the skeleton equation into an oxidation half and a reduction half.
• Balance every element except O and H.
• Balance O by adding H₂O, then balance H by adding H⁺.
• Balance charge by adding electrons to the more positive side.
• Scale the halves so the electrons match, add them, and cancel anything on both sides.
• Check atoms and charge, and confirm no electrons remain.

Converting the method for basic solution

In basic solution, OH⁻ is abundant and the final equation should not contain H⁺. Balance as if the solution were acidic, then add enough OH⁻ to both sides to turn every H⁺ into water. Adding the same species to both sides keeps the equation balanced.

Worked example 2. Hypochlorite oxidizes chromium(III) hydroxide to chromate in base: Cr(OH)₃ + ClO⁻ → CrO₄²⁻ + Cl⁻. Chromium goes from +3 to +6 and chlorine from +1 to −1. Oxidation half: Cr(OH)₃ + H₂O → CrO₄²⁻ + 5H⁺ + 3e⁻. Reduction half: ClO⁻ + 2H⁺ + 2e⁻ → Cl⁻ + H₂O. The least common multiple of 3 and 2 is 6, so double the first half and triple the second.

Adding and cancelling gives 2Cr(OH)₃ + 3ClO⁻ → 2CrO₄²⁻ + 3Cl⁻ + 4H⁺ + H₂O. Add 4OH⁻ to both sides; on the right, 4H⁺ + 4OH⁻ becomes 4H₂O. Final: 2Cr(OH)₃(s) + 3ClO⁻(aq) + 4OH⁻(aq) → 2CrO₄²⁻(aq) + 3Cl⁻(aq) + 5H₂O(l). Check: Cr 2 and 2; Cl 3 and 3; O 6 + 3 + 4 = 13 and 8 + 5 = 13; H 6 + 4 = 10 and 10; charge −7 on each side.

Common mistakes in redox bookkeeping

Most redox errors are bookkeeping errors, and each has a specific check.

As a final test, confirm with oxidation numbers alone that electrons lost equal electrons gained. In worked example 2, two chromium atoms each lose 3 electrons (6 in total) and three chlorine atoms each gain 2 (also 6).

• Naming an atom as the agent: write that Cr₂O₇²⁻ is the oxidizing agent, not chromium.
• Counting the change per atom but not per formula: Cr₂O₇²⁻ → 2Cr³⁺ takes 6 electrons, not 3.
• Putting electrons on the wrong side: they are products in an oxidation half and reactants in a reduction half. If the charge check fails, look here first.
• Balancing oxygen with O, O₂, or O²⁻ instead of H₂O. Free oxide ions do not exist in water.
• Leaving H⁺ in a basic-solution answer, or forgetting to cancel water after adding OH⁻.
• Assuming oxygen is always −2: check for peroxides, superoxides, and O–F bonds.
• Mixing notation: an oxidation number is written sign first (+3); an ion charge is written number first (3+).