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Describe how oxidation and reduction involve electrons, change oxidation numbers, and combine in oxidation-reduction reactions.

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Short answer
- Oxidation is loss of electrons; reduction is gain of electrons.
- When an atom is oxidized its oxidation number increases; when it’s reduced its oxidation number decreases.
- In any redox reaction electrons lost by the species oxidized are gained by the species reduced. We therefore write separate half‑reactions (one showing oxidation, one showing reduction), balance electrons in them, and combine them so the electrons cancel.

Details and rules

1) Definitions
- Oxidation: loss of electrons. Example: Fe2+ → Fe3+ + e−. Oxidation number increases (Fe: +2 → +3).
- Reduction: gain of electrons. Example: Cl2 + 2 e− → 2 Cl−. Oxidation number decreases (Cl: 0 → −1).

2) Oxidation numbers (bookkeeping)
Use oxidation numbers to track electron flow. Basic rules:
- Element in elemental form = 0 (O2, H2, Na).
- Monatomic ion = its charge (Na+ is +1, S2− is −2).
- O almost always −2 (except in peroxides).
- H is +1 with nonmetals, −1 with metals (metal hydrides).
- Sum of oxidation numbers in a neutral molecule = 0; in a polyatomic ion = ion charge.
A change in oxidation number from reactant to product indicates net electron transfer.

3) Half‑reactions and combining them
- Write the oxidation half‑reaction showing electrons on the product side.
- Write the reduction half‑reaction showing electrons on the reactant side.
- Balance atoms other than O and H; balance O with H2O and H with H+ (or use OH− in basic solution); then balance charges by adding electrons.
- Multiply half‑reactions by integers so the number of electrons lost = number gained.
- Add the half‑reactions and cancel identical species (including electrons).

Example (simple aqueous): Zn + Cu2+ → Zn2+ + Cu
- Oxidation half: Zn → Zn2+ + 2 e−
- Reduction half: Cu2+ + 2 e− → Cu
Electrons cancel when you add them, giving the overall equation:
Zn + Cu2+ → Zn2+ + Cu

Example using oxidation numbers: 2 Fe2+ + Cl2 → 2 Fe3+ + 2 Cl−
- Fe2+ → Fe3+ + e− (Fe oxidation: +2 → +3)
- Cl2 + 2 e− → 2 Cl− (Cl reduction: 0 → −1)
Multiply the Fe half by 2 so electrons cancel:
2 Fe2+ + Cl2 → 2 Fe3+ + 2 Cl−

4) Roles of agents
- Reducing agent (reductant): the species that is oxidized (it donates electrons).
- Oxidizing agent (oxidant): the species that is reduced (it accepts electrons).

5) Notes and caveats
- Oxidation numbers are a formalism to track electron transfer; they don’t always represent actual localized charges (especially in covalent molecules).
- Not all changes in oxygen or hydrogen necessarily indicate redox; always check electron flow or oxidation numbers.
- In electrochemical cells, electrons flow through an external circuit from the oxidation half‑cell to the reduction half‑cell.

If you want, I can demonstrate balancing a redox equation step‑by‑step in acidic or basic solution with a worked example.