F. Electrochemistry · ElectrochemistryOxidation Numbers: Electron Bookkeeping
F3.1 F2.1 F2.3About 70 minutes
Learning goals- I can assign oxidation numbers to every atom in an element, ion or compound.
- I can explain what an oxidation number means using electronegativity.
- I can use changes in oxidation number to decide whether a reaction is redox.
- I can identify the oxidizing and reducing agents in reactions between molecules, such as combustion.
Words to know
oxidation number
The charge an atom would have if all of its shared electrons were given to the more electronegative atom in each bond. Also called oxidation state.
electronegativity
A measure of how strongly an atom attracts shared electrons in a bond (you met it in SCH3U).
peroxide
A compound with an O–O single bond, such as H₂O₂, where each oxygen has oxidation number −1.
metal hydride
A compound of a metal and hydrogen, such as NaH or CaH₂, where hydrogen has oxidation number −1.
average oxidation number
When atoms of the same element in a formula have different oxidation numbers, the rules give their average, which can be a fraction (e.g. +8/3 for Fe in Fe₃O₄).
When there are no ions to watch
In the last lesson, the electrons were easy to follow: Zn became Zn²⁺. But look at a natural gas furnace on a cold January night:
CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g)
There are no ions anywhere. Every substance is molecular. Yet this is a redox reaction, and a very important one: it heats most homes in Ontario. To see the electrons, chemists use a bookkeeping system called oxidation numbers.
What an oxidation number means
In a covalent bond, electrons are shared, but not always equally. In Grade 11 (SCH3U, Matter, Chemical Trends, and Chemical Bonding) you learned that the more electronegative atom pulls the shared electrons closer.
An oxidation number pretends the sharing is completely unequal: every shared pair is handed to the more electronegative atom. Then
oxidation number = valence electrons in the free atom − electrons counted for the atom in the compound
It is a bookkeeping charge, not a real charge. Write it with the sign first (+2, −1) to tell it apart from an ion charge, which is written with the sign last (2+, 1−).
The rules
You don't need to draw Lewis structures every time. These rules give the same answers. Apply them in order; an earlier rule wins when two rules disagree.
- An atom in an uncombined element has oxidation number 0 (Na, O₂, Cl₂, S₈, Cu).
- A monatomic ion has an oxidation number equal to its charge (Na⁺ is +1, Fe³⁺ is +3, S²⁻ is −2).
- Fluorine is always −1 in compounds. Group 1 metals are +1 and group 2 metals are +2 in compounds. Aluminium is +3.
- Hydrogen is +1 in compounds, except in metal hydrides (NaH, CaH₂), where it is −1.
- Oxygen is −2 in compounds, except in peroxides such as H₂O₂ (−1) and in OF₂ (+2).
- Chlorine, bromine and iodine are usually −1, but they can be positive when bonded to oxygen or a more electronegative halogen (as in ClO⁻).
- The oxidation numbers in a neutral compound add up to 0. In a polyatomic ion they add up to the ion's charge.
Use rule 7 last, to find the one atom the other rules don't cover.
Worked exampleExample 1: Sulfur in sulfuric acid
Find the oxidation number of sulfur in H₂SO₄.
- Hydrogen is +1 (rule 4); oxygen is −2 (rule 5). Let sulfur be x.
- The compound is neutral, so the sum is 0: 2(+1) + x + 4(−2) = 0.
- 2 + x − 8 = 0, so x = +6.
Worked exampleExample 2: Chromium in the dichromate ion
Find the oxidation number of chromium in Cr₂O₇²⁻.
- Oxygen is −2. Let each chromium be x.
- The ion's charge is 2−, so the sum is −2: 2x + 7(−2) = −2.
- 2x − 14 = −2, so 2x = 12 and x = +6.
Cr = +6. (Remember the sum equals the ion's charge, not 0.)
Worked exampleExample 3: A fractional answer
Magnetite, Fe₃O₄, is a magnetic iron ore. Find the oxidation number of iron.
- Oxygen is −2. Let each iron be x: 3x + 4(−2) = 0.
- 3x = 8, so x = +8/3 ≈ +2.67.
- No single atom can have a charge of 8/3. The rules give an average: magnetite contains one Fe²⁺ for every two Fe³⁺ (2 + 3 + 3 = 8).
Average Fe = +8/3: one iron(II) and two iron(III) per formula unit.
Using oxidation numbers to spot redox
Now we can define redox in a way that works for every reaction:
- If an atom's oxidation number increases, it was oxidized (it lost electrons, or lost its share of them).
- If an atom's oxidation number decreases, it was reduced.
- If no oxidation numbers change, the reaction is not redox.
The size of the change tells you how many electrons each atom lost or gained. For example, manganese going from +7 in MnO₄⁻ to +2 in Mn²⁺ has gained 5 electrons per atom.
Worked exampleExample 4: Combustion of methane
Show that CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g) is a redox reaction. Identify the oxidizing and reducing agents and the number of electrons transferred.
- Assign oxidation numbers on the left. CH₄: H is +1, so C + 4(+1) = 0, C = −4. O₂ is an element: O = 0.
- On the right. CO₂: C + 2(−2) = 0, C = +4. H₂O: H = +1, O = −2.
- Carbon rose from −4 to +4: it was oxidized, losing 8 electrons. Oxygen fell from 0 to −2: it was reduced. Four O atoms each gain 2 electrons: 4 × 2 = 8. ✓ Electrons lost = electrons gained.
- Hydrogen stays +1, so it is not oxidized or reduced.
- The reactant containing the oxidized atom is the reducing agent; the reactant containing the reduced atom is the oxidizing agent.
Redox, with 8 electrons transferred per CH₄. Reducing agent: CH₄(g). Oxidizing agent: O₂(g).
Name the whole species
When an atom inside a molecule or ion is oxidized or reduced, the agent is the whole reactant species: say "MnO₄⁻(aq) is the oxidizing agent", not "Mn".
| Species | Oxidation number of the key atom | Why |
|---|
| O₂, Cu, S₈ | 0 | uncombined element |
| Fe³⁺ | +3 | monatomic ion = its charge |
| H in NaH | −1 | metal hydride |
| O in H₂O₂ | −1 | peroxide |
| Cl in ClO⁻ | +1 | x + (−2) = −1 |
| Mn in MnO₄⁻ | +7 | x + 4(−2) = −1 |
| N in NH₄⁺ | −3 | x + 4(+1) = +1 |
Just for funCarbon's résumé: −4 in methane, 0 in glucose and in diamond, +4 in carbon dioxide. Not many atoms can say they've held nine different oxidation numbers and still kept the same job title.
Hands-on activityOxidation numbers from your kitchen and bathroom
You need: a pencil, paper and the labels of products already in your home. Read labels only: do not open cleaning products, and never mix them.
- Find at least six products whose labels name a chemical compound. Possibilities: baking soda (sodium hydrogen carbonate, NaHCO₃), iodized salt (contains potassium iodide, KI), hydrogen peroxide (H₂O₂), fluoride toothpaste (often sodium fluoride, NaF, or stannous fluoride, SnF₂), bleach (sodium hypochlorite, NaClO), an iron supplement (for example ferrous sulfate, FeSO₄), and vitamin C (ascorbic acid).
- For each, write the formula and assign the oxidation number of every atom, using the rules in order.
- Circle any atom with an unusual oxidation number (hint: H₂O₂ and NaClO both have one).
- Bleach works by oxidizing stains. Which atom in NaClO is reduced when bleach acts, and to what? (It is chlorine, going from +1 to −1 as chloride forms.)
Model answers: NaHCO₃: Na +1, H +1, C +4, O −2. KI: K +1, I −1. H₂O₂: H +1, O −1. NaF: Na +1, F −1. SnF₂: Sn +2, F −1. NaClO: Na +1, Cl +1, O −2. FeSO₄: Fe +2, S +6, O −2.
Your turn
1Find the oxidation number of nitrogen in HNO₃.
1 + x + 3(−2) = 0, so N = +5.
2Find the oxidation number of manganese in KMnO₄.
1 + x + 4(−2) = 0, so Mn = +7.
3Find the oxidation number of phosphorus in PO₄³⁻.
x + 4(−2) = −3, so P = +5.
4Find the oxidation number of hydrogen in CaH₂.
Calcium is +2 (group 2), so 2 + 2x = 0 and H = −1 (a metal hydride).
5Find the oxidation number of carbon in glucose, C₆H₁₂O₆.
6x + 12(+1) + 6(−2) = 0, so 6x = 0 and C = 0 (average).
6In 2Fe₂O₃(s) + 3C(s) → 4Fe(s) + 3CO₂(g), what is oxidized, what is reduced, and what are the agents?
Fe goes from +3 to 0: reduced. C goes from 0 to +4: oxidized. Oxidizing agent: Fe₂O₃; reducing agent: C. (This is the chemistry of a blast furnace, which you met in SCH3U.)
7How many electrons are transferred in the equation in the previous question?
4 Fe atoms each gain 3: 12 electrons. Check: 3 C atoms each lose 4 = 12. ✓
More practice: warm-up
1What is the oxidation number of oxygen in O₂?
2What is the oxidation number of Na⁺?
3What is the oxidation number of chlorine in NaCl?
4What is the oxidation number of oxygen in CO₂?
5What is the oxidation number of carbon in CO₂?
More practice: on your own
1Find the oxidation number of chlorine in the perchlorate ion, ClO₄⁻.
x + 4(−2) = −1, so Cl = +7. (Chlorine is positive because it is bonded to the more electronegative oxygen.)
2Find the oxidation number of sulfur in the thiosulfate ion, S₂O₃²⁻.
2x + 3(−2) = −2, so 2x = 4 and S = +2 (average).
3Find the oxidation number of nitrogen in NH₄⁺ and in N₂O.
NH₄⁺: x + 4 = +1, N = −3. N₂O: 2x − 2 = 0, N = +1.
4Is NaOH(aq) + HCl(aq) → NaCl(aq) + H₂O(l) a redox reaction? Show your reasoning.
Na +1 → +1, O −2 → −2, H +1 → +1, Cl −1 → −1. No oxidation number changes, so it is not redox. It is a neutralization.
5In Cu(s) + 4HNO₃(aq) → Cu(NO₃)₂(aq) + 2NO₂(g) + 2H₂O(l), identify the element oxidized and the element reduced. Why does only part of the nitric acid act as the oxidizing agent?
Cu goes 0 → +2: oxidized. N goes +5 → +4 in NO₂: reduced. Only 2 of the 4 N atoms change; the other 2 stay +5 in the nitrate ions of Cu(NO₃)₂. So half of the HNO₃ is the oxidizing agent and half just supplies spectator nitrate ions.
Challenge
1Oxygen difluoride, OF₂, and potassium superoxide, KO₂, are unusual oxygen compounds. Find the oxidation number of oxygen in each and explain which rule decides it.
OF₂: fluorine is always −1 (rule 3 comes before rule 5), so x + 2(−1) = 0 and O = +2. KO₂: potassium is +1 (rule 3), so 1 + 2x = 0 and O = −1/2 (an average; the O₂⁻ ion is called superoxide).
2In acetic acid, CH₃COOH, the average oxidation number of carbon is 0. Use electronegativity to find the oxidation number of each carbon separately. (Electronegativities: O 3.4, C 2.6, H 2.2.)
CH₃ carbon: it gets the electrons of its 3 C–H bonds (C is more electronegative than H) and shares the C–C bond equally: 4 − (6 + 1) = −3. COOH carbon: it loses its share of the 3 bonds to oxygen (one double, one single) and keeps half of the C–C pair: 4 − 1 = +3. Average: (−3 + 3)/2 = 0. ✓
3Ammonia is oxidized industrially to make nitric acid in steps: 4NH₃ + 5O₂ → 4NO + 6H₂O, then 2NO + O₂ → 2NO₂, then 3NO₂ + H₂O → 2HNO₃ + NO. Trace the oxidation number of nitrogen through the steps, and explain what is unusual about the last step.
N: −3 (NH₃) → +2 (NO) → +4 (NO₂) → +5 (HNO₃) and +2 (NO). In the last step, nitrogen in NO₂ is both oxidized (+4 → +5) and reduced (+4 → +2) at the same time: a disproportionation. Electron check: 2 N each lose 1 e⁻ = 2; 1 N gains 2 e⁻ = 2. ✓
Quiz
1. What is the oxidation number of sulfur in SO₄²⁻?
2. In which compound does hydrogen have an oxidation number of −1?
3. What is the oxidation number of oxygen in H₂O₂?
4. An atom's oxidation number changes from −2 to 0 during a reaction. The atom was:
5. In C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(g), which substance is the reducing agent?
6. Which reaction is a redox reaction?
Big idea (F3.1, F2.3): an oxidation number is an electron-bookkeeping charge. If it goes up, the atom was oxidized; if it goes down, the atom was reduced. This works even for reactions between molecules, such as burning fuels.
How to help: Quiz your teen with formulas from household labels (the activity) and ask for the oxidation number of one atom. Ask them to say the rule they used. Speed comes from practice: aim for 10 quick ones a day for a few days.
Common difficulties:
- Setting the sum to 0 for a polyatomic ion. For ions, the sum equals the ion's charge.
- Forgetting the subscripts: in Cr₂O₇²⁻ there are 2 chromium atoms and 7 oxygen atoms.
- Writing "2+" for an oxidation number. Oxidation numbers are written +2.
- Being surprised by fractions. A fractional answer is an average and is fine.
- Naming an atom ("Mn") instead of the reactant species ("MnO₄⁻") as the agent.
Safety: in the activity, read labels only. Never open or mix cleaning products.