UNIT 2 CHEMISTRY · PEARSON AAQ · C1.2.2
Formulas from Oxidation Numbers
FREE CHEMISTRY REVISION · TOPIC 20
Balance the contributions, then check what the formula represents.
Derive common Period 3 oxide, hydroxide, acid and chloride formulas while keeping ion charges, group brackets and molecular identities clear.
Pearson BTEC Level 3 AAQ Applied Science
Unit 2: Principles and Applications of Chemistry · C1.2.2
What you will learn
Use oxidation numbers to derive formulas of common Period 3 oxides, hydroxides/acids and chlorides. Balance positive and negative contributions, retain polyatomic groups correctly, and distinguish the simplest atom ratio from a molecular formula that requires structural information.
1. Scope: use the common compounds Pearson names
Pearson C1.2.2 requires formulas of common Period 3 oxides, hydroxides/acids and chlorides. The surrounding content identifies Na₂O, MgO, Al₂O₃, P₄O₁₀ and SO₂ as the specified oxygen-reaction products; NaOH, Mg(OH)₂ and Al(OH)₃ as the hydroxides; and NaCl, MgCl₂, Al₂Cl₆, SiCl₄ and PCl₅ as the chloride examples. The acid–base scope also names SiO₂, H₃PO₄, H₂SO₄, HCl, HClO and HClO₄. These are the main examples here.
An element can have more than one oxidation state. A formula cannot always be obtained from the element names alone: sulfur(IV) oxide and sulfur(VI) compounds have different compositions. Use the given name, oxidation number or chemical context. Do not invent common oxides or chlorides for argon simply to fill every position in Period 3.
2. The general balancing method
For a neutral compound, the total oxidation-number contribution must be zero. If A has +a and B has −b, choose positive whole-number atom counts m and n such that m(+a) + n(−b) = 0. Find the lowest common multiple of a and b, then use the smallest whole-number ratio unless a particular molecular formula is required.
1. Write the element symbols in the conventional order.
2. Assign the relevant oxidation numbers or ion charges.
3. Find equal positive and negative totals.
4. Convert the counts to subscripts, omitting subscript 1.
5. Simplify a ratio where appropriate, and check the full sum.
6. For covalent substances, use known molecular information when an empirical ratio is not the complete requested formula.
The “cross-over” shortcut transfers magnitudes as provisional subscripts, but it must be followed by simplification and checking. Mg(+2) and O(−2) give Mg₂O₂ provisionally, then MgO as the simplest oxide ratio. Sodium peroxide Na₂O₂ is a different compound with O at −1; do not confuse it with an unsimplified oxide.
3. Oxides: use O at −2 in these examples
| Central element value | Balance | Formula required |
|---|---|---|
| Na +1 | 2(+1) + (−2) = 0 | Na₂O |
| Mg +2 | (+2) + (−2) = 0 | MgO |
| Al +3 | 2(+3) + 3(−2) = 0 | Al₂O₃ |
| Si +4 | (+4) + 2(−2) = 0 | SiO₂ |
| P +5 | 2(+5) + 5(−2) = 0; ratio 2:5 | P₄O₁₀ is the specified molecular formula |
| S +4 | (+4) + 2(−2) = 0 | SO₂ |
For ionic oxides such as Na₂O and MgO, the formula gives the ratio of ions in the extended solid. In covalent SiO₂ the formula gives an extended network composition, not an isolated Si⁴⁺ ion joined to two separate oxide ions. Oxidation-number balance works for both, but does not prove ionic bonding.
4. Hydroxides: balance the whole OH⁻ group
A hydroxide group has total charge −1 because O is −2 and H is +1. Na⁺ needs one OH⁻: NaOH. Mg²⁺ needs two: Mg(OH)₂. Al³⁺ needs three: Al(OH)₃. Use parentheses only when a whole group is repeated. Never change OH⁻ to a different atom ratio to force a balance.
Check the expanded counts. Al(OH)₃ contains 1 Al, 3 O and 3 H. Its sum is (+3) + 3(−2) + 3(+1) = 0. Writing AlOH₃ instead would give only one O and a different, unbalanced composition for aluminium hydroxide.
5. Acids: combine the known oxyanion or acid family with balance
| Known acid group / ion | Hydrogen balance | Acid formula |
|---|---|---|
| Phosphate PO₄³⁻ | 3(+1) + (−3) = 0 | H₃PO₄ |
| Sulfate SO₄²⁻ | 2(+1) + (−2) = 0 | H₂SO₄ |
| Chloride Cl⁻ | (+1) + (−1) = 0 | HCl |
| Hypochlorite ClO⁻ | (+1) + (−1) = 0 | HClO |
| Perchlorate ClO₄⁻ | (+1) + (−1) = 0 | HClO₄ |
Use H at +1 and O at −2 to check the central values: P +5 in H₃PO₄; S +6 in H₂SO₄; Cl −1, +1 and +7 in HCl, HClO and HClO₄ respectively. More oxygen atoms can require a more positive central oxidation number, but the ion charge of ClO⁻ and ClO₄⁻ remains −1.
Oxidation numbers alone do not uniquely identify every acid formula. If both H and O counts are unknown, a single neutrality equation can have multiple solutions. Use the known oxyanion, the named acid family or additional formula information. For example, P +5 by itself does not establish H₃PO₄ without the phosphate/orthophosphoric-acid context. The ionic balancing method counts composition; it does not claim an undissociated acid molecule contains free H⁺ ions.
6. Chlorides and the empirical–molecular distinction
| Element value | Balance | Formula / structural qualification |
|---|---|---|
| Na +1 | (+1) + (−1) = 0 | NaCl |
| Mg +2 | (+2) + 2(−1) = 0 | MgCl₂ |
| Al +3 | (+3) + 3(−1) = 0 | Empirical AlCl₃; specified molecular Al₂Cl₆ |
| Si +4 | (+4) + 4(−1) = 0 | SiCl₄ |
| P +5 | (+5) + 5(−1) = 0 | PCl₅ |
Al₂Cl₆ contains two Al atoms and six Cl atoms: 2(+3) + 6(−1) = 0. Its simplest ratio is still 1:3. Aluminium chloride can form a covalent dimer under suitable conditions; the balance alone gives AlCl₃ composition, not the dimer size. State Al₂Cl₆ when answering for Pearson’s specified molecular chloride example.
P₄O₁₀ presents the same general lesson: P₂O₅ is its empirical formula, whereas P₄O₁₀ is the molecular formula named in the specified reaction. Do not automatically reduce a requested molecular formula. Conversely, multiplying an ionic formula by an arbitrary factor does not give a new preferred formula unit.
Worked examples
Example 1 · Sodium oxide: an unequal charge pair
Na is +1 and O −2. Two sodium contributions give +2, balancing one oxygen at −2. Ratio 2:1 → Na₂O. Check 2(+1) − 2 = 0. NaO would sum to −1 and is not the required sodium oxide formula.
Example 2 · Magnesium oxide: simplify correctly
Mg is +2 and O −2. One of each already balances: (+2) + (−2) = 0 → MgO. A mechanical cross-over gives 2:2, which reduces to 1:1 for this oxide. Do not identify that provisional Mg₂O₂ with a peroxide.
Example 3 · Aluminium oxide: use a common multiple
The lowest common multiple of 3 and 2 is 6. Two Al contributions of +3 balance three O contributions of −2. Formula Al₂O₃; check +6 − 6 = 0. The signs are used for balancing and are not written as subscript minus signs.
Example 4 · Magnesium and aluminium hydroxides
OH⁻ has charge −1. Mg²⁺ needs two OH⁻ → Mg(OH)₂. Al³⁺ needs three → Al(OH)₃. Parentheses multiply both O and H. Check the complete group charge rather than treating O and H as unrelated formula pieces.
Example 5 · Sulfuric acid from sulfate
Start with sulfate, SO₄²⁻. Two H(+1) contributions balance −2 → H₂SO₄. Confirm the central value: 2(+1) + x + 4(−2) = 0 gives S +6. HSO₄⁻ is a different, negatively charged species rather than the neutral acid formula.
Example 6 · Phosphoric acid from phosphate
PO₄³⁻ needs three H(+1) contributions. Formula H₃PO₄. Check 3(+1) + (+5) + 4(−2) = 0. The known phosphate group is essential context; one oxidation number alone does not determine every H/O count.
Example 7 · Two chlorine oxyacids
For hypochlorite ClO⁻, add one H(+1): HClO, with Cl +1. For perchlorate ClO₄⁻, also add one H(+1): HClO₄, with Cl +7. Both oxyanions are singly charged even though their oxygen counts and chlorine values differ.
Example 8 · From chloride ratio to the required molecule
Al +3 and Cl −1 give empirical AlCl₃. Pearson’s specified dimer is Al₂Cl₆: 2(+3) + 6(−1) = 0. For phosphorus(V), one P(+5) requires five Cl(−1) → PCl₅. The dimer distinction is structural knowledge, not a different oxidation state.
Example 9 · Phosphorus(V) oxide: retain the molecular formula
Balancing +5 against −2 gives a 2:5 ratio, P₂O₅. The specified molecular substance is P₄O₁₀, containing twice that empirical unit. Check 4(+5) + 10(−2) = 0. Reducing it answers an empirical-formula question, not a request for the named molecular formula.
Common misconceptions and exam tips
“Cross-over always gives the final molecular formula.” It gives a provisional ratio; simplify formula units and use molecular information where needed.
“Subscripts may be negative.” Counts are positive whole numbers; signs belong to charges or oxidation numbers.
“OH₂ means two hydroxide groups.” Use (OH)₂ so both atoms are multiplied.
“Al₂Cl₆ means Al has oxidation number +6.” Each Al remains +3; +6 is their combined contribution.
“Oxidation numbers prove the compound is ionic.” Covalent compounds also use this formal accounting.
“P₂O₅ and P₄O₁₀ are interchangeable in every question.” Distinguish empirical and molecular requests.
Write the assigned values, show equal totals, then check the final formula. Do not change subscripts while balancing a reaction equation: formula derivation establishes composition first; reaction coefficients are a later task. Use the precise oxide, acid or chloride named in the question.
Your revision summary
Choose atom or group counts that make the oxidation-number sum zero. Balance oxide O at −2, chloride Cl at −1 and whole hydroxide groups at −1 in these examples. Use known oxyanion identities to derive acid formulas. Oxidation-number balance gives composition, while structures determine when the specified molecular formulas P₄O₁₀ and Al₂Cl₆ must be retained.
Check your understanding
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