CDS Chemistry · Chemical Bonding

Valency and Oxidation Numbers

The rules for working out an oxidation number, why hydrogen and nitrogen take several, and which elements show more than one valency.

All Chemical Bonding notes

Why this matters

Four CDS questions, the largest page in the chapter. Two ask which element or oxide has several or the highest oxidation states; two ask for valencies that change (phosphorus 3 and 5, iron 2 and 3).

Concept 1 of 2: Working out oxidation numbers

An oxidation number is the charge an atom would carry if every bond were fully ionic. A few fixed values (oxygen −2, hydrogen +1) let you find any unknown, because the numbers in a neutral molecule must add up to zero.

Definition

The rules:

A free element is 0 (O₂, Na, H₂).
Oxygen is usually −2 (−1 in peroxides).
Hydrogen is +1 with non-metals (H₂O, HCl) but −1 in metal hydrides (NaH). So hydrogen has more than one oxidation number.
The numbers in a neutral compound add up to 0; in an ion, to its charge.
Nitrogen in its oxides: N₂O +1, NO +2, N₂O₃ +3, NO₂ +4, N₂O₅ +5 (its highest).

Sum rule

\sum (\text{oxidation numbers}) = \text{charge on the species}

Worked example

Find the oxidation number of sulphur in H₂SO₄.

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

CDS · 2018 · CDS (II) 2018 — General Knowledge · Q25Moderate

Example 1 · Chemical Bonding · Valency, Oxidation States and Molecular Formula

Which one of the following nitrogen oxides has the highest oxidation state of nitrogen?

Hydrogen is not always +1

Hydrogen is +1 with non-metals, −1 in metal hydrides such as NaH, and 0 in H₂. 'Hydrogen can have more than one oxidation number' is the true statement.

N₂O₅ is +5, the highest for nitrogen

Work each oxide out with oxygen at −2: N₂O is +1, NO +2, NO₂ +4, N₂O₅ +5. Do not judge by the number of oxygen atoms alone.

Peroxide oxygen is −1

In hydrogen peroxide, H₂O₂, each oxygen is −1, not −2, because the two oxygens are bonded to each other.

Drill 1 more on working out oxidation numbers

Concept 2 of 2: Elements with more than one valency

Some elements can use different numbers of electrons to bond. Phosphorus can share three or all five of its outer electrons. Transition metals such as iron can lose two or three, because their outer s and inner d electrons are close in energy.

Definition

The facts:

Phosphorus: valency 3 and 5 (PCl₃ and PCl₅). It can expand its octet using d orbitals.
Sulphur: 2, 4 and 6 (H₂S, SO₂, SO₃).
Transition metals show variable oxidation states: iron +2 and +3, copper +1 and +2.
Alkali and alkaline earth metals have one state: Na and Li +1, Ca and Mg +2.

Element	Valencies or oxidation states	Examples
Phosphorus	3 and 5	PCl₃, PCl₅Q
Sulphur	2, 4, 6	H₂S, SO₂, SO₃
Iron	+2 and +3	FeSO₄, FeCl₃
Copper	+1 and +2	Cu₂O, CuO
Sodium, lithium	+1 only	NaCl, LiCl
Calcium	+2 only	CaCl₂

Practice this concept2 quick reps

The same idea in a real exam question:

CDS · 2025 · CDS (II) 2025 — General Knowledge · Q38Easy

Example 2 · Chemical Bonding · Valency, Oxidation States and Molecular Formula

Variable oxidation numbers are possible for :

Only the transition metal varies

Among sodium, calcium, lithium and iron, only iron (a transition metal) shows variable oxidation states. The others have one each.

Phosphorus is 3 and 5, not 3 and 4

Phosphorus shares three electrons (PCl₃) or all five (PCl₅). Pairs such as 2, 3 or 4, 5 are distractors.

Drill 1 more on elements with more than one valency

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Working out oxidation numbers
Sum rule
$\sum (\text{oxidation numbers}) = \text{charge on the species}$

Reference tables (1)

Elements with more than one valency6 rows

Element	Valencies or oxidation states	Examples
Phosphorus	3 and 5	PCl₃, PCl₅Q
Sulphur	2, 4, 6	H₂S, SO₂, SO₃
Iron	+2 and +3	FeSO₄, FeCl₃
Copper	+1 and +2	Cu₂O, CuO
Sodium, lithium	+1 only	NaCl, LiCl
Calcium	+2 only	CaCl₂

Watch out for (5)

Hydrogen is not always +1
→ Working out oxidation numbers
N₂O₅ is +5, the highest for nitrogen
→ Working out oxidation numbers
Peroxide oxygen is −1
→ Working out oxidation numbers
Only the transition metal varies
→ Elements with more than one valency
Phosphorus is 3 and 5, not 3 and 4
→ Elements with more than one valency

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