IMAT Chemistry · Inorganic Compounds and Nomenclature

Oxidation Numbers, Common Ions and Writing Formulas

Every atom in a compound gets an oxidation number by fixed rules; they always add up to the overall charge, which lets you check or build any formula.

All Inorganic Compounds and Nomenclature notes

Why this matters

The older papers asked which formula of a compound is wrong (2012), which formula fits a given set of oxidation numbers (2015), and what the formula Br₂ represents (2020). All three are charge-balance checks.

Concept 1 of 3: Rules for assigning oxidation numbers

An oxidation number is the charge an atom would carry if every bond in the compound were fully ionic, with the shared electrons given to the more electronegative atom. It is bookkeeping, not a real charge. Because charge is never lost, the numbers in a neutral compound must add up to zero.

Definition

Apply the rules in this order of priority:

An atom in an element is 0: Na, $\mathrm{O_2}$ , $\mathrm{Br_2}$ , $\mathrm{S_8}$ .
A monatomic ion has its charge: $\mathrm{Fe^{3+}}$ is $+3$ , $\mathrm{Cl^-}$ is $-1$ .
F is always $-1$ . Group 1 metals are $+1$ , Group 2 $+2$ , Al $+3$ .
H is $+1$ with non-metals, but $-1$ in metal hydrides (NaH, $\mathrm{CaH_2}$ ).
O is $-2$ , except in peroxides ( $\mathrm{H_2O_2}$ , $\mathrm{Na_2O_2}$ ) where it is $-1$ , and in $\mathrm{OF_2}$ where it is $+2$ .
The sum is 0 for a neutral compound and equals the charge for an ion. Solve for the one unknown.

Sum of oxidation numbers

\sum (\text{number of atoms} \times \text{oxidation number}) = \text{overall charge}

overall charge0 for a compound, the ion's charge for an ion

Worked example

Find the oxidation number of chromium in potassium dichromate,

\mathrm{K_2Cr_2O_7}

, and of sulfur in the thiosulfate ion,

\mathrm{S_2O_3^{2-}}

Practice this conceptself-check · 4 quick reps

An element in its free state is always zero

\mathrm{Br_2}

\mathrm{O_2}

\mathrm{P_4}

, each atom is 0, however many atoms the molecule has.

\mathrm{Br_2}

is one molecule of the element bromine: not a compound, not two separate atoms, and not ions.

Hydrogen is negative in metal hydrides

In NaH and

\mathrm{CaH_2}

hydrogen is bonded to a less electronegative metal, so it is

-1

(the hydride ion,

\mathrm{H^-}

). Using

+1

there makes the metal's oxidation number come out impossible.

Concept 2 of 3: Common ions and their charges

You cannot write a formula without knowing the charges of its ions. Simple ion charges follow from the group number, but the polyatomic ions have to be learned. There are about fifteen that turn up again and again, and their charges are worth memorising like a times table.

Definition

Simple ions: Group 1 $+1$ , Group 2 $+2$ , $\mathrm{Al^{3+}}$ ; $\mathrm{N^{3-}}$ (nitride), $\mathrm{O^{2-}}$ (oxide), $\mathrm{S^{2-}}$ (sulfide), $\mathrm{F^-}$ , $\mathrm{Cl^-}$ , $\mathrm{Br^-}$ , $\mathrm{I^-}$ (halides).
Common transition metal ions: $\mathrm{Fe^{2+}}$ and $\mathrm{Fe^{3+}}$ , $\mathrm{Cu^+}$ and $\mathrm{Cu^{2+}}$ , $\mathrm{Zn^{2+}}$ , $\mathrm{Ag^+}$ .
A polyatomic ion is a group of covalently bonded atoms carrying an overall charge; it stays together through reactions and in formulas.
Adding $\mathrm{H^+}$ to an anion raises its charge by one: $\mathrm{CO_3^{2-}}$ becomes $\mathrm{HCO_3^-}$ , $\mathrm{PO_4^{3-}}$ becomes $\mathrm{HPO_4^{2-}}$ then $\mathrm{H_2PO_4^-}$ .

Name	Formula	Charge
Ammonium	$\mathrm{NH_4^+}$	1+
Hydroxide	$\mathrm{OH^-}$	1−
Nitrate / nitrite	$\mathrm{NO_3^-}$ / $\mathrm{NO_2^-}$	1−
Hydrogen carbonate	$\mathrm{HCO_3^-}$	1−
Hydrogen sulfate	$\mathrm{HSO_4^-}$	1−
Ethanoate (acetate)	$\mathrm{CH_3COO^-}$	1−
Permanganate	$\mathrm{MnO_4^-}$	1−
Cyanide	$\mathrm{CN^-}$	1−
Carbonate	$\mathrm{CO_3^{2-}}$	2−
Sulfate / sulfite	$\mathrm{SO_4^{2-}}$ / $\mathrm{SO_3^{2-}}$	2−
Chromate / dichromate	$\mathrm{CrO_4^{2-}}$ / $\mathrm{Cr_2O_7^{2-}}$	2−
Phosphate	$\mathrm{PO_4^{3-}}$	3−

Practice this conceptself-check · 3 quick reps

Carbonate is 2−, hydrogen carbonate is 1−

Each added H takes away one negative charge. So a Group 1 metal forms

\mathrm{M_2CO_3}

but

\mathrm{MHCO_3}

; a formula like

\mathrm{NaCO_3}

leaves the carbonate charge unbalanced.

Concept 3 of 3: Writing a correct formula by balancing charges

A compound has no overall charge, so the positive charges must cancel the negative ones exactly. Find the lowest common multiple of the two charges and take enough of each ion to reach it. Keep polyatomic ions whole, in brackets when you need more than one.

Definition

To write the formula of an ionic compound:

Write the cation first, then the anion, each with its charge.
Choose the smallest numbers that make the total charge zero (cross over the charge numbers, then simplify).
Put a polyatomic ion in brackets when there is more than one of it: $\mathrm{Ca(OH)_2}$ , never $\mathrm{CaOH_2}$ .
Check: the oxidation numbers of all the atoms must add to zero.

Charge balance

a \times (\text{cation charge}) + b \times (\text{anion charge}) = 0

$a, b$ smallest whole numbers of cations and anions in the formula

Worked example

Write the formulas of aluminium sulfate and ammonium phosphate.

Practice this conceptself-check · 4 quick reps

Brackets matter: Ca(OH)₂ is not CaOH₂

Without brackets the 2 applies only to the H. Whenever a formula needs more than one polyatomic ion, the whole ion goes in brackets with the number outside:

\mathrm{Ca(OH)_2}

\mathrm{(NH_4)_2SO_4}

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 (2)

Rules for assigning oxidation numbers
Sum of oxidation numbers
$\sum (\text{number of atoms} \times \text{oxidation number}) = \text{overall charge}$
Writing a correct formula by balancing charges
Charge balance
$a \times (\text{cation charge}) + b \times (\text{anion charge}) = 0$

Reference tables (1)

Common ions and their charges12 rows

Name	Formula	Charge
Ammonium	$\mathrm{NH_4^+}$	1+
Hydroxide	$\mathrm{OH^-}$	1−
Nitrate / nitrite	$\mathrm{NO_3^-}$ / $\mathrm{NO_2^-}$	1−
Hydrogen carbonate	$\mathrm{HCO_3^-}$	1−
Hydrogen sulfate	$\mathrm{HSO_4^-}$	1−
Ethanoate (acetate)	$\mathrm{CH_3COO^-}$	1−
Permanganate	$\mathrm{MnO_4^-}$	1−
Cyanide	$\mathrm{CN^-}$	1−
Carbonate	$\mathrm{CO_3^{2-}}$	2−
Sulfate / sulfite	$\mathrm{SO_4^{2-}}$ / $\mathrm{SO_3^{2-}}$	2−
Chromate / dichromate	$\mathrm{CrO_4^{2-}}$ / $\mathrm{Cr_2O_7^{2-}}$	2−
Phosphate	$\mathrm{PO_4^{3-}}$	3−

Watch out for (4)

An element in its free state is always zero
→ Rules for assigning oxidation numbers
Hydrogen is negative in metal hydrides
→ Rules for assigning oxidation numbers
Carbonate is 2−, hydrogen carbonate is 1−
→ Common ions and their charges
Brackets matter: Ca(OH)₂ is not CaOH₂
→ Writing a correct formula by balancing charges

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