Writing Formulae with Polyatomic Ions

Introduction

Many everyday compounds contain groups of atoms that behave as a single unit: sulfate in plaster of Paris, nitrate in fertilisers, carbonate in limestone and hydroxide in drain cleaners. These polyatomic ions combine with other ions just as single-atom ions do. The crossing-valency method you have already met still works, but there is one new rule to learn — when more than one polyatomic ion is needed, the whole group goes inside brackets . This page shows how and why.

Core explanation

Treat the ion as one block. A polyatomic ion such as nitrate, NO₃⁻, is a fixed group: one nitrogen atom and three oxygen atoms carrying an overall charge of 1−. When writing a formula you never break it apart or change its internal subscripts. You simply decide how many of these blocks are needed.

Common polyatomic ions and their valencies:

Ion Formula Valency --- --- --- Ammonium NH₄⁺ 1 Hydroxide OH⁻ 1 Nitrate NO₃⁻ 1 Hydrogencarbonate HCO₃⁻ 1 Sulfate SO₄²⁻ 2 Carbonate CO₃²⁻ 2 Phosphate PO₄³⁻ 3

Balancing charges. A compound has no overall charge, so the total positive charge must equal the total negative charge. Calcium ions are Ca²⁺ and nitrate ions are NO₃⁻. One calcium ion (+2) needs two nitrate ions (−1 each) to balance. The formula is therefore Ca(NO₃)₂.

Why the brackets? Without brackets, CaNO₃₂ would be meaningless, and CaNO₆ would suggest one nitrogen and six oxygens — a different substance altogether. The brackets say "everything inside is one unit", and the subscript 2 outside multiplies every atom within: two nitrogen atoms and six oxygen atoms.

When brackets are NOT needed. If only one polyatomic ion is present, no brackets are written. Sodium nitrate is NaNO₃, not Na(NO₃). Calcium carbonate is CaCO₃, and ammonium chloride is NH₄Cl. Brackets appear only when a subscript greater than 1 must apply to the whole group.

Positive polyatomic ions too. The ammonium ion NH₄⁺ is positive. Ammonium sulfate needs two NH₄⁺ ions to balance one SO₄²⁻ ion, giving (NH₄)₂SO₄. Here the brackets go around the positive ion.

Both ions may need brackets. Calcium phosphate combines Ca²⁺ with PO₄³⁻. Crossing valencies gives three calcium ions and two phosphate ions: Ca₃(PO₄)₂. The calcium is a single atom, so it takes a plain subscript; the phosphate is a group, so it needs brackets.

Step-by-step reasoning

To write the formula of aluminium sulfate:

1. Write the ions: Al³⁺ and SO₄²⁻. 2. Cross the valencies: aluminium takes 2, sulfate takes 3. 3. Sulfate is polyatomic and needs a subscript of 3, so bracket it: (SO₄)₃. 4. Write the formula: Al₂(SO₄)₃. 5. Check charges: 2 × (+3) = +6 and 3 × (−2) = −6. Balanced.

Visual explanation

Imagine each polyatomic ion as a small sealed bag of beads. Ca(NO₃)₂ is one large bead (calcium) beside two identical sealed bags, each holding one nitrogen bead and three oxygen beads. The brackets are the bag; the subscript outside counts the bags.

Real-world analogy

Ordering meals at a café works the same way. "Two breakfast sets" means two of everything in the set — two eggs, two toasts, two coffees. You would not change the contents of a set; you simply order more sets. Brackets in a formula mark the "set", and the number outside tells you how many.

Real-world example

Gardeners use ammonium sulfate, (NH₄)₂SO₄, and ammonium nitrate, NH₄NO₃, as nitrogen fertilisers. The bag label shows the formula, and the brackets in (NH₄)₂SO₄ tell a chemist there are two nitrogen atoms in every formula unit, which matters when calculating how much nitrogen reaches the soil.

Why?

Why must the inside of a polyatomic ion never change? Because the atoms in the ion are held together by strong covalent bonds and form a particular, stable arrangement. SO₄²⁻ is sulfate; SO₃²⁻ is sulfite, a different ion with different properties. Changing a subscript inside the group changes the substance.

Common misconception

"To balance the charge, I can just change the number of oxygen atoms in the ion." This is wrong. Writing Ca(NO₃)₂ as CaN₂O₆ or as CaNO₆ loses the information that nitrate groups are present. Always balance by changing the number of ions , never the ion's own formula.

Worked example

Question: Write the formula of magnesium hydroxide and count the atoms in one formula unit.

Reasoning: The ions are Mg²⁺ and OH⁻. One Mg²⁺ (+2) needs two OH⁻ (−1 each). Hydroxide is polyatomic and needs a subscript of 2, so it is bracketed: Mg(OH)₂. The 2 multiplies both O and H.

Answer: Mg(OH)₂, containing 1 Mg, 2 O and 2 H — five atoms in total.

Quick check

1. Why is sodium sulfate written Na₂SO₄ and not Na₂(SO₄)? Answer: Only one sulfate ion is present, so no brackets are needed; brackets are used only when more than one polyatomic ion is required.

Exam focus

Examiners penalise missing brackets heavily: CaOH₂ instead of Ca(OH)₂ is marked wrong because it means one oxygen and two hydrogens. Learn the formulae and charges of the common polyatomic ions by heart, and always check that total charges add up to zero.

Advanced insight

Brackets also appear in formulae of more complex substances, such as complex ions in coordination chemistry, for example [Cu(H₂O)₆]²⁺, where square brackets enclose the whole complex. In crystal formulae, a dot shows water of crystallisation, as in CuSO₄·5H₂O. These conventions all serve one purpose: showing clearly which atoms belong together.

Summary

Polyatomic ions are fixed groups of atoms carrying a charge. Write formulae by balancing total positive and negative charges, changing only the number of each ion. When more than one polyatomic ion is needed, put it in brackets with the subscript outside; with only one, leave the brackets out. Never alter the subscripts inside the ion.

Practice questions

1. Write the formula of potassium carbonate. Answer: K₂CO₃ — two K⁺ ions balance one CO₃²⁻ ion, and no brackets are needed because there is only one carbonate. 2. Write the formula of iron(III) hydroxide. Answer: Fe(OH)₃ — one Fe³⁺ ion needs three OH⁻ ions, which must be bracketed. 3. Write the formula of ammonium phosphate. Answer: (NH₄)₃PO₄ — three NH₄⁺ ions balance one PO₄³⁻ ion. 4. How many oxygen atoms are in one formula unit of Al₂(SO₄)₃? Answer: Twelve, because the subscript 3 multiplies the four oxygen atoms in each sulfate group. 5. A student writes calcium hydroxide as CaOH₂. Explain the error. Answer: Without brackets the 2 applies only to hydrogen, suggesting one oxygen and two hydrogens; the correct formula is Ca(OH)₂.