Simplifying and Checking Formulae

Introduction

Crossing valencies is a quick way to write formulae, but it sometimes gives an answer that is not in its final form. Cross the valencies of calcium (2) and oxygen (2) and you get Ca₂O₂ — yet calcium oxide is written CaO. This page explains why ionic formulae are reduced to their simplest ratio , how to spot when simplifying is needed, and how to check any formula by making sure its charges balance.

Core explanation

Ionic formulae show ratios. An ionic compound such as calcium oxide is not made of separate small molecules. It is a giant lattice containing billions of Ca²⁺ and O²⁻ ions arranged in a regular pattern. There is no "Ca₂O₂ particle". The formula simply tells us the ratio of ions: one calcium ion for every oxide ion. Because a ratio of 2 : 2 is the same as 1 : 1, the formula is written CaO. The group of ions it describes is called a formula unit .

When to simplify. After crossing valencies, look at the two subscripts. If both can be divided by the same whole number, divide them. For example:

Crossed result Common factor Simplified formula --- --- --- Mg₂O₂ 2 MgO Ca₂(SO₄)₂ 2 CaSO₄ Sn₂O₄ (tin(IV) oxide) 2 SnO₂ Al₃N₃ 3 AlN

Notice that when simplifying a polyatomic ion, you change only the number of ions, never the atoms inside the ion. Ca₂(SO₄)₂ becomes CaSO₄, not CaSO₂.

Checking by charge balance. Every correct ionic formula must be electrically neutral. Multiply the charge of each ion by the number of ions and add. For Al₂O₃: aluminium gives 2 × (+3) = +6 and oxygen gives 3 × (−2) = −6. The total is zero, so the formula is balanced. If the total is not zero, the formula is wrong.

Checking the ratio is the lowest. A formula can be neutral but still not simplest. Mg₂O₂ has charges of +4 and −4, which balance, but the subscripts share a factor of 2. A complete check therefore asks two questions: do the charges cancel, and is there any common factor left?

Molecular formulae are different. For covalent molecules, the formula shows the actual number of atoms in one molecule. Hydrogen peroxide is H₂O₂, and each molecule really does contain two hydrogen and two oxygen atoms. Writing it as HO would describe the empirical formula, not the molecule. So only ionic formulae (and empirical formulae) are simplified in this way.

Step-by-step reasoning

To write and check the formula of lead(IV) oxide:

1. Ions: Pb⁴⁺ and O²⁻. 2. Cross valencies: Pb₂O₄. 3. Both subscripts share a factor of 2, so divide: PbO₂. 4. Check charges: 1 × (+4) + 2 × (−2) = 0. Neutral. 5. No common factor remains between 1 and 2, so PbO₂ is final.

Visual explanation

Picture a very long chequerboard of black and white squares. Whether you look at 2 squares, 20 squares or 2000, the ratio of black to white is always 1 : 1. The formula CaO describes that ratio, not the size of the board.

Real-world analogy

A recipe that uses 4 cups of flour to 2 cups of sugar is the same mixture as one using 2 cups of flour to 1 of sugar — just a larger batch. Cooks would describe the recipe as "two parts flour to one part sugar". Chemists do the same with ionic formulae, stating the simplest ratio.

Real-world example

Tin(IV) oxide, SnO₂, is used as a transparent conducting coating on some glass and in glazes for ceramics. Its formula is always written SnO₂, the simplest ratio, even though a single grain contains trillions of tin and oxide ions in the same 1 : 2 proportion.

Why?

Why is it acceptable to divide the subscripts? Because in an ionic lattice there is no fixed "molecule" size; only the proportion of ions is meaningful. Dividing both numbers by the same factor keeps the proportion unchanged, so the formula still describes exactly the same substance, just more neatly.

Common misconception

"If the charges balance, the formula must be correct." Mg₂O₂ balances but is not written correctly, because the ratio has not been simplified. Equally, simplifying a molecular formula such as C₂H₆ to CH₃ is wrong, because ethane molecules really contain two carbon and six hydrogen atoms.

Worked example

Question: A student writes the formula of barium sulfate as Ba₂(SO₄)₂. Check it and correct it if needed.

Reasoning: Charges: 2 × (+2) + 2 × (−2) = 0, so it is neutral. However, both subscripts share a factor of 2. Dividing gives one Ba²⁺ and one SO₄²⁻. With only one sulfate ion, no brackets are needed.

Answer: BaSO₄.

Quick check

1. Simplify the crossed formula Mg₂(CO₃)₂. Answer: MgCO₃, because the ratio 2 : 2 reduces to 1 : 1 and single ions need no brackets.

Exam focus

When asked to write an ionic formula, examiners expect the simplest ratio: CaO, not Ca₂O₂. Show a charge-balance check in longer answers — it earns credit and catches errors. Do not simplify molecular formulae such as H₂O₂, N₂O₄ or C₆H₁₂O₆.

Advanced insight

Some formulae that look unsimplified are in fact correct because they describe real molecules or ions. Dinitrogen tetroxide, N₂O₄, is a genuine molecule made from two NO₂ units joined together. The mercury(I) ion exists as a pair, Hg₂²⁺, so mercury(I) chloride is written Hg₂Cl₂ rather than HgCl. Chemistry, not arithmetic, decides the final formula.

Summary

Ionic formulae show the simplest whole-number ratio of ions in a lattice, so crossed subscripts with a common factor are divided down. Every correct ionic formula has total positive and negative charges that cancel. Check both neutrality and lowest ratio. Molecular formulae show real atom counts and are not simplified.

Practice questions

1. Simplify Ca₂S₂. Answer: CaS, since the ratio 2 : 2 reduces to 1 : 1. 2. Write the formula of tin(IV) chloride and check its charge balance. Answer: SnCl₄; 1 × (+4) + 4 × (−1) = 0, so it is neutral and already in simplest form. 3. Check the formula AlPO₄ for aluminium phosphate. Answer: Al³⁺ gives +3 and PO₄³⁻ gives −3, so it is balanced and in lowest ratio; it is correct. 4. Explain why hydrogen peroxide is written H₂O₂ and not HO. Answer: It is a molecular compound, and each molecule actually contains two hydrogen and two oxygen atoms, so the formula is not simplified. 5. A student writes sodium oxide as NaO. Use charge balance to correct it. Answer: Na⁺ gives +1 and O²⁻ gives −2, which do not cancel; two sodium ions are needed, so the formula is Na₂O.