Formulae and Equation Writing

Chemical equations can look like strings of symbols and numbers at first, but each part has a precise meaning. For example, 2H₂ + O₂ → 2H₂O tells us what substances react, what product forms and the ratio in which the particles react.

This makes formula and equation writing much more than a chapter to memorise. You will use these skills repeatedly in acids and bases, salts, electrolysis, energetics, reaction rates and mole calculations. The key is to separate the task into stages: first write the correct formulae, then determine the states, then balance the equation, and finally simplify it to an ionic equation if required.

1. Understanding Chemical Symbols and Formulae

Every element is represented by a chemical symbol. Some contain one letter, such as H for hydrogen and C for carbon. Others contain two letters, such as Na for sodium, Mg for magnesium and Cl for chlorine.

The capitalisation matters. The first letter is always uppercase, while any second letter is lowercase.

What does a chemical formula tell us?

A chemical formula tells us which elements are present and the relative numbers of their atoms or ions.

Subscripts belong to the formula

A small number written at the lower right of a chemical symbol is called a subscript. It tells us how many atoms of that element are represented.

In CO₂, the subscript 2 applies only to oxygen. Since no number follows C, there is one carbon atom.

2. Counting Atoms in Formulae

Before writing equations, you must be able to read formulae accurately. This becomes especially important when brackets appear.

Formulae without brackets

Consider Al₂O₃. The formula contains:

• 2 aluminium atoms or ions; and
• 3 oxygen atoms or oxide ions.

Formulae containing brackets

A subscript outside a bracket multiplies every atom inside the bracket.

For example, Ca(OH)₂ contains two complete OH groups. Therefore it contains:

• 1 calcium atom or ion;
• 2 oxygen atoms; and
• 2 hydrogen atoms.

Similarly, Al₂(SO₄)₃ contains three sulfate groups. Therefore it contains:

• 2 aluminium atoms or ions;
• 3 sulfur atoms; and
• 12 oxygen atoms.

3. Writing Formulae for Ionic Compounds

Ionic compounds contain positively charged ions and negatively charged ions. The compound as a whole is electrically neutral, so the total positive charge must exactly balance the total negative charge.

Example: magnesium chloride

Magnesium forms Mg²⁺ ions and chloride ions are Cl⁻.

One Mg²⁺ contributes +2. Two Cl⁻ ions contribute a total of −2.

Therefore:

Mg²⁺ : Cl⁻ = 1 : 2

The formula is MgCl₂.

Example: aluminium oxide

Aluminium ions are Al³⁺ and oxide ions are O²⁻. We need the smallest combination for which the total positive and negative charges are equal.

• 2 Al³⁺ ions give a total charge of +6.
• 3 O²⁻ ions give a total charge of −6.

Therefore the formula is Al₂O₃.

Common ions used at O-Level

When are brackets needed?

Polyatomic ions such as OH⁻, NO₃⁻, CO₃²⁻, SO₄²⁻ and NH₄⁺ behave as complete groups. If more than one of the group is required, place the group in brackets before adding the subscript.

For example, calcium ions are Ca²⁺ and nitrate ions are NO₃⁻. Two nitrate ions are required for each calcium ion:

Ca(NO₃)₂

The brackets show that the entire NO₃ group occurs twice.

Using the crossover method carefully

You may have learnt a shortcut in which the sizes of the charges are crossed over to become subscripts. The shortcut works only if you still understand the charge balance behind it.

Always check three things afterwards:

• the final compound has zero overall charge;
• the ratio has been simplified to the smallest whole numbers; and
• brackets have been used correctly for repeated polyatomic ions.

For example, Mg²⁺ and O²⁻ do not give Mg₂O₂ as the final formula. The 2:2 ratio simplifies to 1:1, so the formula is MgO.

4. Writing Chemical Equations

A chemical equation shows the reactants on the left and the products on the right.

reactants → products

A plus sign separates different substances on the same side of the equation.

For example:

magnesium + hydrochloric acid → magnesium chloride + hydrogen

becomes:

Mg + HCl → MgCl₂ + H₂

At this stage, the formulae are correct but the equation is not yet balanced.

Remember the diatomic elements

Several non-metallic elements exist naturally as molecules containing two atoms. When these elements appear by themselves in an equation, use their molecular formulae.

5. Using State Symbols

State symbols tell us the physical state of a substance under the conditions of the reaction.

How do you decide the correct state?

Use the wording of the question together with your chemical knowledge. In particular, consider:

• whether a substance is naturally solid, liquid or gaseous under the stated conditions;
• whether an ionic compound is dissolved in water;
• whether a precipitate is formed;
• whether a gaseous product is released; and
• whether water is present as a liquid product.

For example:

AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq)

Silver chloride is written AgCl(s) because it forms as an insoluble solid precipitate.

6. Balancing Chemical Equations

During a chemical reaction, atoms are rearranged. They are not created or destroyed. The equation must therefore contain the same number of atoms of every element before and after the reaction.

The most important balancing rule

Never change a subscript in a correct formula.

Instead, place coefficients in front of entire formulae.

A systematic method for balancing

1. Write the correct formula of every reactant and product.
2. Count the number of each type of atom on both sides.
3. Add coefficients to balance one element at a time.
4. Recount all atoms after every change.
5. Use the smallest possible whole-number coefficients.
6. Check the equation once more before moving on.

Worked example 1: hydrogen and oxygen

H₂ + O₂ → H₂O

There are two oxygen atoms on the left but only one on the right. Put 2 before H₂O:

H₂ + O₂ → 2H₂O

The right side now contains four hydrogen atoms, so put 2 before H₂:

2H₂ + O₂ → 2H₂O

Both sides now contain four hydrogen atoms and two oxygen atoms.

Worked example 2: aluminium and oxygen

Al + O₂ → Al₂O₃

Oxygen occurs in groups of 2 in O₂ and groups of 3 in Al₂O₃. The smallest number divisible by both 2 and 3 is 6.

Use 3O₂ and 2Al₂O₃:

Al + 3O₂ → 2Al₂O₃

There are now four aluminium atoms on the right, so put 4 before Al:

4Al + 3O₂ → 2Al₂O₃

Worked example 3: magnesium and hydrochloric acid

Mg + HCl → MgCl₂ + H₂

MgCl₂ contains two chlorine atoms, so place 2 before HCl:

Mg + 2HCl → MgCl₂ + H₂

The two hydrogen atoms from 2HCl now form one H₂ molecule. The equation is balanced.

7. What a Balanced Equation Tells Us

The coefficients in a balanced equation show the relative numbers of particles — and therefore the relative numbers of moles — involved in the reaction.

N₂ + 3H₂ → 2NH₃

This represents:

• 1 nitrogen molecule reacting with 3 hydrogen molecules to form 2 ammonia molecules; or
• 1 mol of N₂ reacting with 3 mol of H₂ to form 2 mol of NH₃.

Do not read the reacting ratio from the subscripts. The subscript 2 in N₂ describes the nitrogen molecule itself; it does not mean that two moles of nitrogen are reacting.

8. Writing Ionic Equations

A full chemical equation shows all the substances involved. However, in many reactions occurring in aqueous solution, some ions remain unchanged throughout the reaction.

These unchanged ions are called spectator ions.

An ionic equation removes the spectator ions so that we can see the particles responsible for the actual chemical change.

How to construct an ionic equation

1. Write the complete balanced chemical equation with state symbols.
2. Separate appropriate aqueous ionic substances into their ions.
3. Keep solids, liquids and gases together.
4. Identify ions that appear unchanged on both sides.
5. Cancel these spectator ions.
6. Write the remaining species as the ionic equation.
7. Check both atoms and total electrical charge.

Worked example: precipitation of silver chloride

Aqueous silver nitrate reacts with aqueous sodium chloride:

AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq)

Separate the soluble aqueous ionic substances:

Ag⁺(aq) + NO₃⁻(aq) + Na⁺(aq) + Cl⁻(aq) → AgCl(s) + Na⁺(aq) + NO₃⁻(aq)

Na⁺ and NO₃⁻ appear unchanged on both sides. They are spectator ions.

After cancelling them:

Ag⁺(aq) + Cl⁻(aq) → AgCl(s)

This equation shows the actual chemical change: dissolved silver ions and chloride ions combine to form insoluble silver chloride.

Check the electrical charge as well as the atoms

In:

Ag⁺(aq) + Cl⁻(aq) → AgCl(s)

the total charge on the left is +1 + (−1) = 0. AgCl is neutral, so the total charge on the right is also 0.

Important ionic equations

Common mistakes with formulae and equations

Formula and equation writing checklist

Formulae and equations become much easier when you stop trying to do everything at once. First identify the substances and write their formulae correctly. Then determine the state symbols and balance the atoms using coefficients. If an ionic equation is required, remove only the spectator ions and check the electrical charge as well as the atoms. Once this sequence becomes familiar, chemical equations begin to read like precise descriptions of what the particles are actually doing.