Formulae and equations

What you'll learn

How to write formulae for common compounds and ionic compounds.
How to assign oxidation numbers in compounds and ions.
How to balance chemical equations using conservation of atoms.
How to write equations with state symbols and simplify them into ionic equations.

Why formulae and equations matter

Chemistry has its own language. A formula tells you what particles are present, and an equation tells you what changes during a reaction.

A chemical equation is not just a sentence in symbols: it must obey conservation of mass, meaning atoms are not created or destroyed during a chemical reaction. You rearrange atoms into new combinations.

Here is the overall workflow for this topic.

Workflow for writing ionic formulae and constructing balanced and ionic equations

Chemical formulae: the basics

A chemical formula shows the elements present in a substance and the ratio of their atoms or ions.

For example, $H2O\text{H}_2\text{O}$ means each water molecule contains two hydrogen atoms and one oxygen atom. $MgCl2\text{MgCl}_2$ means magnesium chloride contains magnesium ions and chloride ions in a 1:2 ratio.

A subscript is the small number written low and to the right of a symbol, such as the 2 in $CO2\text{CO}_2$ . It belongs to the formula and must not be changed when balancing equations.

Definition

Ion

An ion is a particle with an electrical charge. A cation is a positive ion, such as $Na+\text{Na}^+$ . An anion is a negative ion, such as $Cl−\text{Cl}^-$ .

Common ions you need to recognise

You are not expected to work everything out from scratch every time. Some ions are part of the basic language of chemistry.

Common positive ions

Group 1 metal ions: $Li+\text{Li}^+$ , $Na+\text{Na}^+$ , $K+\text{K}^+$
Hydrogen ion: $H+\text{H}^+$
Ammonium ion: $NH4+\text{NH}_4^+$
Group 2 metal ions: $Mg2+\text{Mg}^{2+}$ , $Ca2+\text{Ca}^{2+}$ , $Ba2+\text{Ba}^{2+}$
Zinc ion: $Zn2+\text{Zn}^{2+}$
Copper(II) ion: $Cu2+\text{Cu}^{2+}$
Iron(II) ion: $Fe2+\text{Fe}^{2+}$
Iron(III) ion: $Fe3+\text{Fe}^{3+}$
Aluminium ion: $Al3+\text{Al}^{3+}$

Common negative ions

Halide ions: $F−\text{F}^-$ , $Cl−\text{Cl}^-$ , $Br−\text{Br}^-$ , $I−\text{I}^-$
Hydroxide ion: $OH−\text{OH}^-$
Nitrate ion: $NO3−\text{NO}_3^-$
Oxide ion: $O2−\text{O}^{2-}$
Sulfide ion: $S2−\text{S}^{2-}$
Sulfate ion: $SO42−\text{SO}_4^{2-}$
Carbonate ion: $CO32−\text{CO}_3^{2-}$
Dichromate(VI) ion: $Cr2O72−\text{Cr}_2\text{O}_7^{2-}$
Phosphate ion: $PO43−\text{PO}_4^{3-}$

Common compound formulae

Some covalent compounds and acids are best learned directly:

Water: $H2O\text{H}_2\text{O}$
Ammonia: $NH3\text{NH}_3$
Methane: $CH4\text{CH}_4$
Carbon dioxide: $CO2\text{CO}_2$
Sulfuric acid: $H2SO4\text{H}_2\text{SO}_4$
Nitric acid: $HNO3\text{HNO}_3$
Hydrochloric acid: $HCl\text{HCl}$
Sodium hydroxide: $NaOH\text{NaOH}$
Calcium carbonate: $CaCO3\text{CaCO}_3$

Common Mistake

Charge balancing is for ionic formulae

The “make the total charge zero” method works for ionic compounds. It is not how you find formulae such as $H2O\text{H}_2\text{O}$ , $NH3\text{NH}_3$ or $CH4\text{CH}_4$ , which are covalent molecules.

Writing formulae for ionic compounds

An ionic compound contains positive and negative ions. Overall, the compound must be electrically neutral, so the total positive charge must equal the total negative charge.

Key Idea

Ionic formula rule

Choose the smallest whole-number ratio of ions that gives zero overall charge.

If an ion contains more than one atom, such as nitrate, $NO3−\text{NO}_3^-$ , or sulfate, $SO42−\text{SO}_4^{2-}$ , it is called a polyatomic ion. Keep it together as a unit. Use brackets if you need more than one of it.

Example

Writing aluminium sulfate

Identify the ions. Aluminium forms $Al3+\text{Al}^{3+}$ and sulfate is $SO42−\text{SO}_4^{2-}$ .
Find the smallest charges that cancel. The lowest common multiple of 3 and 2 is 6, so you need two aluminium ions for a total charge of $+ 6$ and three sulfate ions for a total charge of $- 6$ .
Write the formula using brackets around sulfate because more than one sulfate ion is needed: $Al2(SO4)3\text{Al}_2(\text{SO}_4)_3$ .

Common Mistake

Changing the ion instead of using brackets

Do not write something like $Al2S3O12\text{Al}_2\text{S}_3\text{O}_{12}$ for aluminium sulfate. The sulfate ion stays as $SO42−\text{SO}_4^{2-}$ , so the correct formula is $Al2(SO4)3\text{Al}_2(\text{SO}_4)_3$ .

Oxidation numbers

An oxidation number is a bookkeeping number assigned to an atom in a compound or ion. It helps you track electron transfer, especially in redox chemistry later on.

It is not always the real charge on the atom. For example, atoms in covalent compounds do not usually form actual ions, but we can still assign oxidation numbers.

Core oxidation number rules

An uncombined element has oxidation number zero. For example, $Mg\text{Mg}$ , $O2\text{O}_2$ and $Cl2\text{Cl}_2$ all contain atoms with oxidation number zero.
A monatomic ion has oxidation number equal to its charge. For example, $Na+\text{Na}^+$ is +1 and $O2−\text{O}^{2-}$ is -2.
The sum of oxidation numbers in a neutral compound is zero.
The sum of oxidation numbers in a polyatomic ion equals the charge on the ion.
Group 1 metals are usually +1; Group 2 metals are usually +2.
Oxygen is usually -2.
Hydrogen is usually +1 when bonded to non-metals.

Common Mistake

Useful exceptions

Oxygen is not always -2: in peroxides, such as $H2O2\text{H}_2\text{O}_2$ , oxygen is -1. Hydrogen is -1 in metal hydrides, such as $NaH\text{NaH}$ .

Example

Finding the oxidation number of manganese in manganate(VII)

Write the ion and assign the known oxidation number. In $MnO4−\text{MnO}_4^-$ , each oxygen is usually -2, so four oxygens contribute $\times (-2) = -8$ .
Let the oxidation number of manganese be $x$ . The total must equal the ion charge, so $x + (- 8) = - 1$ .
Solve the equation: $x = + 7$ . Manganese has oxidation number +7 in $MnO4−\text{MnO}_4^-$ .

Tip

Roman numerals in names

A Roman numeral in a compound name tells you the oxidation number of that element. For example, iron(III) oxide contains iron with oxidation number +3.

Constructing balanced chemical equations

A chemical equation shows reactants changing into products. Reactants are the substances you start with, written on the left. Products are the substances formed, written on the right.

A coefficient is the number placed in front of a formula. It multiplies the whole formula. For example, in $2H2O2\text{H}_2\text{O}$ , the coefficient 2 means two water molecules.

Key Idea

Balance equations with coefficients, not subscripts

You may change coefficients when balancing an equation. You must not change subscripts inside correct formulae, because that changes the substance.

A reliable balancing method

Write the correct formulae for all reactants and products.
Count atoms of each element on both sides.
Add coefficients to make each atom count equal.
Check again, including atoms inside brackets.
Add state symbols if required.

Example

Balancing aluminium reacting with oxygen

Write the correct formulae first: aluminium is $Al\text{Al}$ , oxygen is diatomic $O2\text{O}_2$ , and aluminium oxide is $Al2O3\text{Al}_2\text{O}_3$ .
Balance oxygen using the lowest common multiple of 2 and 3. Put 3 in front of $O2\text{O}_2$ and 2 in front of $Al2O3\text{Al}_2\text{O}_3$ , giving 6 oxygen atoms on each side.
Balance aluminium. Two formula units of $Al2O3\text{Al}_2\text{O}_3$ contain four aluminium atoms, so put 4 in front of $Al\text{Al}$ .
Add state symbols:

4\text{Al}(s) + 3\text{O}_2(g) \to 2\text{Al}_2\text{O}_3(s)

State symbols

A state symbol tells you the physical state of a substance in an equation.

$(s)$ means solid.
$(l)$ means liquid.
$(g)$ means gas.
$(a q)$ means aqueous, dissolved in water.

For example, sodium chloride solution is $NaCl(aq)\text{NaCl}(aq)$ , but solid sodium chloride is $NaCl(s)\text{NaCl}(s)$ .

Common Mistake

Confusing aqueous and liquid

$(a q)$ means dissolved in water. It does not mean “wet” or “liquid”. Pure water is $H2O(l)\text{H}_2\text{O}(l)$ , not $H2O(aq)\text{H}_2\text{O}(aq)$ .

Ionic equations

An ionic equation shows only the particles that actually change during a reaction. Ions that appear unchanged on both sides are called spectator ions.

This is especially useful for precipitation reactions, acid-base reactions and displacement reactions.

How to write an ionic equation

Write the full balanced equation with state symbols.
Split aqueous ionic substances into their ions.
Do not split solids, liquids, gases or covalent molecules.
Cancel spectator ions that are unchanged on both sides.
Check that atoms and overall charge are balanced.

Example

Writing a net ionic equation for silver chloride precipitation

Write the full equation. Silver nitrate and sodium chloride are aqueous; silver chloride is an insoluble precipitate:

\text{AgNO}_3(aq) + \text{NaCl}(aq) \to \text{AgCl}(s) + \text{NaNO}_3(aq)

Split the aqueous ionic substances into ions, but keep the solid precipitate together:

\text{Ag}^+(aq) + \text{NO}_3^-(aq) + \text{Na}^+(aq) + \text{Cl}^-(aq) \to \text{AgCl}(s) + \text{Na}^+(aq) + \text{NO}_3^-(aq)

Cancel the spectator ions, $Na+\text{Na}^+$ and $NO3−\text{NO}_3^-$ , because they are unchanged on both sides.
Write the net ionic equation and check charge and atoms:

\text{Ag}^+(aq) + \text{Cl}^-(aq) \to \text{AgCl}(s)

Tip

Charge is part of balancing

In ionic equations, both atoms and total charge must balance. If the atoms balance but the charge does not, the ionic equation is wrong.

Linking the ideas together

Formulae, oxidation numbers and equations are closely connected.

Formulae use ratios of atoms or ions.
Ionic formulae use charge balance.
Balanced equations use atom conservation.
Ionic equations remove spectators to show the real chemical change.
Oxidation numbers help describe electron transfer in later redox reactions.

The main skill is being disciplined: first get the formulae correct, then balance the equation, then add state symbols, then simplify to an ionic equation if needed.

Exam technique

In the exam

Write correct formulae before you try to balance; never fix a balancing problem by changing subscripts.
For ionic formulae, make the total charge zero using the smallest whole-number ratio.
In ionic equations, split only aqueous ionic substances and cancel only ions that are identical on both sides.
Always check both atom balance and charge balance before moving on.

Self review

Check yourself

What is the formula of calcium nitrate, and why are brackets needed?
What is the oxidation number of sulfur in $SO42−\text{SO}_4^{2-}$ ?
Write the net ionic equation for the reaction between $BaCl2(aq)\text{BaCl}_2(aq)$ and $Na2SO4(aq)\text{Na}_2\text{SO}_4(aq)$ forming $BaSO4(s)\text{BaSO}_4(s)$ .

What you'll learn

How to write formulae for common compounds and ionic compounds.
How to assign oxidation numbers in compounds and ions.
How to balance chemical equations using conservation of atoms.
How to write equations with state symbols and simplify them into ionic equations.

Why formulae and equations matter

Chemistry has its own language. A formula tells you what particles are present, and an equation tells you what changes during a reaction.

Here is the overall workflow for this topic.

Workflow for writing ionic formulae and constructing balanced and ionic equations

Chemical formulae: the basics

A chemical formula shows the elements present in a substance and the ratio of their atoms or ions.

A subscript is the small number written low and to the right of a symbol, such as the 2 in $CO2\text{CO}_2$ . It belongs to the formula and must not be changed when balancing equations.

Definition

Ion

An ion is a particle with an electrical charge. A cation is a positive ion, such as $Na+\text{Na}^+$ . An anion is a negative ion, such as $Cl−\text{Cl}^-$ .