Chapter 1 of 8

All 8 chapters
  1. 1Chemical formulae, readunderstood
  2. 2Balancing equations, readunderstood
  3. 3The mole, readunderstood
  4. 4Reacting masses and yield, readunderstood
  5. 5Acids, bases and salts, readunderstood
  6. 6The reactivity series, readunderstood
  7. 7Electrolysis, readunderstood
  8. 8Energy changes and rates, readunderstood

S4.7.1 Chapter 1

Chemical formulae

Why is salt written NaCl, but magnesium chloride written MgCl₂?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Write formulae for common compounds using ion charges
  • Count the atoms of each element in a formula

A formula is a short way to write what a substance is made of. It uses the symbols of the elements, and small numbers that say how many.

Water is H₂O. The small 2 sits after the H, so it counts hydrogen atoms. There is no number after the O, so that means 1. One water molecule has 2 hydrogen atoms and 1 oxygen atom.

Three molecules drawn as touching circles with the symbol of each atom inside. Water, H₂O, has one O atom and two H atoms. Carbon dioxide, CO₂, has one C atom between two O atoms. Methane, CH₄, has one C atom with four H atoms round it.OHHOCOCHHHH
Left to right: water H₂O, carbon dioxide CO₂ and methane CH₄. The circles show which atoms are joined, not their true sizes or angles.

A bracket groups atoms that belong together. The small number after the bracket multiplies everything inside it. In Ca(OH)₂ the group OH is there twice.

Three discs in a row. A hatched disc is Ca²⁺. Two plain discs are OH⁻. Under them the sum reads +2 −1 −1 = 0, and under the sum is the formula Ca(OH)₂.Ca²⁺OH⁻OH⁻+2 −1 −1 = 0Ca(OH)₂
Calcium hydroxide. One Ca²⁺ ion goes with two OH⁻ ions, and OH⁻ is a group, so it gets a bracket.

Worked example

How many atoms of each element are in Ca(OH)₂?

  1. Ca has no number after it, so there is 1 calcium atom.
  2. The bracket holds one O and one H. The small 2 after the bracket multiplies both.
  3. O: 1 × 2 = 2 oxygen atoms. H: 1 × 2 = 2 hydrogen atoms.

Answer: 1 Ca, 2 O and 2 H

Now think about salt. Sodium chloride is made of ions, which are atoms or groups of atoms with an electric charge. Na⁺ has a charge of 1+. Cl⁻ has a charge of 1−.

In an ionic compound the charges of all the ions add up to zero. The formula gives the smallest whole-number ratio of the ions that does this. It does not describe a molecule.

A table of positive ions with the columns Ion, Name and Charge. H⁺ hydrogen 1+. Na⁺ sodium 1+. NH₄⁺ ammonium 1+. Mg²⁺ magnesium 2+. Ca²⁺ calcium 2+. Cu²⁺ copper(II) 2+. Al³⁺ aluminium 3+.IonNameChargeH⁺hydrogen1+Na⁺sodium1+NH₄⁺ammonium1+Mg²⁺magnesium2+Ca²⁺calcium2+Cu²⁺copper(II)2+Al³⁺aluminium3+
Positive ions. Metals form positive ions. Hydrogen, H⁺, and ammonium, NH₄⁺, are positive ions too. Copper can form other ions too, so its name carries the charge: copper(II) means 2+.
A table of negative ions with the columns Ion, Name and Charge. Cl⁻ chloride 1−. OH⁻ hydroxide 1−. NO₃⁻ nitrate 1−. O²⁻ oxide 2−. CO₃²⁻ carbonate 2−. SO₄²⁻ sulfate 2−.IonNameChargeCl⁻chloride1−OH⁻hydroxide1−NO₃⁻nitrate1−O²⁻oxide2−CO₃²⁻carbonate2−SO₄²⁻sulfate2−
Negative ions. OH⁻, NO₃⁻, CO₃²⁻ and SO₄²⁻ are each a group of atoms that carries one charge together.

A group of atoms with one charge is a polyatomic ion. NH₄⁺, OH⁻ and SO₄²⁻ are polyatomic ions. They stay together when they join with other ions.

Draw it first

Make magnesium chloride from its ions

  1. Three steps, drawn in the same place. Step 1: a hatched disc Mg²⁺ with the charge +2. Step 2: a plain disc Cl⁻ is added, and the sum reads +2 −1 = +1. Step 3: a second plain disc Cl⁻ is added, the sum reads +2 −1 −1 = 0, and the formula MgCl₂ appears.Mg²⁺+2

    1 Start with the magnesium ion, Mg²⁺. Its charge is +2.

  2. Three steps, drawn in the same place. Step 1: a hatched disc Mg²⁺ with the charge +2. Step 2: a plain disc Cl⁻ is added, and the sum reads +2 −1 = +1. Step 3: a second plain disc Cl⁻ is added, the sum reads +2 −1 −1 = 0, and the formula MgCl₂ appears.Mg²⁺Cl⁻+2 −1 = +1

    2 Add a chloride ion, Cl⁻, with a charge of −1. The sum is +1, not zero. A charge is left over.

  3. Three steps, drawn in the same place. Step 1: a hatched disc Mg²⁺ with the charge +2. Step 2: a plain disc Cl⁻ is added, and the sum reads +2 −1 = +1. Step 3: a second plain disc Cl⁻ is added, the sum reads +2 −1 −1 = 0, and the formula MgCl₂ appears.Mg²⁺Cl⁻Cl⁻+2 −1 −1 = 0MgCl₂

    3 Add a second Cl⁻. Now +2 −1 −1 = 0, so the formula is MgCl₂.

The rule has four parts. Find the smallest numbers of each ion that make the charges add to zero. Write the positive ion first. Write each number small and low, after its symbol. Leave out a 1.

Worked example

Write the formula of aluminium oxide. It is made of Al³⁺ ions and O²⁻ ions.

  1. The ions are Al³⁺ and O²⁻. The charges are 3+ and 2−.
  2. Find the smallest number that both 3 and 2 go into. It is 6.
  3. Aluminium: 6 ÷ 3 = 2 ions.
  4. Oxygen: 6 ÷ 2 = 3 ions.
  5. Write the numbers low, after each symbol: Al₂O₃.

Answer: 2 aluminium ions and 3 oxide ions, so Al₂O₃

See it three ways

As a picture

Five discs in a row. Two hatched discs are Al³⁺. Three plain discs are O²⁻. Under them the sum reads +3 +3 −2 −2 −2 = 0, and under the sum is the formula Al₂O₃.Al³⁺Al³⁺O²⁻O²⁻O²⁻+3 +3 −2 −2 −2 = 0Al₂O₃

In words

Two Al³⁺ ions give a charge of +6. Three O²⁻ ions give −6. The charges cancel, so two aluminium ions go with three oxide ions.

In symbols

2 × (+3) + 3 × (−2) = 0, so the formula is Al₂O₃.

When a polyatomic ion is needed more than once, put it in a bracket. Calcium hydroxide is Ca(OH)₂. Without the bracket, CaOH₂ would mean one oxygen atom and two hydrogen atoms. With one OH⁻ only, as in NaOH, no bracket is needed.

Molecules are different. Water, carbon dioxide and methane are made of non-metal atoms that share electrons. Their formulae count the atoms in one molecule.

Try it

Ion cards: make the charges add to zero

You need: paper, torn into 15 small pieces, a pencil.

  1. Write Na⁺ on three pieces, Al³⁺ on three, and Mg²⁺ on three. Write Cl⁻ on three pieces and O²⁻ on three.
  2. Put cards side by side, positive or negative, until the charges add up to zero.
  3. Use as few cards as you can. Write down the formula each time.
  4. Try every positive card with Cl⁻, and then with O²⁻.

What you will see: Na⁺ takes one Cl⁻. Two Na⁺ take one O²⁻. Mg²⁺ takes two Cl⁻ or one O²⁻. Al³⁺ takes three Cl⁻. Two Al³⁺ take three O²⁻. The cards show why the numbers in a formula are what they are.

If you cannot try it, this is what happens.
Four discs in a row. One hatched disc is Al³⁺. Three plain discs are Cl⁻. Under them the sum reads +3 −1 −1 −1 = 0, and under the sum is the formula AlCl₃.Al³⁺Cl⁻Cl⁻Cl⁻+3 −1 −1 −1 = 0AlCl₃

A wrong idea many people have

In MgCl₂ the small 2 belongs to the magnesium, or is a charge.

Why it feels right: The 2 sits in the middle of the formula, and charges and small numbers look alike.

The test that breaks it: Draw MgCl₂ as discs. Count: there is one Mg²⁺ disc and two Cl⁻ discs. The 2 counted the Cl.

What is true: A small number counts the symbol just before it, or the bracket just before it. A charge is written raised, as in Mg²⁺. A count is written low, as in Cl₂.

Key words

formula
symbols and small numbers that show what a substance is made of.
ion
an atom, or a group of atoms, with an electric charge.
polyatomic ion
a group of atoms that carries one charge together, such as OH⁻.

Back to your guess

The answer is B: The charges of the ions must add up to zero.

The charges must add up to zero. A Mg²⁺ ion has a charge of 2+, and each Cl⁻ ion has 1−. So one magnesium ion needs two chloride ions.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. One Ca²⁺ ion and one Cl⁻ ion are drawn, and their charges do not add up to zero. In calcium chloride, how many Cl⁻ ions go with each Ca²⁺ ion?

    Two discs in a row. A hatched disc is Ca²⁺. A plain disc is Cl⁻. Under them the sum reads +2 −1 = +1.Ca²⁺Cl⁻+2 −1 = +1
    Tap your answer.

    1. Not this one. One Cl⁻ cancels only 1 of the 2 positive charges. The sum is +1, so a charge is left over. Go to S4.6.6. Try another.

    2. Yes, that is right. Ca²⁺ has a charge of +2. Each Cl⁻ has −1. Two Cl⁻ ions give −2, so +2 −1 −1 = 0. The formula is CaCl₂.

    3. Not this one. Three Cl⁻ give −3, which is more than the +2 of the calcium ion. The sum would be −1. Try another.

    See the answer

    2 chloride ions

    Ca²⁺ has a charge of +2. Each Cl⁻ has −1. Two Cl⁻ ions give −2, so +2 −1 −1 = 0. The formula is CaCl₂.

    • If you chose A: One Cl⁻ cancels only 1 of the 2 positive charges. The sum is +1, so a charge is left over. Go to S4.6.6.
    • If you chose C: Three Cl⁻ give −3, which is more than the +2 of the calcium ion. The sum would be −1.

  2. Aluminium ions are Al³⁺ and chloride ions are Cl⁻. What is the formula of aluminium chloride?

    Tap your answer.

    1. Not this one. That is one of each. The charges would be +3 and −1, so +2 is left over. Go to S4.6.6. Try another.

    2. Not this one. The numbers are the wrong way round. Three aluminium ions would give +9, and one chloride ion only −1. Try another.

    3. Yes, that is right. One Al³⁺ has a charge of +3. It needs three Cl⁻ ions, each −1, so the charges add to zero.

    See the answer

    AlCl₃

    One Al³⁺ has a charge of +3. It needs three Cl⁻ ions, each −1, so the charges add to zero.

    • If you chose A: That is one of each. The charges would be +3 and −1, so +2 is left over. Go to S4.6.6.
    • If you chose B: The numbers are the wrong way round. Three aluminium ions would give +9, and one chloride ion only −1.

  3. Sodium ions are Na⁺ and sulfate ions are SO₄²⁻. Which formula is right for sodium sulfate?

    Tap your answer.

    1. Yes, that is right. Two Na⁺ ions give +2. One SO₄²⁻ ion gives −2. The sum is zero, and the sulfate is needed once, so it needs no bracket.

    2. Not this one. One Na⁺ and one SO₄²⁻ give +1 −2 = −1. The charges do not add to zero. Try another.

    3. Not this one. Two sulfate ions would give −4, and one sodium ion only +1. It is the sodium that is needed twice. Try another.

    See the answer

    Na₂SO₄

    Two Na⁺ ions give +2. One SO₄²⁻ ion gives −2. The sum is zero, and the sulfate is needed once, so it needs no bracket.

    • If you chose B: One Na⁺ and one SO₄²⁻ give +1 −2 = −1. The charges do not add to zero.
    • If you chose C: Two sulfate ions would give −4, and one sodium ion only +1. It is the sodium that is needed twice.

  4. One Ca²⁺ ion needs two OH⁻ ions. Which formula for calcium hydroxide shows this?

    Tap your answer.

    1. Not this one. Here the small number counts only the H. That is 1 Ca, 1 O and 2 H. OH is a group, so it needs a bracket. Try another.

    2. Not this one. This has two calcium atoms and one OH. The count is on the wrong symbol. Try another.

    3. Yes, that is right. The bracket groups O and H, and the 2 after it multiplies both. The formula has 1 Ca, 2 O and 2 H.

    See the answer

    Ca(OH)₂

    The bracket groups O and H, and the 2 after it multiplies both. The formula has 1 Ca, 2 O and 2 H.

    • If you chose A: Here the small number counts only the H. That is 1 Ca, 1 O and 2 H. OH is a group, so it needs a bracket.
    • If you chose B: This has two calcium atoms and one OH. The count is on the wrong symbol.

  5. How many oxygen atoms are in one unit of Al₂(SO₄)₃?

    Tap your answer.

    1. Not this one. The 3 after the bracket is the number of sulfate groups. Each group has 4 oxygen atoms. Try another.

    2. Yes, that is right. Each SO₄ has 4 oxygen atoms, and there are 3 of them: 4 × 3 = 12. The count also includes 2 Al and 3 S.

    3. Not this one. That is the oxygen in one sulfate group. The bracket holds 3 groups. Try another.

    See the answer

    12 oxygen atoms

    Each SO₄ has 4 oxygen atoms, and there are 3 of them: 4 × 3 = 12. The count also includes 2 Al and 3 S.

    • If you chose A: The 3 after the bracket is the number of sulfate groups. Each group has 4 oxygen atoms.
    • If you chose C: That is the oxygen in one sulfate group. The bracket holds 3 groups.

  6. What does the formula MgCl₂ tell you?

    Tap your answer.

    1. Yes, that is right. The low 2 sits after Cl, so it counts chlorine. The formula gives the ratio of the ions in the lattice: 1 Mg²⁺ to 2 Cl⁻.

    2. Not this one. A charge is written raised, as in Cl⁻, and the chloride ion is 1−. The low 2 after Cl counts chloride ions. Go to S4.6.6. Try another.

    3. Not this one. There is only one Mg, and magnesium chloride is a lattice of ions, not a molecule. The formula gives the ratio of the ions. Go to S4.6.6. Try another.

    See the answer

    There are two chloride ions for each magnesium ion.

    The low 2 sits after Cl, so it counts chlorine. The formula gives the ratio of the ions in the lattice: 1 Mg²⁺ to 2 Cl⁻.

    • If you chose B: A charge is written raised, as in Cl⁻, and the chloride ion is 1−. The low 2 after Cl counts chloride ions. Go to S4.6.6.
    • If you chose C: There is only one Mg, and magnesium chloride is a lattice of ions, not a molecule. The formula gives the ratio of the ions. Go to S4.6.6.

  7. A molecule is drawn as circles. Which formula matches it?

    A molecule drawn as touching circles. One circle with the symbol C has four circles with the symbol H touching it.CHHHH
    Tap your answer.

    1. Not this one. That would be four carbon atoms and one hydrogen. Count the circles: one C and four H. Try another.

    2. Yes, that is right. One C circle and four H circles. The small number goes low, after the symbol it counts: CH₄.

    3. Not this one. That is one carbon and one hydrogen. Count again: there are four H circles. Try another.

    See the answer

    CH₄

    One C circle and four H circles. The small number goes low, after the symbol it counts: CH₄.

    • If you chose A: That would be four carbon atoms and one hydrogen. Count the circles: one C and four H.
    • If you chose C: That is one carbon and one hydrogen. Count again: there are four H circles.

  8. How many atoms in all are in one unit of Ca(OH)₂?

    See the answer

    5 atoms

    Ca 1, O 2 and H 2. The bracket multiplies the O and the H by 2. 1 + 2 + 2 = 5.

  9. A positive ion has a charge of 3+ and a negative ion has a charge of 2−. How many of each ion are in one unit of the compound?

    See the answer

    2 positive ions and 3 negative ions

    The smallest number that 3 and 2 both go into is 6. 6 ÷ 3 = 2 positive ions and 6 ÷ 2 = 3 negative ions.

Keep it

Copy this into your exercise book.

Write the positive ion first. Use the smallest numbers that make the charges add to zero. Write them low, after the symbol. Put a bracket round a group that is counted more than once.

Draw: MgCl₂ as one Mg²⁺ disc and two Cl⁻ discs, with the sum +2 −1 −1 = 0 under them.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

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