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C. Chemical Reactions · Chemical Reactions

Writing and Balancing Chemical Equations

C2 C3 A1.12About 70 minutes
Learning goals
  • I can turn a word equation that uses IUPAC names into a skeleton equation with correct formulas and state symbols.
  • I can balance chemical equations, including ones with polyatomic ions and ones that need doubling.
  • I can explain how a balanced equation shows the law of conservation of mass.
  • I can read a balanced equation in terms of particles (atoms, molecules and formula units).

Words to know

reactant
A substance present at the start of a reaction; written on the left of the arrow.
product
A substance formed by a reaction; written on the right of the arrow.
skeleton equation
An equation with the correct formulas for every reactant and product, but not yet balanced.
coefficient
A whole number written in front of a formula that tells how many particles (or moles) of that substance take part.
subscript
A small number inside a formula that tells how many atoms or ions of each kind are in one particle. Changing it changes the substance.
state symbol
A label after a formula: (s) solid, (l) liquid, (g) gas, (aq) aqueous, meaning dissolved in water.
diatomic element
An element whose particles are two-atom molecules: H₂, N₂, O₂, F₂, Cl₂, Br₂ and I₂.
law of conservation of mass
In a chemical reaction, the total mass of the products equals the total mass of the reactants, because atoms are rearranged, not created or destroyed.

A recipe that must add up

A pancake recipe says: 2 cups of flour + 2 eggs + 1½ cups of milk → about 12 pancakes. The recipe tells you what goes in, what comes out, and how much of each.

A chemical equation is a chemist's recipe. It is more strict than a kitchen recipe, though. In a kitchen you can lose a little batter on the spoon. In a chemical reaction, no atom is ever lost or created. Every atom that goes in must come out, so the equation has to balance exactly.

This whole unit is about chemical reactions: what kinds there are, how to predict what they make, and how they affect our health and environment. Every lesson uses balanced equations, so we start by making sure your equation skills are solid.

Remember from Grade 10

In the Grade 10 Chemical Reactions unit you named compounds (including multivalent metals like iron(III), polyatomic ions like sulfate, and acids), wrote word equations, tested the law of conservation of mass, balanced equations, and met the five reaction types. In this course's Matter, Chemical Trends, and Chemical Bonding unit you reviewed IUPAC names and formulas again. This lesson adds speed and harder cases: polyatomic ions, odd numbers of oxygen atoms and fractions.

The parts of a chemical equation

Read the arrow as "yields" or "produces". Reactants go on the left; products go on the right.

  • A coefficient is the big number in front of a formula. 2H₂O means two molecules of water.
  • A subscript is the small number inside a formula. The 2 in H₂O means each water molecule has two hydrogen atoms.
  • A state symbol tells the state: (s) solid, (l) liquid, (g) gas, (aq) aqueous (dissolved in water).

Multiply the coefficient by the subscript to count atoms. In 3H₂SO₄ there are 3 × 2 = 6 hydrogen atoms, 3 sulfur atoms and 3 × 4 = 12 oxygen atoms.

2H₂(g)+O₂(g)→2H₂O(l)coefficientsubscriptstate symbolyieldsstate symbolreactants (what you start with)product (what forms)(s) solid(l) liquid(g) gas(aq) dissolved in water
The parts of a balanced chemical equation. The coefficient counts whole particles; the subscript is part of the formula and can never be changed when you balance.

Seven elements come in pairs

Seven elements exist as diatomic molecules when they are not combined with other elements: H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂. A memory trick is HOFBrINCl (say "Hof-brinkle"). On the periodic table they make a "7" shape starting at nitrogen (N, O, F, then down Cl, Br, I), plus hydrogen.

Two more elements are usually written as larger molecules: phosphorus as P₄ and sulfur as S₈. All other elements are written as single symbols: Fe, Cu, Na, C, He.

This matters because a free element in an equation must be written the way it really exists. Oxygen gas is O₂(g), never O(g).

From words to a balanced equation

Follow four steps every time:

  1. Word equation. Write the names of all reactants and products.
  2. Skeleton equation. Replace each name with its correct formula. For an ionic compound, use the ion charges so the total charge is zero. Add state symbols.
  3. Balance. Put coefficients in front of formulas so each kind of atom has the same count on both sides.
  4. Check. Count every atom on each side. Make sure the coefficients are the lowest whole-number ratio.
1. Word equationnames of allreactants and products2. Skeletoncorrect formulasand state symbols3. Balancechange coefficientsonly, never subscripts4. Checkcount every atomlowest whole numbers
The four steps for writing a balanced chemical equation. Most mistakes happen in step 2 (a wrong formula), so slow down there.

Why balance? Conservation of mass

In a chemical reaction, bonds break and new bonds form. The atoms are rearranged, but they do not disappear and new ones do not appear. Since each atom keeps its mass, the total mass of the products equals the total mass of the reactants. This is the law of conservation of mass, first stated clearly by the French chemist Antoine Lavoisier in the late 1700s.

A balanced equation shows this law: the same atoms appear on both sides, just in new combinations. Look at the particle picture of hydrogen burning in oxygen.

HHHH+OOOHHOHH+2H₂ + O₂2H₂O4 H atoms, 2 O atoms4 H atoms, 2 O atoms
Two hydrogen molecules react with one oxygen molecule to give two water molecules. Count the circles: 4 H and 2 O on each side, so mass is conserved.

Balancing strategies that save time

  • Start with the most complicated formula and balance the elements in it that appear only once on each side.
  • Treat a polyatomic ion as one unit if it appears unchanged on both sides. For example, count SO₄ groups instead of separate S and O atoms.
  • Leave elements that appear by themselves (like O₂, Fe, H₂) until last. You can change their coefficient without upsetting anything else.
  • Odd and even. If an element has an odd count on one side and must be even on the other (oxygen in O₂ is always even), double the formula with the odd count.
  • Fractions are allowed while you work. If you need 7/2 O₂, write it, then multiply every coefficient by 2 at the end.
  • Never change a subscript. Changing H₂O to H₂O₂ turns water into hydrogen peroxide, a different substance.
Worked example

Balancing with ion charges

Write a balanced equation: aluminium metal reacts with aqueous copper(II) chloride to produce aqueous aluminium chloride and solid copper.

  1. Formulas. Aluminium is Al. Copper(II) is Cu²⁺ and chloride is Cl⁻, so copper(II) chloride is CuCl₂. Aluminium is Al³⁺, so aluminium chloride is AlCl₃. Copper is Cu.
  2. Skeleton: Al(s) + CuCl₂(aq) → AlCl₃(aq) + Cu(s).
  3. Chlorine is 2 on the left and 3 on the right. The lowest common multiple of 2 and 3 is 6, so write 3CuCl₂ and 2AlCl₃.
  4. Now there are 3 Cu atoms on the left, so write 3Cu on the right, and 2 Al atoms on the right, so write 2Al on the left.
  5. Check: Al 2 = 2, Cu 3 = 3, Cl 6 = 6. ✔

2Al(s) + 3CuCl₂(aq) → 2AlCl₃(aq) + 3Cu(s)

Worked example

Polyatomic ions as units

Balance: Ca(OH)₂(aq) + H₃PO₄(aq) → Ca₃(PO₄)₂(s) + H₂O(l)

  1. Calcium: 3 on the right, so put 3 in front of Ca(OH)₂.
  2. Phosphate (PO₄) stays together. There are 2 phosphate groups on the right, so put 2 in front of H₃PO₄.
  3. Hydrogen on the left: 3 × 2 = 6 (from hydroxide) + 2 × 3 = 6 (from the acid) = 12. Water has 2 H, so we need 6 H₂O.
  4. Oxygen check: left 3 × 2 = 6 (hydroxide) + 2 × 4 = 8 (phosphate) = 14. Right: 2 × 4 = 8 (phosphate) + 6 (water) = 14. ✔

3Ca(OH)₂(aq) + 2H₃PO₄(aq) → Ca₃(PO₄)₂(s) + 6H₂O(l)

Worked example

Odd oxygen: use a fraction, then double

Ethane gas (C₂H₆) burns in oxygen to form carbon dioxide gas and water vapour. Write the balanced equation.

  1. Skeleton: C₂H₆(g) + O₂(g) → CO₂(g) + H₂O(g).
  2. Carbon: 2 on the left, so 2CO₂.
  3. Hydrogen: 6 on the left, so 3H₂O.
  4. Oxygen on the right: 2 × 2 + 3 × 1 = 7 atoms. Oxygen comes in pairs, so we need 7/2 O₂: 7/2O₂. (Read it as "three and a half".)
  5. Multiply everything by 2 to get whole numbers: 2C₂H₆ + 7O₂ → 4CO₂ + 6H₂O.
  6. Check: C 4 = 4, H 12 = 12, O 14 = 4 × 2 + 6 = 14. ✔

2C₂H₆(g) + 7O₂(g) → 4CO₂(g) + 6H₂O(g)

Worked example

Reading an equation as particles

In a blast furnace, iron(III) oxide reacts with carbon monoxide: Fe₂O₃(s) + 3CO(g) → 2Fe(l) + 3CO₂(g). Describe this equation in words, using particles.

  1. Fe₂O₃ is an ionic compound, so its particle is a formula unit. CO and CO₂ are molecules. Iron is a metal element, so its particles are atoms.
  2. Read the coefficients: 1 formula unit of iron(III) oxide reacts with 3 molecules of carbon monoxide to produce 2 atoms of liquid iron and 3 molecules of carbon dioxide.
  3. Check balance: Fe 2 = 2; C 3 = 3; O 3 + 3 = 6 on the left and 3 × 2 = 6 on the right. ✔
  4. The same ratio works for any amount: 1 million formula units of Fe₂O₃ need 3 million molecules of CO. In the Quantities in Chemical Reactions unit you will use this idea with moles.

One formula unit of solid iron(III) oxide reacts with three molecules of carbon monoxide gas to yield two atoms of liquid iron and three molecules of carbon dioxide gas.

The most common mistakes

  • Writing a diatomic element as one atom (O instead of O₂).
  • Getting an ionic formula wrong: calcium chloride is CaCl₂, not CaCl, because Ca²⁺ needs two Cl⁻.
  • Changing a subscript to make the numbers work.
  • Putting a coefficient inside a formula (H₂ 2O means nothing). The coefficient goes in front.
  • Forgetting to reduce: 4H₂ + 2O₂ → 4H₂O is balanced but should be 2H₂ + O₂ → 2H₂O.
Hands-on activity

Model it at home: atoms you can hold

You need: three kinds of small objects in different colours or shapes (for example dried beans, macaroni and coins, or LEGO bricks), a sheet of paper, and a pencil. If young children or pets are in the house, put the small objects away when you finish.

  1. Choose a key, for example: bean = H, macaroni = O, coin = C. Write it at the top of the paper.
  2. Draw a line down the middle and an arrow. Build one methane molecule (CH₄: 1 coin + 4 beans) and one O₂ molecule on the left.
  3. Build CO₂ and H₂O on the right using only the atoms from the left side. You will run out of oxygen. Add more O₂ "molecules" (pairs of macaroni) and more H₂O until every object on the left is used exactly once on the right.
  4. Write the balanced equation from your model. (You should get CH₄ + 2O₂ → CO₂ + 2H₂O.)
  5. Repeat for N₂ + H₂ → NH₃ (use a fourth object for N, or turn coins over).

What to look for: the number of each object never changes; only the groupings change. That is conservation of mass.

Just for fun

I tried to balance H₂ + O₂ → H₂O by changing the water to H₂O₂. It balanced perfectly. Unfortunately, I now had a glass of hydrogen peroxide instead of a drink. Change coefficients, not subscripts!

Your turn

1

Write the formula: (a) iron(III) chloride (b) sodium sulfate (c) ammonium phosphate.

2

Balance: Na(s) + Cl₂(g) → NaCl(s)

3

Balance: N₂(g) + H₂(g) → NH₃(g)

4

Balance: KClO₃(s) → KCl(s) + O₂(g)

5

Balance: AgNO₃(aq) + CaCl₂(aq) → AgCl(s) + Ca(NO₃)₂(aq)

6

Write a balanced equation with states: solid magnesium burns in oxygen gas to form solid magnesium oxide.

7

How many atoms of each element are shown by 3Al₂(SO₄)₃?

More practice: warm-up

1

Name the seven diatomic elements.

2

What does (aq) mean?

3

In 4NH₃, what is the coefficient and how many hydrogen atoms are shown?

4

Balance: H₂(g) + Cl₂(g) → HCl(g)

5

Balance: Zn(s) + HCl(aq) → ZnCl₂(aq) + H₂(g)

More practice: on your own

1

Balance: Fe(s) + O₂(g) → Fe₂O₃(s)

2

Balance: C₃H₈(g) + O₂(g) → CO₂(g) + H₂O(g)

3

Balance: Al(s) + H₂SO₄(aq) → Al₂(SO₄)₃(aq) + H₂(g)

4

Write the balanced equation: aqueous lead(II) nitrate and aqueous potassium iodide react to form solid lead(II) iodide and aqueous potassium nitrate.

5

A student writes 2H₂O → 2H₂ + 2O. What is wrong? Fix it.

Challenge

1

Balance: C₈H₁₈(l) + O₂(g) → CO₂(g) + H₂O(g) (octane, a part of gasoline).

2

Balance: Fe₂(SO₄)₃(aq) + KOH(aq) → Fe(OH)₃(s) + K₂SO₄(aq)

3

Burning 4.0 g of hydrogen in excess oxygen produces 36.0 g of water. What mass of oxygen reacted? Which law did you use, and why must it hold?

Check your understanding

Quiz

1.

Which is the correct formula for oxygen gas in an equation?

2.

When you balance an equation, what are you allowed to change?

3.

Which equation is correctly balanced?

4.

What is the coefficient of O₂ when C₃H₈ + O₂ → CO₂ + H₂O is balanced with lowest whole numbers?

5.

What does (aq) after a formula tell you?

6.

How many oxygen atoms are in 2Ca(NO₃)₂?

For parents and teachers

This lesson is the foundation for the whole unit. If your teen struggles here, every later lesson will feel hard, so it is worth spending extra time.

How to help: ask your teen to explain out loud the difference between a coefficient and a subscript, and to count atoms for you. A periodic table and a list of common ions (both easy to find printed in any Grade 11 chemistry textbook or online) should be beside them for every lesson in this unit.

Common difficulties:

  • Wrong formulas. Most "balancing" errors are really formula errors. Check ion charges first.
  • Forgetting diatomic elements (O₂, H₂, Cl₂ and so on).
  • Giving up on combustion equations with an odd number of oxygen atoms. Encourage the fraction-then-double method.

The modelling activity uses small objects; put them away from younger children afterwards.