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C. Chemistry: Chemical Reactions · Chemical Reactions

Balancing Chemical Equations

C3.4 C3.2 C2.2 A1.12About 75 minutes
Learning goals
  • I can explain why only coefficients, never subscripts, may be changed when balancing.
  • I can use an atom-count table to check whether an equation is balanced.
  • I can balance chemical equations step by step, including ones with polyatomic ions.
  • I can reduce coefficients to the lowest whole-number ratio.

Words to know

balanced equation
An equation with the same number of atoms of each element on both sides.
coefficient
A whole number placed in front of a formula to show how many molecules or formula units react or form.
atom-count table
A table listing how many atoms of each element are on each side of an equation.
lowest whole-number ratio
Coefficients that cannot all be divided by the same whole number.

Making the books balance

A store owner counting money at the end of the day expects the cash in the drawer to match the sales. If it does not, something is wrong. A chemist counting atoms expects the same thing: every atom on the left side of an equation must show up on the right side. In the last lesson you learned why (atoms are conserved, so mass is conserved). In this lesson you will learn how to balance equations, step by step (expectations C3.2 and C3.4).

The golden rule

You may change coefficients. You may never change subscripts.

A subscript is part of a substance's identity. Changing H₂O to H₂O₂ does not balance the equation; it turns water into hydrogen peroxide, a completely different chemical. A coefficient only changes how many molecules there are, which is exactly what we are allowed to adjust.

2H₂O: change a COEFFICIENTOHHOHHtwo water moleculesstill water ✔H₂O₂: change a SUBSCRIPTOOHHone hydrogen peroxide moleculea different substance ✘
Putting a 2 in front of H₂O gives two water molecules. Changing the subscript to make H₂O₂ makes hydrogen peroxide, so it would describe a different reaction.

A step-by-step method

  1. Write the skeleton equation with correct formulas (remember diatomic elements: H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂).
  2. Count the atoms of each element on each side. A small table helps.
  3. Balance one element at a time by placing coefficients. Good order:
  • Start with an element that appears in only one compound on each side, often a metal or carbon.
  • If a polyatomic ion appears unchanged on both sides (such as SO₄ or NO₃), balance it as one unit.
  • Leave elements that appear on their own (such as O₂, H₂, Fe) until last, because changing their coefficient does not upset anything else.
  1. Recount every element. Changing one coefficient can unbalance something you already fixed.
  2. Check the coefficients are the lowest whole-number ratio. If they can all be divided by 2, do it.
1. Skeleton: H₂ + O₂ → H₂OHH+OOOHHH: 2 → 2O: 2 → 1O does not match2. Fix O: put 2 before H₂OHH+OOOHHOHHH: 2 → 4O: 2 → 2now H does not match3. Fix H: put 2 before H₂HHHH+OOOHHOHHH: 4 → 4O: 2 → 2balanced!
Balancing H₂ + O₂ → H₂O with models. Each change of a coefficient adds whole molecules, never single atoms. Recount after every step.
Worked example

Example 1: Aluminium and oxygen

Balance: Al + O₂ → Al₂O₃ (aluminium reacts with oxygen to form the protective layer of aluminium oxide on aluminium foil).

  1. Count: left Al 1, O 2; right Al 2, O 3.
  2. Oxygen: 2 on the left and 3 on the right. The lowest number both divide into is 6. Put 3 in front of O₂ (3 × 2 = 6) and 2 in front of Al₂O₃ (2 × 3 = 6): Al + 3O₂ → 2Al₂O₃.
  3. Now aluminium: the right has 2 × 2 = 4 Al. Put 4 in front of Al: 4Al + 3O₂ → 2Al₂O₃.
  4. Recount: Al 4 = 4; O 6 = 6. ✔ The coefficients 4, 3, 2 cannot all be divided by the same number.

4Al + 3O₂ → 2Al₂O₃

Worked example

Example 2: Burning methane (natural gas)

Balance: CH₄ + O₂ → CO₂ + H₂O

  1. Count: left C 1, H 4, O 2; right C 1, H 2, O 3.
  2. Carbon is already balanced (1 = 1).
  3. Hydrogen: 4 on the left, 2 on the right. Put 2 in front of H₂O: CH₄ + O₂ → CO₂ + 2H₂O.
  4. Oxygen last (it appears on its own as O₂): the right now has 2 + 2 = 4 O. Put 2 in front of O₂ (2 × 2 = 4).
  5. Recount: C 1 = 1; H 4 = 4; O 4 = 4. ✔

CH₄ + 2O₂ → CO₂ + 2H₂O

Worked example

Example 3: Polyatomic ions as units

Balance: Pb(NO₃)₂(aq) + KI(aq) → PbI₂(s) + KNO₃(aq)

  1. The nitrate group NO₃ appears unchanged on both sides, so count it as one unit.
  2. Count: left Pb 1, NO₃ 2, K 1, I 1; right Pb 1, NO₃ 1, K 1, I 2.
  3. Nitrate: 2 on the left, 1 on the right. Put 2 in front of KNO₃.
  4. Now K: the right has 2, the left has 1. Put 2 in front of KI. This also gives 2 I on the left, matching PbI₂.
  5. Recount: Pb 1 = 1; NO₃ 2 = 2; K 2 = 2; I 2 = 2. ✔

Pb(NO₃)₂(aq) + 2KI(aq) → PbI₂(s) + 2KNO₃(aq). (The bright yellow solid PbI₂ is a precipitate, a sign of this reaction.)

Worked example

Example 4: An odd-even problem

Balance: C₂H₆ + O₂ → CO₂ + H₂O (ethane burning)

  1. Carbon: put 2 in front of CO₂. Hydrogen: 6 on the left, so put 3 in front of H₂O.
  2. Oxygen on the right: 2 × 2 + 3 × 1 = 7. But O₂ comes in pairs, and 7 is odd: no whole number times 2 equals 7.
  3. Fix it by doubling everything else: 2C₂H₆ + O₂ → 4CO₂ + 6H₂O. Now the right side has 4 × 2 + 6 = 14 O.
  4. Put 7 in front of O₂ (7 × 2 = 14).
  5. Recount: C 4 = 4; H 12 = 12; O 14 = 14. ✔

2C₂H₆ + 7O₂ → 4CO₂ + 6H₂O

ElementLeft side (4Al + 3O₂)Right side (2Al₂O₃)
Al42 × 2 = 4
O3 × 2 = 62 × 3 = 6
An atom-count table for Example 1. Multiply each coefficient by each subscript.
Hands-on activity

Pasta-atom balancing

You need: three or four kinds of dry pasta or cereal shapes (for example macaroni = O, spirals = H, small shells = C, wheels = a metal such as Al), several small cups or paper squares, a pencil and paper.

  1. Each cup is one molecule or formula unit. Fill cups to match a formula: an O₂ cup has 2 macaroni; an H₂O cup has 1 macaroni and 2 spirals.
  2. Set up the skeleton equation H₂ + O₂ → H₂O with one cup of each on the "reactant" and "product" sides of the table.
  3. Count each kind of pasta on each side. Fix the imbalance only by adding whole cups (you may never change what is inside a cup: that is the subscript rule).
  4. Write the balanced equation when the counts match.
  5. Repeat for CH₄ + O₂ → CO₂ + H₂O and Al + O₂ → Al₂O₃.

What to look for: H₂ + O₂ → H₂O needs 2 H₂ cups and 2 H₂O cups: 2H₂ + O₂ → 2H₂O. Methane needs 1 CH₄, 2 O₂, 1 CO₂ and 2 H₂O cups. Aluminium needs 4 Al, 3 O₂ and 2 Al₂O₃ cups. If you were tempted to put an extra piece inside a cup, notice how that would change the substance.

Just for fun

I tried to balance H₂ + O₂ → H₂O by changing H₂O to H₂O₂. Now the equation balances, but my glass of water has turned into hair bleach. (Hydrogen peroxide really is used to lighten hair. Stick to coefficients.)

Your turn

1

Balance: H₂ + Cl₂ → HCl

2

Balance: Na + Cl₂ → NaCl

3

Balance: N₂ + H₂ → NH₃

4

Balance: Mg + O₂ → MgO

5

Balance: H₂O₂ → H₂O + O₂

6

Balance: Fe + O₂ → Fe₂O₃

7

Is this balanced? If not, fix it: CaCO₃ → CaO + CO₂

More practice: warm-up

1

When balancing, which numbers may you change?

2

How many H atoms are in 3H₂O?

3

How many O atoms are in 2CO₂?

4

Is 2H₂ + O₂ → 2H₂O balanced?

5

Why should coefficients be in the lowest whole-number ratio?

More practice: on your own

1

Balance: K + H₂O → KOH + H₂

2

Balance: Zn + HCl → ZnCl₂ + H₂

3

Balance: C₃H₈ + O₂ → CO₂ + H₂O

4

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

5

Balance: KClO₃ → KCl + O₂

Challenge

1

Balance the equation for cellular respiration: C₆H₁₂O₆ + O₂ → CO₂ + H₂O

2

Balance the burning of octane (in gasoline): C₈H₁₈ + O₂ → CO₂ + H₂O

3

Balance: Al + CuSO₄ → Al₂(SO₄)₃ + Cu, treating sulfate as a unit.

Check your understanding

Quiz

1.

Which is the correctly balanced equation for hydrogen and oxygen reacting to form water?

2.

What coefficient goes in front of O₂ to balance CH₄ + __O₂ → CO₂ + 2H₂O?

3.

Balance: __Al + __O₂ → __Al₂O₃. What are the coefficients?

4.

When balancing, why should you usually leave elements that appear on their own (like O₂ or Fe) until last?

5.

How many oxygen atoms are on the right side of 2C₂H₆ + 7O₂ → 4CO₂ + 6H₂O?

6.

In Pb(NO₃)₂ + 2KI → PbI₂ + 2KNO₃, why can nitrate be balanced as one unit?

For parents and teachers

Big idea: C3.4 asks students to write balanced chemical equations, and C3.2 asks them to explain why we balance (atoms and mass are conserved). Balancing is a skill that improves with practice: most students need many examples before it feels natural.

Common difficulties:

  • Changing subscripts to force a balance. This is the most serious error, because it changes the substances.
  • Forgetting to recount after every change.
  • Multiplying wrongly: 3Al₂O₃ has 6 Al and 9 O (multiply the coefficient by each subscript).
  • Odd numbers of oxygen atoms in combustion problems: double everything and try again.
  • Not reducing to lowest terms.

How to help: ask your teen to talk you through each step, using an atom-count table. The pasta activity lets them "feel" that only whole molecules can be added. Use dry food that will not be eaten afterwards, or put it back in its package only if hands were clean.