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Practice sheet · Chemistry Path · Lens 1: Math

Balancing equations

Practice for The Math of Chemistry, 03 Balancing equations (book p.10) and Equations as sentences (p.76). Pencil-and-paper only: none of these reactions are experiments to try at home.
Warm-upCoreLevel Up
Name Date Time I spent
Remember

Atoms in = atoms out. Change the big numbers in front (coefficients) only. Never change the small subscripts: H2O2 is a different chemical from H2O.

Count, then fix. Start with the element in the fewest formulas; save H and O for last. A number after brackets multiplies what is inside: Mg(OH)2 has 2 O and 2 H. Use the smallest whole numbers; leave a box empty for 1.

Warm-up

Count and balance

Two or three formulas.
1

Count the atoms

The coefficient multiplies the whole formula.

3H2O:  H  O     2CO2:  C  O
Ca(OH)2, slaked lime:  Ca  O  H

2

Hydrogen meets chlorine

Hydrogen and chlorine gases make hydrogen chloride.

H2 + Cl2 → HCl

3

Table salt from scratch

Sodium metal and chlorine gas make sodium chloride (watch-only: it is violent).

Na + Cl2 → NaCl

4

Burning magnesium

Magnesium metal burns with a blinding white light, making magnesium oxide.

Mg + O2 → MgO

Core

Everyday reactions

Balance, then check with a count.
5

Barbecue propane

Propane burns in a gas grill, like natural gas on p.10.

C3H8 + O2 → CO2 + H2O

6

Rust

Iron + oxygen, simplified (real rust also holds water).

Fe + O2 → Fe2O3

7

Photosynthesis

The overall equation for plants (the real process has many steps).

CO2 + H2O → C6H12O6 + O2

Chemistry Practice · Chemistry Path · Unizon1/2
Chemistry Path · Unizon · PracticeBalancing equations
8

Splitting water

Electricity splits water into hydrogen and oxygen gas (electrolysis).

H2O → H2 + O2

9

Is the volcano balanced?

Baking soda + vinegar (p.13). Fill in the count table. Is it already balanced?

NaHCO3 + CH3COOH → NaCH3COO + H2O + CO2

NaHCO
Left
Right
10

Antacid

Milk of magnesia, Mg(OH)2, neutralizes stomach acid, HCl: an acid + base reaction that makes a salt + water.

Mg(OH)2 + HCl → MgCl2 + H2O

Level Up

Bigger molecules

Tip: if O comes out odd, double everything.
11

Lighter fuel

Butane burns in a lighter.

C4H10 + O2 → CO2 + H2O

12

Rising bread

Yeast turns sugar into ethanol and the CO2 bubbles that lift dough.

C6H12O6 → C2H5OH + CO2

13

In the engine

Gasoline is a mix; octane stands in for it here.

C8H18 + O2 → CO2 + H2O

14

Spot the mistake

Hydrogen peroxide fizzes into water and oxygen gas, O2. Someone wrote H2O2 → H2O + O. The atoms match, so what is wrong? Balance it properly:

H2O2 → H2O + O2

Make your own problem

Your turn to be the chemist

  1. Pick a reaction from the book or real life (cooking, cleaning, burning, rusting).
  2. Write it as a word equation first, then in symbols, unbalanced (p.76 shows how).
  3. Swap with someone. Balance theirs, then check each other with a count table.

My problem, and my worked answer:

Chemistry Practice · Chemistry Path · Unizon2/2
Chemistry Path · Unizon · PracticeBalancing equations

Try every problem first, then check here. Wrong answers are useful: find the step where your work and the key split apart.

The key never prints with Print my work or Print blank. Open it to get its own Print the answer key button.

Answer key

Worked solutions. A coefficient of 1 is usually left unwritten. Other whole-number multiples balance too, but use the smallest set.

Warm-up
1
H 6, O 3 · C 2, O 4 · Ca 1, O 2, H 2 The coefficient multiplies every atom; the 2 after the brackets doubles O and H.
2
H2 + Cl2 → 2HCl Left has 2 H and 2 Cl, so make 2 HCl.
3
2Na + Cl2 → 2NaCl Cl2 needs 2 NaCl, then 2 NaCl needs 2 Na.
4
2Mg + O2 → 2MgO O2 needs 2 MgO, then 2 MgO needs 2 Mg.
Core
5
C3H8 + 5O2 → 3CO2 + 4H2O C: 3 CO2. H: 8 ÷ 2 = 4 H2O. O on the right: 3 × 2 + 4 = 10, so 5 O2. Check: C 3 = 3, H 8 = 8, O 10 = 10.
6
4Fe + 3O2 → 2Fe2O3 O2 gives pairs, Fe2O3 gives threes: meet at 6 O (3 O2, 2 Fe2O3). That is 4 Fe.
7
6CO2 + 6H2O → C6H12O6 + 6O2 C: 6 CO2. H: 12 ÷ 2 = 6 H2O. O on the left: 12 + 6 = 18; glucose has 6, so 12 more = 6 O2.
8
2H2O → 2H2 + O2 2 H2O gives 2 O for one O2, and 4 H for 2 H2. (The reverse of the book’s p.10 example.)
9
Yes, balanced as written Na 1 = 1 · H 1 + 4 = 5 and 3 + 2 = 5 · C 1 + 2 = 3 and 2 + 1 = 3 · O 3 + 2 = 5 and 2 + 1 + 2 = 5. Every coefficient is 1.
10
Mg(OH)2 + 2HCl → MgCl2 + 2H2O Cl: 2 HCl. Then H on the left: 2 + 2 = 4, so 2 H2O. O: 2 = 2. Mg: 1 = 1.
Level Up
11
2C4H10 + 13O2 → 8CO2 + 10H2O With 1 C4H10: 4 CO2 + 5 H2O needs 13 O = 6.5 O2. Double it all: 2, 13, 8, 10. Check O: 26 = 16 + 10.
12
C6H12O6 → 2C2H5OH + 2CO2 H: 12 ÷ 6 = 2 C2H5OH. That uses 4 of the 6 C, so 2 CO2. Check O: 6 = 2 + 4.
13
2C8H18 + 25O2 → 16CO2 + 18H2O With 1 C8H18: 8 CO2 + 9 H2O needs 25 O = 12.5 O2. Double: 2, 25, 16, 18. Check O: 50 = 32 + 18.
14
2H2O2 → 2H2O + O2 The atoms in “H2O + O” do match, but oxygen gas is O2, not a lone O. You can’t change a formula to make it fit; change the coefficients instead.
Make your own: a good problem uses real formulas (look them up), and the balanced answer uses the smallest whole numbers. Check every element, not just the tricky ones.
Chemistry Practice · Chemistry Path · UnizonAnswer key