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πŸ“– Lesson 9 ⏱ ~30 min Year 10 Β· Unit 2 ⚑ +115 XP

Writing and Balancing Equations

In 2022, CSIRO's mineral processing teams balanced over 10 million chemical equations to optimise recovery rates at Australian mine sites, each one must be atom-perfect.

Today's hook: In 2022, CSIRO's mineral processing division reported that incorrect stoichiometry in hydrometallurgical plants wastes up to 15% of reagent chemicals, costing Australian mining companies hundreds of millions of dollars annually. A chemical equation off by even one atom means the wrong amount of reactant is added, producing waste instead of product. Every balanced equation is a precise recipe: the atoms on the left must exactly match the atoms on the right. If you were designing a chemical plant, how would you check that every equation your team uses is correct?
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Warm-up
Think First
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If you split water into hydrogen and oxygen, you get two hydrogen atoms for every oxygen atom in the formula Hβ‚‚O. Now imagine writing a recipe for making water from those gases, how many molecules of each gas would you need to use, and why? Try to sketch or write your best guess.

The law of conservation of mass says atoms are never created or destroyed in a chemical reaction. So when you write a chemical equation, what rule must every correct equation obey? Why do you think chemists bother writing equations instead of just describing reactions in words?

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Learning objectives
What you'll master
3 areas

● Know

  • How to write word equations for chemical reactions
  • The basics of symbolic equations using chemical formulas
  • What state symbols are: (s), (l), (g), (aq)

● Understand

  • Why equations must be balanced to obey conservation of mass
  • That only coefficients (numbers in front) can be changed to balance equations
  • How atom counting verifies that an equation is balanced

● Can do

  • Write word equations for synthesis, decomposition, combustion and displacement reactions
  • Balance simple symbolic equations by counting atoms
  • Identify whether a given symbolic equation is balanced
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Vocabulary Β· tap to flip
Words You Need
6 terms
Core term Concept Skill Reference
Word equation
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Word equation
A way of describing a chemical reaction using the names of reactants and products.
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Symbolic equation
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Symbolic equation
A chemical equation using chemical formulas and symbols to represent reactants and products.
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Balanced equation
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Balanced equation
An equation with the same number of each type of atom on both sides, obeying conservation of mass.
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Coefficient
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Coefficient
A number placed in front of a chemical formula to show how many molecules or formula units are involved.
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Subscript
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Subscript
A small number written after an element symbol in a formula, showing how many atoms of that element are in the molecule.
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State symbol
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State symbol
A symbol showing the physical state of a substance: (s) solid, (l) liquid, (g) gas, (aq) aqueous (dissolved in water).
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Cross-lesson links: Every reaction type you studied in Lessons 6–8 (synthesis, decomposition, displacement, combustion) gets expressed using the equation skills you build here, this lesson is the language toolkit for the whole unit. Balanced equations also underpin Lesson 15, where you write the Haber process equation and understand why exact ratios matter for industrial yield.
Core learning
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Stop & Check, Word Equations
Quick Check
+5 XP

Write H2 + O2 β†’ H2O on a piece of paper and count the atoms: two hydrogens and two oxygens on the left, two hydrogens and only one oxygen on the right, one oxygen atom has vanished, which is impossible. A balanced chemical equation is a quantitative description of a reaction. It tells you not just what reacts and what forms, but in what proportions. Balancing equations is one of the most fundamental skills in chemistry.

The rules for balancing:

  1. Write the correct formulas for all reactants and products.
  2. Count the atoms of each element on both sides.
  3. Add coefficients (numbers in front of formulas) to make atom counts equal for every element.
  4. Never change subscripts within formulas - that changes the substance identity.
  5. Start with elements that appear in only one reactant and one product.
  6. Save hydrogen and oxygen for last, as they often appear in multiple compounds.

Balanced equations obey the law of conservation of mass because equal numbers of each type of atom appear on both sides. Atoms are rearranged, not created or destroyed.

Balancing Hβ‚‚ + Oβ‚‚ β†’ Hβ‚‚O Step by Step Step 1: Unbalanced Hβ‚‚ + Oβ‚‚ β†’ Hβ‚‚O H: 2 | O: 2 left side H: 2 | O: 1 right side O not balanced! β†’ Step 2: Add coefficient Hβ‚‚ + Oβ‚‚ β†’ 2Hβ‚‚O H: 2 | O: 2 left side H: 4 | O: 2 right side H not balanced! β†’ Step 3: Balanced! 2Hβ‚‚ + Oβ‚‚ β†’ 2Hβ‚‚O H: 4 | O: 2 left side H: 4 | O: 2 right side Both sides equal Law of Conservation of Mass H H H H O O = H H O H H O Same atoms in β†’ same atoms out Only change COEFFICIENTS, never change SUBSCRIPTS
Example

Balance the equation for ammonia synthesis: N2 + H2 -> NH3.

Nitrogen: 2 on left, 1 on right. Put coefficient 2 in front of NH3: N2 + H2 -> 2NH3.

Now hydrogen: 2 on left, 6 on right. Put coefficient 3 in front of H2: N2 + 3H2 -> 2NH3.

Final check: N: 2 = 2. H: 6 = 6. Balanced.

This tells us that one nitrogen molecule reacts with three hydrogen molecules to produce two ammonia molecules. In industrial practice, this ratio determines the stoichiometric feed rates for the Haber process.

Real-world anchor

Australian chemical engineering: Process engineers at plants like the Yara Pilbara ammonia facility use balanced equations to calculate exact feedstock requirements, predict product yields, and optimise reactor conditions. A 1% error in stoichiometric calculations could cost millions of dollars annually in wasted feedstock or lost production. Balanced equations are not just academic exercises - they are the foundation of industrial chemical accounting.

Watch out

You can balance equations by changing the formulas of compounds. This is false and represents a fundamental misunderstanding. The formulas (like H2O or CO2) are determined by chemical bonding and valency. They describe what the substance is. You cannot change H2O to H2O2 to balance an equation because H2O2 is hydrogen peroxide, a completely different substance with different properties. Only coefficients can be adjusted.

Fill the blanks+4 XP

Balance this equation for the combustion of propane.

C3H8(g) + O2(g) -> CO2(g) + H2O(g)
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Using formulas and counting atoms
Symbolic Equations and Balancing
+5 XP

Beyond simple balancing, chemists use several notations to convey more information about reactions.

State symbols indicate the physical state of each substance: (s) solid, (l) liquid, (g) gas, (aq) aqueous (dissolved in water). State symbols matter because they affect reaction energetics and feasibility. Water as H2O(l) and H2O(g) have different enthalpies.

Ionic equations show only the ions and molecules that actually participate in the reaction, omitting spectator ions that do not change. For example, the reaction between HCl and NaOH:

Full equation: HCl(aq) + NaOH(aq) -> NaCl(aq) + H2O(l)

Ionic equation: H+(aq) + OH-(aq) -> H2O(l)

The Na+ and Cl- ions are spectators - they appear on both sides unchanged. The ionic equation reveals the essential chemistry: acid + base -> water.

Example

A precipitation reaction between silver nitrate and sodium chloride:

Full: AgNO3(aq) + NaCl(aq) -> AgCl(s) + NaNO3(aq)

Ionic: Ag+(aq) + Cl-(aq) -> AgCl(s)

The Na+ and NO3- ions are spectators. The net ionic equation shows that any soluble silver salt reacting with any soluble chloride will produce silver chloride precipitate. This generality is why ionic equations are powerful - they reveal patterns that full equations obscure.

Real-world anchor

Australian analytical chemistry: Forensic chemists at the Australian Federal Police and state forensic laboratories use ionic equations to interpret evidence. When analysing white powders, they add reagents and observe precipitation, gas evolution, or colour changes. The ionic equations tell them which ions must be present or absent. This qualitative analysis underpins drug testing, environmental monitoring, and materials identification.

Watch out

State symbols are optional decorations. This is false. State symbols carry essential information. H2O(l) and H2O(g) are chemically identical but physically and energetically different. A reaction producing water vapour releases less energy than one producing liquid water because condensation releases additional heat. In equilibrium expressions, only aqueous and gaseous species appear - solids and pure liquids are omitted. State symbols are not decorative; they are chemically meaningful.

Spot the slip-up+5 XP

Find the error in this balanced equation.

The student wrote: 2H2 + O2 -> 2H2O2
  1. Hydrogen: 4 atoms on each side. Balanced.
  2. Oxygen: 2 atoms on left, 4 atoms on right. Balanced.
  3. Wait - the product is hydrogen peroxide, not water.
  4. The equation is actually balanced, but the product formula is wrong.
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Stop & Check, Balancing Practice
Quick Check
+5 XP

Here is a worked example for balancing the reaction between magnesium and oxygen:

Step 1: Mg + O2 β†’ MgO

Count: Left = 1 Mg, 2 O. Right = 1 Mg, 1 O. Oxygen is unbalanced.

Step 2: Try 2MgO on the right: Mg + O2 β†’ 2MgO

Count: Left = 1 Mg, 2 O. Right = 2 Mg, 2 O. Magnesium is now unbalanced.

Step 3: Add 2Mg on the left: 2Mg + O2 β†’ 2MgO

Count: Left = 2 Mg, 2 O. Right = 2 Mg, 2 O. Balanced!

State symbols (introduced briefly)

State symbols tell us the physical state of each substance:

  • (s) = solid
  • (l) = liquid
  • (g) = gas
  • (aq) = aqueous (dissolved in water)

Example: 2Mg(s) + O2(g) β†’ 2MgO(s)

Think about it
Why is balancing equations important? (Hint: revisit the law of conservation of mass from Lesson 1.)
A student is balancing: Hβ‚‚ + Oβ‚‚ β†’ Hβ‚‚O. They change Hβ‚‚O to Hβ‚‚Oβ‚‚ to make the oxygen balance. What is wrong with this approach?
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Heads-up Β· common traps
Spot the Trap
3 myths
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Wrong: "You can change subscripts to balance an equation." No οΏ½ changing subscripts changes the substance. H 2 O is water; H 2 O 2 is hydrogen peroxide. Only coefficients can be changed.

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Right: Only coefficients, the numbers placed in front of a formula, can be adjusted when balancing. Changing a subscript changes the identity of the substance entirely; Hβ‚‚O and Hβ‚‚Oβ‚‚ are completely different chemicals.

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Wrong: "A balanced equation is just for show, it doesn't matter if it's unbalanced." No οΏ½ an unbalanced equation violates the law of conservation of mass. Atoms cannot be created or destroyed in chemical reactions.

βœ“

Right: A balanced equation is chemically necessary, it reflects the law of conservation of mass. An unbalanced equation is simply incorrect because it implies atoms are being created or destroyed, which cannot happen.

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Wrong: "State symbols are optional and don't mean anything." State symbols give important information about the conditions of the reaction and help scientists predict how substances will behave.

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Right: State symbols are chemically meaningful, (s), (l), (g) and (aq) tell you the physical state of each substance and affect how the reaction proceeds, the energy change involved, and how equilibrium expressions are written.

Australian Context

Chemistry in Australian Industry

Australia's mining and metallurgical industries rely heavily on balanced chemical equations. When BHP extracts iron from iron ore, engineers use balanced equations to calculate exactly how much coke (carbon) is needed to reduce the iron oxide, and how much carbon dioxide will be produced.

At the Tomago aluminium smelter near Newcastle, chemists use symbolic equations to understand the electrolysis of aluminium oxide. Balanced equations ensure that raw materials are used efficiently and waste is minimised. Without balanced equations, industrial chemistry would be guesswork, costing money and creating unnecessary pollution.

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From the lesson
Copy Into Books

✍ Copy Into Your Books

β–Ύ

Word Equations

  • reactant + reactant β†’ product + product
  • Use substance names
  • Always check arrow direction

Balancing Rules

  • Count atoms on each side
  • Change only COEFFICIENTS
  • Never change SUBSCRIPTS
  • Recheck all atoms at the end

State Symbols

  • (s) = solid
  • (l) = liquid
  • (g) = gas
  • (aq) = aqueous (dissolved)
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From the lesson
Diagram
Diagram
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From the lesson
Activity 1
Activity 1

Write Word Equations

Write a word equation for each reaction described.

1 Calcium carbonate decomposes when heated to produce calcium oxide and carbon dioxide.
Answer in your book.
2 Zinc metal displaces copper from copper sulfate solution.
Answer in your book.
3 Hydrochloric acid reacts with sodium hydroxide to produce sodium chloride and water.
Answer in your book.
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From the lesson
Activity 2
Activity 2

Balance by Atom Counting

Count the atoms on each side and determine if the equation is balanced. If not, write the balanced version.

1 N2 + H2 β†’ NH3
Answer in your book.
2 Fe + O2 β†’ Fe2O3
Answer in your book.
3 CH4 + O2 β†’ CO2 + H2O
Answer in your book.
Reflect
Revisit your thinking
reflect

At the start of this lesson, the hook told you that a chemical equation is the most compact "recipe" in science, get even one atom wrong and an entire industrial plant produces waste instead of product.

Now that you can write and balance equations yourself, can you see why getting every coefficient right really matters? What was the trickiest part of balancing, and how has your picture of what a chemical equation actually represents changed since the start of this lesson?

Interactive Tool, Balance Equations Lab Open fullscreen β†—
A balanced equation means the number of ______ is equal on both sides.
Quick check Β· multiple choice
1
Quick check
What does a word equation show?
+10 XP
2
Quick check
In the equation H 2 + Cl 2 β†’ 2HCl, what does the '2' in front of HCl mean?
+10 XP
3
Quick check
What coefficients balance the equation __Mg + __O 2 β†’ __MgO?
+10 XP
4
Quick check
How many oxygen atoms are on each side of 2H 2 + O 2 β†’ 2H 2 O?
+10 XP
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Quick check
A student writes C + O 2 β†’ CO 2 and says it is balanced. Another writes H 2 + O 2 β†’ H 2 O and says it is balanced. Who is correct and why?
+10 XP
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From the lesson
Additional content
Short answer
SA
Short answer Β· explain in your own words
Show your reasoning
3 questions
Understand Core 2 marks

Q1. 1. Explain the difference between a word equation and a symbolic equation. Give one example of each for the same reaction. 4 MARKS

Apply Core 3 marks

Q2. 2. Balance the equation for the reaction between nitrogen and hydrogen to form ammonia: N 2 + H 2 β†’ NH 3 . Show your working by counting atoms on each side. 4 MARKS

Analyse Core 3 marks

Q3. 3. A student argues that you can balance H 2 + O 2 β†’ H 2 O by changing the formula to H 2 O 2 . Explain why this is incorrect and demonstrate the correct way to balance this equation. 4 MARKS

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From the lesson
Revisit

Revisit Your Thinking

Go back to your Think First answer. Has your understanding changed?

  • Were your atom counts for H2 + O2 β†’ H2O correct?
  • Can you now balance this equation properly?
Update your thinking in your book.
Model answers (click to reveal)

Answers

β–Ύ

MCQ 1

BA word equation shows the names of the reactants and products in a chemical reaction.

MCQ 2

BThe '2' in front of HCl is a coefficient, meaning two molecules of hydrogen chloride are produced.

MCQ 3

A2Mg + O2 β†’ 2MgO is balanced: 2 Mg and 2 O on each side.

MCQ 4

CLeft side has 2 oxygen atoms (from O2). Right side has 2 Γ— 1 = 2 oxygen atoms (from 2H2O). The equation is balanced.

MCQ 5

DC + O2 β†’ CO2 is balanced: 1 C and 2 O on each side. H2 + O2 β†’ H2O is NOT balanced: 2 O on the left but only 1 O on the right. It should be 2H2 + O2 β†’ 2H2O.

Short Answer 1

Model answer: A word equation uses the names of substances to describe a reaction. For example: hydrogen + oxygen β†’ water. A symbolic equation uses chemical formulas and symbols instead of names. For the same reaction: H2 + O2 β†’ H2O. Symbolic equations are more concise and allow chemists to balance reactions by counting atoms, while word equations are clearer for beginners and ensure everyone understands which substances are involved.

Short Answer 2

Model answer: In N2 + H2 β†’ NH3, the left side has 2 nitrogen atoms and 2 hydrogen atoms. The right side has 1 nitrogen atom and 3 hydrogen atoms. To balance nitrogen, place a 2 in front of NH3: N2 + H2 β†’ 2NH3. Now the right side has 2 nitrogen atoms and 6 hydrogen atoms. To balance hydrogen, place a 3 in front of H2: N2 + 3H2 β†’ 2NH3. Final check: left = 2 N, 6 H; right = 2 N, 6 H. Balanced.

Short Answer 3

Model answer: Changing H2O to H2O2 is incorrect because H2O is water and H2O2 is hydrogen peroxide, they are completely different substances. In balancing, you can only change coefficients (numbers in front), never subscripts (small numbers in formulas). The correct way to balance H2 + O2 β†’ H2O is: count atoms (2 H, 2 O on left; 2 H, 1 O on right). Place a 2 in front of H2O: H2 + O2 β†’ 2H2O. Now right side has 4 H, 2 O. Place a 2 in front of H2: 2H2 + O2 β†’ 2H2O. Now both sides have 4 H and 2 O.

Quick-fire challenge
Game time
+25 XP
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Interactive
Lesson Game
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