Chemical reactions · Model
Symbol equations and balancing
Written straight out, the equation for making water destroys an oxygen atom. Fixing it teaches you the one number in chemistry you are allowed to change.
Start here
Count the oxygens. One of them has gone missing.
H2 + O2 H2O. Two oxygen atoms on the left. One on the right. Last lesson you proved that atoms are never destroyed — so this equation, exactly as written, is a claim that one of them was.
What has to change to fix it?
The number of particles. Two hydrogen particles react with one oxygen particle and make two water particles — and writing a 2 in front of H2O says so. What you must not touch is the small number inside a formula: changing H2O to H2O2 also balances the oxygen, and it does it by quietly replacing the water with bleach.
A symbol equation says which substances react and how many particles of each. The small numbers inside a formula are part of the substance's name — H2O is water. The big numbers in front say how many of that particle take part, and those are the only numbers you are allowed to change.
An equation is balanced when every kind of atom appears the same number of times on both sides. It has to be, because atoms are not created or destroyed.
Your turn · balance four equations
Change only the big numbers. Watch the counters.
Hydrogen burns in oxygen to make water. The products are known; only the numbers in front are in question.
1H2
1O2
1H2O
H atoms
2 left · 2 right
Matched.Too few on the right.Too few on the left.
O atoms
2 left · 1 right
Matched.Too few on the right.Too few on the left.
Balanced.
Two hydrogen particles to one oxygen particle, making two waters. That two-to-one ratio is the fact a word equation could never tell you.
Balanced, but not in its smallest numbers. Every number in front is 2 times what it needs to be — and an equation is always written with the smallest whole numbers that work.
Magnesium ribbon burns in air to make magnesium oxide.
1Mg
1O2
1MgO
Mg atoms
1 left · 1 right
Matched.Too few on the right.Too few on the left.
O atoms
2 left · 1 right
Matched.Too few on the right.Too few on the left.
Balanced.
One oxygen particle carries two oxygen atoms, so it can oxidise two magnesium atoms. That is why the 2 lands in front of the Mg and the MgO together.
Balanced, but not in its smallest numbers. Every number in front is 2 times what it needs to be — and an equation is always written with the smallest whole numbers that work.
Sodium burns in chlorine to make sodium chloride — table salt.
1Na
1Cl2
1NaCl
Na atoms
1 left · 1 right
Matched.Too few on the right.Too few on the left.
Cl atoms
2 left · 1 right
Matched.Too few on the right.Too few on the left.
Balanced.
The same shape of answer as the magnesium one, for the same reason: chlorine travels in pairs, so it takes two sodium atoms to use one chlorine particle up.
Balanced, but not in its smallest numbers. Every number in front is 2 times what it needs to be — and an equation is always written with the smallest whole numbers that work.
Methane burns on a gas hob to make carbon dioxide and water. Four terms this time.
1CH4
1O2
1CO2
1H2O
C atoms
1 left · 1 right
Matched.Too few on the right.Too few on the left.
H atoms
4 left · 2 right
Matched.Too few on the right.Too few on the left.
O atoms
2 left · 3 right
Matched.Too few on the right.Too few on the left.
Balanced.
Balance the carbon and hydrogen first and the oxygen falls out last — four oxygen atoms needed on the right, so two O2 particles on the left. Working in that order saves a lot of guessing.
Balanced, but not in its smallest numbers. Every number in front is 2 times what it needs to be — and an equation is always written with the smallest whole numbers that work.
All four. In every one of them you changed how many particles react and never what a particle is — and in every one of them the counters ended up matching, because they were always going to have to.
The move that looks like it works
There is a much quicker way to balance the hydrogen and oxygen equation. Add a small 2 to the water instead of a big 2 in front of it, and the counters agree immediately. Try it and see what it costs.
H2O2H2O22H2O
The counters agree: two hydrogens and two oxygens on each side. And you are no longer describing the reaction you were asked about. H2O2 is hydrogen peroxide — it bleaches hair, burns skin at high concentration and has been used as rocket fuel. One small digit, and the equation now says that burning hydrogen produces bleach. It does not.
The oxygens now match — and the hydrogens do not, until hydrogen gets a 2 as well: 2H2 + O2 makes 2H2O, four hydrogens and two oxygens on each side. The substances are untouched: water is still water, and all you have changed is how many of each particle take part. That is the only kind of change balancing is allowed to make.
Key fact
Balancing changes how many particles react, never what the particles are. Big numbers in front are yours to change; small numbers inside a formula belong to the substance.
Think again
“Balancing is just a maths puzzle — as long as the numbers add up, the equation is right.”
Every balanced equation does have matching counts on both sides. Commit before you read on.
Matching counts are necessary and nowhere near sufficient. H2 + O2 makes H2O2 is perfectly balanced and completely false, because that reaction does not happen and that substance is not water. The chemistry decides what the products are; the balancing only makes the arithmetic honest afterwards.
So the order of work matters. Find out what the products actually are, write their formulae, and only then adjust the numbers in front. An equation that balances beautifully around the wrong product is worth nothing — and it is a mistake that a calculator will never catch for you.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Recall
In a symbol equation, which numbers are you allowed to change when balancing?
Rung 2 · The one that catches people
A student balances the equation as H2 + O2 makes H2O2, and points out that both sides now have two hydrogens and two oxygens. What is wrong?
Rung 3 · Explain
Balance the equation for magnesium burning in oxygen, and explain why a 2 is needed in front of both the Mg and the MgO — and why putting a small 2 in the MgO would be wrong.
Rung 4 · Take it somewhere new
A hydrogen car burns hydrogen with oxygen from the air. The engineers need to know how much oxygen to supply for a given amount of hydrogen. Explain what the balanced equation tells them that a word equation cannot, and what would happen if they supplied too little.
Key note
A symbol equation says which substances react and how many particles of each. It is balanced when every kind of atom appears the same number of times on both sides — which it must, because atoms are never created or destroyed. Balance by changing the big numbers in front of formulae only: the small numbers inside a formula are part of the substance, and changing one changes what the equation is about.
Going further
The big numbers are not decoration; they are the reason this notation was worth inventing. 2H2 + O2 makes 2H2O says that hydrogen and oxygen react in a two-to-one ratio, so a hydrogen fuel cell needs exactly twice as many hydrogen particles as oxygen ones, and a plant scaling that up needs the ratio right to the tonne. Word equations cannot carry that. This is the whole reason your course spends a year learning symbols.
Two conventions worth having now. The numbers in front must be whole — you may not write half a particle, even though 1/2 O2 would sometimes be tidier — and they are written in the smallest whole numbers that work, so 4H2 + 2O2 makes 4H2O is balanced and would still be marked down. At GCSE two more things get added to the same line: state symbols in brackets, and the fact that this identical logic runs the calculation of how much product a reaction can make.
Before this lesson
At GCSE this becomes
- Balanced equations with state symbols, half equations and ionic equations — and using the ratio to calculate reacting masses.
Where to next
- Next: Combustion
Types of reaction
- Previous: Mass in a reaction
Ask Mr Badmus AI
Still not sure why the small numbers are off limits?
Lesson content © MrBadmusAI.