How to balance a chemical equation without guessing
HESI A2 topic: Chemical equations
- In a reaction, atoms are never created or destroyed, so both sides match.
- Change only coefficients, never subscripts; subscripts define the substance.
- Atoms = coefficient × subscript: 3H₂SO₄ has 12 oxygen atoms.
- Balance oxygen, or any element in several formulas, last.
- A fraction is fine midway; multiply everything to get whole numbers.
Key facts
- The law of conservation of mass: matter is not created or destroyed in a chemical reaction, so the total mass of reactants equals the total mass of products.
- Atoms in a formula = coefficient × subscript; for example, 3H₂SO₄ contains 12 oxygen atoms.
- Only coefficients may change when balancing; subscripts define the substance.
Show all 6 key factsShow fewer
- Balance an element that appears in more than one formula on a side last, often oxygen.
- A fractional coefficient is fine as a middle step; multiply every coefficient by the same number to get whole numbers.
- Reaction patterns: synthesis A + B → AB, decomposition AB → A + B, single replacement A + BC → AC + B, double replacement AB + CD → AD + CB, combustion fuel + O₂.
Quick check1 question · 2 more at the end
How many oxygen atoms are represented by 3H₂SO₄?
Correct answer: A.
To count atoms, multiply the coefficient by the subscript. Each H₂SO₄ unit has 4 oxygen atoms, and the coefficient 3 means three units, so 3 × 4 = 12 oxygen atoms. The same 3H₂SO₄ also contains 6 hydrogen atoms and 3 sulfur atoms.
A Correct: 3 units × 4 oxygen atoms per unit = 12 oxygen atoms.
B Seven comes from adding the coefficient and the subscript (3 + 4) instead of multiplying them.
C Twenty-four also multiplies by the hydrogen subscript (3 × 2 × 4); each subscript applies only to the atom written just before it.
D Four is the number of oxygen atoms in one H₂SO₄ unit; it ignores the coefficient 3.
Full lesson
Each part starts with its main idea. Open a part when you want the details.
The short answer: A balanced equation has the same number of each kind of atom on both sides, because the law of conservation of mass says atoms are only rearranged in a reaction. To balance one, count atoms, change only the coefficients in front of formulas, balance an element that appears in several formulas last, and reduce to the smallest whole numbers.
1 What does "balanced" actually mean?A balanced equation has the same number of each kind of atom on both sides of the arrow. 1 min
A balanced equation has the same number of each kind of atom on both sides of the arrow. That rule comes from the law of conservation of mass (also called conservation of matter). A reaction rearranges atoms into new substances, but it never creates or destroys them. So the total mass of the reactants always equals the total mass of the products.
If a burning sample seems to lose mass in an open dish, the missing mass left as gas, such as carbon dioxide and water vapor. Run the same reaction in a sealed container and the mass does not change.
2 Coefficients or subscripts: which can you change?You can change only the coefficients, the large numbers written in front of formulas. 1 min
You can change only the coefficients, the large numbers written in front of formulas. The subscripts, the small numbers inside a formula, tell you what the substance is. Turning H₂O into H₂O₂ would "balance" the oxygen but describe hydrogen peroxide instead of water.
To count atoms, multiply the coefficient by each subscript. In 3H₂SO₄ there are 3 × 2 = 6 hydrogen atoms, 3 sulfur atoms, and 3 × 4 = 12 oxygen atoms.
3 How do you balance an equation step by step?Work through it in a fixed order so you never have to guess. 1 min
Work through it in a fixed order so you never have to guess.
- Write correct formulas: Al + O₂ → Al₂O₃.
- Count each element on both sides. Aluminum: 1 and 2. Oxygen: 2 and 3.
- Oxygen is 2 on the left and 3 on the right. The smallest number both divide into is 6, so write 3O₂ on the left and 2Al₂O₃ on the right.
- Recount: aluminum is now 1 on the left and 4 on the right, so write 4Al.
- Final check: 4Al + 3O₂ → 2Al₂O₃ has 4 aluminum and 6 oxygen atoms on each side.
Two habits help. Leave an element that shows up in several formulas, often oxygen, until last. And at the end, make sure the coefficients cannot all be divided by a common number.
4 What if you end up with a fraction?A fraction is allowed as a middle step; you just clear it at the end. 1 min
A fraction is allowed as a middle step; you just clear it at the end. Take butane burning: C₄H₁₀ + O₂ → CO₂ + H₂O.
- Carbon: 4 on the left, so write 4CO₂.
- Hydrogen: 10 on the left, so write 5H₂O.
- Oxygen on the right is now 8 + 5 = 13 atoms. Oxygen comes as O₂, so you need 13/2 O₂.
- Multiply everything by 2: 2C₄H₁₀ + 13O₂ → 8CO₂ + 10H₂O.
5 How do you recognize the reaction type?Look at how many substances are on each side and whether a lone element appears. 1 min
Look at how many substances are on each side and whether a lone element appears.
| Type | Pattern | Clue |
|---|---|---|
| Synthesis | A + B → AB | Ends with one product |
| Decomposition | AB → A + B | Starts with one reactant |
| Single replacement | A + BC → AC + B | A lone element trades places, e.g. Zn + 2HCl → ZnCl₂ + H₂ |
| Double replacement | AB + CD → AD + CB | Two compounds swap partners |
| Combustion | Fuel + O₂ → products + heat | O₂ reacts with a fuel; carbon-hydrogen fuels give CO₂ + H₂O |
Synthesis joins parts into something larger, and decomposition breaks something down. Single and double replacement are both exchange reactions: bonds break and new ones form. A double replacement that makes an insoluble solid is called a precipitation reaction.
Common mistakes
The traps students fall into most. Read these before you practice.
Watch out: Balance atoms, not molecules; the number of molecules on each side can differ.
Watch out: A coefficient multiplies every atom in the formula after it, not just the first element.
Watch out: Changing a subscript makes a different substance; H₂O₂ is hydrogen peroxide, not water.
Watch out: Mass seems to vanish when a gas escapes from an open container, but it is not destroyed; in a sealed container the mass stays the same.
How to remember it
Memory hook: "Count, coefficient, check." Count every atom, change only coefficients, then check every element one last time. If oxygen is in several places, save it for last.
Self-check:
- How many oxygen atoms are in 2Ca(NO₃)₂? (Hint: the subscript outside the parentheses multiplies everything inside.)
- Balance H₂ + Cl₂ → HCl and name the reaction type.
- Explain why a candle burned in a sealed jar weighs the same before and after.
Show answers
- 12 oxygen atoms.
- One Ca(NO₃)₂ has 3 × 2 = 6 oxygen atoms.
- The coefficient 2 doubles that: 2 × 6 = 12.
- H₂ + Cl₂ → 2HCl, a synthesis reaction.
- Left side: 2 H and 2 Cl. Right side: 1 H and 1 Cl.
- Write 2HCl. Now each side has 2 H and 2 Cl.
- Two reactants join into one product, so it is synthesis.
- Atoms are only rearranged, and no gas can escape.
- The law of conservation of mass says no atoms are created or destroyed.
- In an open dish, the CO₂ and water vapor leave as gas.
- In a sealed jar they stay inside, so the total mass does not change.