You may only change the large numbers in front of formulas, never the small numbers inside them. The small numbers define the substance, and the large numbers say how much of it reacts.
Many students know this rule and still break it when an equation will not balance. Changing a subscript feels like a shortcut, but it swaps one substance for another and the equation stops being true.
Why does changing a subscript cause a problem?
Think of H₂O as a fixed recipe: two hydrogen atoms joined to one oxygen atom, which is water. H₂O₂ has two oxygen atoms and is a different compound with different properties. No amount of counting makes them the same thing.
| Written as | What it means | Is it the same substance as H₂O? |
|---|---|---|
| H₂O | 1 molecule of water | Yes |
| 2H₂O | 2 molecules of water | Yes, there are two of them |
| H₂O₂ | 1 molecule of a different compound | No |
The equation balance reasoning trainer keeps every subscript fixed and shows you the atom count, which is a safe place to practise this habit. The mole and equation-ratio tutor then uses the balanced equation to show why the coefficients matter for calculations.
Worked example 1: a short equation
Question. Balance: Mg + O₂ → MgO.
The mistaken solution. The left side has 2 oxygen atoms and the right has 1. The student changes MgO to MgO₂ so that both sides have 2 oxygen atoms. The counts match, but MgO₂ is not magnesium oxide, so the equation is wrong.
The repaired solution. Build an atom table and change coefficients only.
| Element | Left | Right (MgO) |
|---|---|---|
| Mg | 1 | 1 |
| O | 2 | 1 |
Oxygen is short on the right, so put a 2 in front of MgO. Now the right side has 2 O and 2 Mg, so magnesium is short on the left. Put a 2 in front of Mg.
2Mg + O₂ → 2MgO
| Element | Left | Right |
|---|---|---|
| Mg | 2 | 2 |
| O | 2 | 2 |
Worked example 2: an equation that needs a plan
Question. Balance: C₃H₈ + O₂ → CO₂ + H₂O.
Start with the elements that appear in only one substance on each side, and leave oxygen until last because it appears in two products.
- Carbon. The left has 3 C, so put 3 in front of CO₂. The right now has 3 C.
- Hydrogen. The left has 8 H, so put 4 in front of H₂O, which gives 4 × 2 = 8 H on the right.
- Oxygen. The right now has 3 × 2 = 6 from CO₂ and 4 × 1 = 4 from H₂O, a total of 10 O. The left has O₂, so put 5 in front of it to get 10 O.
C₃H₈ + 5O₂ → 3CO₂ + 4H₂O
| Element | Left | Right |
|---|---|---|
| C | 3 | 3 |
| H | 8 | 8 |
| O | 10 | 10 |
Check. The formulas are identical to the ones given, and each total matches. Only coefficients were added.
A routine that keeps subscripts safe
- Copy the formulas once and never rewrite them. Write the equation with gaps in front of each formula where coefficients will go.
- Draw the atom table. One row per element, one column per side.
- Start with an element that appears once on each side. Leave a free element such as O₂ or H₂ until last.
- Change one coefficient at a time and update the table. This shows you which change caused which effect.
- Finish with a full recount from the final equation. Do not rely on the last line of your working.
If a fraction appears, for example 3/2 O₂, double every coefficient to clear it. Check the final set has no common factor, so 4, 2, 4 would be reduced to 2, 1, 2.
Check yourself
1. Balance: Na + Cl₂ → NaCl.
Show answer
Chlorine: the left has 2 Cl, the right has 1, so put 2 in front of NaCl. Now sodium is 1 on the left and 2 on the right, so put 2 in front of Na.
2Na + Cl₂ → 2NaCl. Na 2 = 2 and Cl 2 = 2.
2. Balance: CH₄ + O₂ → CO₂ + H₂O.
Show answer
Carbon is already 1 and 1. Hydrogen: the left has 4, so put 2 in front of H₂O. Oxygen on the right is 2 + 2 = 4, so put 2 in front of O₂.
CH₄ + 2O₂ → CO₂ + 2H₂O. C 1 = 1, H 4 = 4, O 4 = 4.
3. A student balances N₂ + H₂ → NH₃ by writing N₂ + H₂ → N₂H₂. Explain in one or two sentences why this is not allowed, then balance the equation correctly.
Show answer
N₂H₂ is a different substance from ammonia, NH₃, so the equation would no longer describe the reaction given. Only coefficients may change.
Nitrogen: put 2 in front of NH₃, which gives 2 N and 6 H on the right. Put 3 in front of H₂ to get 6 H on the left.
N₂ + 3H₂ → 2NH₃. N 2 = 2 and H 6 = 6.
Where to go next
The lesson on balancing atoms without changing subscripts builds the atom table habit, and checking a balanced equation independently gives a final-line routine. Once your equations are reliable, the mole ratio help page shows how to use them in calculations, and the Chemistry original practice page has mixed questions.
If you understand the rule but still reach for the subscript under pressure, a teacher can watch your first ten seconds on an equation and point to the habit that triggers it. That is the kind of reasoning check we offer in online one-to-one Chemistry tuition.