Think of a reaction as taking apart one set of LEGO models and building new ones from exactly the same bricks. No brick vanishes and no new brick appears; the bricks are only reconnected. Atoms behave the same way. When methane burns on a gas stove, every carbon atom and every hydrogen atom that went into the flame comes out again, now attached to oxygen as carbon dioxide and water. A balanced equation is simply an honest bookkeeping record of that rearrangement. A chemical equation is a shorthand sentence describing a reaction: what you start with (reactants, on the left of the arrow) and what you end up with (products, on the right). The arrow reads as "yields" or "produces", and a plus sign on the left reads as "reacts with". Getting from a plain-language description to a correctly balanced equation happens in stages, and skipping a stage is where most errors creep in.
Three stages of writing an equation
- Word equation: names only, no formulas. E.g. "hydrogen gas reacts with oxygen gas to produce water".
- Skeleton equation: correct chemical formulas substituted in, but not yet balanced. E.g. .
- Balanced equation: whole-number coefficients added so the same number of each atom appears on both sides. E.g. .
Why we change coefficients, never subscripts
- Says HOW MANY units of the substance take part
- means two water molecules: 4 H and 2 O in total
- Multiplies every atom in the formula that follows it
- Free to change while balancing
- Says WHAT the substance is
- is hydrogen peroxide, not water
- Applies only to the atom or bracket it follows
- Fixed by bonding and ion charges; never change it to balance
The subscripts come from the chemistry you already know: ion charges for ionic compounds (criss-cross) and known molecular formulas such as , and . Once the skeleton equation has the right formulas, the only way left to fix the atom count is to use more or fewer whole units of each substance. That is why the coefficient is the only thing you may adjust. The atom-inventory table below is the tool that tells you which coefficient needs to change next.
A systematic balancing strategy
- Write the correct skeleton equation first — never change a subscript to balance an equation, since that changes the substance itself.
- Make an atom inventory: list each element (or each unchanged polyatomic ion) and count it on both sides.
- If a polyatomic ion appears unchanged on both sides, balance it as a single unit rather than atom-by-atom.
- Balance metals first, then other nonmetals (excluding H and O), then hydrogen, and balance oxygen last — oxygen is often easiest to fix once everything else is set, because it usually appears in several formulas and often also as a free element () whose coefficient changes nothing else.
- Only ever change the coefficient (the number in front of a formula) — never a subscript. Update the inventory after every change.
- Once balanced, check that all coefficients share no common factor (reduce to lowest whole-number ratio) and recount every atom on both sides to confirm.
| Element | Left: | Right: | Fix |
|---|---|---|---|
| C | 2 | 1 | put 2 in front of |
| H | 6 | 2 | put 3 in front of |
| O | 2 | 2(2) + 3(1) = 7 | need , then double everything |
- Fraction trick (for stubborn equations): when the last element to balance is a free diatomic element (, , ), use a fraction such as temporarily, then multiply every coefficient by the denominator to get whole numbers.
- Odd–even trick: if one side has an odd number of an atom and the other side can only ever give an even number (because of a subscript 2), double the formula with the odd count first.
- Polyatomic units: in , count as one unit; bracketed subscripts multiply everything inside the brackets.
- Water as HOH: in acid–base or hydroxide reactions, writing water as H–OH lets you balance groups as units too.
States, conditions and the final check
A completed equation should also show the physical state of each substance, in brackets immediately after its formula: solid (s), liquid (l), gas (g), or aqueous — dissolved in water — (aq). These are required for full marks and are essential once you study reaction types and precipitates. Conditions such as heat (), electricity or a catalyst are written above the arrow; they are not reactants and are never balanced.