Balancing equations

Write down "zinc reacts with dilute sulphuric acid to give zinc sulphate and hydrogen" as a chemical equation, and you get $\text{Zn} + \text{H}_2\text{SO}_4 \longrightarrow \text{ZnSO}_4 + \text{H}_2$ . Count the atoms and this particular equation is already correct — but change the metal to magnesium reacting with oxygen, $\text{Mg} + \text{O}_2 \longrightarrow \text{MgO}$ , and the atom count on the two sides no longer agrees. Nature does not allow atoms to appear or vanish during a reaction, so an equation that leaves atoms unaccounted for is simply wrong, however sensible the chemistry sounds in words.

Balancing is the fix: adjusting whole-number multipliers in front of formulae — never touching the formulae themselves — until every element has the same count of atoms on both sides. This article builds the reasoning behind that rule from the Law of Conservation of Mass, works through the systematic hit-and-trial method step by step, and re-solves the magnesium example carefully so you can see exactly why each coefficient goes where it does.

The core insight

Because atoms are conserved in any chemical reaction, an equation is balanced only when adjustable whole-number coefficients (never the formula subscripts) make the count of every element equal on both the reactant and product sides.

The core idea

A chemical equation is a sentence written in the language of formulae, and like any sentence it can be grammatically fine yet factually wrong. The fact it must obey is the Law of Conservation of Mass: matter is neither created nor destroyed in a chemical reaction, so the reactants simply rearrange into products without a single atom being gained or lost anywhere along the way.

\text{atoms of element } X \text{ on the reactant side} = \text{atoms of element } X \text{ on the product side}

where: $X$ stands for any element present in the equation — the equality must hold separately for every element, not just for the total mass. An equation that satisfies this test for every element it contains is called a balanced equation; one that fails it for even a single element is only a skeleton equation — a correct list of reactants and products, but not yet a correct account of quantities. The only tool allowed for fixing a mismatch is the coefficient: a whole number written in front of an entire formula, which multiplies every atom inside that formula. Placing a 2 in front of $\text{H}_2\text{O}$ gives $2\text{H}_2\text{O}$ , meaning 4 hydrogen atoms and 2 oxygen atoms — the formula itself, $\text{H}_2\text{O}$ , is untouched. This is the one rule that cannot be bent: subscripts inside a formula must never be changed to balance an equation, because a subscript defines what the substance is. Turning $\text{H}_2\text{O}$ into $\text{H}_2\text{O}_2$ does not balance oxygen — it silently swaps water for hydrogen peroxide, a different compound with different properties, which is not balancing at all but a factual error dressed up as a fix.

Figure

Two balance pans compare atom counts, reactant side pan tips level with product side pan once a coefficient of two is placed before MgO showing two magnesium and two oxygen atoms matching on both sides

Why it works

There is no algebraic shortcut prescribed at this level — the accepted method is deliberately called hit-and-trial, meaning a disciplined trial-and-error process, not guessing at random.

Step 1. Write the skeleton equation using the correct chemical formulae for every reactant and product, exactly as chemistry gives them; nothing here may later be edited except by adding coefficients in front.

Step 2. Count the atoms of each element separately on the reactant side and on the product side, listing the counts element by element so nothing is missed.

Step 3. Compare the two lists and identify every element whose count does not already match between the two sides.

Step 4. Place a whole-number coefficient in front of the formula (or formulae) containing the mismatched element, choosing the smallest number that brings the two counts into agreement, and remember that this coefficient multiplies every atom in that formula at once.

Step 5. Recount all elements after every single change, not just the one just adjusted, because fixing one element's balance very often disturbs an element that matched a moment ago.

Step 6. Repeat Steps 3 to 5 until every element balances simultaneously, then check whether all the coefficients share a common factor and, if they do, divide through so the equation is written in its simplest whole-number form. A practical habit that speeds this up: balance elements that appear in only one reactant formula and one product formula first, and leave elements that appear in several formulae, or as free diatomic molecules such as $\text{O}_2$ or $\text{H}_2$ , for later — those are the ones most likely to need a second adjustment once earlier counts shift.

Worked example

Problem. Balance the skeleton equation for magnesium burning in oxygen: $\text{Mg} + \text{O}_2 \longrightarrow \text{MgO}$ .

Step 1. Count atoms on the reactant side: Mg = 1 (one magnesium atom), O = 2 (the subscript on $\text{O}_2$ shows two oxygen atoms bonded together as a molecule).

Step 2. Count atoms on the product side: Mg = 1, O = 1, since a single $\text{MgO}$ unit contains one atom of each element.

Step 3. Compare the two counts: magnesium matches, 1 on each side, but oxygen does not — 2 on the reactant side against only 1 on the product side.

Step 4. Fix oxygen by placing a coefficient of 2 in front of $\text{MgO}$ , since the subscript inside $\text{MgO}$ itself must never be altered: this gives $\text{Mg} + \text{O}_2 \longrightarrow 2\text{MgO}$ , and now the product side has O = 2, matching the reactant side.

Step 5. Recount magnesium after that change: $2\text{MgO}$ now contains 2 magnesium atoms on the product side, but the reactant side still shows only 1 magnesium atom, so magnesium has gone out of balance as a direct consequence of fixing oxygen.

Step 6. Fix magnesium by placing a coefficient of 2 in front of Mg on the reactant side, giving $2\text{Mg} + \text{O}_2 \longrightarrow 2\text{MgO}$ , and then perform a final full recount: reactant side Mg = 2, O = 2; product side Mg = 2, O = 2. Every element now matches, and the coefficients 2, 1, 2 share no common factor greater than 1, so this is already the simplest form.

2\text{Mg}(s) + \text{O}_2(g) \longrightarrow 2\text{MgO}(s)

The balanced equation is $2\text{Mg} + \text{O}_2 \longrightarrow 2\text{MgO}$ , and it took exactly one re-adjustment: fixing oxygen first disturbed magnesium, which was then fixed in turn — a small but typical illustration of why every element must be rechecked after every change, right up to the final recount.

Competitive stretch

Compare this with the zinc–sulphuric acid equation from earlier, $\text{Zn} + \text{H}_2\text{SO}_4 \longrightarrow \text{ZnSO}_4 + \text{H}_2$ : counting gives Zn = 1, H = 2, S = 1, O = 4 on the reactant side and Zn = 1, S = 1, O = 4, H = 2 on the product side — every element already matches with coefficient 1 throughout, so no adjustment is needed at all. This is the trap version of the trap list below: assuming a skeleton equation must always need balancing, when the only way to know is to count.

Common traps

Changing a subscript inside a formula (turning $\text{H}_2\text{O}$ into $\text{H}_2\text{O}_2$ , for instance) to force a match, instead of adjusting a coefficient in front — this is never allowed, since it changes which substance the formula represents.
Balancing one element, feeling satisfied, and forgetting to recheck the other elements afterward — as the worked example shows, fixing oxygen is exactly what threw magnesium out of balance.
Forgetting that a coefficient in front of a formula multiplies every atom inside it, not just the first symbol — $2\text{Ca(OH)}_2$ means 2 calcium atoms, 4 oxygen atoms and 4 hydrogen atoms, not just 2 calcium atoms.
Leaving coefficients un-simplified when they share a common factor, such as writing $4\text{Mg} + 2\text{O}_2 \longrightarrow 4\text{MgO}$ instead of dividing through to the simplest form $2\text{Mg} + \text{O}_2 \longrightarrow 2\text{MgO}$ .

Ask the tutor: Stuck partway through balancing an equation, or want to check whether your final coefficients are already in simplest form — ask the AI tutor to walk through it with you, element by element.

Why can we change coefficients but never the subscripts inside a formula

A subscript is part of the definition of the substance itself — it tells you how many atoms of each element are bonded together in one unit, and changing it turns the substance into something chemically different, such as water into hydrogen peroxide. A coefficient, written separately in front of the whole formula, just says how many identical units of that same substance are involved in the reaction, so changing it only adjusts quantity, never identity. Balancing is entirely a quantity problem, so only quantity — the coefficient — is allowed to move.

Is there a fixed order in which elements should be balanced first

Not a fixed rule, which is exactly why the method is called hit-and-trial rather than a formula. A useful habit is to balance elements appearing in only one reactant and one product formula first, and leave elements that appear in several formulae, or as free diatomic molecules like O2 or H2, until later, since those tend to need a second adjustment once other counts shift, as seen with magnesium in the worked example. Different equations may need a different starting element, so recounting after every change is what actually keeps the process reliable, not the order chosen.

Once every element matches, is the equation automatically finished

Almost — one more check remains. After every element balances, look at the set of coefficients and see whether they share a common factor; if they do, divide every coefficient by that factor so the equation is written in its simplest whole-number form, the way 4Mg + 2O2 to 4MgO should be simplified to 2Mg + O2 to 2MgO. An equation with unsimplified coefficients is technically balanced but not written in the conventional final form expected in an answer.