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CHM 151 · Ch 3 · Stoichiometry

Balancing Equations

Atoms aren't created or destroyed, so every atom that goes in has to come out. Coefficients make the books balance.

the idea

Change the coefficients, never the subscripts.

A chemical equation is a recipe that has to obey conservation of mass: the same number of each kind of atom on both sides. Subscripts define what the substance is. H₂O is water, and H₂O₂ is hydrogen peroxide, a different chemical. Coefficients say how many of each, and they're the only thing you're allowed to change.

Plant version: it's a mass balance on a batch. If 100 lb of ingredients go into the vat, 100 lb comes out as product, waste, and losses. Nothing appears or disappears. Balancing an equation is the same reconciliation done atom by atom. Changing a subscript would be like "fixing" the reconciliation by relabeling cream as skim.

1 · Start with the messiest

Balance the element that appears in the fewest, most complicated formulas first.

2 · Save H and O for last

Especially O, which usually shows up everywhere. Pure elements (O₂, Fe, H₂) are the easiest to adjust at the end.

3 · Clear fractions

If you need 7/2 O₂, that's fine mid-way. Then multiply everything by 2 so all coefficients are whole numbers in lowest terms.
try it

Balance it yourself

Use + and − on each coefficient. The tally below shows the atoms on each side, and every row has to match.

tool

Auto-balancer

Type any equation with + and → (or ->). Parentheses work, and so do charges written with ^, like Cu + Ag^+ → Cu^2+ + Ag. Phase labels like (aq) are ignored.

reaction patterns

Three patterns to recognize on sight

Combination

A + B → AB
Two or more reactants, one product.
2Mg + O₂ → 2MgO

Decomposition

AB → A + B
One reactant breaks apart, often with heat.
CaCO₃ → CaO + CO₂

Combustion

fuel + O₂ → CO₂ + H₂O
A hydrocarbon (or CHO compound) burns in oxygen. Always the same two products when burning is complete.

practice

Balance these

engineering version

A balanced equation is a feed spec.

Your boiler burns natural gas: CH₄ + 2O₂ → CO₂ + 2H₂O. The coefficients say every mole of methane needs exactly two moles of O₂. Air is about 21% O₂, so that's roughly 9.5 volumes of air per volume of gas. Burners are tuned with a little excess air on top of that. Too little and the combustion is incomplete, making carbon monoxide (2CH₄ + 3O₂ → 2CO + 4H₂O). That's why CO alarms belong near fired equipment.

Same logic in the vat: C₁₂H₂₂O₁₁ + H₂O → 4C₃H₆O₃. One lactose (with one water) becomes four lactic acids. It only balances because of that water molecule, which is why the product weighs slightly more than the lactose consumed.

exam traps

Common mistakes