Balancing Chemical Equations Guide

Overview

These notes explain how to balance chemical equations using coefficients, with worked examples and special tips for polyatomic ions.

Atoms are neither created nor destroyed, so each element must have equal atoms on both sides.
You may only change coefficients (numbers in front of formulas), never subscripts (small numbers in formulas).
If no subscript is written after an element symbol, it is assumed to be 1.
If no coefficient is written in front of a formula, it is assumed to be 1.
Always recount atoms after changing any coefficient, because changes affect all atoms in that formula.

Step 1: Count atoms of each element on both sides of the equation.
Step 2: Compare counts and identify which elements are unbalanced.
Step 3: Change coefficients to make atom counts equal for each element.
Step 4: Recount atoms; repeat adjustments until all elements are balanced.
Step 5: Check that no subscripts have been changed and that all coefficients are in the simplest whole-number ratio.

Start: Left side has 8 sulfur atoms and 2 oxygen atoms.
Right side has 1 sulfur atom and 2 oxygen atoms.
Oxygen is already balanced (2 on each side); sulfur is not (8 vs. 1).
Put coefficient 8 in front of sulfur on the product side.
This gives 8 sulfur atoms on the right, but now also 16 oxygens on the right.
To fix oxygen, put coefficient 8 in front of the oxygen-containing reactant with 2 oxygens.
Now left side has 8 sulfurs and 16 oxygens; right side has 8 sulfurs and 16 oxygens.
The equation is now balanced using only coefficients.

Initial counts: Left has 2 hydrogens and 2 oxygens.
Right has 2 hydrogens and 1 oxygen.
To balance oxygen, place coefficient 2 in front of the oxygen-containing product.
Now right side has 2 oxygens but 4 hydrogens.
To balance hydrogen, place coefficient 2 in front of the hydrogen-containing reactant.
Now each side has 4 hydrogens and 2 oxygens.
The equation is balanced.

Some equations contain the same polyatomic ion on both sides (examples: SO₄, NO₃).
When a polyatomic ion appears unchanged on both sides, you can count it as one “chunk.”
Example counts:
- Calcium: 1 on left, 1 on right.
- SO₄ group: 1 on left, 1 on right (treated as one unit).
- Na: 2 on left.
- NO₃: 1 on left; on the right, a subscript 2 outside parentheses gives 2 NO₃ groups.
To balance sodium and nitrate:
- Put coefficient 2 in front of the sodium–nitrate compound on the product side.
- Na: 1 × 2 = 2 on the right, matching left.
- NO₃: 1 × 2 = 2 on the right, matching the 2 NO₃ groups.
All species are now balanced.
Treating polyatomic ions as one item simplifies counting and balancing.

Species	Left Side Count	Right Side Count (before)	Right Side Coefficient Used	Right Side Count (after)
Ca	1	1	2	1 × 2 = 2 (if in that term)
SO₄	1	1	2	1 × 2 = 2 (if in that term)
Na	2	1	2	1 × 2 = 2
NO₃	1	2 (due to subscript 2)	2	2 × 1 = 2 or matched value

(Counts reflect the logic described: ions on both sides, coefficient effect, and subscripts outside parentheses.)

Initial counts on left: 1 carbon, 4 hydrogens, 2 oxygens.
Initial counts on right:
- 1 carbon in CO₂.
- 2 oxygens in CO₂.
- 2 hydrogens in H₂O.
- Plus 1 more oxygen from another oxygen-containing reactant or product, total 3 oxygens on that side.
Start by balancing hydrogen:
- Put coefficient 2 in front of H₂O (or hydrogen-containing product).
- Now right side has 2 × 2 = 4 hydrogens, matching left.
Recount oxygens on the right:
- 2 oxygens from CO₂.
- Plus 2 × 1 oxygen from water gives 2 more oxygens.
- Total oxygens on right = 4.
To balance oxygens, put coefficient 2 in front of the O₂ (or oxygen-containing reactant with 2 oxygens) on the left.
Now left side has 2 × 2 = 4 oxygens, matching the 4 oxygens on the right.
Carbons and hydrogens remain balanced; the equation is balanced.

Coefficient: Number written in front of a chemical formula; multiplies all atoms in that formula.
Subscript: Small number written after an element symbol inside a formula; gives number of atoms of that element.
Reactants: Substances present on the left side of the equation; they undergo change.
Products: Substances present on the right side of the equation; they are formed in the reaction.
Polyatomic ion: Group of atoms that acts as a single charged unit and appears unchanged on both sides of some equations.

Practice counting atoms carefully, including atoms in polyatomic ions and atoms repeated in different products.
Work additional balancing problems, increasing difficulty to gain speed and confidence.
Always double-check atom counts for every element after setting final coefficients.