Balancing Equations & Reaction Types — Reference Sheet

Conservation of mass

The Law of Conservation of Mass says matter is never created or destroyed in a chemical reaction. Every atom present in the reactants has to show up somewhere in the products. Atoms get rearranged into new substances, but the total count of each element stays exactly the same on both sides of the equation. A balanced equation is just the bookkeeping that proves this is true: the same number of atoms of each element on the reactant side (left of the arrow) as on the product side (right of the arrow). The small whole numbers you place in front of formulas are called coefficients. They multiply the whole formula that follows them.

Coefficients vs. subscripts

Only change the coefficient (the number in front, like the 2 in 2H₂O) when balancing. Never change a subscript (the number inside a formula, like the 2 in H₂O) — that would turn water into a different substance entirely. Subscripts are fixed by the compound's chemical identity; coefficients are the only thing you're allowed to adjust.

Balancing by inspection

Balancing by inspection (also called trial and error) is the standard method for balancing simple equations by hand. There's no single formula — you adjust coefficients step by step until every element matches on both sides. A reliable order to work in:

Step	What to do
1	Write the unbalanced (skeleton) equation with correct formulas for every reactant and product.
2	Count the atoms of each element on each side. Make a running tally if it helps.
3	Balance elements that appear in only one reactant and one product first. Save elements that appear in several formulas for later.
4	Balance polyatomic ions (like SO₄²⁻ or NO₃⁻) as a single unit if they stay intact through the whole reaction.
5	Balance H and O last — they usually appear in the most formulas.
6	Check every element again. If any coefficients share a common factor, divide them all down to the smallest whole-number ratio.

Worked example. Balance the combustion of propane: C₃H₈ + O₂ → CO₂ + H₂O 1. Carbon: 3 C on the left (in C₃H₈), so put a 3 in front of CO₂ → C₃H₈ + O₂ → 3CO₂ + H₂O 2. Hydrogen: 8 H on the left, so put a 4 in front of H₂O (4 × 2 = 8) → C₃H₈ + O₂ → 3CO₂ + 4H₂O 3. Oxygen: right side now has (3 × 2) + (4 × 1) = 10 O atoms. Left side has O₂, so 10 O atoms means 5 O₂ → C₃H₈ + 5O₂ → 3CO₂ + 4H₂O 4. Final check: C: 3 = 3 ✓ H: 8 = 8 ✓ O: 10 = 10 ✓ Balanced equation: C₃H₈ + 5O₂ → 3CO₂ + 4H₂O

Half coefficients are fine mid-work

If balancing oxygen leaves you needing a fraction (like 7/2 O₂), that's allowed as a temporary step. Multiply every coefficient in the whole equation by 2 (or whatever clears the fraction) to get back to whole numbers.

States of matter in equations

A state symbol in parentheses after a formula shows the physical state of that substance under the reaction conditions. Including them makes an equation more complete and is required for full-credit answers on most tests.

Symbol	Meaning	Example
(s)	solid	NaCl(s)
(l)	liquid	H₂O(l)
(g)	gas	CO₂(g)
(aq)	aqueous — dissolved in water	NaCl(aq)

Example with states shown: 2H₂(g) + O₂(g) → 2H₂O(l) An aqueous solution means the substance is dissolved in water, which matters most for reactions between ions in solution (single and double replacement reactions below).

Synthesis and decomposition

These two reaction types are opposites of each other, which makes them easy to tell apart once you spot the pattern of reactants and products.

Type	General form	Description	Example
Synthesis (combination)	A + B → AB	Two or more simple substances combine into one more complex product.	2Na(s) + Cl₂(g) → 2NaCl(s)
Decomposition	AB → A + B	One compound breaks apart into two or more simpler products.	2H₂O₂(aq) → 2H₂O(l) + O₂(g)

Spotting the pattern

Synthesis: two things go in, one thing comes out. Decomposition: one thing goes in, two or more things come out. If you see a single compound on one side of the arrow and multiple substances on the other, you're looking at synthesis or decomposition — check which side the single compound is on.

Single and double replacement

These two reaction types swap atoms or ions between compounds rather than simply combining or breaking apart.

Type	General form	Description	Example
Single replacement	A + BC → AC + B	One element replaces another element in a compound.	Zn(s) + 2HCl(aq) → ZnCl₂(aq) + H₂(g)
Double replacement	AB + CD → AD + CB	The positive ions (cations) of two compounds swap partners.	AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq)

In single replacement, a free element (Zn) displaces an element already in a compound (H, from HCl), and that displaced element comes out on its own. In double replacement, no free elements are involved at all — two compounds trade partners, usually in aqueous solution, and a solid precipitate, a gas, or water often forms as one of the products.

Recognizing a precipitate reaction

In the AgNO₃ + NaCl example, AgCl forms as a solid (s) precipitate that separates out of solution while NaNO₃ stays dissolved (aq). A double replacement reaction that produces an insoluble solid is often called a precipitation reaction.

Combustion reactions

A combustion reaction is a fuel reacting with oxygen gas, O₂, releasing energy as heat and light. The fuel is usually a hydrocarbon (a compound of only carbon and hydrogen, like CH₄ or C₃H₈), though oxygen-containing fuels like ethanol also burn. Complete combustion of a hydrocarbon always produces carbon dioxide and water when there's enough oxygen available.

Type	General form	Example
Complete combustion	CₓHᵧ + O₂ → CO₂ + H₂O	CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g)

Incomplete combustion

With a limited oxygen supply, combustion can be incomplete, producing carbon monoxide (CO) or even soot (solid carbon, C) instead of all CO₂. Incomplete combustion is why running an engine or a heater in an unventilated space is dangerous — carbon monoxide is toxic and odorless.

Identifying reaction type at a glance

Clue in the equation	Likely reaction type
Two elements or simple compounds → one product	Synthesis
One compound → two or more products	Decomposition
One element + one compound → one new element + one new compound	Single replacement
Two compounds (often both aqueous) → two new compounds	Double replacement
A hydrocarbon or fuel + O₂ → CO₂ + H₂O	Combustion

This table is a quick first pass, not a guarantee — some reactions can look like more than one type until you check the actual atom count and confirm the equation balances. Always balance the equation as the final check, regardless of what type you think it is.

Try it yourself

Download equations-to-balance.txtequations-to-balance.txt

Six unbalanced skeleton equations, one of each reaction type on this sheet, written with the word "yields" in place of the reaction arrow.

Open it in a text editor, Google Sheets, or Excel

It's a plain text file, so any text editor works. Balance each equation by inspection using the step order in the table above (elements in one reactant and one product first, polyatomic ions as a unit, H and O last).

1. Balance this equation: Fe + O₂ → Fe₂O₃ 2. Classify this reaction and balance it: AgNO₃(aq) + CaCl₂(aq) → AgCl(s) + Ca(NO₃)₂(aq) 3. Write and balance the complete combustion of butane, C₄H₁₀, with O₂ Using equations-to-balance.txt: 4. For each of the 6 equations, write the balanced equation using the smallest whole-number coefficients. 5. For each equation, name its reaction type: synthesis, decomposition, single replacement, double replacement, or combustion.