Chemistry 2e · Stoichiometry of Chemical Reactions

Writing and Balancing Chemical Equations

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In 30 seconds
Why this matters
The college version
Eli explains
Worked example
Key takeaway
Check yourself
Study tools
Sources & references

In 30 seconds

A is chemistry's shorthand for a reaction: it states which substances disappear (reactants), which substances appear (products), and in what proportions. The general skeleton is

$reactants \to products$

For example, the reaction of methane with oxygen is written

$CH 4 (g) + 2 O 2 (g) \to CO 2 (g) + 2 H 2 O (g)$

Reading it aloud: one molecule of methane plus two molecules of oxygen yield one molecule of carbon dioxide plus two molecules of water. The numbers in front of the formulas — the coefficients — are the heart of the equation: they encode the relative amounts in which substances react. Because atoms are neither created nor destroyed in ordinary chemical reactions (the law of ), every equation must be balanced: the same number of atoms of each element must appear on both sides. Balancing is not a cosmetic exercise — it is what turns a qualitative description into a quantitative recipe that stoichiometry (later in this chapter) uses to predict masses of products.

Why this matters

Every quantitative prediction in chemistry — how much a reaction makes, how much you must weigh out, what volume of gas evolves, how much titrant neutralizes an unknown — begins with a correct, balanced equation. An unbalanced equation gives wrong mole ratios, and wrong mole ratios give wrong answers downstream, no matter how careful the arithmetic. Balancing also enforces the physical reality that mass is conserved: if a reaction appears to "lose" or "gain" atoms, the equation (or your understanding of the reaction) is wrong. In industry, balancing is embedded in process design: combustion engineering, pharmaceutical synthesis, and wastewater treatment all run on stoichiometric ratios derived from balanced equations. Writing the correct state symbols — (s), (l), (g), (aq) — tells you what you should see: a precipitate, a gas, or an aqueous solution. And because every later topic in this chapter assumes you can balance quickly and correctly, this skill is the gatekeeper for the whole chapter.

The college version

Core Concepts

Anatomy of an equation

A complete chemical equation has four parts: the reactant formulas (left of the arrow), the product formulas (right of the arrow), the coefficients that balance the counts, and the state symbols in parentheses — (s) solid, (l) liquid, (g) gas, (aq) dissolved in water. An arrow → means "yields"; a double arrow ⇌ indicates a reversible reaction (Chapter 13). Formulas must be correct before balancing begins — you cannot fix a wrong formula by changing subscripts. Subscripts define the compound (H₂O is water; H₂O₂ is hydrogen peroxide — very different chemicals); coefficients count molecules or formula units. Changing a changes the substance; changing a changes only the amount.

The law of conservation of mass

Balancing rests on one physical law: in a chemical reaction, atoms are rearranged, not created or destroyed — established by Lavoisier's experiments in the 18th century. Consequently, the total mass of reactants equals the total mass of products, and the count of each element's atoms is identical on both sides. A balanced equation is simply the bookkeeping that guarantees this.

The balancing algorithm

A reliable strategy is:

Write the correct formulas for all reactants and products (with state symbols).
Count atoms of each element on both sides.
Balance elements one at a time, starting with the most complex formula and saving elements that appear as free elements (e.g., O₂, N₂) for last.
Use coefficients — never change subscripts.
Reduce coefficients to the smallest whole-number set, then re-count to verify.

Fractions are allowed as intermediate steps (multiply through at the end); the final check is a full atom count on both sides.

Diatomic elements and common pitfalls

Seven elements exist as diatomic molecules in their standard states: H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂ (remember "H₂N₂O₂F₂Cl₂Br₂I₂" or the mnemonic "Have No Fear Of Ice Cold Beer"). Students who write "H" or "O" instead of H₂ or O₂ in equations will never balance them. Another classic pitfall: balancing oxygen first in a combustion reaction, when oxygen usually appears as a free element and should be balanced last.

How It Works / Step-by-Step Process

Translate the word description into correct formulas with state symbols.
Count atoms of each element on the reactant side and the product side.
Choose the most complex formula and balance its elements first, adjusting coefficients.
Balance remaining elements, leaving free elements (O₂, N₂, H₂) for last.
Reduce to smallest whole-number coefficients; verify by counting every element again.

Common Confusions

Do Not Confuse	With	Difference
Coefficients	Subscripts	Coefficients (outside) change amounts; subscripts (inside) define the substance — only coefficients may change
Changing subscripts to balance	Changing coefficients	"Fixing" an equation by editing H₂O to H₃O changes the substance — that's inventing chemistry, not balancing
Balanced equation	Reaction mechanism	Balancing only ensures atom conservation; it says nothing about how fast or by what steps the reaction occurs
Reactant side total	Product side total	The numbers of atoms must match; the numbers of molecules need not (and usually don't)
H (hydrogen atom)	H₂ (hydrogen molecule)	Free hydrogen is diatomic H₂; writing H breaks the count
→	⇌	A single arrow means the reaction goes one way; a double arrow means reversibility (equilibrium)

Eli explains

The same idea, in plain words

Explain it like I’m 10

Think of a recipe: to bake one cake you need 2 eggs, 1 cup of flour, and 1 cup of sugar — that's the "recipe equation." A chemical equation is the same idea for molecules: it says how many of each kind of molecule you need so that nothing is wasted and nothing appears from nowhere. Just like you can't turn a cake recipe into a pie by changing "2 eggs" to "2 pies," you can't fix a chemical equation by changing a molecule's formula — you can only add more of the molecules that are already there.

Worked example

Example 1: Balancing the combustion of propane

Problem: Balance the equation for propane burning in oxygen: C₃H₈(g) + O₂(g) → CO₂(g) + H₂O(g).

Step 1 — Count atoms:

Element	Reactants	Products
C	3	1
H	8	2
O	2	3

Step 2 — Balance carbon first: put a 3 before CO₂ (3 C on each side).

Step 3 — Balance hydrogen: put a 4 before H₂O (8 H on each side). Now the product side has 3 × 2 + 4 × 1 = 10 oxygen atoms.

Step 4 — Balance oxygen last: O₂ is a free element, so set its coefficient to give 10 O atoms: a coefficient of 5 gives 5 × 2 = 10.

Step 5 — Verify:

$C 3 H 8 (g) + 5 O 2 (g) \to 3 CO 2 (g) + 4 H 2 O (g)$

C: 3 = 3 ✓ H: 8 = 8 ✓ O: 10 = 10 ✓. Balanced, with the smallest whole-number coefficients.

Example 2: Balancing a single-replacement reaction

Problem: Balance: Al(s) + CuCl₂(aq) → AlCl₃(aq) + Cu(s).

Counts: Al 1 = 1; Cu 1 = 1; Cl 2 ≠ 3. Balance chlorine first: 2 and 3 share a least common multiple of 6, so use coefficients 3 (CuCl₂) and 2 (AlCl₃):

$Al (s) + 3 CuCl 2 (aq) \to 2 AlCl 3 (aq) + Cu (s)$

Now Cl: 6 = 6 ✓, but Al: 1 ≠ 2 and Cu: 3 ≠ 1. Fix the remaining two elements:

$2 Al (s) + 3 CuCl 2 (aq) \to 2 AlCl 3 (aq) + 3 Cu (s)$

Final check — Al: 2 = 2 ✓, Cu: 3 = 3 ✓, Cl: 6 = 6 ✓. Balanced.

Example 3: Balancing with a fraction, then clearing

Problem: Balance: N₂(g) + H₂(g) → NH₃(g).

Nitrogen: put 2 before NH₃. Hydrogen: 2 on the left vs 6 on the right, so use coefficient 3 for H₂:

$N 2 (g) + 3 H 2 (g) \to 2 NH 3 (g)$

Check — N: 2 = 2 ✓, H: 6 = 6 ✓. If you had used a fractional step (e.g., 3/2 H₂), multiply everything by 2 to clear the fraction — always end with whole numbers.

Key takeaways

A balanced equation has equal numbers of each element's atoms on both sides — the physical basis is conservation of mass.
Coefficients (large numbers before formulas) are the only thing you may change when balancing; subscripts are part of the substance's identity.
Write correct formulas with state symbols first; balance the most complex species first, free elements (O₂, N₂, H₂) last.
Seven elements are diatomic in standard states: H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂.
Final coefficients must be the smallest whole-number set.
The balanced equation's coefficients are the mole ratios used in all stoichiometry later in this chapter.

Check yourself

6 review questions from the chapter. Try each one, then open the answer.

State the physical law that requires chemical equations to be balanced.
Show answer
The law of conservation of mass — atoms are rearranged, never created or destroyed in a chemical reaction.
Balance: Mg(s) + O₂(g) → MgO(s).
Show answer
2Mg(s) + O₂(g) → 2MgO(s). (Mg: 2 = 2 ✓, O: 2 = 2 ✓.)
Why can't you balance an equation by changing subscripts?
Show answer
Subscripts define which compound the formula represents; changing them changes the substance, so the equation would describe a different reaction entirely.
Which element do you usually balance last in a combustion reaction, and why?
Show answer
Oxygen — it appears as the free element O₂, so it is easiest to balance after the compound elements are set.
Name the seven diatomic elements in their standard states.
Show answer
H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂.
Balance: Fe(s) + Cl₂(g) → FeCl₃(s).
Show answer
2Fe(s) + 3Cl₂(g) → 2FeCl₃(s). (Fe: 2 = 2 ✓, Cl: 6 = 6 ✓.)

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Study tools & related lessonsKey vocabulary · Related

Key vocabulary

Chemical equation: Symbolic statement of a reaction: reactants → products
Reactant: A substance consumed in a reaction (left of the arrow)
Product: A substance formed by a reaction (right of the arrow)
Coefficient: The number before a formula, giving relative amounts
Subscript: The small number inside a formula (e.g., the 2 in H₂O)
State symbol: (s), (l), (g), (aq) after a formula
Conservation of mass: Atoms are rearranged, never created or destroyed
Diatomic element: An element that exists as pairs, e.g., O₂, N₂, H₂

Sources & references

openstax.org — Chemistry 2e

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