Chemistry: Atoms First 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 chemical equation is the chemist's shorthand for a reaction: it names the starting materials (reactants), the products formed, and — once balanced — the exact mole ratios in which they combine. Writing a correct equation is the first step of every stoichiometry problem, because the coefficients are the numbers that carry quantitative meaning. An unbalanced equation is like a recipe that lists ingredients but no amounts: it describes what reacts but not how much. Balancing an equation applies the law of — atoms are neither created nor destroyed in a chemical reaction, so every element must appear with the same number of atoms on both sides. This topic covers how to translate word descriptions and formulas into proper equations, the meaning of coefficients versus subscripts, and the systematic trial-and-error method for balancing.

Why this matters

Every quantitative calculation in chemistry — how much a reaction makes, how much to weigh out, what volume of solution is needed — begins with a correct, balanced equation. In industry, engineers use balanced equations to scale reactions from grams in a flask to tons in a reactor. In health care, balanced equations underlie metabolic biochemistry, drug synthesis, and clinical lab tests (e.g., the glucose oxidase reaction used in blood glucose meters). In environmental science, balanced equations describe combustion of fuels and formation of pollutants. Getting the equation wrong, or reading a as a , produces wildly wrong answers — for example, treating O₂ as two oxygen atoms instead of a diatomic molecule changes a whole calculation. Mastering equation writing and balancing is therefore the gatekeeper skill for the rest of this chapter and nearly every later chapter in the book.

The college version

Core Concepts

Anatomy of a chemical equation

A chemical equation shows reactants on the left and products on the right, separated by an arrow (→) that means "yields" or "produces":

$reactants \to products$

Each substance is written with its correct chemical formula, and the physical state is often noted in parentheses: (s) solid, (l) liquid, (g) gas, (aq) aqueous (dissolved in water). For example, the reaction of solid magnesium with oxygen gas to form solid magnesium oxide is:

$2 Mg(s) + O 2 (g) \to 2 MgO(s)$

The numbers in front of formulas — the coefficients — show the relative number of formula units (or moles) of each substance. The equation above says two formula units of Mg react with one molecule of O₂ to give two formula units of MgO.

Coefficients vs. subscripts: the most important distinction

A coefficient (the big number in front) tells you how many units of a substance take part. A subscript (the small number inside a formula) tells you how many atoms of an element are in one unit of that substance. You may change coefficients to balance an equation, but you must never change subscripts — changing a subscript changes the identity of the substance. Writing O₃ instead of O₂ changes oxygen gas into ozone, a completely different molecule. Think of it this way: coefficients change the number of molecules, subscripts change the kind of molecule.

The law of conservation of mass and balancing

A balanced equation has equal numbers of each type of atom on both sides. Balancing is done by adjusting coefficients using a systematic process:

Write the correct formulas for all reactants and products (unbalanced ).
Count atoms of each element on both sides.
Adjust coefficients — starting with the most complex formula — to equalize atom counts.
Check every element again; reduce coefficients to the smallest whole-number ratio if needed.
Verify that the sum of atoms of each element matches on both sides.

Balancing is trial-and-error, but there are useful heuristics: balance metals and nonmetals first, then hydrogen and oxygen last, and treat polyatomic ions that appear unchanged on both sides as single units. Pure elements like H₂, N₂, O₂, F₂, Cl₂, Br₂, and I₂ exist as diatomic molecules and must be written that way in equations.

Special symbols in equations

Beyond state symbols, equations may carry condition symbols: a triangle (Δ) over the arrow means heat is supplied; the formula of a catalyst (e.g., Pt) above the arrow means the reaction requires that catalyst; an upward arrow (↑) indicates a gas product escaping, and a downward arrow (↓) indicates a precipitate. These symbols convey the conditions of the reaction, which are as important as the substances themselves — some reactions only proceed when heated, and others only in the presence of a catalyst.

Common Confusions

Do Not Confuse	With	Difference
Coefficient (2 in 2H₂O)	Subscript (2 in H₂O)	Coefficient = number of molecules; subscript = atoms per molecule. Only coefficients change when balancing
Changing coefficients	Changing subscripts	Coefficients adjust amounts; changing a subscript creates a different substance (O₂ → O₃)
NH₃ vs N₂ + H₂	Same substance	NH₃ is a product molecule; N₂ and H₂ are the diatomic reactants — they are different chemical species
The arrow meaning "equals"	The arrow meaning "yields"	Equations show a direction of change; they are not algebraic equalities and generally do not run backward without different conditions
(g) gas vs (aq) aqueous	Both "in air"	(g) is a pure gas phase; (aq) means dissolved in water as ions — very different reactivity
A balanced equation meaning equal masses	Equal atom counts	Balancing conserves atoms, not necessarily total visible mass units on paper; mole ratios are what the coefficients give

Eli explains

The same idea, in plain words

Explain it like I’m 10

A chemical equation is like a recipe for making cookies: it tells you what ingredients (reactants) you start with and what cookies you get (products). The big numbers in front are like saying "use 2 cups of flour" — they tell you how much. The little numbers inside a formula are like saying "this recipe needs eggs, not just egg whites" — they describe what the ingredient actually is. You can change how many cups you use, but you can't change what an egg is. And just like a recipe must use up all the ingredients you put in, a balanced equation must have the same atoms on both sides — atoms can't just disappear.

Worked example

Example 1: Balancing the formation of ammonia (Haber process)

Balance the skeleton equation for ammonia synthesis: N₂(g) + H₂(g) → NH₃(g).

Step 1 — Count atoms: left side has 2 N and 2 H; right side has 1 N and 3 H. Neither element matches.

Step 2 — Balance nitrogen first: put a coefficient 2 in front of NH₃ so both sides have 2 N:

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

Step 3 — Recount hydrogen: right side now has 2 × 3 = 6 H atoms. Put coefficient 3 in front of H₂ to supply 6 H:

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

Step 4 — Verify: 2 N = 2 N; 6 H = 6 H. Balanced. The coefficients (1, 3, 2) are the smallest whole numbers, and the equation says 1 mol N₂ reacts with 3 mol H₂ to produce 2 mol NH₃.

Example 2: Balancing the combustion of propane

Propane (C₃H₈) burns in oxygen to produce carbon dioxide and water. Write and balance the equation.

Step 1 — Write the skeleton: C₃H₈(g) + O₂(g) → CO₂(g) + H₂O(g).

Step 2 — Balance carbon: 3 C on the left, so put 3 in front of CO₂:

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

Step 3 — Balance hydrogen: 8 H on the left, so put 4 in front of H₂O (4 × 2 = 8 H):

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

Step 4 — Balance oxygen last: right side now has 3 × 2 + 4 × 1 = 10 O atoms. Put 5 in front of O₂:

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

Step 5 — Verify: C: 3 = 3; H: 8 = 8; O: 10 = 10. Balanced. Notice that oxygen, which appears as a free element, was balanced last — a strategy that avoids reworking earlier coefficients.

Example 3: From word description to balanced equation

Write a balanced equation for: aqueous solutions of lead(II) nitrate and potassium iodide react to form solid lead(II) iodide and aqueous potassium nitrate.

Step 1 — Convert words to formulas with states:

$Pb(NO 3) 2 (aq) + KI(aq) \to PbI 2 (s) + KNO 3 (aq)$

Step 2 — Balance: treat the nitrate ion NO₃^- as a unit. Put 2 in front of KI and 2 in front of KNO₃:

$Pb(NO 3) 2 (aq) + 2 KI(aq) \to PbI 2 (s) + 2 KNO 3 (aq)$

Step 3 — Verify: Pb: 1 = 1; N: 2 = 2; O: 6 = 6; K: 2 = 2; I: 2 = 2. Balanced. The (s) on PbI₂ flags the yellow precipitate — a signature of this classic double-replacement reaction (Topic 2).

Key takeaways

Reactants → products; never reverse the arrow carelessly.
Coefficients = how many units; subscripts = atoms per unit. Change coefficients, never subscripts.
A balanced equation satisfies conservation of mass: equal atom counts for every element on both sides.
Seven elements exist as diatomic molecules: H₂, N₂, O₂, F₂, Cl₂, Br₂, I₂.
State symbols: (s), (l), (g), (aq); Δ = heat; ↑ = gas formed; ↓ = precipitate formed.
Balancing order heuristic: most complex formula first, single elements last; leave H and O for near the end.
Coefficients represent mole ratios — this is what makes stoichiometry (Topic 3) possible.

Check yourself

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

Balance: Fe(s) + O₂(g) → Fe₂O₃(s).
Show answer
4 Fe(s) + 3 O₂(g) → 2 Fe₂O₃(s). Check: Fe 4 = 4; O 6 = 6.
Why can you never change a subscript to balance an equation?
Show answer
Because subscripts are part of the substance's identity. Changing them (e.g., H₂O → H₂O₂) names a different compound; balancing must preserve chemical identities and only adjust how many units react.
What do the symbols (s), (l), (g), (aq), and Δ stand for?
Show answer
(s) solid, (l) liquid, (g) gas, (aq) dissolved in water (aqueous), Δ = heat supplied.
How many oxygen atoms are on each side of the balanced equation for the combustion of propane?
Show answer
Left side: 5 × 2 = 10; right side: 3 × 2 (from CO₂) + 4 × 1 (from H₂O) = 10. Equal, as required by conservation of mass.
Write the balanced equation for the reaction of aqueous silver nitrate with aqueous sodium chloride, given that silver chloride precipitates and sodium nitrate stays dissolved.
Show answer
AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq) — already balanced as written.
A student writes 2 H₂ + O₂ → 2 H₂O. What mole ratio of hydrogen to oxygen does this equation represent, and is it balanced?
Show answer
The equation is balanced (4 H = 4 H; 2 O = 2 O). The mole ratio of H₂ to O₂ is 2:1 — two moles of hydrogen react with one mole of oxygen.

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Study tools & related lessonsKey vocabulary · Related

Key vocabulary

Reactant: A starting substance that is consumed in a reaction
Product: A substance formed by a reaction
Coefficient: The number in front of a formula, telling how many units react
Subscript: The small number inside a formula, telling atoms per unit
Skeleton equation: Unbalanced equation with correct formulas
Aqueous (aq): Dissolved in water
Conservation of mass: Atoms are neither created nor destroyed

Sources & references

openstax.org — Chemistry Atoms First 2e

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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