Chemistry: Atoms First 2e · Atoms, Molecules, and Ions

Chemical Formulas

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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 a compact code that tells you which elements are present in a substance and in what ratio. This topic distinguishes the three main types of formulas: molecular formulas, which give the exact number of atoms of each element in one molecule (H₂O, C₆H₁₂O₆); empirical formulas, which give the simplest whole-number ratio of atoms (CH₂O for glucose); and structural formulas, which show how the atoms are connected (H–O–H for water). It also explains the used for ionic compounds such as NaCl, and how to compute a by summing atomic masses. Learning to read and interpret formulas is a prerequisite for naming compounds, balancing equations, and every quantitative calculation that follows.

Why this matters

Formulas are the language of chemistry. A single set of atoms can be arranged into different molecules, and the formula is the first clue to which one you have — H₂O₂ (hydrogen peroxide) and H₂O (water) are completely different substances with different properties, and mistaking one for the other is dangerous in any lab or industrial setting. Empirical formulas are how chemists report the results of elemental analysis, and formula masses are the stepping stone to molar masses and stoichiometry in later chapters. In health and industry, formulas on labels (like CO₂, NaCl, or C₃H₈O for isopropyl alcohol) carry essential information about what a substance is and how to handle it.

The college version

Core Concepts

Molecular formulas

A states the actual number of atoms of each element in one molecule of a covalent compound. Subscripts indicate atom counts; a of 1 is omitted. Examples: water H₂O (two H, one O), glucose C₆H₁₂O₆ (six C, twelve H, six O), and hydrogen peroxide H₂O₂ (two H, two O). By convention, carbon is written first, then hydrogen, then the remaining elements, as in C₂H₆O for ethanol.

Empirical formulas

An gives the simplest whole-number ratio of atoms in a compound, not the actual count. Glucose C₆H₁₂O₆ has the empirical formula CH₂O because the ratio 6:12:6 reduces to 1:2:1. Hydrogen peroxide H₂O₂ reduces to HO, and benzene C₆H₆ reduces to CH. Two very different molecules can share the same empirical formula: glucose, acetic acid (C₂H₄O₂), and formaldehyde (CH₂O) all have empirical formula CH₂O. The empirical formula alone cannot distinguish them.

Structural formulas

A shows how atoms are connected, using lines for bonds: water is H–O–H and carbon dioxide is O=C=O. Connectivity matters because some molecules with the same molecular formula have different arrangements and different properties; such compounds are called isomers and are studied in depth in organic chemistry (Chapter 21).

Formula units for ionic compounds

Ionic compounds such as sodium chloride do not exist as discrete molecules. Instead, they form a repeating lattice of ions, and the formula — called a formula unit — states the simplest ratio of ions that gives a neutral compound. NaCl is one Na⁺ per Cl⁻; CaCl₂ is one Ca²⁺ per two Cl⁻; Al₂O₃ is two Al³⁺ per three O²⁻. The charges of the ions must balance to zero in the formula unit.

Formula mass

The formula mass is the sum of the atomic masses of all atoms in a formula, expressed in atomic mass units (u). For a covalent substance, the same sum is called its molecular mass. Because atomic masses come from the periodic table (rounded appropriately), the formula mass is

$M = \sum (number of atoms of element i) \times (atomic mass of element i)$

This quantity is used in Chapter 6 to define molar mass and begins all stoichiometric calculations.

How It Works / Step-by-Step Process

Identify the type of substance: covalent (molecule) or ionic (formula unit).
For empirical formulas, divide all subscripts of the molecular formula by their greatest common factor.
For formula mass, list each element, multiply its subscript by its atomic mass, and sum the products.
Interpret parentheses as a multiplier: the subscript outside parentheses applies to everything inside.
Check the result: the formula mass should lie in a plausible range and the element ratio should match the intended compound.

Common Confusions

Do Not Confuse	With	Difference
Molecular formula	Empirical formula	Molecular = actual atom count (C₆H₁₂O₆); empirical = simplest ratio (CH₂O). Several molecules can share one empirical formula.
Subscript	Coefficient	A subscript (H₂) means two atoms within the formula; a coefficient (2H₂O) means two whole molecules or units.
H₂O	H₂O₂	Water versus hydrogen peroxide — different atom counts, different properties; mixing them up is a serious safety error.
Formula unit	Molecule	Ionic solids (NaCl) are described by formula units; only covalent substances form discrete molecules.
Ca(NO₃)₂	CaNO₃	The subscript outside parentheses doubles the entire nitrate group; misreading it changes the atom count and the formula mass.
Same empirical formula	Same substance	Identical empirical formulas (CH₂O) can belong to different molecules with different properties.

Eli explains

The same idea, in plain words

Explain it like I’m 10

A chemical formula is like a grocery list that says how many of each ingredient are in one molecule: H₂O means two hydrogens and one oxygen. Sometimes the same list of ingredients can be doubled, like a recipe for two cakes instead of one — the simplest version of the recipe is the empirical formula. And for salt, the formula just shows the simplest matching pair of positive and negative pieces.

Worked example

Worked Example 1: Molecular versus empirical formulas

(a) Find the empirical formula of hydrogen peroxide (H₂O₂). (b) Show that glucose and acetic acid share an empirical formula.

(a) Divide both subscripts of H₂O₂ by their greatest common factor, 2:

$H 2 O 2 \to HO$

So the empirical formula of hydrogen peroxide is HO, even though each molecule contains two H and two O.

(b) Glucose is C₆H₁₂O₆; dividing by 6 gives CH₂O. Acetic acid is C₂H₄O₂; dividing by 2 also gives CH₂O. Both molecules share the empirical formula CH₂O, which is why knowing only the empirical formula is not enough to identify a substance. Their molecular formulas — C₆H₁₂O₆ versus C₂H₄O₂ — carry the distinguishing information.

Worked Example 2: Formula mass of calcium nitrate

Calculate the formula mass of calcium nitrate, Ca(NO₃)₂, using atomic masses Ca = 40.08 u, N = 14.01 u, O = 16.00 u.

The parentheses mean the subscript 2 multiplies the whole nitrate group: one Ca, two N, and 2 × 3 = 6 O. Sum each element's contribution:

$M = (1 \times 40.08) + (2 \times 14.01) + (6 \times 16.00) u$

$M = 40.08 + 28.02 + 96.00 = 164.10 u$

The formula mass of Ca(NO₃)₂ is 164.10 u. Check: 164.10 u is consistent with a calcium salt of a heavy anion, and the 6 O atoms dominate the total, as expected.

Worked Example 3: From percent to formula — the hydrogen in water

Water has the molecular formula H₂O, and its formula mass is

$M = (2 \times 1.008) + 15.999 = 18.015 u$

The hydrogen fraction by mass is therefore

$2 \times 1.008 18.015 = 0.1119 = 11.19 %$

This is the same 11.19% hydrogen quoted for the law of definite proportions in the Early Ideas in Atomic Theory topic — the formula is the quantitative link between a compound's composition and its identity.

Key takeaways

Molecular formula = exact atom count per molecule; empirical formula = simplest whole-number ratio.
To convert molecular → empirical, divide every subscript by the greatest common factor.
The same empirical formula can belong to several different molecules (CH₂O: glucose, acetic acid, formaldehyde).
Ionic compounds are described by formula units (simplest neutral ion ratio), not molecules.
Subscripts count atoms; a coefficient outside a formula counts whole formula units (2H₂O = two water molecules).
Formula mass = sum of (subscript × atomic mass) over all elements; report in u.
Read subscripts and parentheses carefully: Ca(NO₃)₂ has two nitrate groups, so six O atoms.

Check yourself

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

What is the difference between a molecular formula and an empirical formula?
Show answer
A molecular formula gives the exact number of atoms of each element in one molecule; an empirical formula gives the simplest whole-number ratio of the atoms.
Convert C₆H₆ (benzene) to its empirical formula.
Show answer
C₆H₆ reduces to CH (divide both subscripts by 6).
How many atoms of each element are in Ca(NO₃)₂?
Show answer
One calcium, two nitrogen, and six oxygen atoms (the subscript 2 multiplies the entire nitrate group, 2 × 3 = 6 O).
Why is it correct to call NaCl a formula unit rather than a molecule?
Show answer
NaCl is an ionic compound that forms a repeating lattice of ions, not discrete molecules; the formula states the simplest neutral ratio of ions, which is what "formula unit" means.
Which molecule has the larger formula mass: H₂O or H₂O₂? Explain using the atom counts.
Show answer
H₂O₂. Its atom count is H₂O₂ = 2(1.008) + 2(15.999) = 34.014 u, whereas H₂O = 2(1.008) + 15.999 = 18.015 u; the extra oxygen roughly doubles the mass.

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Study tools & related lessonsKey vocabulary · Related

Key vocabulary

chemical formula: Notation listing elements and atom ratios in a substance
molecular formula: Exact number of atoms of each element per molecule
empirical formula: Simplest whole-number ratio of atoms in a compound
structural formula: Drawing showing how atoms are connected
formula unit: Simplest neutral ratio of ions in an ionic compound
subscript: Small number showing how many atoms of an element
formula mass: Sum of atomic masses of all atoms in a formula

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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