ChemistryDifficulty 2-4

Molecules

A molecule is a group of atoms held together by covalent bonds that acts as a single particle — such as water, H₂O, or carbon dioxide, CO₂. A molecular formula says which atoms a molecule contains and how many; its three-dimensional shape, which VSEPR theory predicts from repelling electron groups, strongly affects how it behaves. Chemists count molecules in moles: exactly 6.022 140 76 × 10²³ of them.

Geometry from experiment and from VSEPR

Spectroscopically derived geometries (NIST CCCBDB; water's value is flagged as an equilibrium geometry) confirm VSEPR's qualitative predictions: CO₂ is linear (D∞h symmetry) with r(C–O) = 1.162 Å, while H₂O is bent (C2v) with r(O–H) = 0.958 Å and ∠HOH = 104.48°. The compression from the ideal tetrahedral 109.5° is attributed in the VSEPR picture to the two lone pairs on oxygen.

Amount of substance

Since the SI definition fixes the Avogadro constant at exactly 6.022 140 76 × 10²³ mol⁻¹, the mole is a pure count. Molar masses then follow from standard atomic weights: 2(1.0080) + 15.999 = 18.015 g mol⁻¹ for water, matching NIST's 18.0153.

Common misconception: A molecular formula underdetermines structure: isomers share a formula but differ in connectivity and properties, so structural or spectroscopic data are needed to identify a molecule.

Full explanation — the complete reference version every reading depth is based on

Molecules and formulas

Covalent compounds are made of separate molecules. The formula H₂O says each water molecule has two hydrogen atoms and one oxygen atom. A molecular formula gives the actual numbers of atoms; an empirical formula gives only the simplest ratio — acetic acid (in vinegar) is C₂H₄O₂ but its empirical formula is CH₂O.

Common misconception: Not every chemical formula describes a molecule. Sodium chloride is an ionic lattice, so 'NaCl' is a formula unit — the 1:1 ratio of ions — and there is no such thing as a single NaCl molecule in solid salt.

Shape matters

VSEPR (valence-shell electron-pair repulsion) theory predicts shapes by assuming the electron groups around a central atom spread out as far apart as possible. Carbon dioxide has two electron groups around carbon and no lone pairs, so it is linear (180°). Water's oxygen carries two bonds and two lone pairs, so the molecule is bent; its measured H–O–H angle is about 104.5°.

CO₂: linear, O–C–O 180°, C–O 1.162 Å.
H₂O: bent, H–O–H 104.48°, O–H 0.958 Å.
CH₄: tetrahedral, ideal H–C–H angle 109.5°.

Structure is not decided by the formula alone: isomers share a molecular formula but connect their atoms differently, and often have very different properties.

Counting molecules: the mole

Molecules are far too small to count one by one, so chemists use the mole: exactly 6.022 140 76 × 10²³ entities. The mass of one mole of a substance in grams equals its molecular mass, found by adding atomic weights.

M(\mathrm{H_2O}) = 2(1.0080) + 15.999 = 18.015\ \mathrm{g\,mol^{-1}}

Molar mass of water from CIAAW abridged atomic weights (ScienceVerse calculation; NIST lists 18.0153).

Worked example: 18.015 g of water is one mole, so it contains about 6.022 × 10²³ water molecules — each with three atoms, so about 1.807 × 10²⁴ atoms in total (ScienceVerse calculation).

Info: Molecules connect chemistry to biology: DNA is a very large molecule, and a molecule's shape and polarity decide how it interacts with others.

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Sources and methodology

Covalent compounds consist of individual molecules, and the formula H₂O states that each water molecule contains two hydrogen atoms and one oxygen atom. (awaiting scientific review)
- 1.4: Compounds and How We Represent Them (Chemistry: Physical Principles), CC BY 4.0 — Textbook
A molecular formula gives the actual number of atoms of each element in a molecule, while an empirical formula gives the simplest whole-number ratio: acetic acid's molecular formula is C₂H₄O₂ and its empirical formula is CH₂O. (awaiting scientific review)
- 1.4: Compounds and How We Represent Them (Chemistry: Physical Principles), CC BY 4.0 — Textbook
Compounds with the same molecular formula but different structures are called isomers, and they often have very different properties. (awaiting scientific review)
- 1.4: Compounds and How We Represent Them (Chemistry: Physical Principles), CC BY 4.0 — Textbook
The formula NaCl represents a formula unit — the simplest 1:1 ratio of ions in an ionic lattice — rather than a molecule. (awaiting scientific review)
- 1.4: Compounds and How We Represent Them (Chemistry: Physical Principles), CC BY 4.0 — Textbook
VSEPR theory predicts a molecule's shape by assuming that the electron groups around a central atom repel each other and arrange themselves as far apart as possible. (awaiting scientific review)
- 3.6: Molecular Structure and Polarity (Chemistry: Physical Principles), CC BY 4.0 — Textbook
The equilibrium H–O–H bond angle of a water molecule is about 104.5° (104.4776° in NIST's CCCBDB), with O–H bond lengths of 0.958 Å. (awaiting scientific review)
- NIST CCCBDB (SRD 101), Release 22: experimental data for H2O (water), including geometry — Primary dataset
A carbon dioxide molecule is linear, with an O–C–O angle of 180° and C–O bond lengths of 1.162 Å. (awaiting scientific review)
- NIST CCCBDB (SRD 101), Release 22: experimental data for CO2 (carbon dioxide), including geometry — Primary dataset
Four electron groups around a central atom give a tetrahedral arrangement with ideal angles of 109.5°, and because lone pairs repel more strongly than bonding pairs, molecules with lone pairs on the central atom have actual bond angles slightly smaller than the ideal. (awaiting scientific review)
- 3.6: Molecular Structure and Polarity (Chemistry: Physical Principles), CC BY 4.0 — Textbook
VSEPR has limitations and does not always predict the shapes of complex molecules, but it is very useful for simple molecules. (awaiting scientific review)
- 3.6: Molecular Structure and Polarity (Chemistry: Physical Principles), CC BY 4.0 — Textbook
One mole contains exactly 6.022 140 76 × 10²³ specified elementary entities, which may be atoms, molecules, ions, electrons or other particles. (awaiting scientific review)
- SI base unit: mole (mol) — Government or standards body
The Avogadro constant has the exact value 6.022 140 76 × 10²³ mol⁻¹ (CODATA 2022). (awaiting scientific review)
- CODATA 2022 recommended value: Avogadro constant — Government or standards body
CIAAW's abridged standard atomic weights are 1.0080 for hydrogen, 12.011 for carbon and 15.999 for oxygen. (awaiting scientific review)
- Abridged Standard Atomic Weights 2024 — Government or standards body
NIST's Chemistry WebBook lists the molecular weight of water as 18.0153. (awaiting scientific review)
- NIST Chemistry WebBook (SRD 69): Water — phase change data — Primary dataset

Claims marked “awaiting scientific review” cite the sources listed but have not yet been signed off by a scientific reviewer.

Content status: published 1 October 2026.

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