Mole and Avogadro Constant — Amount of Substance

One-sentence answer: The mole counts 6.02214076×10²³ entities exactly; it links macroscopic mass to microscopic count via molar mass.

Objectives

• Define amount of substance (n) and mole (mol) per IUPAC Gold Book.
• Use $N = n N_A$ and $n = m/M$ with unit-consistent substitution.
• Distinguish mole (count) from mass (inertia) and from concentration.

Prerequisites

• SI Units — base units; Atomic mass conceptual

Intuition (plain language)

Macroscopic: you weigh grams on a balance. Particle level: chemical change is counted in atoms, ions, or molecules. The mole is the bridge: one mole contains exactly $6.02214076\times10^{23}$ specified entities (atoms, molecules, formula units, electrons — you must state which). This number is the Avogadro constant $N_A$, exact by definition since 2019 (SI).

Representations

• Macroscopic: $m$ (mass, g) measured on a balance.
• Particle level: $N$ (number of entities) — e.g., 12.0 g of $^{12}$C contains $N_A$ atoms.
• Symbolic: $n = N/N_A = m/M$, where $M$ is molar mass (g·mol⁻¹).

Definitions and constants

From IUPAC Gold Book and NIST CODATA 2022:

• Amount of substance (n, unit mol) — proportional to number of specified entities: $n = N/N_A$.
• Avogadro constant $N_A = 6.02214076\times10^{23}$ mol⁻¹ exactly (defines the mole; not measured).

Symbol	Quantity	Unit	Notes
$N_A$	Avogadro constant	mol⁻¹	exact: $6.02214076\times10^{23}$ mol⁻¹ (nist-constants-2022)
$n$	amount of substance	mol	$n = N/N_A = m/M$
$M$	molar mass	g·mol⁻¹	sum of atomic weights (CIAAW, see periodic table)

Worked example — entities from mass

Problem: How many formula units in 12.0 g of NaCl ($M = 58.44$ g·mol⁻¹)?

Solution:

1. Relation: $n = m/M$.
2. Substitute with units: $n = 12.0\,\text{g} / 58.44\,\text{g·mol}^{-1} = 0.205$ mol.
3. Dimensional check: $\text{g} / (\text{g·mol}^{-1}) = \text{mol}$ ✓.
4. Entities: $N = n N_A = 0.205 \times 6.02214076\times10^{23} = 1.23\times10^{23}$ formula units of NaCl.

Answer: $0.205$ mol → $1.23\times10^{23}$ units.

The same steps power the calculators: grams↔moles and moles↔particles.

Pause and predict

If you double the mass to 24.0 g, predict the effect on $N$ before calculating — then verify $N$ also doubles, confirming $N \propto m$ at fixed $M$.

Common mistakes and misconceptions

• Confusing mass with amount (moles) — moles count specified entities via $N_A$.
• Omitting the entity type (“moles of what?” — NaCl formula units, H₂O molecules, e⁻).
• Using atomic mass (g/mol per atom) where formula mass is required.
• Treating $N_A$ as measured with significant-figure uncertainty — since 2019 it is defined exact.

Quick knowledge check

Which is larger: 1 mol of H₂O molecules or 1 mol of NaCl formula units?

Answer: Counts are equal — both are $N_A$ entities — but masses differ: ~18.015 g vs 58.44 g. Same amount, different entity mass. See worked example and revisit misconceptions.

Summary

• The mole is an SI count of $N_A$ specified entities; $N_A$ is exact.
• Use $n=m/M$ and $N=nN_A$ with the entity stated and units checked.
• Link to tools: Molar mass for $M$, then the examples above.

Sources

• IUPAC Gold Book — amount of substance, mole, Avogadro constant — goldbook.iupac.org (iupac-gold). Accessed 2026-08-21, reviewed 2026-08-23.
• CODATA 2022 via NIST — $N_A = 6.02214076×10^{23}$ mol⁻¹ exact — physics.nist.gov/cuu/Constants (nist-constants-2022). Version 2022-CODATA, reviewed 2026-08-23.
• CIAAW atomic weights for $M$ (see /sources).

Author and dates

• Author: Chemistry Fundamentals Editorial Team
• Reviewer: Editorial Review Board (chemistry reviewer; transparent placeholder — see Editorial Policy)
• Published: 2026-08-21 — Last reviewed: 2026-08-23 — Review due: 2027-08-23
• Correction? See Corrections Policy — Contact