Avogadro Constant

Summary: The Avogadro constant (6.02 × 10²³) is the number of particles — atoms, molecules, or ions — present in one mole of any substance, serving as the fundamental bridge between the atomic-scale and macroscopic-scale in quantitative chemistry.

Tags: stoichiometry mole avogadro quantitative-chemistry cambridge-igcse-0620

Created: 2026-07-13

The Avogadro constant, with a value of 6.02 × 10²³, defines the number of specified particles contained in exactly one mole of any substance. Named after the Italian scientist Amedeo Avogadro (1776–1856), who first proposed that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules, the constant provides chemists with a direct numerical link between the submicroscopic world of individual particles and the macroscopic quantities measured in the laboratory. Whether counting atoms in an element, molecules in a covalent compound, or ions in an ionic lattice, one mole always contains 6.02 × 10²³ of those entities — just as a dozen always means twelve, a mole always means 6.02 × 10²³. This universality makes the Avogadro constant indispensable for converting between the amount of substance in moles and the actual number of particles present, using the relationship N = n × L (where N is number of particles, n is moles, and L denotes the Avogadro constant). In examination settings, candidates are expected to apply this constant to calculate numbers of atoms, molecules, or ions from a given number of moles, and vice versa, often as part of multi-step stoichiometric problems involving mass or gas volume. The magnitude of 6.02 × 10²³ is vast — it is far larger than the number of grains of sand on every beach on Earth — which underscores just how extraordinarily small individual atoms and molecules are.

Definition

The Avogadro constant (symbol L or N_A) is the number of constituent particles per mole of a substance. Its value is:

L = 6.02 × 10²³ mol⁻¹

For IGCSE, this value is used in its standard form, rounded to three significant figures. The units of the Avogadro constant (mol⁻¹) indicate that it expresses a number of particles per mole — multiplying by a number of moles therefore yields a dimensionless count of particles.

What the Avogadro Constant Counts

One of the most important points to grasp is that the Avogadro constant applies to any specified particle type. The particle must always be clearly identified, because the number obtained depends on what is being counted:

Atoms in a Compound

When asked “how many atoms” are in one mole of a compound, you must multiply by the number of atoms per formula unit. For example, one mole of H₂O contains 3 × 6.02 × 10²³ = 1.806 × 10²⁴ atoms, because each water molecule has three atoms (two hydrogen, one oxygen). Similarly, one mole of H₂SO₄ contains 7 × 6.02 × 10²³ = 4.214 × 10²⁴ atoms.

The Mole-Avogadro Relationship

The Avogadro constant is the heart of Mole calculations. The core equation is:

number of particles = number of moles × Avogadro constant

N = n × L

This equation can be rearranged to find moles from a given number of particles:

n = N / L

Worked Example 1: Moles to Particles

How many molecules are in 2.5 mol of carbon dioxide, CO₂?

• N = n × L
• N = 2.5 × 6.02 × 10²³
• N = 1.505 × 10²⁴ molecules of CO₂

Worked Example 2: Particles to Moles

How many moles are 3.01 × 10²³ atoms of magnesium?

• n = N / L
• n = (3.01 × 10²³) / (6.02 × 10²³)
• n = 0.500 mol of Mg atoms

Worked Example 3: Ions in Ionic Compounds

How many chloride ions are in 0.200 mol of calcium chloride, CaCl₂?

Each formula unit of CaCl₂ contains two Cl⁻ ions:

• Moles of Cl⁻ ions = 0.200 × 2 = 0.400 mol
• Number of Cl⁻ ions = 0.400 × 6.02 × 10²³ = 2.408 × 10²³

Using the Avogadro Constant with Mass and Gas Volume

The Avogadro constant is rarely used in isolation — it forms part of a chain of conversions in quantitative chemistry:

1. Mass to particles: mass (g) → moles (using Relative Atomic Mass or Molar Mass) → number of particles (using Avogadro constant)
2. Gas volume to particles: gas volume (dm³) → moles (using Molar Gas Volume, 24 dm³ mol⁻¹ at r.t.p.) → number of particles
3. Concentration to particles: concentration (mol dm⁻³) and volume → moles → number of particles

Worked Example 4: Full Chain

How many atoms are present in 4.6 g of sodium? (Aᵣ of Na = 23)

1. Moles of Na = mass / Aᵣ = 4.6 / 23 = 0.20 mol
2. Number of Na atoms = 0.20 × 6.02 × 10²³ = 1.204 × 10²³ atoms

Magnitude and Scale

The Avogadro constant is an enormous number. Understanding its scale helps internalize why chemists use moles rather than counting individual particles:

• 6.02 × 10²³ grains of rice would cover the entire land surface of the Earth to a depth of several metres.
• One mole of water molecules (18 cm³, about one tablespoon) contains more molecules than there are stars in the observable universe.
• If you started counting particles at a rate of one per second, it would take approximately 19 quadrillion years to reach 6.02 × 10²³.

Keywords

• Avogadro constant — 6.02 × 10²³ particles per mole
• Mole — the amount of substance containing exactly 6.02 × 10²³ specified particles
• Particle — the entity being counted, which may be an atom, molecule, ion, electron, or formula unit

Sources

• Cambridge IGCSE Chemistry 0620 Syllabus, Section 3.3: The Mole and the Avogadro Constant. Cambridge Assessment International Education.
• Harwood, R. and Lodge, I. (2014). Cambridge IGCSE Chemistry Coursebook. 3rd ed. Cambridge University Press. Chapter 5.
• Gallagher, R. and Ingram, P. (2021). Complete Chemistry for Cambridge IGCSE. 4th ed. Oxford University Press. Chapter 3.

Common Misconceptions