The Mole and the Avogadro Constant

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Define and use the term mole in terms of the Avogadro constant

Main Content

https://cambridgeassistant.com

What is a Mole?

A mole (symbol: mol) is simply a way of counting particles — just like "a dozen" means 12 of something, "a mole" means a specific very large number of particles.

Definition of a mole:
A mole is the amount of substance that contains 6.02 × 10²³ particles (atoms, molecules, ions, or electrons).

This special number is called the Avogadro constant.

Think of it this way:

  • 1 dozen eggs = 12 eggs
  • 1 mole of atoms = 6.02 × 10²³ atoms

The reason we use moles in chemistry is because atoms and molecules are incredibly tiny. Instead of saying "I have 602,000,000,000,000,000,000,000 atoms of carbon," we can simply say "I have 1 mole of carbon atoms." Much easier!

The Avogadro Constant

The Avogadro constant (symbol: N_A or L) is the number of particles in one mole of any substance.

Value: N_A = 6.02 × 10²³ mol⁻¹

This constant applies to:

  • Atoms (e.g., sodium atoms, carbon atoms)
  • Molecules (e.g., water molecules, oxygen molecules)
  • Ions (e.g., chloride ions, sodium ions)
  • Electrons

Important fact: The Avogadro constant is named after the Italian scientist Amedeo Avogadro. It's a fixed number that never changes, no matter what substance you're dealing with.

Connecting Moles to Mass

Here's a very useful relationship:

One mole of any element has a mass in grams equal to its relative atomic mass (A_r).

Examples:

  1. Sodium (Na):

    • Relative atomic mass (A_r) = 23.0
    • Therefore, 1 mole of sodium = 23.0 g
    • This 23.0 g contains 6.02 × 10²³ sodium atoms

  2. Carbon (C):

    • Relative atomic mass (A_r) = 12.0
    • Therefore, 1 mole of carbon = 12.0 g
    • This 12.0 g contains 6.02 × 10²³ carbon atoms

For molecules and compounds, we use the relative molecular mass (M_r) or relative formula mass instead.

Examples:

  1. Hydrogen gas (H₂):

    • Each hydrogen atom has A_r = 1.0
    • H₂ has 2 hydrogen atoms, so M_r = 2 × 1.0 = 2.0
    • Therefore, 1 mole of H₂ = 2.0 g
    • This 2.0 g contains:
      • 6.02 × 10²³ molecules of H₂
      • 1.204 × 10²⁴ atoms of hydrogen (because each molecule has 2 atoms, so 2 × 6.02 × 10²³)

  2. Water (H₂O):

    • M_r = (2 × 1) + 16 = 18
    • Therefore, 1 mole of water = 18 g
    • This contains 6.02 × 10²³ water molecules

  3. Sodium chloride (NaCl):

    • M_r = 23.0 + 35.5 = 58.5
    • Therefore, 1 mole of NaCl = 58.5 g
    • This contains:
      • 6.02 × 10²³ formula units of NaCl
      • 6.02 × 10²³ sodium ions (Na⁺)
      • 6.02 × 10²³ chloride ions (Cl⁻)
      • Total atoms = 1.204 × 10²⁴ (since each formula unit has 1 Na + 1 Cl = 2 atoms)

Sign in to view full notes