15.1 The Mole

2026 Syllabus Objectives

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

  1. Understand that amount of substance is an SI base quantity with the base unit mol.
  2. Use molar quantities, knowing that one mole of any substance is the amount that contains a number of particles equal to the Avogadro constant, Nₐ.

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1. Amount of Substance — An SI Base Quantity

In physics, we measure many things: length in metres, mass in kilograms, time in seconds. These are called SI base quantities — the fundamental building blocks of measurement that everything else is built from.

Amount of substance is one of these SI base quantities. It tells us how much of a substance we have, not in terms of mass or volume, but in terms of how many particles (atoms, molecules, etc.) are present.

The SI base unit for amount of substance is the mole, written as mol.

Think of the mole the same way you think of the word "dozen." A dozen always means 12 of something — it doesn't matter if it's 12 eggs or 12 cars. Similarly, a mole always means a specific, fixed number of particles.

2. What Is a Mole?

One mole is defined as the amount of substance that contains as many particles as there are atoms in exactly 12 grams of carbon-12 (a specific type of carbon atom).

This sounds specific, but all you really need to know is: one mole = a very large, fixed number of particles.

That fixed number is called the Avogadro constant.

3. The Avogadro Constant (Nₐ)

The Avogadro constant, given the symbol Nₐ, is the number of particles in exactly one mole of any substance.

NA=6.02×1023 mol−1N_A = 6.02 \times 10^{23} \text{ mol}^{-1}

This is an enormous number — over 600 billion trillion! The reason we need such a huge number is that individual atoms and molecules are incredibly tiny. You need an astronomically large number of them to have an amount you can actually see and work with in a lab.

Key point: The Avogadro constant applies to any substance and any type of particle — atoms, molecules, ions, electrons, etc.

Examples:

  • 1 mole of helium atoms contains 6.02 × 10²³ helium atoms.
  • 1 mole of water molecules contains 6.02 × 10²³ water molecules.
  • 1 mole of sodium atoms contains 6.02 × 10²³ sodium atoms.
  • 2 moles of nitrogen atoms contains 2 × 6.02 × 10²³ = 1.20 × 10²⁴ nitrogen atoms.

It doesn't matter what the substance is — one mole always contains Nₐ particles.

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