6.4 Avogadro's Number and Mole

This topic introduces the mole — the chemist's counting unit — and Avogadro's number, which connects the microscopic world of atoms to the macroscopic world we can measure.

Definition

Mole

A mole is an amount of a substance that contains 6.022 × 10²³ particles of that substance.

Simple explanation: A mole is just a counting unit — like "dozen" or "pair" — but much, much larger.

Avogadro's Number

This experimentally determined number is known as Avogadro's number. It is represented by N_A.

N_A = 6.022 × 10²³

Simple explanation: Avogadro's number tells you how many particles are in one mole of a substance.

Main Idea

How do you count your shoes? Since shoes come in pairs, you'll probably count them in pairs rather than individually. Likewise, eggs, oranges, etc. are counted in dozens, but paper with the ream. So the unit of counting depends on what you are counting.

Chemists also use a practical unit for counting atoms, molecules, and ions. They use a counting unit called mole to measure the amount of a substance.

• a dozen eggs = 12 eggs
• a ream of paper = 500 papers

a mole of a substance = 6.022 × 10²³ representative particles of that substance.

Simple explanation: The mole is just a convenient way to count very large numbers of tiny particles.

Core Concept

What Is a Mole?

Simple explanation: One mole always contains the same number of particles — 6.022 × 10²³ — no matter what the substance is.

Representative Particles

The term representative particles in a substance refers to:

• Atoms — for elements (e.g., C, S, Na)
• Molecules — for molecular compounds (e.g., H₂O, CO₂)
• Formula units — for ionic compounds (e.g., NaCl, MgO)
• Ions — for charged species (e.g., Na⁺, Cl⁻)

Simple explanation: The "particles" in a mole can be atoms, molecules, formula units, or ions — depending on the substance.

Detailed Explanation

The Size of the Mole

The book gives a striking example:

> "Entire population cannot count 1 mole of coins in a year. They need about one million years to count them."

This shows just how large Avogadro's number is.

Simple explanation: 6.022 × 10²³ is an incredibly huge number — you could never count that many things one by one.

Why Chemists Use the Mole

Chemists use the mole because:

• Atoms and molecules are too small to count individually.
• Chemical reactions involve huge numbers of particles.
• The mole provides a bridge between the microscopic world (atoms) and the macroscopic world (grams).

Simple explanation: The mole lets chemists "count" atoms by weighing them.

Mass of One Mole

The mass of one mole of a substance is called its molar mass.

• Molar mass of carbon = 12 g/mol
• Molar mass of sulphur = 32.1 g/mol
• Molar mass of water = 18 g/mol

Simple explanation: One mole of carbon weighs 12 grams; one mole of water weighs 18 grams.

Examples from the Book

The book asks:

Q: What is the mass of one mole of C-atoms? A: 12 g

Q: How many atoms are there in 32.1 g of S-atoms? A: 6.022 × 10²³ atoms (one mole)

Q: Does a dozen eggs have the same mass as a dozen bananas? A: No — a dozen is a count, not a mass. Similarly, one mole of carbon has a different mass than one mole of sulphur.

Q: Does a mole of carbon atoms have a different mass than a mole of sulphur atoms? A: Yes — carbon's molar mass is 12 g/mol, sulphur's is 32.1 g/mol.

Simple explanation: One mole always has the same number of particles, but different substances have different masses per mole.

Intermediate Level

Why 6.022 × 10²³?

Avogadro's number was chosen so that:

1 mole of a substance = its relative atomic/molecular mass in grams

• Carbon: relative atomic mass = 12 amu → 1 mole = 12 g
• Sulphur: relative atomic mass = 32.1 amu → 1 mole = 32.1 g
• Water: relative molecular mass = 18 amu → 1 mole = 18 g

Simple explanation: The mole connects atomic mass units (amu) to grams in a convenient way.

The Mole and Chemical Reactions

Chemical equations tell us the ratio of moles of reactants and products.

Example:

2H₂ + O₂ → 2H₂O

• 2 moles of H₂ react with 1 mole of O₂
• to produce 2 moles of H₂O

Simple explanation: The mole lets us count particles in chemical reactions.

Molar Mass

The molar mass of a substance is the mass of one mole of that substance.

Simple explanation: Molar mass is the mass in grams of one mole of a substance.

Avogadro's Number and Molar Mass

Key relationship:

Number of moles = Mass of substance (g)Molar mass (g/mol)

Simple explanation: If you know the mass of a substance and its molar mass, you can find the number of moles.

Important Points

• - Mole: amount of a substance that contains 6.022 × 10²³ particles.
• - Avogadro's number: 6.022 × 10²³ particles per mole.
• - Representative particles: atoms, molecules, formula units, or ions.
• - **1 mole of C** = 6.022 × 10²³ C atoms = 12 g
• - **1 mole of S** = 6.022 × 10²³ S atoms = 32.1 g
• - **1 mole of H₂O** = 6.022 × 10²³ H₂O molecules = 18 g
• - Molar mass: mass of one mole of a substance.
• - The mole is the chemist's counting unit.
• - The mole connects the microscopic world (atoms) to the macroscopic world (grams).

Remember

• - **Mole** = 6.022 × 10²³ particles.
• - **Avogadro's number** = 6.022 × 10²³.
• - **1 mole of C** = 12 g.
• - **1 mole of S** = 32.1 g.
• - **1 mole of H₂O** = 18 g.
• - Molar mass = mass of one mole.
• - Representative particles: atoms, molecules, formula units, ions.
• - Mole = chemist's counting unit.

Common Mistakes

• 1. Thinking a mole is a mass. A mole is a count — like a dozen.
• 2. Thinking 1 mole of all substances has the same mass. Different substances have different molar masses.
• 3. Forgetting Avogadro's number. It is 6.022 × 10²³.
• 4. Confusing moles with molecules. 1 mole = 6.022 × 10²³ molecules (for a molecular substance).
• 5. Thinking "representative particles" always means molecules. It depends on the substance — atoms, molecules, formula units, or ions.
• 6. Forgetting the difference between relative atomic mass (amu) and molar mass (g/mol). They are numerically equal but have different units.

Quick Revision

• Mole: an amount of a substance that contains 6.022 × 10²³ particles of that substance.
• Avogadro's number (N_A): 6.022 × 10²³ — experimentally determined number of particles per mole.
• Representative particles: atoms, molecules, formula units, or ions.
• Just as a dozen = 12 and a ream = 500, a mole = 6.022 × 10²³.
• Examples:
• 1 mole of carbon = 6.022 × 10²³ atoms = 12 g
• 1 mole of sulphur = 6.022 × 10²³ atoms = 32.1 g
• 1 mole of water = 6.022 × 10²³ molecules = 18 g
• Molar mass: mass of one mole of a substance (in g/mol).

60-Second Revision

• **Mole** = 6.022 × 10²³ particles.
• **Avogadro's number** = 6.022 × 10²³.
• **1 mole of C** = 12 g; **1 mole of H₂O** = 18 g.
• Molar mass = mass of one mole.
• Warning: a mole is a count, not a mass.