The Mole Concept

This lesson introduces the mole — the chemist's unit for counting particles. The mole concept links the mass of a substance (which you can weigh) to the number of particles it contains. It is one of the most important ideas in GCSE Chemistry and is required by the Edexcel specification (1CH0).

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Why Do We Need the Mole?

Atoms and molecules are incredibly small. Even a tiny grain of salt contains billions upon billions of particles. It would be impractical to count individual atoms, so chemists use a special counting unit called the mole (symbol: mol).

The mole is to chemistry what the "dozen" is to eggs — a convenient way to count a fixed number of items.

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What Is a Mole?

One mole of any substance contains exactly 6.02 × 10²³ particles.

This number is called Avogadro's constant (sometimes written as Avogadro's number).

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

So:

• 1 mol of carbon atoms contains 6.02 × 10²³ carbon atoms
• 1 mol of water molecules contains 6.02 × 10²³ water molecules
• 1 mol of sodium chloride formula units contains 6.02 × 10²³ NaCl units

Exam Tip: You must know that Avogadro's constant is 6.02 × 10²³. Questions may ask you to state it or use it in calculations.

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The Key Formula: Moles, Mass and Mr

The mole links mass (in grams) to relative formula mass (Mr):

$\text{moles} = \frac{\text{mass (g)}}{M_r}$moles=Mr​mass (g)​

This can be rearranged:

$\text{mass (g)} = \text{moles} \times M_r$mass (g)=moles×Mr​

$M_r = \frac{\text{mass (g)}}{\text{moles}}$Mr​=molesmass (g)​

The Mole Triangle

You can use a triangle diagram to help you rearrange the formula:

graph TD
    A["mass (g)"] --- B["moles × Mr"]
    style A fill:#f9f,stroke:#333,stroke-width:2px
    style B fill:#bbf,stroke:#333,stroke-width:2px

How to use the triangle:

• Cover what you want to find
• The remaining parts tell you the calculation:
  • Cover moles → mass ÷ Mr
  • Cover mass → moles × Mr
  • Cover Mr → mass ÷ moles

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Worked Examples

Example 1: Finding Moles from Mass

Question: Calculate the number of moles in 24 g of carbon (Ar of C = 12).

Solution:

• moles = mass ÷ Mr
• moles = 24 ÷ 12
• moles = 2 mol

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Example 2: Finding Moles from Mass (Compound)

Question: Calculate the number of moles in 22 g of carbon dioxide, CO₂.

Solution:

• First, calculate Mr of CO₂ = 12 + (2 × 16) = 12 + 32 = 44
• moles = mass ÷ Mr
• moles = 22 ÷ 44
• moles = 0.5 mol

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Example 3: Finding Mass from Moles

Question: Calculate the mass of 0.25 mol of calcium carbonate, CaCO₃.

Solution:

• First, calculate Mr of CaCO₃ = 40 + 12 + (3 × 16) = 40 + 12 + 48 = 100
• mass = moles × Mr
• mass = 0.25 × 100
• mass = 25 g

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Example 4: Finding Mr from Mass and Moles

Question: 0.1 mol of a substance has a mass of 5.85 g. Calculate the Mr.

Solution:

• Mr = mass ÷ moles
• Mr = 5.85 ÷ 0.1
• Mr = 58.5

(This is the Mr of NaCl — sodium chloride!)

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Example 5: Finding the Number of Particles

Question: How many molecules are there in 2 mol of water?

Solution:

• Number of particles = moles × Avogadro's constant
• Number of molecules = 2 × 6.02 × 10²³
• Number of molecules = 1.204 × 10²⁴

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Example 6: Multi-step Problem

Question: How many molecules are there in 9 g of water (H₂O)?

Solution:

1. Calculate Mr of H₂O = (2 × 1) + 16 = 18
2. Calculate moles: 9 ÷ 18 = 0.5 mol
3. Calculate number of molecules: 0.5 × 6.02 × 10²³ = 3.01 × 10²³ molecules

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Key Relationships

What you know	What you want	Formula
Mass and Mr	Moles	moles = mass ÷ Mr
Moles and Mr	Mass	mass = moles × Mr
Mass and moles	Mr	Mr = mass ÷ moles
Moles	Number of particles	N = moles × 6.02 × 10²³
Number of particles	Moles	moles = N ÷ 6.02 × 10²³

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The Mass of One Mole

A crucial insight: the mass of one mole of a substance (in grams) is numerically equal to its Mr.

Substance	Formula	Mr	Mass of 1 mol
Hydrogen gas	H₂	2	2 g
Water	H₂O	18	18 g
Carbon dioxide	CO₂	44	44 g
Sodium chloride	NaCl	58.5	58.5 g
Calcium carbonate	CaCO₃	100	100 g
Copper sulfate	CuSO₄	160	160 g

Exam Tip: When a question says "mass of 1 mole", it is simply asking for the Mr value expressed in grams. For example, the mass of 1 mole of CO₂ is 44 g.

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Common Mistakes

1. Forgetting to calculate Mr first — You must find Mr before you can convert between mass and moles.
2. Using Ar instead of Mr — Ar is for single atoms; Mr is for compounds or molecules.
3. Wrong rearrangement — Practice using the triangle to make sure you divide or multiply correctly.
4. Confusing moles with mass — Moles is a count (amount); mass is measured in grams.

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Summary

• A mole is the chemist's counting unit. 1 mol = 6.02 × 10²³ particles (Avogadro's constant).
• The key formula is: moles = mass ÷ Mr
• This can be rearranged to: mass = moles × Mr, or Mr = mass ÷ moles.
• The mass of one mole of a substance in grams is numerically equal to its Mr.
• Show all working in calculations and always calculate Mr first when dealing with compounds.

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