Moles | Chemistry | MrBadmusAI

📖 In-Depth Theory

The Mole — A Counting Unit for Chemistry

Atoms and molecules are far too small to count individually — there are billions of billions of them in even a tiny sample.

Chemists use the MOLE (symbol: mol) as a counting unit for particles.

One MOLE of any substance contains the SAME NUMBER of particles (atoms, molecules or ions):

6.02 × 10²³ particles — this is the AVOGADRO CONSTANT (Nₐ).

This number is chosen because:

1 mole of carbon-12 atoms has a mass of exactly 12 grams.

So 1 mole of any substance has a mass equal to its relative formula mass in grams.

Examples:

1 mole of water (H₂O, Mr = 18) has mass 18 g and contains 6.02 × 10²³ molecules.

1 mole of NaCl (Mr = 58.5) has mass 58.5 g and contains 6.02 × 10²³ formula units.

1 mole of Fe (Ar = 56) has mass 56 g and contains 6.02 × 10²³ atoms.

Calculating Moles from Mass

The key equation linking moles, mass and Mr:

moles (mol) = mass (g) ÷ Mr

Rearranging:

mass (g) = moles (mol) × Mr

Mr = mass (g) ÷ moles (mol)

EXAMPLES:

How many moles in 44 g of CO₂? (Mr of CO₂ = 44)

n = 44 ÷ 44 = 1 mol

How many moles in 9 g of water? (Mr of H₂O = 18)

n = 9 ÷ 18 = 0.5 mol

What mass of CaCO₃ is 0.25 mol? (Mr of CaCO₃ = 100)

mass = 0.25 × 100 = 25 g

What mass of NaOH contains 3.01 × 10²³ molecules? (Mr = 40)

Moles = 3.01 × 10²³ ÷ 6.02 × 10²³ = 0.5 mol

Mass = 0.5 × 40 = 20 g

Moles and Number of Particles

The Avogadro constant links moles to actual numbers of particles:

Number of particles = moles × Avogadro constant (6.02 × 10²³)

Moles = number of particles ÷ 6.02 × 10²³

EXAMPLES:

How many molecules in 2 mol of H₂O?

2 × 6.02 × 10²³ = 1.204 × 10²⁴ molecules.

How many atoms in 0.1 mol of iron?

0.1 × 6.02 × 10²³ = 6.02 × 10²² atoms.

PERCENTAGE MASS:

Percentage mass of element in compound:

% mass = (Ar × number of those atoms ÷ Mr) × 100

Example: % mass of oxygen in H₂SO₄ (Mr = 98):

% O = (16 × 4 ÷ 98) × 100 = (64 ÷ 98) × 100 = 65.3%

⚠️ Common Mistake

Make sure mass is in GRAMS before dividing by Mr. If given mass in kg, multiply by 1000 first. Also: 1 mole of H₂O contains 6.02 × 10²³ MOLECULES — but 3 × 6.02 × 10²³ ATOMS (2 H + 1 O per molecule). Always be clear about what particles are being counted.

📐 Variables

nAmount in moles (n) is measured in mol (mol)

mMass (m) is measured in grams (g)

MrRelative formula mass (Mr) is measured in ()

NₐAvogadro constant (Nₐ) is measured in mol⁻¹ (6.02 × 10²³)

📐 Key Equations

moles (mol) = mass (g) ÷ Mr

mass (g) = moles (mol) × Mr

number of particles = moles × 6.02 × 10²³

% mass = (Ar × number of atoms ÷ Mr) × 100

📌 Key Note

1 mole = 6.02 × 10²³ particles (Avogadro constant). n = m ÷ Mr. The molar mass = Mr in g/mol. % mass = (Ar × atoms ÷ Mr) × 100.

🎯 Matching Activity — Moles Calculations

Match each calculation to the correct answer. — drag the symbols on the right to match the component names on the left.

Moles in 40 g NaOH (Mr=40)

Drop here

Mass of 2 mol CO₂ (Mr=44)

Drop here

Moles in 5.6 g Fe (Ar=56)

Drop here

Particles in 0.5 mol

Drop here

% mass of Ca in CaCO₃ (Mr=100)

Drop here

3.01 × 10²³ — 0.5 × 6.02 × 10²³

40% — (40 ÷ 100) × 100 = 40%

0.1 mol — n = 5.6 ÷ 56 = 0.1

88 g — mass = 2 × 44 = 88

1 mol — n = 40 ÷ 40 = 1

⚽ FIFA Worked Examples

Moles from Mass

Calculate the number of moles in 27 g of aluminium (Ar = 27).

F

moles = mass ÷ Mr

I

moles = 27 ÷ 27

F

moles = 1

A

1 mol of aluminium

🎯 Test Yourself

Question 1 of 2

1. How many moles are in 9.8 g of sulfuric acid (H₂SO₄)? Mr = 98.

2. What mass of calcium carbonate (CaCO₃, Mr = 100) contains 3.01 × 10²³ formula units?

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🧪 Moles

The Mole — A Counting Unit for Chemistry

Calculating Moles from Mass

Moles and Number of Particles

Mr. Badmus AI