Ch 2 · The mole and the Avogadro constant · AS & A Level Chemistry 9701

Topic 2 of 4 in Atoms, molecules and stoichiometry — AS & A Level Chemistry 9701 — 43 lessons.

Introduction

Atoms and molecules are far too numerous and too small to count individually, so chemists work in a unit that groups an enormous, fixed number of particles together: the mole. This lesson defines the mole and the Avogadro constant and builds the routine conversions between mass, moles and number of particles used throughout quantitative chemistry.

Key ideas — Defining the mole and the Avogadro constant

One mole of a substance is the amount of substance that contains the same number of particles (atoms, molecules, ions, electrons or formula units, as specified) as there are atoms in exactly 12 g of carbon-12. This number is the Avogadro constant, L (or N_A), with value 6.02 × 10^23\ mathrmmol^-1. A mole is therefore simply a very large, fixed counting unit, analogous to using "a dozen" to mean 12 of anything, except that one mole represents 6.02 × 10^23 particles.

🧑‍🏫 Teacher's explanation

Imagine you are trying to count grains of sand on a beach or stars in the sky. It is impossible to count them one by one. Instead, chemists use a 'counting unit' that is so large it makes sense for the microscopic world. Just as a 'dozen' tells you there are exactly 12 items, a 'mole' tells you there are exactly 6.02 × 10^23 particles.

📖 Definitions

🔍 Worked example — Easy

Calculate the number of molecules in 45 g of water (H_2O). (A_r values: H = 1, O = 16)

🔍 Worked example — Standard

How many moles are present in 3.01 × 10^23 atoms of Magnesium (Mg)? (A_r of Mg = 24)

🔍 Worked example — Exam-style

A sample of pure Iron (Fe) contains 1.204 × 10^24 atoms. Calculate the mass of this sample. (A_r of Fe = 56)

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — Why chemistry uses the mole

Chemical reactions occur between individual particles in fixed whole-number ratios (as shown by a balanced equation), but samples of matter that can be weighed on a balance contain numbers of particles far too large to count. The mole bridges this gap: because relative atomic and molecular masses are defined on the same scale as the mole (one mole of any substance has a mass in grams numerically equal to its A_r or M_r, called its molar mass, M, in mathrmg\ mol^-1), chemists can weigh out a measurable mass of a substance and know precisely how many moles, and therefore how many particles, are present, allowing reacting quantities to be calculated directly from a balanced equation.

🧑‍🏫 Teacher's explanation

Imagine you are a baker. You know that a recipe requires exactly 12 eggs to make a batch of cakes. However, eggs are small and hard to count one by one when you are working with thousands of them. Instead, you might think in terms of 'dozens'. If you know you have 5 dozen eggs, you automatically know you have 5 × 12 = 60 eggs. The mole is simply the 'chemist's dozen'.

📖 Definitions

🔍 Worked example — Standard

A sample contains 3.01 × 10^23 atoms of Magnesium. Calculate the mass of this sample. (A_r: Mg=24)

🔍 Worked example — Exam-style

How many moles of H_2O are present in 45.0g of water? (M_r: H=1, O=16)

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — Converting between mass, moles and number of particles

Three quantities are linked by two equations:

🧑‍🏫 Teacher's explanation

Think of a 'mole' just like a 'dozen'. If I tell you I have 2 dozen eggs, you know I have 24 eggs because the 'unit' (a dozen) is defined as 12. In chemistry, atoms are too tiny to count one by one, so we use the 'mole' as a massive counting unit. One mole is exactly 6.02 × 10^23 particles.

📖 Definitions

🔍 Worked example — Easy

Calculate the number of moles in 10.0 g of Calcium Carbonate, CaCO_3. (A_r: Ca=40, C=12, O=16)

🔍 Worked example — Exam-style

A sample of pure Iron (Fe) contains 3.01 × 10^24 atoms. Calculate the mass of this sample. (A_r: Fe=56, L = 6.02 × 10^23)

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — Care with what is being counted

When interconverting moles and number of particles, the type of particle specified must be tracked carefully, since one mole of a compound contains one mole of formula units but a different number of moles of each type of atom or ion within it. For example, one mole of CaCl_2 contains one mole of mathrmCa^2+ ions but two moles of Cl^- ions, and hence 1 × L calcium ions but 2 × L chloride ions. Similarly, one mole of O_2 gas contains one mole of oxygen molecules but two moles (and therefore 2 × L) of oxygen atoms.

🧑‍🏫 Teacher's explanation

Think of a 'mole' just like a 'dozen'. If I tell you I have 3 dozen eggs, you know I have 36 eggs. But if I tell you I have 3 dozen donuts, and each donut is made of 3 sprinkles, you have to be careful: do I have 36 donuts or 108 sprinkles? In chemistry, the 'dozen' is the Avogadro constant (L or N_A), and the 'donuts' are molecules.

Ch 2 · The mole and the Avogadro constant · AS & A Level Chemistry 9701

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