A dozen means 12. A century means 100. A mole means 602,200,000,000,000,000,000,000. Chemists chose this number for a very specific reason — and once you understand why, every calculation in this module falls into place.
📚 Core Content
Atoms are extraordinarily small. A single carbon atom has a mass of roughly 2 × 10⁻²³ grams — far too small to weigh on any lab balance. Yet chemical reactions happen between specific numbers of atoms. If you want to react hydrogen with oxygen to make water, you need exactly two hydrogen atoms for every one oxygen atom. Counting individual atoms is impossible, so chemists needed a bridge between the atomic world and the measurable world.
The solution was to define a counting unit large enough that a mole of something has a mass you can actually put on a scale. That unit is the mole — the SI unit for amount of substance.
One mole is defined as the amount of substance that contains exactly 6.022 × 10²³ elementary entities (atoms, molecules, ions, or formula units). This number is called Avogadro's number, symbol NA.
It's genuinely difficult to grasp. Here's one comparison that helps: if you had Avogadro's number of grains of sand, they would cover the entire continent of Australia to a depth of approximately 100 metres. Every grain of sand in every beach on Earth contains nothing close to this many atoms of silicon.
This is the only formula in this lesson. It connects three quantities: the number of particles (N), the amount in moles (n), and Avogadro's number (NA). If you know any two, you can find the third.
For example, if you have 2 mol of carbon atoms: N = 2 × 6.022 × 10²³ = 1.204 × 10²⁴ atoms. The moles unit cancels because NA is mol⁻¹, leaving a dimensionless count of particles.
🧮 Worked Examples
🧪 Activities
1 A sample contains 0.75 mol of NaCl. How many formula units does it contain?
2 A balloon contains 1.806 × 10²⁴ molecules of helium gas. How many moles is this?
3 A student dissolves 3.0 mol of glucose (C₆H₁₂O₆) in water. Her lab partner claims the solution contains exactly 3.0 × 6.022 × 10²³ individual glucose molecules. Is the lab partner correct? Calculate the actual number and state whether they agree.
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Complete these problems in your workbook.
| Analogy | Quantity | Comparable to Nₐ? |
|---|---|---|
| Grains of sand covering Australia at 100 m depth | ~6 × 10²³ | Your answer |
| Seconds elapsed since the Big Bang | ~4 × 10¹⁷ | Your answer |
| Blades of grass on all of Earth's land surfaces | ~7 × 10¹⁸ | Your answer |
| Stars in the observable universe | ~10²³ | Your answer |
Type your responses below:
Answer A and B in your workbook.
❓ Multiple Choice
1. The mole is best defined as:
2. Which expression correctly gives the number of particles N in a sample of n moles?
3. What are the correct units of Avogadro's number, NA?
4. How many atoms are in 0.25 mol of iron (Fe)?
5. A student has two samples: 2 mol of H₂O and 2 mol of CO₂. Which statement is correct?
✍️ Short Answer
6. Explain why chemists use the mole as a unit of measurement rather than counting individual atoms. In your answer, refer to the scale of atoms and the purpose of Avogadro's number. 3 MARKS
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Answer in your workbook.
7. A sample of helium gas contains 9.033 × 10²³ atoms. Calculate the number of moles of helium in the sample. Show all working. 3 MARKS
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Answer in your workbook.
8. A student claims that 1 mol of hydrogen gas (H₂) and 1 mol of oxygen gas (O₂) contain the same number of molecules. Is the student correct? Justify your answer with reference to Avogadro's number, and explain why the masses of the two samples differ despite having the same number of molecules. 4 MARKS
Type your answer below:
Answer in your workbook.
Question A: Grains of sand covering Australia is most useful for most students — it's a physical object they can picture, and the scale (~6 × 10²³) is almost exactly Avogadro's number. Stars in the observable universe (~10²³) is also comparable. Accept any well-reasoned answer.
Question B: Seconds since the Big Bang (~4 × 10¹⁷) is NOT comparable to NA. It is about 6 orders of magnitude smaller than 6.022 × 10²³. This highlights that Avogadro's number is so large it dwarfs even the age of the universe measured in seconds.
1. B — The mole is the SI unit for amount of substance containing NA entities.
2. A — N = n × NA is the correct expression.
3. C — NA has units of mol⁻¹ (per mole), so when multiplied by n (mol) the units cancel.
4. D — N = 0.25 × 6.022 × 10²³ = 1.506 × 10²³ atoms.
5. B — Both samples are 2 mol, so both contain 2 × 6.022 × 10²³ = 1.204 × 10²⁴ molecules. The mole is defined by particle count, not mass.
Q6 (3 marks): Atoms are far too small to count individually in the laboratory — a single carbon atom has a mass of approximately 2 × 10⁻²³ g [1]. Chemists use the mole because it represents a number of particles (NA = 6.022 × 10²³) large enough that one mole of any substance has a measurable mass [1]. Avogadro's number provides the conversion factor between the atomic scale (individual particles) and the laboratory scale (grams of substance) [1].
Q7 (3 marks):
Known: N = 9.033 × 10²³ atoms, NA = 6.022 × 10²³ mol⁻¹ Formula: n = N ÷ NA n = 9.033 × 10²³ ÷ 6.022 × 10²³ n = 1.5 mol ✓Q8 (4 marks): The student is correct [1]. Both 1 mol of H₂ and 1 mol of O₂ contain exactly NA = 6.022 × 10²³ molecules, because the mole is defined by particle count, not mass [1]. However, the masses differ because the two molecules have different molar masses — H₂ has a molar mass of 2 g/mol, while O₂ has a molar mass of 32 g/mol [1]. The same number of particles can have very different masses depending on the mass of each individual particle [1].
Tick when you've finished all activities and checked your answers.