The Mole Concept
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.
Download this lesson's worksheet
Use the PDF for classwork, homework or revision. It includes key ideas, activities, questions, an extend task and success-criteria proof.
A recipe calls for 'a dozen eggs'. A chemist counts atoms in 'moles'. What do you think a mole is, and why would scientists need a special word for a quantity of atoms?
Type your initial response below — you will revisit this at the end of the lesson.
Write your initial response in your book. You will revisit it at the end of the lesson.
Formula Reference — This Lesson
Know
- What a mole is and why it exists
- Avogadro's number and its units
- The difference between N and n
Understand
- How Nₐ bridges atomic and lab scales
- Why the mole was defined using carbon-12
- When to use N = n × Nₐ
Can Do
- Calculate N from n using N = n × Nₐ
- Calculate n from N by rearranging
- State and apply Avogadro's number correctly
📚 Core Content
Misconceptions to Fix
Wrong: The limiting reagent is the one present in the smallest mass.
Right: The limiting reagent is the reactant that runs out first based on mole ratios, not mass.
Why Do Chemists Use the Mole?
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.
The Definition
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.
How Big Is Avogadro's Number?
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.
The Formula: N = n × NA
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
Worked Example 1 — Finding N (number of particles)
Stepwise-
1Identify known valuesn = 2.5 mol | NA = 6.022 × 10²³ mol⁻¹
-
2Identify what we needN = ? (number of carbon atoms)
-
3Write the formulaN = n × NA
-
4Substitute valuesN = 2.5 × 6.022 × 10²³
-
5CalculateN = 1.506 × 10²⁴
Worked Example 2 — Finding n (moles)
Stepwise-
1Identify known valuesN = 3.01 × 10²⁴ molecules | NA = 6.022 × 10²³ mol⁻¹
-
2Identify what we needn = ? (amount in moles)
-
3Rearrange the formulan = N ÷ NA
-
4Substitute valuesn = 3.01 × 10²⁴ ÷ 6.022 × 10²³
-
5Calculaten = 5.0 mol
Common Mistakes — Don't Lose Easy Marks
📓 Copy Into Your Books
▼📖 Key Definitions
- Mole — SI unit for amount of substance
- N — number of particles (atoms, molecules, formula units) — no units
- n — amount of substance, measured in mol
- NA — Avogadro's number = 6.022 × 10²³ mol⁻¹
📐 Formula & Rearrangements
- N = n × NA (find number of particles)
- n = N ÷ NA (find moles)
- NA = N ÷ n (find Avogadro's number)
🔢 Key Values
- NA = 6.022 × 10²³ mol⁻¹
- 1 mole of carbon-12 = 12.000 g
- Units: mol × mol⁻¹ = no units ✓
💡 When to Use This
- Converting moles → number of particles
- Converting number of particles → moles
- Any question giving you N or n and asking for the other
🧪 Activities
Applying N = n × Nₐ
-
1 A sample contains 0.75 mol of NaCl. How many formula units does it contain?
N = n × NA = 0.75 × 6.022 × 10²³N = 4.517 × 10²³ formula units -
2 A balloon contains 1.806 × 10²⁴ molecules of helium gas. How many moles is this?
n = N ÷ NA = 1.806 × 10²⁴ ÷ 6.022 × 10²³n = 3.0 mol -
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.
Yes, the lab partner is correct. N = n × NA = 3.0 × 6.022 × 10²³N = 1.807 × 10²⁴ molecules3.0 × 6.022 × 10²³ = 1.807 × 10²⁴ — this is exactly what the formula gives, so the lab partner's statement is equivalent and correct.
Type your working below before revealing answers above:
Complete these problems in your workbook.
The Scale of Avogadro's Number
| 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.
Revisit Your Initial Thinking
Earlier you were asked: What do you think a mole is, and why would scientists need a special word for a quantity of atoms?
The key insight: atoms are so tiny that even a pinhead of iron contains around 10²⁰ atoms — far too many to count individually. The mole (NA = 6.022 × 10²³) was chosen because one mole of carbon-12 atoms has a mass of exactly 12 g, linking the atomic scale to the laboratory scale. It's not a mysterious number — it's a bridge between the world of atoms and the world of grams and beakers.
Now revisit your initial response. What did you get right? What has changed in your thinking?
Look back at your initial response in your book. Annotate it with what you now understand differently.
Multiple Choice
5 random questions from a replayable lesson bank — feedback shown immediately
✍️ Short Answer
Extended Questions
8. 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
Type your answer below:
Answer in your workbook.
9. 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
Type your answer below:
Answer in your workbook.
10. 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.
11. In 2019, scientists redefined the mole so that it is now based on fixing the exact numerical value of Avogadro's number (NA = 6.02214076 × 10²³ mol⁻¹), rather than tying it to a physical sample of carbon-12. (a) Distinguish between the old and new definitions of the mole. (2 marks) (b) Evaluate whether this redefinition affects any Year 11 chemistry calculations in practice. Justify your answer with at least one example. (2 marks) (c) Suggest one advantage of fixing NA as an exact constant rather than defining it by reference to a physical substance. (1 mark) 5 MARKS
Type your answer below:
Answer in your workbook.
✅ Comprehensive Answers
▼📊 Activity 2 — Scale Analysis
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.
❓ Multiple Choice
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.
6. B (Band 5 — Evaluate) — The claim is wrong in general. The mole concept links amount (mol) to mass via molar mass. 1 g of carbon-12 contains NA atoms because the molar mass of carbon-12 is exactly 12 g/mol and the sample is 1/12 mol — a special case. Iron has a molar mass of ~56 g/mol, so 1 g of iron is only 1/56 mol, containing NA/56 ≈ 1.07 × 10²² atoms.
7. B (Band 6 — Create) — 1.00 mol of H₂O contains 1.00 mol of O atoms (one O per molecule). Each CO₂ molecule contains 2 O atoms, so 1 mol of CO₂ provides 2 mol of O atoms. To match 1.00 mol of O atoms: n(CO₂) = 1.00 ÷ 2 = 0.50 mol.
📝 Short Answer Model Answers
Q8 (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].
Q9 (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 ✓Q10 (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].
Q11 (5 marks — Band 6): (a) Old definition: the mole was the amount of substance containing the same number of entities as atoms in exactly 12 g of carbon-12 — this tied NA to a physical sample [1]. New definition: NA is fixed exactly at 6.02214076 × 10²³ mol⁻¹, making the mole defined by a counting number rather than a physical artefact [1]. (b) No practical effect — the value of NA changed by less than 1 part in 10⁸, far below the precision of any Year 11 calculation. For example, n = N ÷ NA gives the same answer to 4 significant figures before and after the redefinition [1]. All formulas and worked examples remain identical [1]. (c) Fixing NA removes dependence on a physical standard that could be destroyed or change over time — the definition is now based on a universal constant that can be realised anywhere in the universe without reference to a specific object [1].
Science Jump — The Mole Concept
Climb platforms, hit checkpoints, and answer questions on the mole concept, Avogadro's number and the relationship between moles and particles. Quick recall from lessons 1–1.
Mark lesson as complete
Tick when you've finished all activities and checked your answers.