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.
Practise this lesson
Four printable worksheets that build from the foundations up to exam-style questions, start at whatever level suits you.
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?
$$N = n \times N_A$$
Key facts
- what a mole is and why it exists
- Avogadro's number (NA) and its units
- the difference between capital N and lowercase n
Concepts
- how NA bridges atomic and lab scales
- why the mole was defined using carbon-12
- when to use $N = n \times N_A$
Skills
- calculate N from n using $N = n \times N_A$
- calculate n from N by rearranging
- state and apply Avogadro's number correctly
Chemistry has a counting problem. The atomic world and the lab world don't speak the same language, until the mole bridges them.
- A single carbon atom weighs ~2 × 10⁻²³ g
- Far too small to weigh on any lab balance
- Reactions need exact numbers of atoms (e.g. 2 H + 1 O → H₂O)
- Reagents are weighed in grams on a balance
- You can scoop 12 g of carbon, but not 1 atom
- Quantities are large enough to see and measure
How big is Avogadro's number?
N vs n, get these right from day one
- The raw number of particles
- Like 1.2 × 10²⁴, a huge number
- No units (it's a pure count)
- The amount in moles
- Like 2 mol, a small number
- Units: mol
A mole is a counting unit (6.022 × 10²³ entities, symbol NA) chosen so that one mole of carbon-12 has a mass of exactly 12 g, bridging the atomic scale to the lab scale. Capital N = raw particle count (no units); lowercase n = amount in mol.
Pause, copy the highlighted definition into your book before moving on.
Did you get this? True or false: a mole is a counting unit (like a dozen), not a unit of mass.
Quick check: Which statement best explains why chemists use the mole?
Convert between moles and number of particles. The interactive scores you in real time.
We just saw that a mole is a counting unit equal to 6.022 × 10²³ entities, and that N and n are different symbols. That raises a question: how do you actually calculate one from the other? This card answers it → with the single formula that links them.
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 mol unit cancels because NA is mol⁻¹, leaving a dimensionless count of particles.
The formula N = n × NA converts moles to particle count; rearranged, n = N ÷ NA. Units cancel correctly: mol × mol⁻¹ = dimensionless count. Always cover the unknown in the triangle to read the correct rearrangement.
Add the highlighted point to your notes before the check below.
Did you get this? True or false: when you multiply n (mol) × NA (mol⁻¹) the units cancel and N has no units.
Fill the blanks: drag each token into the matching blank.
The formula linking moles to particles is N = ___ × ___. Capital N is the ___ ; lowercase n is the ___ .
Worked examples · reveal as you go
How many atoms are in 2.5 mol of carbon?
A sample contains 3.01 × 10²⁴ molecules of water. How many moles is this?
Common errors · the 3 traps that cost marks
Confusing N and n
Capital N is the raw count of particles, a number like 1.2 × 10²⁴ with no units. Lowercase n is the amount in moles, like 2 mol. They are not interchangeable.
Fix: Always label which quantity you're calculating before you substitute.
Dropping units, especially mol⁻¹
NA has units of mol⁻¹. When you multiply n (mol) × NA (mol⁻¹), the mol units cancel and you're left with a dimensionless count.
Fix: Write units at every step and confirm they cancel to what you expect.
Thinking a mole is a mass
A mole is a counting unit (like a dozen), not a unit of mass. Saying "a mole of carbon weighs 12 grams" is true only because 1 mol of C-12 is defined that way, not because a mole is itself a mass.
Fix: Always state what entity you are counting (atoms, molecules, ions, formula units).
Quick-fire practice · 5 reps +2 XP per reveal
A sample contains 0.75 mol of NaCl. How many formula units does it contain?
A balloon contains 1.806 × 10²⁴ molecules of helium gas. How many moles is this?
3.0 mol of glucose (C₆H₁₂O₆) is dissolved in water. How many individual glucose molecules are present?
A sample contains 1.204 × 10²² atoms of magnesium. Calculate n in moles.
How many oxygen atoms are in 0.50 mol of carbon dioxide (CO₂)? Be careful, each CO₂ molecule has 2 O atoms.
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.
True or false? One mole of any substance contains 6.022 × 10²³ particles, so 1 mol of carbon dioxide (CO₂) contains the same number of molecules as 1 mol of water (H₂O).