🧪 Elements
22 lessons

The Mole: Chemistry's Dozen

Atoms are too small to count, so chemists count in batches of 6 × 10²³ — a batch sized so the scale does the counting for you.

lesson 2 of 3 in this unit

Builds on: 0.1 Atoms: The Alphabet of Matter2.1 Chemical Reactions & Balancing

A counting unit, nothing more

A pair is 2, a dozen is 12, a mole is 6.022 × 10²³ — that’s the whole definition. The number (Avogadro’s number, NA) looks absurd, but it’s chosen with surgical cunning: one mole of any substance weighs its atomic/molecular mass in grams. Carbon-12 atoms have mass number 12 → one mole of carbon weighs 12 g. Water molecules weigh 18 u → one mole of water is 18 g, about one gulp.

n = m / Mmoles = mass in grams ÷ molar mass in g/mol (read M off the periodic table)

This is the bridge between the invisible and the weighable. You cannot count molecules, but you can weigh 18 g of water — and then you know, with certainty, that you hold 6.022 × 10²³ molecules. The scale becomes a particle counter.

Molar mass from a formula

Add up the atomic masses from the periodic table. Water H₂O: 2 × 1.008 + 16.00 = 18.02 g/mol. Carbon dioxide CO₂: 12.01 + 2 × 16.00 = 44.01 g/mol. Table sugar C₁₂H₂₂O₁₁: 342.3 g/mol. That’s the entire skill — addition with a map.

Counting particles

N = n · NAparticles = moles × 6.022 × 10²³
How big is 6 × 10²³ really?

A mole of marshmallows would cover Germany roughly 1000 km deep. A mole of water molecules fits in a shot glass. That contrast — a number too big to imagine, hiding inside amounts you handle daily — is why chemistry needs the mole: reality operates in armies, and the mole is the army’s name.

⚗️ LabThe Particle Counter

A scale on the left, the conversion chain on the right.

  • Set water to exactly 18 g — read off precisely one mole.
  • Same 100 g of water vs. iron: which holds more particles, and why?
  • Watch the particle count: it never leaves the 10²³–10²⁴ neighbourhood for lab-sized amounts.
18 g

Work it by hand — 0 / 4

No multiple choice here: compute the value and type it. Suffixes like 2.5k, 20m or 100µ are understood; answers within ±2% count.

1. How many moles are in 90 g of water (M = 18.02 g/mol)?
2. What is the mass of 0.25 mol of CO₂ (M = 44.01 g/mol)?
3. What is the molar mass of glucose, C₆H₁₂O₆ (C = 12.01, H = 1.008, O = 16.00)?
4. How many molecules are in 2.5 mol of water? (Answer in molecules; suffixes like 1.5e24 work.)

Check your understanding

1. One mole of a substance always contains…

2. Why is Avogadro's number chosen to be exactly that odd value?

3. What is the molar mass of CO₂ (C = 12.01, O = 16.00)?

4. You have 100 g of water and 100 g of iron. Which contains more particles?