The Mole & Molar Mass

Atoms are far too small to count one by one — so chemists count them by weighing. The mole is how.

High schoolIntro Gen ChemUni Year 1
⏱️ About 20 min

You can't pick up a single atom and drop it on a balance. Atoms are far too small and far too many. So chemists do something clever: they count atoms by weighing them in bulk. The bridge that makes this work is one of the most useful ideas in all of chemistry — the mole.

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The big idea: A mole is just a counting number, like a dozen — it's 6.022 × 10²³ of anything. Its power is that one mole of an element weighs its atomic mass in grams. That single fact — the molar mass — lets you convert freely between grams (which you can weigh) and number of particles (which you can't).
🎯 By the end, you'll be able to
  • Explain a mole as a count of particles (6.022 × 10²³), not a mass
  • Find the molar mass of an element or compound from atomic masses
  • Convert between mass, moles, and number of particles
  • Use the mole as the hub that connects grams to atoms and molecules
📎 Helpful to know first

A mole is a number, not a weight

Here is the single most important thing to get straight: a mole is a count. Just as a dozen means 12 of something and a pair means 2, a mole means 6.022 × 10²³ of something. That's it.

A dozen eggs and a dozen elephants are both 12 things, even though they weigh wildly different amounts. In the same way, a mole of hydrogen atoms and a mole of lead atoms are both 6.022 × 10²³ atoms — they just weigh different amounts. The number is fixed; the mass depends on what you're counting.

🔑 Avogadro's number
One mole = 6.022 × 10²³ particles. This is Avogadro's number. Why such a strange value? It was chosen so that one mole of an element weighs its atomic mass in grams — the neat link we use next.

Molar mass: the gram value of a mole

The molar mass of a substance is the mass of one mole of it, in grams per mole (g/mol). And here's the gift the mole gives us: the molar mass of an element is just its atomic mass from the periodic table, read in grams.

Carbon's atomic mass is 12.01, so one mole of carbon weighs 12.01 g. For a compound, add up the molar masses of all its atoms. Water, H₂O, is 2 × 1.008 + 16.00 = 18.02 g/mol — one mole of water is about 18 g, a little over a tablespoon.

\[ M(\text{H}_2\text{O}) = 2(1.008) + 16.00 = 18.02\ \text{g/mol} \]
Molar mass of a compound = sum of the molar masses of every atom in the formula.
✨ The mole is the hub
Think of moles as the central station everything routes through. Grams ↔ moles uses molar mass (÷ or × M). Moles ↔ particles uses Avogadro's number (× or ÷ 6.022 × 10²³). You almost never go grams → particles directly; you go through moles.
\[ n = \frac{m}{M} \qquad\text{and}\qquad N = n \times N_A \]
n = moles, m = mass (g), M = molar mass (g/mol); N = number of particles, Nₐ = 6.022 × 10²³.
📝 Worked example: How many water molecules are in 9.00 g of water?
  1. First go grams → moles. Molar mass of H₂O = 2(1.008) + 16.00 = 18.02 g/mol.
  2. n = m / M = 9.00 g ÷ 18.02 g/mol = 0.4995 ≈ 0.500 mol.
  3. Now moles → molecules using Avogadro's number: 0.500 mol × 6.022 × 10²³ molecules/mol.
  4. = 3.01 × 10²³ molecules. (Notice we routed through moles, not straight from grams.)
✓ ≈ 3.01 × 10²³ water molecules.
✏️ Practice: How many moles are in 36.0 g of water (H₂O)? Use molar mass 18.02 g/mol. Round to 2 decimals.
mol
Solution
  1. Use n = m / M.
  2. n = 36.0 g ÷ 18.02 g/mol.
  3. = 2.00 mol. (So 36 g of water is about two moles — roughly 1.2 × 10²⁴ molecules.)
✏️ Practice: What is the mass of 0.250 mol of carbon dioxide, CO₂? First find its molar mass from C = 12.01 and O = 16.00. Give grams to 1 decimal.
g
Solution
  1. Molar mass of CO₂ = 12.01 + 2(16.00) = 12.01 + 32.00 = 44.01 g/mol.
  2. Rearrange n = m / M to get m = n × M.
  3. m = 0.250 mol × 44.01 g/mol = 11.0 g.

Check your understanding

1. Which statement about a mole is correct?
A mole is a count — 6.022 × 10²³ of something — exactly like 'a dozen' means 12. It is not a mass; the mass of a mole depends on what you're counting.
2. A mole of helium atoms and a mole of iron atoms. What is the same about them?
Both contain 6.022 × 10²³ atoms — the same count. They weigh different amounts because helium and iron atoms have different masses.
3. To convert from grams of a substance to number of molecules, you should:
Moles are the hub. Convert grams to moles with the molar mass, then moles to molecules with Avogadro's number. You can't jump straight from grams to particles.
🔎 Related lessons
Previous: Naming Compounds Next: Empirical & Molecular Formulas Solution Stoichiometry & Molarity
✅ Key takeaways
  • A mole is a count: 6.022 × 10²³ particles (Avogadro's number) — like a dozen, but bigger.
  • Molar mass (g/mol) is the mass of one mole; for an element it's the atomic mass in grams.
  • For a compound, add the molar masses of all its atoms (H₂O = 18.02 g/mol).
  • Moles are the hub: grams ↔ moles via molar mass; moles ↔ particles via Avogadro's number.
  • n = m / M converts mass to moles; N = n × Nₐ converts moles to particles.
➡️ The mole lets us weigh a sample and know how many atoms of each kind it holds. Turn that around and you can work out a compound's formula from lab masses alone — that's empirical and molecular formulas, coming next.
Want to test yourself on this? Try the Chemistry practice test →