Avogadro's Number
Avogadro's number (6.022 × 10²³) defines how many particles are in one mole.
Learn to convert between moles and individual atoms or molecules.
The Formula
N = n × Nₐ
Nₐ = 6.022 × 10²³ particles/mol
Nₐ = 6.022 × 10²³ particles/mol
Avogadro's number is the number of atoms, molecules, or particles in exactly one mole of a substance. It connects the macroscopic world (grams) to the microscopic world (individual particles).
Variables
| Symbol | Meaning |
|---|---|
| N | Number of particles (atoms, molecules, or formula units) |
| n | Number of moles (mol) |
| Nₐ | Avogadro's number (6.022 × 10²³ particles per mole) |
Example 1
How many molecules are in 3 moles of water?
Apply the formula: N = n × Nₐ
N = 3 × 6.022 × 10²³
N = 1.807 × 10²⁴ molecules
Example 2
A sample contains 1.2044 × 10²⁴ atoms of iron. How many moles is that?
Rearrange: n = N / Nₐ
n = (1.2044 × 10²⁴) / (6.022 × 10²³)
n = 2 mol of iron
When to Use It
Use Avogadro's number to convert between moles and individual particles.
- Converting moles to number of atoms or molecules
- Converting a particle count back to moles
- Understanding the scale of chemical reactions at the atomic level
- Combine with the mole formula (n = m/M) to go from grams to particles
Key Notes
- Dividing molar mass (g/mol) by Nₐ gives the mass of a single atom or molecule in grams — for example, one carbon-12 atom has a mass of 12 / (6.022×10²³) ≈ 1.993 × 10⁻²³ g
- Since the 2019 SI redefinition, Nₐ = 6.02214076 × 10²³ mol⁻¹ exactly by definition — it is no longer an experimental measurement but a fixed fundamental constant
- A mole was defined so that 12 g of carbon-12 contains exactly Nₐ atoms — this is why molar mass in g/mol numerically equals atomic mass in unified atomic mass units (u or Da)
- For scale: if you spent 1 million dollars per second, spending 1 Avogadro's number of dollars would take roughly 19 million times the age of the universe