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Gas Laws- Avogadro’s

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What is Avogadro’s Number?

Avogadro’s number is the number of particles (atoms, molecules, ions, or other units) contained in exactly one mole of a substance. It is named after the Italian scientist Amedeo Avogadro.

NA = 6.022 × 1023 mol-1

This means that one mole of anything — carbon atoms, water molecules, even grains of sand — contains exactly this many particles.

Why Do We Need It

Atoms and molecules are far too small and numerous to count individually. Avogadro’s number acts as a bridge between the atomic scale (mass of a single atom) and the macroscopic scale (mass you can measure on a balance in the lab).

1  mole  = 6.022 × 10 23  particles

The Mole Conversion Formula

n = N N A
  • n = number of moles
  • N = number of particles
  • NA = Avogadro’s number (6.022 × 1023)

Rearranged to solve for the number of particles:

N = n × N A

Example 1: Moles to Particles

How many molecules are in 2 moles of water (H₂O)?

N = 2  mol  × 6.022 × 10 23

= 1.2044 × 1024 molecules of H₂O

Example 2: Particles to Moles

How many moles are in 3.011 × 1023 atoms of carbon?

n = 3.011 × 10 23 6.022 × 10 23

= 0.5 mol of carbon

Example 3: Grams to Particles (Using Molar Mass)

How many atoms are in 18 grams of carbon (molar mass = 12 g/mol)?

Step 1 — Convert grams to moles:

n = 18 g 12 g/mol = 1.5  mol

Step 2 — Convert moles to atoms:

N = 1.5 × 6.022 × 10 23

= 9.033 × 1023 atoms of carbon

Practice Problems

Problem 1

How many molecules are in 4 moles of CO₂?

N = 4 × 6.022 × 1023 = 2.4088 × 1024 molecules

Problem 2

How many moles are in 1.2044 × 1024 atoms of iron?

n = 1.2044 × 1024 ÷ 6.022 × 1023 = 2 mol

Problem 3

How many atoms are in 0.25 mol of gold?

N = 0.25 × 6.022 × 1023 = 1.5055 × 1023 atoms

Problem 4

A sample contains 6.022 × 1022 molecules of NH₃. How many moles is this?

n = 6.022 × 1022 ÷ 6.022 × 1023 = 0.1 mol

Problem 5

How many hydrogen atoms are in 2 moles of water (H₂O)? (Remember: each water molecule has 2 hydrogen atoms.)

Molecules of H₂O = 2 × 6.022 × 1023 = 1.2044 × 1024
Hydrogen atoms = 1.2044 × 1024 × 2 = 2.4088 × 1024 H atoms

Useful Formulas

QuantityFormula
Particles from molesN=n×NA
Moles from particlesn=NNA
Moles from massn = mass ÷ molar mass
Avogadro’s number 6.022 × 1023 mol–1