Moles to particles
Now the other direction. If the number of moles is known, multiplying by the Avogadro constant gives the number of particles.
Example 1 — 4 moles of carbon
Problem
Find the number of atoms in 4 mol of carbon.
Solution
number of atoms in 1 mol of carbon = 6.022 × 1023
number of atoms in 4 mol of carbon = 6.022 × 1023 × 4
= 2.409 × 1024
Example 2 — 0.1 mole of carbon dioxide
Problem
Find the number of molecules contained in 0.1 mol of carbon dioxide.
Solution
number of molecules in 1 mol = 6.022 × 1023
number of molecules in 0.1 mol = 6.022 × 1023 × 0.1
= 6.022 × 1022
Multiplying by 0.1 just drops the index by one: 1023 becomes 1022.
Example 3 — from a mass to molecules
Problem
The relative molecular mass of oxygen (O2) is 32. Find the number of molecules contained in 10 g of oxygen.
Solution
number of molecules in 32 g of O2 = 6.022 × 1023
number of molecules in 10 g of O2 = 6.022 × 1023 × (10 g ÷ 32 g)
= 1.88 × 1023
Both steps were used here: 10 ÷ 32 for the number of moles, then multiplying by the constant. Every mass-to-particles problem has that shape.