Question

How many atoms of gold are in a 5 gram sample of pure gold?

Answer 1

The answer is 1.505 × 10²² atoms

Avogadro's number is the number of units (atoms, molecules) in 1 mole of substance: 6.02 × 10²³ units per 1 mole

Number of moles (n) is the quotient of mass (m) and molar mass(Mr)
n = m/Mr

m = 5 g
Mr(Au) = 197 g/mol

n = 5g / 197g/mol = 0.025 mol = 2.5 × 0.01 = 2.5 × 10⁻² mol


If 6.02 × 10²³ atoms are in 1 mol, x atoms are in  2.5 × 10⁻² mol:
6.02 × 10²³ atoms : 1 mol = x :  2.5 × 10⁻² mol

x = 6.02 × 10²³ atoms * 2.5 × 10⁻² mol : 1 mol
x = 15.05 × 10²³⁻² atoms = 15.05 × 10²¹ atoms = 1.505 × 10²² atoms