First we find the number of moles of cocaine hydrochloride;
Number of moles = mass/ molar mass
Mass = 20.5mg = 0.025 g
Molar mass of cocaine hydrochloride = 339.816 g/mol
Number of moles = 0.025 / 339.816
= 7.35692 x 10⁻⁵ moles
In 1 mole there is Avogadro's number of molecules, so in 7.35692 x 10⁻⁵ moles there are;
7.35692 x 10⁻⁵ x 6.02 x 10²³ = 4.429 x 10¹⁹ molecules
And in C₁₇H₂₂ClNO₄, number of atoms = 17C + 22H + 1Cl + 1N + 4O = 45
So, number of atoms in a sample of cocaine hydrochloride = 45 x 4.429 x 10¹⁹ = 1.99 x 10²⁵ atoms
