1)First, let's use the chemical formula of iron (III) oxide (Fe₂O₃) to find the number of molecules of Fe₂O₃.
So one molecule of iron oxide contains 2 atom of Fe and 3 atom of Oxygen.
So you might find that:
1 molecule of Fe₂O₃ ------ 3 atoms of Oxygen
x molecule of Fe₂O₃ ------ 1.0×10⁹ atoms of Oxygen
x = 1.0×10⁹/3
x = 3.3 × 10⁸ molecules of Fe₂O₃
2) Now you use the Avogrado's constant to transform molecules into moles.
6.022 × 10²³ molecules ----- 1 mol
3.3 × 10⁸ molecules of Fe₂O₃ ----- x mol
x = 3.3 × 10⁸/6.022 × 10²³
x = 5.5 × 10⁻¹⁶ moles of Fe₂O₃
3) Finally, let's use the molar mass of Fe₂O₃ to find out the mass.
Molar mass of Fe₂O₃: (2x55.9) + (3x16) = 159.8
159.8 g ----- 1 mol
x g ----- 5.5 × 10⁻¹⁶ moles of Fe₂O₃
x = 8.8 x 10^-14 grams
Answer: The mass of iron (III) oxide ( Fe2O3) that contains a billion (1.0x10^9) oxygen atoms is 8.8 x 10^-14 grams
