The balanced chemical equation for rusting iron is:
4Fe + 3O2 = 2Fe2O3
If we divide 1.0x10^9 by Avogadro's number, we get the amount of moles of oxygen which is 1.6611x10^-15 moles.
From the chemical equation we know that it takes 3 moles of oxygen to produce 2 moles of iron oxide. So if we multiply the moles of oxygen calculated by 2/3, we can get the moles of iron oxide.
(1.611x10^-15)(2/3) = 1.107419x10^-15 moles of iron oxide.
If we multiply the moles of iron oxide by the molar mass of iron oxide, we get how many grams of iron oxide would be produced by 1 billion oxygen atoms. Which is the same thing as how many grams of iron oxide contain 1 billion oxygen atoms.
(1.107419x10^-15)(159.69) = 1.8x10^-13 grams of Fe2O3