Video: Calculating the Mass of a Metal Oxide Sample from the Amount of Oxygen in the Sample and the Atomic Masses of the Metal and Oxygen

A student is given a sample of iron(III) oxide (Fe₂O₃). They find that it contains 15 moles of oxygen. What is the total mass of this Fe₂O₃ sample, taking the atomic mass of iron as 56 g/mol and the atomic mass of oxygen as 16 g/mol? [A] 102 g [B] 160 g [C] 480 g [D] 800 g [E] 1600 g

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Video Transcript

A student is given a sample of iron(III) oxide (Fe₂O₃). They find that it contains 15 moles of oxygen. What is the total mass of this Fe₂O₃ sample, taking the atomic mass of iron as 56 grams per mole and the atomic mass of oxygen as 16 grams per mole? A) 102 grams, B) 160 grams, C) 480 grams, D) 800 grams, or E) 1600 grams.

We need to find the total mass of a sample of Fe₂O₃ that contains 15 moles of oxygen. The first thing we can do is find the molar mass of Fe₂O₃, which we can find by summing the atomic masses of each of the elements in iron(III) oxide. There are two iron atoms, which each have an atomic mass of 56 grams per mole, and three oxygen atoms, which each have an atomic mass of 16 grams per mole. This gives us a molar mass for iron(III) oxide of 160 grams per mole.

Now that we know the molar mass of Fe₂O₃, we want to find the total mass of our Fe₂O₃ sample that contains 15 moles of oxygen. We know how many moles of oxygen are in our sample of Fe₂O₃. But we don’t know how many moles of Fe₂O₃ we have. According to the chemical formula for Fe₂O₃, for every one mole of Fe₂O₃ that we have, we have three moles of oxygen. So we can use this to convert between moles of oxygen to moles of Fe₂O₃.

Now, we’re in moles of Fe₂O₃ and we want to find the total mass of our Fe₂O₃ sample. And we can convert from moles to grams by multiplying by the molar mass. Multiplying everything through, we get 800 grams. This matches answer choice D.

So the total mass of the Fe₂O₃ sample is 800 grams.