Video: Calculating the Mass Percentage of Iron in a Compound of Iron and Oxygen Given the Mole Ratio of Fe to O

Which of the following is the percentage by mass of iron in a compound of iron and oxygen if the mole ratio of Fe : O is 2 : 3? A) 30% Fe B) 35% Fe C) 40% Fe D) 60% Fe E) 70% Fe

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Video Transcript

Which of the following is the percentage by mass of iron in a compound of iron and oxygen if the mole ratio of Fe to O is two to three? A) 30 percent iron, B) 35 percent iron, C) 40 percent iron, D) 60 percent iron, or E) 70 percent iron.

The easiest way to think about percentage by mass is to first consider the mass of the whole sample. We know that the compound is made of iron and oxygen. So, we know the mass of the sample will be made up of an iron contribution and an oxygen contribution. But we don’t yet know what the proportions are. But we have been given the ratio of the elements inside the compound. So, we know that the formula of the compound is Fe₂O₃. Of course, Fe₄O₆, Fe₆O₉, Fe₈O₁₂ are also valid, but we’d get the same proportion of iron. So, we don’t need to worry about exactly what the formula would be. The formula Fe₂O₃ will do.

We calculate our percentage mass of iron in this compound by taking the mass due to iron dividing it by the total mass and multiplying by 100 percent. There remains one question: How big should the sample mass be, a gram, a mole’s worth, a pound? Well, you could do it in many different ways, but I’m going to show you a way that simplifies the calculation. I’ll work with the smallest unit I can, one lot of Fe₂O₃. And then, all I need to figure out is the mass of two iron atoms.

Now, bear in mind that I said iron atoms, not iron ions. This is because when we think about percentage by mass, we generally consider the mass we can get out of a substance in the pure elemental form, which would be iron atoms. However, it doesn’t make a great deal of difference because iron ions have about the same mass as iron atoms.

We can now look up the atomic masses of these elements on the periodic table. An atom of iron has a mass of 56 unified atomic mass units, thereabouts amusing, rounded numbers because the answers are fairly rounded anyway. And it will help with the mental arithmetic in a little bit. And the atomic mass of oxygen is 16 unified atomic mass units. One unified atomic mass unit is equivalent to a 12th of the mass of a carbon 12 atom. However, it really doesn’t make a difference here. As long as we use the same mass units, we’re going to figure out the right percentage of iron in our sample.

To calculate the mass of one unit of Fe₂O₃, we simply take the atomic mass of iron and multiply it by two, the atomic mass of oxygen and multiply it by three and sum the two together, giving us 160 unified atomic mass unit. This means that one unit of the Fe₂O₃ has the mass of about 13 carbon atoms. We’ve now figured out our sample mass. And because we did the calculations step by step, we also have the iron mass. This is the mass due to the two atoms of iron in our structure.

All we need to do is plug the right values into the equation. Our percentage mass of iron in our sample is equal to 112 unified atomic mass unit divided by 160 unified atomic mass unit multiplied by 100 percent. The greatest common factor of 112 and 160 is 16, giving us seven over 10 times 100 percent which is 70 percent. You could have simplified the fraction in more steps, if it’s easier. 112 divided by 160 is the same as 56 divided by 80. We’ve simply divided the numerator and denominator by two. One more time gives us 28 over 40 and then 14 over 20 until we arrive at seven 10ths.

Therefore, the percentage by mass of iron in a compound of iron and oxygen in the molar ratio of two to three, iron to oxygen is 70 percent iron.

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