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.