Example comparing mass percentages of element in comounds

So we have four different compounds here, and we also have their molar masses. What I would like you to do is think about which of these compounds has the highest percentage of sulfur by mass. So pause this video and see if you can figure that out.

All right, now one way to approach this is to say, for each of these compounds—if we say per mole of each compound—we could figure out how many grams. I would say, what is the mass of sulfur divided by the total mass of the compound?

Now, the mass of sulfur, we can see that for a mole of each of these compounds, you have exactly one mole of sulfur in all of these formulas. You see exactly one sulfur. So in all of these situations, the mass of sulfur is going to be the same. This is going to be the same for all compounds. It wouldn't be the same for all compounds if some of them had two sulfurs, or some of them had three, or maybe some of them had none. But all of them have one sulfur.

So for a mole of each of these compounds, you're going to have a mole of sulfur, and so they're going to have the same mass of sulfur. We could take out a periodic table, and we could look it up, and we could say, "Oh, look, the average atomic mass of sulfur is 32.06." So if I had a mole of it, it would be 32.06 grams.

We could put the 32.06 grams up here if we like. This would be 32.06 grams in all of these cases because, once again, if you have a mole of each of these compounds, you're going to have a mole of sulfur because you only see one sulfur in these—in each of these formulas.

But the big picture is, in all the cases, I'm going to have the same value in the numerator. So if I want to have the highest percentage, I would want to minimize the value in the denominator. So I would really want to see which one would have the lowest denominator or which one would have the lowest mass for a mole of the molecules.

Another way of thinking about it: which of them will have the lowest molar mass? You could see very clearly that this compound right over here has the lowest molar mass. So we're done! This has the highest percentage of sulfur by mass because, per mole, it has the same mass of sulfur as everything else, but it has the lowest total mass. So it's going to have the highest percentage of sulfur.

A quick way to do it: we just looked at the lowest molar mass. You could have gone and taken 32.06 and divided by each of these values and figured out a percentage, but they're not asking us to figure out the percentage. They're saying which one has the highest percentage, and that would be this second compound right over there.