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# Another mass composition problem

## Video transcript

I said I would get you a more
interesting mass composition to empirical formula problem,
one that doesn't just have a straight-up 2:1 ratio. And so here it is. I have a bag of stuff. Or let's call this a
bottle of stuff. Maybe it's in its liquid form. And it happens to be 2.04%
hydrogen, 65.3% oxygen, and 32.65% sulfur. What is the empirical formula,
what's our best stab at the empirical formula, of
this substance? So what we would do, like we
do in all these problems, let's just assume we've got
100 grams of the stuff. So we have 100 grams
of the stuff. So we assume 100 grams. Let me
do that in a good yellow. So let's say, assume I have 100
grams. How many grams of hydrogen do I have? If I have 100 grams total, 2.04%
of that is hydrogen, so I have 2.04 grams of hydrogen. I have 65.3 grams of oxygen. And I have 32.65 grams
of sulfur. Now, what we need to do now is
figure out how many moles of hydrogen is this. How many moles of oxygen. And how many moles of sulfur. Then we can compare the ratios
and we should be able to know the empirical formula. What is the mass of 1
mole of hydrogen? Let me write that. So 1 mole of hydrogen. Well we know what the mass
number for hydrogen is. It's 1. And especially, the atomic
weight, also for hydrogen, if we were to take it on Earth. The composition, you
pretty much just find hydrogen nucleuses. If it's neutral, it
has an electron, but it has no neutrons. So it has an atomic mass of
one atomic mass unit. So one mole of hydrogen. If you have a ton of hydrogens
together, or a mole of them, not a ton, I shouldn't say, you
have 6.02 times 10 to the 23 hydrogens. Then you take hydrogen's atomic
mass number in atomic mass units. And you say, well, it'll
be that many grams of hydrogen, right? So if you immediately look up
here, if we have 2.04 grams of hydrogen, how many moles
of hydrogen do we have? Well, one mole is one
gram, so we have 2.04 moles of hydrogen. Notice, this said what the
mass of the hydrogen is. This tells us how many hydrogen
molecules we have. Remember, this is 2.04 times
6.02 times 10 to the 23 hydrogen atoms. Moles
of hydrogen. Maybe I should write
that down. So one mole of hydrogen. There you go. And then oxygen. One mole of oxygen. Oxygen's mass number, in
case you forgot, is 16. Right there. Oxygen's mass number is 16. So one mole of oxygen has a mass
of 16 grams. 6.02 times 10 to the 23 oxygen atoms
has a mass of 16 grams. So how many moles
do we have here? Let's see. So if we take 65.3
grams of oxygen. And we have 16 grams per mole,
so you divide by 16. It equals 4.08125. I don't want to get
too precise here. But let me just write that. 4.08 moles of oxygen. So I'm going to write that
in oxygen color. So I have 4.08 moles
of oxygen. And then finally, sulfur. What is sulfur's atomic mass? The one thing I'll never
forget about sulfur is its smell. There's a city in Louisiana
which we used to drive to all the time -- I think we had some
family friends there-- called Port Sulfur. And they did a lot of sulfur
processing there. And lucky for the residents,
at least at the time-- I apologize if they fixed the
issue-- it smelled like sulfur, which smells
like rotten eggs. But anyway, one mole
of sulfur. So sulfur's atomic mass
is 32 atomic mass units per sulfur atom. So a whole mole of it is going
to have a mass of 32 grams. So a mole of sulfur-- not a mule. Maybe I should invent a new
unit called the mule. So a mole of sulfur is
32 grams. So how many moles do we have? We have a little bit more than
one, but let's be precise here, because everything else is
a little bit of a decimal. So if we have 32.65 grams of
sulfur and we divide by the number of grams per mole--
divided by 32 grams per mole-- we have 1.02 moles of sulfur. This was hydrogen up here. So here, you should hopefully
see a pretty good ratio, here. For every one sulfur atom-- I
mean, the ratio worked exactly out and that's because I did
this problem before. I actually made up this problem
before we worked, so I made it so the numbers
worked out. But one mole of sulfur, for
every mole of sulfur, so for every 6.02 times 10 to the 23
sulphur atoms, you have two moles of hydrogen, right? This ratio is 1:2. Two times 1.02 is 2.04. And then, for every one mole
of sulfur, you have four moles of oxygen. Right? Literally, if you multiply this
times four you get 4.08. So the ratio of hydrogen to
sulfur to oxygen is for every one sulfur, we have
two hydrogens and we have four oxygens. So the empirical formula
of this is H2. And then we have one sulfur. And then we have four oxygens. And this is sulfuric acid, one
of the things you would least like poured on you
most of the time. Anyway, hope you found
that useful.