A couple of videos ago we figured out how to go from the
empirical formula to the mass composition.
And all I mean by that, mass composition, is that you could
start with the empirical formula H2O, which is also its
molecular formula.
And then we were able to figure out what percentage of
this was water and what
percentage of this was hydrogen.
The way we did it is we said, OK, oxygen's mass is 16 atomic
mass units.
Hydrogen is one.
The mass of the entire molecule is 2 times hydrogen.
2 times 1.
Plus 16 for that one oxygen, so it's 18.
And then we said, the composition of
oxygen is just 16/18.
So oxygen is 16/18.
I don't have my calculator anymore.
I think the number was something on the order of 88%
or 88.9% oxygen.
So now let's see if we can go the other way.
Let's see if we could start with mass composition, the
percent composition of the different elements, and then
go to empirical formula.
And I think the first video I made, I
spelled empirical wrong.
Which is good reason for me not to do spelling videos.
I think I spelled this with an e right here, because I
pronounce it empricial.
But it's spelled with an i.
Empirical formula.
So back to the empirical formula.
So let's do some exercises here to see
if we can get someplace.
So let's say that I start off with-- I need space, my
periodic table is right down there.
Let's say I am told that I have a bag of stuff.
And 75% of that bag, let's say it is mercury.
Hg.
And say that the other 25% of the bag is chlorine.
So the question that I'm asked is, what is the empirical
formula of the stuff that I have here, assuming that it's
all one molecule or one type of molecule?
So what is the empirical formula?
So the way to think about this is, let's assume that you have
100 grams of this stuff.
Right?
And the reason why I'm picking 100 is because 100 is a useful
number to deal with.
So if I have 100 grams of the stuff, all right.
So let's say I assume that you have 100 grams. If you have
100 grams, how many grams of mercury do you have?
Well that means that 75% of that, that means you have 75
grams of mercury, Hg.
And that means you have 25 grams of chlorine.
You might be saying, where did get these numbers from?
Well, I got the numbers because I assumed 100 grams. I
could have assumed 112 grams or 7 grams, but those would
have been harder numbers to work with.
So I'm just assuming 100 grams. So the question is, in
75 grams of mercury, how many moles of mercury do I have?
So I need to convert from grams to moles.
Let's go the other way.
One mole of mercury-- this is at least how my brain thinks--
let me pick a suitable color-- so one mole of mercury so 6.02
times 10 to the 23 mercury atoms.
What's the mass of that?
Well it's equal to whatever mercury's mass number is in
grams. So let's go look up mercury's mass number.
So mercury is a transition metal.
It's one of the few metals that are liquid at room
temperature.
Right there we have mercury.
Its mass number, let's pick the 200.
It has a mass number of 200.
Obviously, there's some mercury out there that has a
mass of 201.
But for simplicity, let's say it's 200.
So 1 mole of mercury is 200 grams. How did I get that?
Mercury's mass number.
One atom of mercury has a mass of 200 atomic mass units.
So one mole of mercury-- 6.02 times 10 to the 23 mercury
atoms-- has that many grams of mass.
So instead of 200 atomic mass units per atom, we have 200
grams per mole of that atom.
It's an easy calculation.
You just look up it atomic mass number and say it's that
many grams. You have a mole of the substance.
Fair enough.
And what about one mole of chlorine?
We do the same exercise.
We go down to our periodic table.
Chlorine has a mass number of, let's say, 35.
It has various isotopes on this planet.
But let's say the mass number is 35.
So one chlorine atom weighs-- well now, we shouldn't say
weighs, we have to be very careful.
One chlorine atom has a mass of 35 atomic mass units.
So 6.02 times 10 to the 23 chlorine atoms, or one mole of
chlorine atoms will have a mass of 35.
35 grams.
So how many moles of mercury do I have?
Let me get my calculator going.
So I have 75 grams of mercury.
One mole of mercury would have a mass of 200 grams. So I
could just take 75 divided by 200 and it tells me how many
moles I have. 75 divided by 200 is equal to
0.375 moles of mercury.
How did I figure that?
One mole of mercury would be 200 grams. I only have 75
grams of mercury, so I have a small fraction of it, roughly
0.375 moles of mercury.
I've just expressed the number of atoms of mercury I have.
Moles tells me it's 6.02 times 10 to the 23 atoms of mercury.
So I have 0.375 times Avogadro's number of mercury
atoms. Fair enough.
Now let's do the chlorine.
I have 25 grams of chlorine.
One mole of chlorine is 35 grams. So I
have 25 over 35 moles.
So what's that?
So 25 divided by 35 is equal to 0.714 moles of chlorine.
Now these numbers, they're not exact.
Because if you take twice this number up here, you don't get
twice this number right here.
If you get twice this, you don't get this.
But this is roughly twice as many moles of chlorine as I do
of mercury.
So that tells me that for every mercury atom-- remember,
moles is just a number-- for every mercury atom I have, I
have two chlorine atoms. So the empirical formula here is
for every mercury I have two chlorines.
I have two chlorines, right there.
And the numbers didn't work out almost exactly right.
Especially in the real world, when you're actually trying to
figure out things empirically, your numbers seldom will.
And maybe there's some random other things running out there
in terms of other things that are contributing to the mass.
But this is close enough to know that the ratio of mercury
to chlorine is roughly 1:2.
Right?
This is a number.
For every one chlorine atom, you have roughly two.
You have twice as many.
I guess the other way of thinking about it is you have
twice as many chlorine atoms in the
bag as you have mercury.
Roughly.
Although this is a little bit more.
This is close to 0.75.
But it's close enough for you to know that you're dealing
with mercury chloride.
Right there.
Let's do another one of these.
Let's see how the numbers turn out for this one.
Let's say you have another bag that is 9% magnesium.
And let's say the remainder of the bag, 91%, is iodine.
91% is iodine.
So the way to do all of these is, you do the same thing.
Assume you have 100 grams. So if you have 100 grams, of
which you have 9 grams of magnesium.
And you have 91 grams of iodine.
And then figure out how much a mole of magnesium-- what would
be the mass of a mole of magnesium and
then a mole of iodine.
So let me write here.
One mole of magnesium.
And we want to figure out one mole of iodine.
Let's figure those out.
So magnesium's mass number is, let's just go with 24.
Let's say we have the isotope that's 24.
Magnesium is 24 and since we're already down here,
what's iodine.
127.
It's 127.
Iodine is one of the halogens.
So let's see.
You have 127 and you have 24.
Let me write those down.
So you have 127 and you have 24.
So one atom of iodine has a mass of 127 atomic mass units.
So a whole mole all of it, 6.02 times 10 to the 23 iodine
atoms will have a mass of 127 grams. You just take the
atomic weight, or the atomic mass, and the mass will be
that many grams when you have this many of the atom.
So then one mole of magnesium will be 24 grams.
So now we just figure out how many moles of each of these we
have. We have 9 grams of magnesium.
So what fraction of a mole is that?
A mole is 24 grams. So this is equal to
9/24 moles of magnesium.
And what is 9 over 24?
9 divided by 24 is equal to 0.375.
So this is equal to 0.375, which is similar to what we
had in the last problem when that 0.375 showed up.
And 91 grams of iodine is what?
91 grams of iodine.
Well, in a whole mole of iodine you're going to have
127 grams. So we have 91/127 moles of iodine.
And what's 91 over 127?
I have a feeling we're going to have very similar numbers.
121 divided by 127 is equal to 0.716.
I should do another problem with better ratios than this.
These have the same ratios as the last problem, 0.72,
roughly, moles of iodine.
And this is moles of magnesium.
So we have roughly twice the number of iodine atoms as we
do of magnesium atoms. Right?
For every one magnesium atom we have roughly two iodine
atoms. I know this isn't exactly 1:2,
but it's pretty close.
So the formula here is magnesium iodide.
Right there.
And that's the empirical formula.
We don't know, maybe in every atom maybe you had two
magnesiums and four iodines.
We don't know.
All we know is that the ratio of magnesium to
iodine here is 1:2.
In the next video, I'm going to try to look for ones that
have more interesting ratios, because I don't want to do two
problems that both have the same ratio.
But hopefully you found this a little bit helpful.