- [Instructor] I have about 3.21 grams
of sulfur powder over here.
My question to you is how many atoms of sulfur are there?
At first, this question sounds ridiculous.
I mean, there's gonna be lots and lots of atoms.
How in the world are we going to count that?
That's what we're gonna find out in this video.
We're gonna do that by introducing the idea of mole.
So let's begin.
To come up with the idea of moles,
we first need a new unit of mass to deal
with the masses of atoms.
See, atoms are very tiny.
Their masses are going to be incredibly tiny.
So kilograms and grams is going
to be very inconvenient to use.
So we come up with a new unit called the atomic mass unit,
AMU or u.
It's a very tiny unit of mass.
Just like grams or kilograms, it's a unit of mass.
But, of course, whenever we learn about a new unit,
we need to ask ourselves, "How big is that unit?"
What is the definition of that unit? How big is 1u?
Well, here's how we define what a u is.
You take a single atom of carbon 12.
Now, its mass by definition is 12u.
This is not something that we have measured.
This is something that we fixed.
We fixed the mass of a carbon 12 atom to be two 12u.
Exactly. Okay?
Now, what is 1u?
Well, if the mass of a carbon 12 atom is 12u,
1u is 1/12 of its mass, right?
So we define one atomic mass unit, 1u as 1/12
of the mass of a single atom of the carbon 12 isotope.
Does that make sense?
Well, I'm sure at this point
you may be having some questions,
like why did we decide to use carbon as a reference
and not any other elements?
Well, it turns out that we actually started with hydrogen
because it's one of the lightest elements.
Then we ran into some problems
and then we switched to oxygen
because again, it's extremely abundant.
Then again, we ran into some other problems,
and then finally, we decided to go with carbon,
which is also abundant.
We'll not delve into the histories
and details of what really happened,
but yeah, we have to choose some element as a reference,
and we ended up choosing carbon as a reference.
Another question you could be having
is why do we fix the mass of a single atom of this carbon 12
to be 12u?
Why not any other number? Why 12?
Well, for that, you can see that over here.
Carbon has how many protons and neutrons in it?
Well, it has a total of, I mean,
it has six protons and six neutrons.
So it has a total of 12 protons and neutrons, 12 particles.
I think of protons and neutrons together over here
because they have pretty much similar mass.
I mean, a neutron is actually slightly heavier
than a proton, but for our purposes,
to get an intuition over here, they're masses.
We can pretty much think of them
to be almost equal to each other.
So it has a total of 12 particles, right?
Now, by fixing the mass of those 12 particles to be 12u,
look at what we are doing.
We are basically saying, "Hey,
let's fix the mass of a single proton
or a neutron to be about 1u.
That was the whole intention. Okay?
So you can also think 1u is kind of a representation
of a mass of a single proton or a neutron,
but again, this is not exact because masses of protons
and neutrons are not exactly equal to each other.
So a proton and neutron will have a mass very close
to 1u, but it's not exactly 1u,
but it's a good way to think about what a u represents.
It represents sort of the mass of a proton or neutron.
Anyways, now that we understand this, here's a question.
What do you think is the mass of a single atom
of oxygen 16 isotope?
A single atom of this,
what will be its mass in u, atomic mass unit?
Well, it has a total of 16 particles, 16 protons
and neutrons together, and since each particle,
each proton and neutron has a mass of 1u,
and there are total 16, oxygen mass will be about 16u.
Again, you can see it's not gonna be exactly 16u
because mass of each proton and neutron is not exactly 1u,
but it's gonna be very close to that.
Similarly, if you take an isotope of say chlorine,
a particular isotope, the most abundant isotope of fluorine,
which has 35 protons and neutrons together in it,
well, then its mass would be close to 35u.
Makes sense, right?
Okay, now, here's a question we're gonna ask ourselves.
Let's go back to carbon.
Each carbon has a mass of 12u, by definition.
Now, how many carbon atoms do I need
to take together says that the total mass of all
of those carbon atoms together becomes 12 grams.
You can imagine it's going to be lots
and lots of atoms, right?
Because each atom has a very tiny mass
and we want together 12 grams.
So we probably need to take billions
and billions and billions of atoms.
But the big question is how many atoms do I need to take
is that they all add up to give me 12 grams of mass?
Well, it turns out we figured it out.
Again, we'll not get into the details
of how we figured it out, okay?
The history is actually pretty interesting,
but again, we'll not talk about that over here,
but we figured it out, and it turns out to be this number.
You need to take about 6.022,
and there are some other decimals over here,
some numbers here, times 10 to the power 23,
which is a huge number, okay?
If you take these many carbon atoms together,
carbon 12 atoms together, they will together have a mass
of 12 grams.
This number is what we call the Avogadro number
named after the scientist Amedeo Avogadro
who worked a lot on this idea.
But anyways, you can now see the significance
of this number.
I can now count the number of atoms in a carbon isotope.
If you give me 12 grams of carbon,
I know it has these many number of carbon atoms in it.
Carbon 12, okay?
These many number of carbon 12 atoms in it.
If you give me 24 grams of carbon,
there must be twice the amount.
If you give me six grams of carbon,
then there must be half the amount.
You tell me the mass of the carbon 12 isotope
that I'm holding in my hand,
and I can now use this number to tell you
how many atoms there are.
Beautiful, isn't it?
In other words, this becomes the conversion factor
for our tiny unit of mass, from our tiny unit of mass u
to our more familiar big unit of mass, grams.
If you take u and you multiply with this number,
you get grams.
And whenever you have an Avogadro number of things
with you, we call it a mole.
Just like how when you have 12 things with you,
we call it a dozen, these many things,
if you have together, it could be anything.
It could be these many atoms.
Then we'll call it a mole of atoms,
or it could be these many babies.
Then we'll say we have a mole of babies.
It's a ridiculous number but you get the idea.
And this word mole actually comes from the Latin molecule,
which translates to a very tiny amount of something.
But anyways, what is a mole?
A mole represents Avogadro number,
these many number of things.
It could be number of atoms, molecules, particles, anything.
And what's so special about this number?
It's a conversion factor from the tiny unit
of mass u to grams.
You take this number, multiply it by this number,
and you will now get it in grams.
Okay, now, let's see if you understand this.
What do you think would be the mass of one mole
of oxygen 16 atoms?
If I had an Avogadro number of oxygen 16 atoms together,
what do you think collectively would its mass be?
Well, an Avogadro number
of 12us will give me a mass of 12 grams.
So an Avogadro number of 16us
will give me me a mass of 16 grams.
That's what we mean by a conversion factor, okay?
It works for any atom which has any mass.
You just multiply it by this,
and now you'll get the mass in grams.
Similarly, if I had an Avogadro number of chlorine 35,
if I had one more of chlorine 35 atoms with me,
then it'll have 35 grams of mass.
Make sense?
And so another way to talk about all
of these things, whatever I just said now,
another way to talk about this is we say the molar mass
of carbon 12 is 12 grams.
Carbon 12 has a mass of 12 grams per mole.
Makes sense, right?
We would say oxygen 16 will have 16 grams per mole.
I mention oxygen 16
because remember, there are other isotopes as well.
Different isotopes will have different masses,
so their molar mass would be different.
So oxygen 16 isotope has a molar mass
of 16 grams per mole,
and chlorine 35 has a molar mass
of 35 grams per mole, okay?
Same thing, whatever I just said, a technical way
of stating the same thing over here.
All right, the last thing we need to do
to make this more practical is to remember
that over here we considered pure cases.
I took a pure carbon 12 isotopes
where every single atom was carbon 12,
or I took a pure chlorine isotope
where every single atom was chlorine 35,
but in reality, that's not the case.
If I take a chunk of chlorine,
a lot of it will be chlorine 35,
but there'll be some other isotopes as well.
Like, another abundant isotope next to chlorine 35
is chlorine 37.
And that sounds really complicated, but what's important
and powerful is that that doesn't matter to us.
This whole idea still works. Okay?
Here's what I mean.
Let me take an example.
If you look at our periodic table,
and you can see that the atomic mass of chlorine is given
to be not 35.
It's 35.45.
So significant deviation from 35. Why?
Because this also accounts for the fact
that if you take a chunk of chlorine,
it'll also contain a lot of chlorine 37 in it.
So what we do is sort of like take an average.
This is a weighted average, we say,
so this is the average atomic mass of chlorine.
So since I know the average atomic mass
of chlorine is 35.45, if I now take one mole of chlorine,
not pure as it exists as a mixture in nature,
then one mole will have a mass of 35.45 grams.
That's it.
Similarly, if I take one mole of carbon,
which, you know, it's not exactly 12 grams
because there are other isotopes, it'll be 12.01 grams.
You see what I mean? A mole is a conversion factor.
Take one mole of anything, it'll be this number in grams.
And so now we can try and answer our original question.
We asked ourselves, if you have 3.21 grams of sulfur,
how many atoms there are?
Why don't you pause the video
and see if you can now answer this question yourself.
If I take one mole of sulfur,
if I take Avogadro number of sulfur atoms,
it'll have a mass of 32.1 grams, roughly 32.1 grams.
So 32.1 grams represents one mole of sulfur.
But how much sulfur do I have?
I have not 32.1, I have 3.21 grams,
which is just 1/10 of a mole.
That's why I took 3.21 to just keep the calculation simpler.
We can do it in our head. This is 1/10 of a mole.
So how many atoms you must be having?
1/10 of a mole, so 1/10 of the Avogadro number.
So the answer would be the Avogadro number,
which is 6.02 times 10 to the power 23
divided by 10, 1/10 of it.
So it'll be 6.02 times 10 to the power 22.
Okay, here's our final question.
If I take one mole of carbon dioxide,
what do you think will its mass be?
What is the molar mass of one mole of carbon dioxide?
Can you pause the video and try to think about this?
Okay, let's do this step by step.
I know if I have one mole of carbon dioxide,
then it must be having an Avogadro number of molecules
of carbon dioxide, right?
Remember, if I had half a mole of carbon dioxide, it means
that I would have half the Avogadro number
of carbon dioxide.
Makes sense, right? Okay.
Anyways, now comes the question
how many carbon atoms must be there
and how many oxygen atoms must be there?
What do you think?
Well, a single carbon dioxide molecule
has one atom of carbon.
If I have five molecules of carbon dioxide,
I have five carbon atoms,
which means if I have these many molecules
of carbon dioxide, I should have exactly that many amount
of carbon atoms, meaning I have one mole
of carbon atoms with me.
Okay, what about the number of oxygen atoms?
Well, each carbon dioxide molecule has atoms of oxygen.
And so if I had five, for example, molecules
of carbon dioxide, I would have twice the amount,
10 atoms of oxygen.
And therefore, if I have these many molecules
of carbon dioxide, I would have twice the amount,
which means I have two moles of oxygen atoms with me.
And I can now look at the periodic table
to find the mass of one mole of carbon.
It's 12.0107 grams,
and for oxygen,
it would be 15.9994 grams.
That would be the mass of one mole of oxygen.
But then we have to multiply it by two
because over here, we have two moles.
Simplifying this will give me the molar mass
of carbon dioxide.
So one mole of carbon dioxide will have this much mass.
Or we can also say that carbon dioxide has a mass
of 44.0095 grams per mole.
Same thing. It's the same thing, okay?
They all mean the same thing.
Of course, we can round it off
and we are actually doing a numerical.