Calculations using Avogadro's number (part 1) | Chemistry | Khan Academy

- [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.