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- [Instructor] I have about 3.21 grams

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of sulfur powder over here.

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My question to you is how many
atoms of sulfur are there?

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At first, this question sounds ridiculous.

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I mean, there's gonna be
lots and lots of atoms.

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How in the world are
we going to count that?

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That's what we're gonna
find out in this video.

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We're gonna do that by
introducing the idea of mole.

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So let's begin.

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To come up with the idea of moles,

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we first need a new unit of mass to deal

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with the masses of atoms.

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See, atoms are very tiny.

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Their masses are going
to be incredibly tiny.

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So kilograms and grams is going

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to be very inconvenient to use.

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So we come up with a new unit
called the atomic mass unit,

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AMU or u.

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It's a very tiny unit of mass.

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Just like grams or kilograms,
it's a unit of mass.

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But, of course, whenever
we learn about a new unit,

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we need to ask ourselves,
"How big is that unit?"

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What is the definition of
that unit? How big is 1u?

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Well, here's how we define what a u is.

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You take a single atom of carbon 12.

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Now, its mass by definition is 12u.

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This is not something
that we have measured.

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This is something that we fixed.

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We fixed the mass of a
carbon 12 atom to be two 12u.

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Exactly. Okay?

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Now, what is 1u?

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Well, if the mass of a
carbon 12 atom is 12u,

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1u is 1/12 of its mass, right?

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So we define one atomic
mass unit, 1u as 1/12

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of the mass of a single atom
of the carbon 12 isotope.

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Does that make sense?

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Well, I'm sure at this point

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you may be having some questions,

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like why did we decide to
use carbon as a reference

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and not any other elements?

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Well, it turns out that we
actually started with hydrogen

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because it's one of the lightest elements.

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Then we ran into some problems

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and then we switched to oxygen

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because again, it's extremely abundant.

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Then again, we ran into
some other problems,

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and then finally, we
decided to go with carbon,

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which is also abundant.

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We'll not delve into the histories

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and details of what really happened,

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but yeah, we have to choose
some element as a reference,

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and we ended up choosing
carbon as a reference.

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Another question you could be having

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is why do we fix the mass of a
single atom of this carbon 12

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to be 12u?

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Why not any other number? Why 12?

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Well, for that, you
can see that over here.

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Carbon has how many
protons and neutrons in it?

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Well, it has a total of, I mean,

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it has six protons and six neutrons.

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So it has a total of 12 protons
and neutrons, 12 particles.

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I think of protons and
neutrons together over here

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because they have pretty
much similar mass.

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I mean, a neutron is
actually slightly heavier

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than a proton, but for our purposes,

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to get an intuition over
here, they're masses.

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We can pretty much think of them

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to be almost equal to each other.

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So it has a total of 12 particles, right?

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Now, by fixing the mass of
those 12 particles to be 12u,

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look at what we are doing.

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We are basically saying, "Hey,

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let's fix the mass of a single proton

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or a neutron to be about 1u.

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That was the whole intention. Okay?

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So you can also think 1u
is kind of a representation

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of a mass of a single proton or a neutron,

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but again, this is not exact
because masses of protons

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and neutrons are not
exactly equal to each other.

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So a proton and neutron
will have a mass very close

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to 1u, but it's not exactly 1u,

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but it's a good way to think
about what a u represents.

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It represents sort of the
mass of a proton or neutron.

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Anyways, now that we understand
this, here's a question.

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What do you think is the
mass of a single atom

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of oxygen 16 isotope?

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A single atom of this,

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what will be its mass
in u, atomic mass unit?

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Well, it has a total of
16 particles, 16 protons

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and neutrons together,
and since each particle,

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each proton and neutron has a mass of 1u,

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and there are total 16,
oxygen mass will be about 16u.

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Again, you can see it's
not gonna be exactly 16u

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because mass of each proton
and neutron is not exactly 1u,

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but it's gonna be very close to that.

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Similarly, if you take an
isotope of say chlorine,

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a particular isotope, the most
abundant isotope of fluorine,

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which has 35 protons and
neutrons together in it,

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well, then its mass would be close to 35u.

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Makes sense, right?

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Okay, now, here's a question
we're gonna ask ourselves.

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Let's go back to carbon.

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Each carbon has a mass
of 12u, by definition.

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Now, how many carbon atoms do I need

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to take together says
that the total mass of all

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of those carbon atoms
together becomes 12 grams.

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You can imagine it's going to be lots

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and lots of atoms, right?

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Because each atom has a very tiny mass

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and we want together 12 grams.

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So we probably need to take billions

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and billions and billions of atoms.

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But the big question is how
many atoms do I need to take

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is that they all add up to
give me 12 grams of mass?

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Well, it turns out we figured it out.

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Again, we'll not get into the details

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of how we figured it out, okay?

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The history is actually
pretty interesting,

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but again, we'll not talk
about that over here,

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but we figured it out, and it
turns out to be this number.

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You need to take about 6.022,

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and there are some other
decimals over here,

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some numbers here, times
10 to the power 23,

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which is a huge number, okay?

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If you take these many
carbon atoms together,

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carbon 12 atoms together,
they will together have a mass

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of 12 grams.

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This number is what we
call the Avogadro number

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named after the scientist Amedeo Avogadro

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who worked a lot on this idea.

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But anyways, you can
now see the significance

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of this number.

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I can now count the number
of atoms in a carbon isotope.

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If you give me 12 grams of carbon,

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I know it has these many
number of carbon atoms in it.

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Carbon 12, okay?

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These many number of
carbon 12 atoms in it.

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If you give me 24 grams of carbon,

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there must be twice the amount.

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If you give me six grams of carbon,

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then there must be half the amount.

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You tell me the mass of
the carbon 12 isotope

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that I'm holding in my hand,

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and I can now use this number to tell you

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how many atoms there are.

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Beautiful, isn't it?

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In other words, this becomes
the conversion factor

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for our tiny unit of mass,
from our tiny unit of mass u

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to our more familiar
big unit of mass, grams.

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If you take u and you
multiply with this number,

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you get grams.

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And whenever you have an
Avogadro number of things

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with you, we call it a mole.

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Just like how when you
have 12 things with you,

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we call it a dozen, these many things,

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if you have together,
it could be anything.

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It could be these many atoms.

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Then we'll call it a mole of atoms,

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or it could be these many babies.

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Then we'll say we have a mole of babies.

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It's a ridiculous number
but you get the idea.

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And this word mole actually
comes from the Latin molecule,

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which translates to a very
tiny amount of something.

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But anyways, what is a mole?

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A mole represents Avogadro number,

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these many number of things.

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It could be number of atoms,
molecules, particles, anything.

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And what's so special about this number?

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It's a conversion factor
from the tiny unit

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of mass u to grams.

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You take this number,
multiply it by this number,

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and you will now get it in grams.

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Okay, now, let's see
if you understand this.

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What do you think would
be the mass of one mole

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of oxygen 16 atoms?

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If I had an Avogadro number
of oxygen 16 atoms together,

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what do you think collectively
would its mass be?

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Well, an Avogadro number

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of 12us will give me a mass of 12 grams.

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So an Avogadro number of 16us

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will give me me a mass of 16 grams.

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That's what we mean by a
conversion factor, okay?

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It works for any atom which has any mass.

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You just multiply it by this,

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and now you'll get the mass in grams.

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Similarly, if I had an
Avogadro number of chlorine 35,

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if I had one more of
chlorine 35 atoms with me,

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then it'll have 35 grams of mass.

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Make sense?

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And so another way to talk about all

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of these things, whatever I just said now,

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another way to talk about
this is we say the molar mass

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of carbon 12 is 12 grams.

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Carbon 12 has a mass of 12 grams per mole.

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Makes sense, right?

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We would say oxygen 16 will
have 16 grams per mole.

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I mention oxygen 16

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because remember, there
are other isotopes as well.

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Different isotopes will
have different masses,

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so their molar mass would be different.

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So oxygen 16 isotope has a molar mass

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of 16 grams per mole,

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and chlorine 35 has a molar mass

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of 35 grams per mole, okay?

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Same thing, whatever I
just said, a technical way

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of stating the same thing over here.

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All right, the last thing we need to do

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to make this more practical is to remember

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that over here we considered pure cases.

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I took a pure carbon 12 isotopes

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where every single atom was carbon 12,

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or I took a pure chlorine isotope

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where every single atom was chlorine 35,

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but in reality, that's not the case.

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If I take a chunk of chlorine,

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a lot of it will be chlorine 35,

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but there'll be some
other isotopes as well.

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Like, another abundant
isotope next to chlorine 35

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is chlorine 37.

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And that sounds really
complicated, but what's important

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and powerful is that that
doesn't matter to us.

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This whole idea still works. Okay?

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Here's what I mean.

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Let me take an example.

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If you look at our periodic table,

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and you can see that the atomic
mass of chlorine is given

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to be not 35.

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It's 35.45.

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So significant deviation from 35. Why?

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Because this also accounts for the fact

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that if you take a chunk of chlorine,

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it'll also contain a lot
of chlorine 37 in it.

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So what we do is sort
of like take an average.

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This is a weighted average, we say,

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so this is the average
atomic mass of chlorine.

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So since I know the average atomic mass

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of chlorine is 35.45, if I
now take one mole of chlorine,

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not pure as it exists
as a mixture in nature,

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then one mole will have
a mass of 35.45 grams.

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That's it.

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Similarly, if I take one mole of carbon,

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which, you know, it's not exactly 12 grams

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because there are other
isotopes, it'll be 12.01 grams.

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You see what I mean? A mole
is a conversion factor.

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Take one mole of anything,
it'll be this number in grams.

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And so now we can try and
answer our original question.

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We asked ourselves, if you
have 3.21 grams of sulfur,

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how many atoms there are?

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Why don't you pause the video

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and see if you can now answer
this question yourself.

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If I take one mole of sulfur,

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if I take Avogadro number of sulfur atoms,

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it'll have a mass of 32.1
grams, roughly 32.1 grams.

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So 32.1 grams represents
one mole of sulfur.

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But how much sulfur do I have?

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I have not 32.1, I have 3.21 grams,

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which is just 1/10 of a mole.

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That's why I took 3.21 to just
keep the calculation simpler.

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We can do it in our head.
This is 1/10 of a mole.

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So how many atoms you must be having?

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1/10 of a mole, so 1/10
of the Avogadro number.

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So the answer would be
the Avogadro number,

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which is 6.02 times 10 to the power 23

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divided by 10, 1/10 of it.

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So it'll be 6.02 times 10 to the power 22.

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Okay, here's our final question.

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If I take one mole of carbon dioxide,

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what do you think will its mass be?

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What is the molar mass of
one mole of carbon dioxide?

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Can you pause the video and
try to think about this?

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Okay, let's do this step by step.

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I know if I have one
mole of carbon dioxide,

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then it must be having an
Avogadro number of molecules

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of carbon dioxide, right?

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Remember, if I had half a mole
of carbon dioxide, it means

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that I would have half the Avogadro number

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of carbon dioxide.

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Makes sense, right? Okay.

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Anyways, now comes the question

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how many carbon atoms must be there

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and how many oxygen atoms must be there?

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What do you think?

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Well, a single carbon dioxide molecule

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has one atom of carbon.

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If I have five molecules
of carbon dioxide,

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I have five carbon atoms,

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which means if I have these many molecules

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of carbon dioxide, I should
have exactly that many amount

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of carbon atoms, meaning I have one mole

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of carbon atoms with me.

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Okay, what about the
number of oxygen atoms?

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Well, each carbon dioxide
molecule has atoms of oxygen.

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And so if I had five,
for example, molecules

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of carbon dioxide, I would
have twice the amount,

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10 atoms of oxygen.

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And therefore, if I have
these many molecules

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of carbon dioxide, I would
have twice the amount,

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which means I have two moles
of oxygen atoms with me.

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And I can now look at the periodic table

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to find the mass of one mole of carbon.

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It's 12.0107 grams,

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and for oxygen,

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it would be 15.9994 grams.

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That would be the mass
of one mole of oxygen.

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But then we have to multiply it by two

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because over here, we have two moles.

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Simplifying this will
give me the molar mass

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of carbon dioxide.

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So one mole of carbon dioxide
will have this much mass.

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Or we can also say that
carbon dioxide has a mass

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of 44.0095 grams per mole.

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Same thing. It's the same thing, okay?

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They all mean the same thing.

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Of course, we can round it off

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and we are actually doing a numerical.