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Before I continue, I want to
introduce you to what might be

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an unfamiliar concept, although
if you've taken

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chemistry, you might know a
little bit about it-- it's

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called a mole.

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This isn't the thing that grows
on your face with the

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hair in it, or the animal that
digs in your backyard,

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although those are also
called moles.

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We're talking about the
SI unit called a mole.

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A mole is just a number.

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It's like saying a mole of
something means a certain

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number of something, just like
a dozen-- it's like saying

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that a dozen eggs is 12 eggs.

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Just like that, a mole would
be 6-- I always forget the

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exact number, but it's 6.023,
or something of that nature.

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You could look it up--
I think it's 6.023

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times 10 to the twentieth.

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Let me look up the exact number,
just because I think

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that 23 I'm misremembering.

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The mole is 6.022 times 10 to
the 23 of something, so it's a

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very number of something.

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Normally, we don't deal in moles
of eggs-- I don't think

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there has been a mole of eggs
ever produced in the history

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of the universe.

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10 to the 23 is a very, very,
very large number.

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Where is it useful?

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A mole is useful for counting
atoms, and so what is a mole

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of atoms or molecules?

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What's that many molecules?

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It's 6 followed by roughly 23
0's of molecules-- a very,

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very big number.

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What's interesting about a mole
is that when I have a

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mole of something, its mass--
let's say its mass in grams. A

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mole of carbon: its mass in
grams is going to be equal

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to-- so if I have this many
carbon molecules, its mass in

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grams is x grams. It'll have a
mass of x grams, where x is

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the atomic mass number of an
atom of carbon, although if I

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was talking about a mole of a
molecule, I would figure out

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the atomic mass of the
entire molecule.

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What's an atomic mass number?

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Let me see if I can do a Web
search on a periodic table.

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I'm showing you what I do here,
and it's not fancy.

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Let me go to Google, and let's
look up periodic table, and

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let's see if we can
find a good one--

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this one looks good.

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If we go to carbon, which is
right here, we see that its

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atomic number is 6, and
that's the number of

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protons that it has.

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The atomic mass number-- it's
the mass of the entire atom.

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And just so you know-- we're
delving into a little bit of

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chemistry here-- but most of
the mass of an atom is the

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protons and the neutrons.

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The neutrons and the protons
weigh roughly the same thing,

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and then the electrons are
much, much, much smaller.

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If you factor in the mass of the
protons and the neutrons,

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you pretty much have the
mass of the particle.

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Just a little more chemistry
here is that although on

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average most of the most of
the atoms have roughly the

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same number of protons and
neutrons-- some don't.

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Some, you could have a carbon
atom that has seven neutrons,

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another one with five, another
one with six, and those are

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actually all called isotopes,
and I won't go into all of

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that-- they're just
the same atom with

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different numbers of neutrons.

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In general, the atomic mass is
equal to the mass of the

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protons and the neutrons, and
they tend to be equal.

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So if the atomic number
is 6, the atomic

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mass tends to be 12.

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So why is this useful?

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We can say if we have niobium--
let's say I have a

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mole of niobium.

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If we look here on the periodic
table, it has an

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atomic mass number of 41, and
its average atomic mass-- if

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we were to average all of the
isotopes based on the

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weighting of how they exist
in nature-- it's

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92.9, so roughly 93.

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It's actually a little bit more
than double its atomic

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number, but let's say 93.

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If we had a mole of niobium--
if we had 6.022 times 10 to

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the 23 of niobium, it would
have a mass of 92 grams.

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That's pretty easy-- look
at any element.

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Let's say chromium: we see its
atomic mass number is roughly

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52, and we see that there.

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If I have a mole of it-- if I
have roughly 6 times 10 the 23

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three of it, that much will
have a mass of 52 grams.

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That's how we think
about a mole.

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If I tell you I have a mole of
something, I'm also telling

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you how many of that molecule
I have, and I'm also telling

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you what the mass of that mole
that quantity will be,

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assuming that you
have a periodic

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table in front of you.

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With that said, and with that
out of the way, let's make

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some more progress with
our thermodynamics.

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We said in the last several
videos that pressure times

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volume is somehow
proportional--

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let's call that K.

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And this is an arbitrary number,
it's not some special

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constant-- to the total kinetic
energy of a system.

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We also said that that is
roughly proportional-- that's

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another constant-- times the
number of molecules we have

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times the temperature, because
temperature we viewed as

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kinetic energy per molecule.

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In general, we could also say
that this is proportional to

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this, which is proportional to
this, that pressure times

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volume is proportional.

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We'll use R, because you'll see
where that's coming from

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in a second.

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It's proportional, it's equal
to some constant times the

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number of molecules n.

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Here I just take the absolute
numbers-- if I had five

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molecules, I'd put a five here,
but now this n, I'm

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counting in moles.

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If this n is 1, that means that
I have 6.022 times 10 to

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the 23 molecules.

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One mole equals 6.022 times 10
to the 23, so I'm just saying

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that this is another way to
write the number of molecules,

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and then that's times
temperature.

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Then if we rearrange
it-- PV equals nRT.

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We have a relationship, that
if I know the pressure, the

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volume, and the number of
molecules, I can figure out

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the temperature, or if I know
the number of molecules, the

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temperature, and the pressure,
I can figure out the volume,

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assuming I know what R is.

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I'm about to tell you
what that is.

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R is called the universal gas
constant, and it is R is 8.31

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joules per mole-Kelvin.

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That kind of tells you what
you need in this formula.

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This should end up being
joules, so if you have

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pressure in pascals and volume
in meters cubed, you'll end up

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with joules there.

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This should be in moles--
this is 8.31 joules per

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mole-Kelvin.

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And then this, as we always
said, should be in Kelvin.

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Honestly, if you just memorize
two things in all of

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thermodynamics, you'll probably
be able to do 95% of

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problems, but you actually
should have the intuition of

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how they work.

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Just remember that PV over T
is equal to a constant, or

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that if you change them, they
relate to each other in that

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they all equal a constant, so
P1 times V1 divided by T1 is

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equal to P2 times V2
divided by T2.

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You also should just need to
memorize PV is equal to nRT,

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where R is equal to 8.31
joules per mole Kelvin.

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I know you might not have a
lot of intuition of this

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formula yet, because I haven't
used it, but I'm going to do

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that in the next video.

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These are literally the two
most important things you

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should know in thermodynamics,
and hopefully you have a

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little intuition at this point
of what they mean.

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See you soon.

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