Before I continue, I want to introduce you to what might be
an unfamiliar concept, although if you've taken
chemistry, you might know a little bit about it-- it's
called a mole.
This isn't the thing that grows on your face with the
hair in it, or the animal that digs in your backyard,
although those are also called moles.
We're talking about the SI unit called a mole.
A mole is just a number.
It's like saying a mole of something means a certain
number of something, just like a dozen-- it's like saying
that a dozen eggs is 12 eggs.
Just like that, a mole would be 6-- I always forget the
exact number, but it's 6.023, or something of that nature.
You could look it up-- I think it's 6.023
times 10 to the twentieth.
Let me look up the exact number, just because I think
that 23 I'm misremembering.
The mole is 6.022 times 10 to the 23 of something, so it's a
very number of something.
Normally, we don't deal in moles of eggs-- I don't think
there has been a mole of eggs ever produced in the history
of the universe.
10 to the 23 is a very, very, very large number.
Where is it useful?
A mole is useful for counting atoms, and so what is a mole
of atoms or molecules?
What's that many molecules?
It's 6 followed by roughly 23 0's of molecules-- a very,
very big number.
What's interesting about a mole is that when I have a
mole of something, its mass-- let's say its mass in grams. A
mole of carbon: its mass in grams is going to be equal
to-- so if I have this many carbon molecules, its mass in
grams is x grams. It'll have a mass of x grams, where x is
the atomic mass number of an atom of carbon, although if I
was talking about a mole of a molecule, I would figure out
the atomic mass of the entire molecule.
What's an atomic mass number?
Let me see if I can do a Web search on a periodic table.
I'm showing you what I do here, and it's not fancy.
Let me go to Google, and let's look up periodic table, and
let's see if we can find a good one--
this one looks good.
If we go to carbon, which is right here, we see that its
atomic number is 6, and that's the number of
protons that it has.
The atomic mass number-- it's the mass of the entire atom.
And just so you know-- we're delving into a little bit of
chemistry here-- but most of the mass of an atom is the
protons and the neutrons.
The neutrons and the protons weigh roughly the same thing,
and then the electrons are much, much, much smaller.
If you factor in the mass of the protons and the neutrons,
you pretty much have the mass of the particle.
Just a little more chemistry here is that although on
average most of the most of the atoms have roughly the
same number of protons and neutrons-- some don't.
Some, you could have a carbon atom that has seven neutrons,
another one with five, another one with six, and those are
actually all called isotopes, and I won't go into all of
that-- they're just the same atom with
different numbers of neutrons.
In general, the atomic mass is equal to the mass of the
protons and the neutrons, and they tend to be equal.
So if the atomic number is 6, the atomic
mass tends to be 12.
So why is this useful?
We can say if we have niobium-- let's say I have a
mole of niobium.
If we look here on the periodic table, it has an
atomic mass number of 41, and its average atomic mass-- if
we were to average all of the isotopes based on the
weighting of how they exist in nature-- it's
92.9, so roughly 93.
It's actually a little bit more than double its atomic
number, but let's say 93.
If we had a mole of niobium-- if we had 6.022 times 10 to
the 23 of niobium, it would have a mass of 92 grams.
That's pretty easy-- look at any element.
Let's say chromium: we see its atomic mass number is roughly
52, and we see that there.
If I have a mole of it-- if I have roughly 6 times 10 the 23
three of it, that much will have a mass of 52 grams.
That's how we think about a mole.
If I tell you I have a mole of something, I'm also telling
you how many of that molecule I have, and I'm also telling
you what the mass of that mole that quantity will be,
assuming that you have a periodic
table in front of you.
With that said, and with that out of the way, let's make
some more progress with our thermodynamics.
We said in the last several videos that pressure times
volume is somehow proportional--
let's call that K.
And this is an arbitrary number, it's not some special
constant-- to the total kinetic energy of a system.
We also said that that is roughly proportional-- that's
another constant-- times the number of molecules we have
times the temperature, because temperature we viewed as
kinetic energy per molecule.
In general, we could also say that this is proportional to
this, which is proportional to this, that pressure times
volume is proportional.
We'll use R, because you'll see where that's coming from
in a second.
It's proportional, it's equal to some constant times the
number of molecules n.
Here I just take the absolute numbers-- if I had five
molecules, I'd put a five here, but now this n, I'm
counting in moles.
If this n is 1, that means that I have 6.022 times 10 to
the 23 molecules.
One mole equals 6.022 times 10 to the 23, so I'm just saying
that this is another way to write the number of molecules,
and then that's times temperature.
Then if we rearrange it-- PV equals nRT.
We have a relationship, that if I know the pressure, the
volume, and the number of molecules, I can figure out
the temperature, or if I know the number of molecules, the
temperature, and the pressure, I can figure out the volume,
assuming I know what R is.
I'm about to tell you what that is.
R is called the universal gas constant, and it is R is 8.31
joules per mole-Kelvin.
That kind of tells you what you need in this formula.
This should end up being joules, so if you have
pressure in pascals and volume in meters cubed, you'll end up
with joules there.
This should be in moles-- this is 8.31 joules per
mole-Kelvin.
And then this, as we always said, should be in Kelvin.
Honestly, if you just memorize two things in all of
thermodynamics, you'll probably be able to do 95% of
problems, but you actually should have the intuition of
how they work.
Just remember that PV over T is equal to a constant, or
that if you change them, they relate to each other in that
they all equal a constant, so P1 times V1 divided by T1 is
equal to P2 times V2 divided by T2.
You also should just need to memorize PV is equal to nRT,
where R is equal to 8.31 joules per mole Kelvin.
I know you might not have a lot of intuition of this
formula yet, because I haven't used it, but I'm going to do
that in the next video.
These are literally the two most important things you
should know in thermodynamics, and hopefully you have a
little intuition at this point of what they mean.
See you soon.