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# The mole and Avogadro's number

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Let's talk about a concept
that probably confuses chemistry students the
most on some level. But on some level it's also one
of the simplest concepts. And that's the idea of a mole,
which in chemistry is different than the thing digging
up your backyard, or the thing you want to get
removed from your left eye. A mole in chemistry
is just a number. It's just a number, and
the number is 6.02 times 10 to the 23. So it's a very huge number. And this is also called
Avogadro's number. Maybe I will do a video
on Avogadro. But that's all you
need to know. A mole is just a number. There are kind of
more Byzantine definitions of a mole. This actually is not-- actually,
let me copy and paste it from Wikipedia. This is Wikipedia's definition
of a mole. And you hopefully at the end of
this video you'll see that they're equivalent. But if you're just getting
exposed to the concept, this to me, it's just not
an easy concept. Basically, a "a mole is defined
as the amount of substance of a system that
contains as many elemental entities as there are atoms in
12 grams of carbon 12." Well, I just told you that a mole is
6.02 times 10 to the 23. So if you just take the
last part, atoms in 12 grams of carbon 12. So that means that there are 1
mole of carbon 12-- let me write it like that--
carbon 12. There are 1 mole of carbon 12
atoms in 12 grams of carbon. And so that's why a
mole is useful. So I could have just instead
of writing 1 mole, I could have replaced this as there's
6.02 times 10 to the 23 carbon atoms, carbon 12 atoms in
12 grams of carbon. How do you figure that out? Or I guess, what else
does this mean? I mean, we just added in carbon,
they said it's the amount of substance of any
molecule, if you convert between atomic mass
units and grams. This I find very confusing. How can we apply this
in other places? So the first thing to realize
is a mole is just a way of translating between grams
and atomic mass units. One carbon 12 atom is what? What's its mass number? It's 12. That's why it's called carbon
12 instead of carbon 14. So its mass is 12 atomic
mass units. So if you have something that
has a mass of 12 atomic mass units and you have a mole of
them, or you have 6.02 times 10 to the twenty three of
them, all of those atoms combined will have a
mass of 12 grams. So another way to think about
it is 1 gram is equal to 1 mole of atomic mass units. I'll write amu's like that. Or you can write 1 gram is equal
to 6.02 times 10 to the 23 atomic mass units. And the reason why this is
useful-- and it's kind of addressed in this Wikipedia
definition there-- is it helps us translate between the atomic
world-- where we deal with atomic mass units and we
deal with, oh, we've got an extra neutron now, let's add
one to our atomic mass number-- and translating between
that atomic world and our everyday world where
we deal in grams. And just so you know, a
gram is still a pretty small amount of mass. It's 1/1,000 of a kilogram. A kilogram is about 2 pounds. So this is about 1/500
of a pound. So this is not much. So there's a ton of atoms in a
very small amount of-- in 1 gram of carbon, or at least in
12 grams of carbon, you have a ton of atoms. You have 6.02
times 10 to the 23. And just to hit the point home,
I probably should have talked about this in the atom. This is a huge number. To maybe visualize it, if you
think of-- I was told that in the diameter of a hair, if this
is a hair and this is diameter of the hair, if you
go this way there 1 million carbon atoms. 1 million
carbon atoms that way. Or if you were to take an apple
and you were to try to figure out what fraction, if
you were to make one of the atoms of an apple-- and
obviously, an apple has a bunch of different types of
atoms in it-- but if you were to take one of the atoms and
make it the size of the apple, then the apple would be
the size of the earth. So an apple atom is
to an apple as an apple is to the earth. So these are obviously-- it's
hard for us to even process things of this size. When you just have one gram of--
well, let's say you have 1 gram of hydrogen. 1 gram of hydrogen. If you have 1 gram of hydrogen,
that means you have 1 mole of hydrogen. How do I know that? Because hydrogen's atomic
mass number is 1. So in general, if you just take
any element-- so what is the mass of, let me just pick,
1 mole of aluminum? So if I were to take 6.02 times
10 to the 23 aluminum atoms, what is the mass
of that collection? Well, each of them have an
atomic mass number of 13. So it's 13 amu's-- I don't
have to put the s there-- times six point-- well, I won't write that way, actually. That'll probably just
confuse you. The easy way to think about is
if you have a mole of an atom, you take its mass-- I was taking
its atomic number, that's not good-- you take
its mass number. In this case let's
say it's 27. So we're dealing with
aluminum 27. You take its mass number, and if
you have 1 mole of it, then the mass of that will
be 27 grams. So that literally, when you have
one mole of an atom it's a direct translation between its
mass number and grams. 1 mole of iron, let's say iron
56-- there's obviously many isotopes or iron-- let's say
we're dealing with iron 56. You normally don't hear it like
that, but let's say we're dealing with the isotope
of iron that has a mass number of 56. So if I have 1 mole of this, 1
mole of this atom right here, that's going to have a mass of--
the math isn't difficult here-- 56 grams. And if you
think about it, how many atomic mass units is this? Well, this is 56 atomic
mass units per atom. Then you have a mole of those,
so you have 6.02 times 10 to the 23 times 56 atomic
mass units. And then you divide it by
the number of atomic mass units per gram. And you end up with 56 grams. But the easy way to think about
it is you just take whatever the mass number is. If you have silicon, if you have
a mole of silicon, a mole of silicon will have a mass--
I don't want to say weight because this should apply to
any planet-- of 28 grams. What about 2 moles of silicon? And I'll write its
mass number. Let's say silicon has
a mass number of 28. Two moles of silicon. Well, 1 more would have a mass
of 28 grams, so 2 moles is going to have a mass
of 56 grams. If I were to say, let's say I
had 4 moles of oxygen, which has a mass number of 16. What is the mass of that? This is a huge number of oxygen
atoms-- what would be the mass of that? Well, it would be 4 times-- 1
mole of oxygen would have a mass of 16 grams, so 4
moles has 64 grams. It's confusing because we're not
used to using a word like moles as a number, but all
it is is a number. And the easy way to think
about is that it lets us translate between this atomic
mass unit number and grams. And you say, well, how do
I get that many grams? Well, I have to have 6.02 times
10 to the 23 carbon atoms for that collection of
carbon to have a mass of 12 grams. That's all
that mole means. It's just a number. And I encourage you to kind of
play around with a lot of what we talked about. Because it's super important to
have the intuition behind moles, otherwise you'll get
confused later on when we start getting into energies
in terms of it requires kilojoules per mole, and what is
the energy of this reaction and all that type of stuff. So just really try to make sure
you digest this as well as possible. And let me know if you don't
and I'll maybe make another video on this because
it's so important.