Chem143 The Mole

The mole, Avogadro's number, and molar mass.

>> In this video, we're
going to talk about the mole.

No, no, not the animal,
but rather a number.

Avogadro's number is this number
right here, 6.022 times 10

to the 23rd or at least
the four sig figs it is.

Where this number comes from is
it's defined as being the number

of atoms of carbon-12 in
exactly 12 grams of carbon-12.

Remember, we have
different isotopes.

It ends up that the element
carbon has several different

isotopes, one of
those being carbon-12

in which there are six protons
and six neutrons in the nucleus.

Well, if had exact
12 grams of carbon,

we could count how many atoms
there were in that 12 grams.

That would-- That's
Avogadro's number.

That's how it's defined.

And it ends up to at
least to four sig figs,

that number is 6.022
times 10 to the 23rd.

Definitely memorize the number.

And memorize it to four sig figs
like I have it here for you.

It's also a conversion
factor, because the mole

that we're talking
about here is defined--

1 mole of anything is defined

as being Avogadro's
number of that thing.

So just basically
fill in the blank.

One mole of blank is equal

to 6.022 times 10 to
the 23rd of blank.

For example, 1 mole of
sand grains is equal

to 6.022 times 10 to
the 23rd grains of sand.

Now, in reality as
chemists, most of the time,

we fill in the blank
with something

like atoms or molecules.

But it could be anything.

It's-- You think
about it like a dozen.

If I said I was going to
the store and I was going

to buy two dozen eggs,
well, everybody knows

that I'd be getting 24 eggs.

So we could say one dozen of
blank is equal to 12 of blank.

Same thing, right?

And it is a conversion factor.

This conversion factor
right here lets us convert

between moles of things
and numbers of things.

For example, let's say we
have 1.75 moles of pennies

and we want to find how
many pennies we have.

It's really best to threat this

as a dimensional analysis
problem because later on,

we're going to build on this
concept and make problems,

self-problems where it's--
has several steps to it

and this will be
one of the steps.

So, we want to know how many
pennies there are in 1.75 moles.

So, our answer-- the units
of our answer will be numbers

of pennies and our starting
point is 1.75 moles of pennies.

Our conversion factor, well,

it will be the definition
of a mole.

One mole of pennies is
equal to 6.022 times 10

to the 23rd pennies,
where I've just filled

in the blank here
now with pennies.

Notice, OK, mole, M-O-L-E,
we have an abbreviation

which isn't very
much an abbreviation.

But if we drop the E, M-O-L
is the abbreviation for mole.

So, finishing the problem,
1.75 moles of pennies.

Using our conversion factor,
realizing that we have

to cancel moles of pennies,
so we put 1 mole of pennies

on the bottom, putting
Avogadro's number of pennies

on the top, and you can see
that the units cancel out.

And we get our answer, 1.053
times 10 to the 24th pennies.

We're only allowed three sig
figs because of the 1.75.

This has four, this has three,
so we keep three sig figs.

Now, molar mass, a
really important concept.

The molar mass of anything
is the mass of 1 mole

of that thing, how much one mole

of that thing weighs
typically in grams.

And this right here in white
is a really important concept.

The molar mass of
any element, it's--

is the same number as
its average atomic mass.

Remember, we did average
atomic mass a while back.

So for example, we-- if we
look at the periodic table,

we can get the average
atomic mass of any element.

If we look for-- up that carbon,
we see that it's 12.011 amu

for its average atomic mass.

So now, we also know the
molar mass of carbon,

it's 12.011 grams per mole.

The units of molar mass
are grams per mole.

We could also say, as
a conversion factor,

that 1 mole of carbon is equal
to 12.011 grams of carbon.

And we'll do that right now.

So, here's a problem.

We have 4.592 grams of
lithium, we want to find out,

calculate how many moles
of lithium we have.

Well, going between
grams and moles now,

the conversion factor
is the molar mass.

One mole of lithium is equal
to 6.941 grams of lithium.

Where I get this number?

I got it from the
periodic table.

I looked up the average
atomic mass of lithium,

I saw that it was 6.941 amu.

And so, that told me right
there that the molar mass

of lithium is 6.941 grams per
mole, or as a conversion factor,

1 mole of lithium is equal
to 6.941 grams of lithium.

So doing my dimensional
analysis,

the units that I want
will be moles of lithium.

So I leave it blank here in
front of moles of lithium.

And my starting point is
how many grams I have,

so 4.952 grams of lithium.

I looked at my conversion factor
here, I've grams of lithium

on top here as my starting
point so I need grams

of lithium in the bottom.

That puts moles of
lithium on top.

And again, units cancel.

We get moles of lithium.

And so, we get 0.66157
moles of lithium.

Four sig figs in this
number, four in this,

so we keep four sig
figs, we round it.

So, before we go on, we've now
seen two different conversion

factors and they're really,

really important
conversion factors.

First is Avogadro's
number, let's go back there.

Avogadro's number converts
between moles of things

and numbers of things.

Write that down because people
get this confused all the time.

And then-- so that's
Avogadro's number,

a mole of anything is equal to
Avogadro's number of that thing,

the individual things.

Now, molar mass converts
between grams and moles, right,

not numbers of thing
and moles but grams.

You see the difference there?

And so, if we know the
molar mass of something,

we can convert between moles
of that and grams of that,

just like we did here.

Now, if we have a compound, the
molar mass of that compound,

it's just the sum of the
molar masses of the atoms

that make up that compound.

For example, calcium nitrate.

In one molecule of
calcium nitrate,

we have one form of unit rather.

We have 1 atom of calcium,
2 atoms of nitrogen,

and 2 times 3 is
6 atoms of oxygen.

Well, the molar mass of calcium
nitrate will just be the--

1 times the molar
mass of calcium

because there's one calcium,
and 2 times the molar mass

of nitrogen, and 6 times
the molar mass of oxygen.

So looking up at the periodic
table, finding the molar masses,

remember it's the same number
as average atomic mass,

we find calcium is 40.078
grams per mole and there's one

of those guys, two nitrogens
each is 14.007 grams per mole,

and six oxygen each is
15.999 grams per mole.

Multiplying this out-- I'm
going to warn you guys here.

Be careful with sig figs.

Show the individual
steps and I multiply it--

oh, by the way, these
numbers, right, they're exact

because we're counting things.

The 1 and the 2 and the
6 are exact numbers.

But the others aren't, right?

This guy has five sig figs,
this has five and this has five.

So we multiply each out,
we keep five sig figs,

40.078, 28.014, 95.994.

But next when we add, we look
at where the last sig fig is,

it ends up the way
it worked out.

Here, the last sig fig was
three places to the right

of the decimal on each of
these, so we keep three places

to the right of the decimal.

And our answer, 164.086
grams per mole.

Notice, we have six sig figs
now even though all these guys

had five.

So now, we know the molar
mass of calcium nitrate,

164.086 grams per mole,

which means we have
another conversion factor.

We can convert between grams
and moles for calcium nitrate.

We now know that 1 mole of
calcium nitrate is equal

to 164.086 grams
of calcium nitrate.

So let's use that in a problem.

Let's say we have 5.794 grams
of calcium nitrate and we want

to find out how many moles
of calcium nitrate there are.

Well, there's our
conversion factor

which is our molar mass we
just calculated, that's right.

So typically, if you
have a problem like this,

you won't already know the
molar mass so you have to do

that calculation first to
get your conversion factor.

So we know 1 mole of
calcium nitrate is equal

to 164.086 grams
of calcium nitrate.

So setting up our
dimensional analysis,

the units of our answer will
be moles of calcium nitrate.

So we leave it blank in front
of moles of calcium nitrate.

And our starting
point is 5.794 grams

of calcium nitrate right here.

Well, we need grams of calcium
nitrate in the bottom so we come

up here, take that,
put it down there.

The other side of the
equal sign goes on top.

And we-- our units cancel,

grams of calcium
nitrate here cancel here.

And we end up with moles
of calcium nitrate here.

And because we have four sig
figs in the 5.794 and six

in the 164.086, the
one is exact,

we keep four sig
figs in our answer.

So the answer is 0.3531
moles of calcium nitrate.