Chem143 The Mole II

Calculating moles of an element in a molecule from the mass of the molecule, and calculating the number of atoms of an element in a molecule given the mass of the molecule.

>> In this video, we're
going to have some more fun

with the mole, more
calculations.

So first of all, we already know
that when we look at the formula

for a compound, for example
caffeine whose formula is a

C8H10N4O2, that in one molecule
of caffeine, this formula,

if there are 8 atoms of
carbon, 10 atoms of hydrogen,

4 atoms of nitrogen
and 2 atoms of oxygen.

Now that we know about the
mole, what we can say is

that in one mole, 1.0 mole,
2 sigfigs of caffeine,

we have 1 mole of
caffeine times 8 carbon

for every 1 caffeine gives
us 8.0 moles of carbon,

so 2 sigfigs here,
2 sigfigs here.

And 1 mole of caffeine, we get
10 moles of hydrogen and so on,

so 4 moles of nitrogen
and 2 moles of oxygen.

The 1.0 is only 2 sigfigs,
that's the measure--

how much we have,
we have to measure.

But these subscripts here,
the 8, the 10, the 4 and 2,

they're all exact because
we're counting this.

So anyway, 8, 10, 4 and 2.

Now, we can use this.

So we want to know how many
moles of hydrogen there are

in 125 milligrams of caffeine.

Well-- OK.

So let's think about
this kind of approaches

like backwards from the answer.

We know how many moles--

if we know how many moles
of caffeine we have,

then we know how many
moles of hydrogen

because of what I just showed
you on the previous slide.

These numbers here, they're
all conversion factors.

Look, we can say that--

OK, there's a lot of
conversion factors here.

For example, we could say that
1 mole of caffeine is equal

to 8 moles of carbon for--

you know, so we can
convert between moles

of caffeine and moles of carbon.

We can convert between moles of
caffeine and moles of hydrogen,

moles of caffeine and moles of
nitrogen and moles of caffeine

and moles of oxygen
and we can also convert

between the different elements,
we know for caffeine anyway

that 8 moles of carbon is
equal to 10 moles of hydrogen,

so we can convert between moles
of carbon and moles of hydrogen,

nitrogen, oxygen and so on.

So going back here, if
we know how many moles

of caffeine we have, we
can find moles of hydrogen

because the conversion factor
is 1 mole of caffeine is equal

to 10 moles of hydrogen.

So how do we get
moles of caffeine?

Well, we're not giving moles,
we're giving milligrams.

Well, let's see, if we know
grams, we can get moles, right?

Remember what that
conversion factor is

between grams and moles?

It's called molar mass,
not Avogadro's number,

remember Avogadro's number
converts between moles of things

and numbers of things.

We'll see that in a minute.

But we need the molar mass.

So the first thing we're going

to need is the molar
mass of caffeine.

And you guys know how to
calculate that from the formula,

there's 8 carbons, 10 hydrogens,
4 nitrogens and 2 oxygens.

So we'll just look on
the periodic table,

find the molar mass of
carbon, multiply times 8,

add to that the molar
mass of hydrogen times 10,

nitrogens times 4
and oxygen times 2.

We add those up and we get
194.19, 4 grams per mole.

This 4 is a subscript by
the way because in hydrogen,

when we multiply it by 10,
we're only allowed 4 sigfigs,

10 times 1.008 is 10.08 to 4
sigfigs, which is two places

to the right of the decimal.

That's why we keep this.

All right, so now we
know the molar mass.

So what? Well, now, we
can go from milligrams

to grams using our
prefixes, right?

We know that milli means
times 10 to the minus 3.

So this converts
milligrams to grams.

And then moles of--

we can convert 2 moles

of caffeine using the
molar mass of caffeine.

And just to make sure,
cross out all the units

to make sure they cancel
and sure enough they do.

We have the moles of
caffeine but we want in moles

of hydrogen, so what
we do is take the moles

of caffeine using the
conversion factor that we get

from just looking
at the formula,

10 moles of hydrogen
per 1 mole of caffeine.

Moles of caffeine cancel.

And there we go, 6.44
to 3 sigfigs times 10

to the minus 3 moles of hydrogen
in 125 milligrams of caffeine.

We could also calculate how many
atoms of an element there are

in caffeine if we know
how much-- how many--

what mass of caffeine we have.

So let's say we wanted
to know how many atoms

of carbon there are in a 125
milligrams of caffeine, well,

here's-- OK, kind of
approaching this backwards.

If we knew how many moles of
carbon we could find atoms

of carbon, what's that
conversion factor called?

It's Avogadro's number, right?

Moles of things, numbers of
things is Avogadro's number,

so we know that conversation
factor.

All right.

So how do we get
moles of carbon?

Well, if we know moles of
caffeine, we know moles

of carbon because from the
formula, there are 8 moles

of carbon and 1 mole
of caffeine,

it's conversion factor.

And we already saw that if we
know milligrams of caffeine,

we can get moles of caffeine.

So let's do that first.

I'm going to use-- I'm not
going to show that calculation

of the molar mass because
we already did that,

194 grams per mole.

So 125 milligrams converting to
grams and then grams to moles,

and we have 6.43, 6 times 10 to
the minus 4 moles of caffeine.

Then using the conversion factor
for carbon, convert to moles

of carbon, moles of caffeine
cancel, we get moles of carbon,

45.149 times 10 to the
minus 3 moles of carbon.

Now, to go from moles to numbers
of things, atoms in this case,

we use Avogadro's number, moles
of carbon times 6.022 times 10

to the 23 atoms of
carbon per 1 mole.

Moles probably cancel.

And we have the answer,
3.10 times 10

to the 21st atoms of carbon.