>> narrator: In this video,
we'll take a Closer Look
at hydrates
and molecular formulas.
A hydrated salt is a salt
that has crystallized
from an aqueous solution.
Chemicals that form hydrates
can be used to absorb
water vapor to keep air dry
where it's important,
such as around
sensitive equipment.
It may look dry,
but when it's heated,
it liberates very large
quantities of water.
During the heating process,
the crystals change color
and are converted into
an anhydrous form.
Which just means
they lack water
in their crystal structure.
To calculate a hydrate's
empirical formula,
first determine the moles
of water that have been
driven off.
Then, find the moles
of the anhydrous, or dry,
salt that are left.
Next, determine the lowest
whole number mole ratio
of the anhydrous salt
to the water.
Write the formula for
the hydrate by writing
the moles of anhydrous salt,
separated by the moles
of water associated with it,
separated by a dot.
Here's a practice problem
which asks you to calculate
the empirical formula
for a hydrate.
A 15.67 gram sample of
a magnesium carbonate hydrate
was heated,
driving off the water only.
After heating was complete,
the mass was 7.58 grams.
What is the empirical
formula of the hydrate?
The first step is to
figure out the mass of water
that was driven off.
To do that, take the mass
of the hydrated salt,
which was 15.67 grams,
and subtract the mass
of the anhydrous salt,
what was left after heating.
8.09 grams of water
were driven off
during the heating process.
Next, take that mass of water,
8.09 grams,
and convert it to moles,
using the molar mass of water,
which is 18.02 grams.
After dividing the mass
of water driven off
by the molar mass of water,
we have 0.449 moles of water
that were driven off.
Now, take the mass of the
anhydrous magnesium carbonate,
7.58 grams,
and convert that to moles,
using the molar mass
of magnesium carbonate,
which is 84.31 grams.
So, 7.58 grams of
magnesium carbonate
divided by 84.31
is 0.0899 moles of
magnesium carbonate.
Now you are ready to figure out
the empirical formula
for this hydrated salt.
Divide 0.0899 moles
of magnesium carbonate
into 0.449 moles of water.
That will give you the ratio
of the moles of water
to moles of the anhydrous
magnesium carbonate,
and that ratio is
five moles of water
for every one mole
of magnesium carbonate.
This is how you
write the formula for
the hydrated compound.
Again, this dot does not
mean multiplied by.
This is just the way you
represent hydrated compounds.
Empirical formulas represent
the reduced subscript formula
for a compound,
but may not always represent
the actual number of each
element present in a molecule
or formula unit of a substance.
We use empirical formulas to
calculate molecular formulas,
which are true formulas
that show the number
of all the atoms that
are present in a molecule.
To calculate a molecular
formula, first find
the empirical formula,
if it's not already given.
Then determine the
empirical formula mass.
You find this the same way
that you calculate
the molar mass
for any other compound.
Just add up the molar masses
of all the elements that
make up the empirical formula.
The next step is to divide
that molecular mass
from the compound by
the empirical formula mass.
Then, multiply each subscript
in the empirical formula
by the number you found
in the previous step,
when you divided
the molecular mass by
the empirical formula mass.
And here are
a couple of equations
to illustrate that process.
This first box says to
take the molar mass
and divide it by
the empirical formula mass
to get some number, an integer,
"n," if you will.
Then distribute that integer
to all the subscripts
in the empirical formula.
Here's a problem in which
we have to calculate
the molecular formula.
This problem tells us
that the empirical formula
for ethylene is CH2.
We need to find
the molecular formula
if the molar mass
of the compound is
28.1 grams per mole.
The empirical formula mass
is found from taking 12
from carbon,
plus the two from hydrogen,
and we get 14.03 grams per mole
as the empirical formula mass.
The molecular mass,
which was given in the problem,
is 28.1.
When you divide those two,
we get 2.00.
That becomes the subscript
that we distribute to
all of the subscripts
from the empirical formula.
The two distributes here
to the two from hydrogen.
So we multiply two times two
to get the new subscript
of four for hydrogen.
And the two distributes here
to the carbon.
Multiply two times
the understood one,
and you get the new subscript
of two for carbon.
So the molecular formula
for this compound is C2H4.
Now here's one for you to try.
The empirical formula
of a compound is NO2.
The molar mass of the compound
is 92.0 grams per mole.
What is the molecular formula?
When you're ready,
pause the video
and work the problem.
When you're ready, press play
and see if you got it.
Here's the answer.
If you got N204
for the molecular formula
for this compound,
good work.
The process was to take
the molar mass that was
given in the problem, 92.0,
and divide that by 46,
which was simply the mass
of nitrogen dioxide, NO2.
And you get an integer of two.
Take that two and distribute it
to all the subscripts
inside the empirical formula.
So the two gets distributed
to the nitrogen.
That's how we got the N2.
And then the two distributed
to the two from oxygen,
ends up being two times two,
or four, for oxygen.
And, N2O4 is the molecular
formula for this compound.
That's a Closer Look
at hydrates
and molecular formulas.
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