### Video Transcript

Oxalic acid is an organic compound
found in many plants, including rhubarb. It is found to contain 26.7 percent
carbon and 71.1 percent oxygen, with the rest being hydrogen. If the molar mass of oxalic acid is
90 grams per mole, what is its molecular formula?

The molecular formula tells us the
amount of each type of atom that’s in a molecule. This problem gives us the
percentage of carbon, oxygen, and hydrogen in the compound, which we’ll be able to
use to create a ratio of carbon to oxygen to hydrogen. If we express this in the simplest
whole number ratio of atoms, we would have the compound’s empirical formula. And then, we could use the molar
mass of the compound to determine the molecular formula from the empirical
formula.

So to solve this problem, we’ll
first find the ratio of carbon to hydrogen to oxygen that’s in the compound, which
we’ll use to create the empirical formula. And then, finally, we’ll find the
molecular formula. The problem tells us that our
sample is 26.7 percent carbon and 71.1 percent oxygen. Since the rest of the compound is
hydrogen, we can find the percentage of hydrogen in our compound by subtracting the
percentage of carbon and oxygen from 100 percent, which gives us 2.2. So, our sample is 2.2 percent
hydrogen.

If we assume that our sample is 100
grams, we can easily go from these mass percentages into the masses of each
element. 26.7 percent carbon corresponds to
26.7 grams of carbon, since 26.7 percent of 100 is 26.7. Now, we want the ratio of carbon to
hydrogen to oxygen, which we can’t find using these masses, since there’s a
different amount of carbon atoms and hydrogen atoms in one gram of each element. So, we’re going to need to convert
these masses into moles, which we can do by dividing each path by the molar mass of
the element.

The molar mass of carbon is 12.01
grams per mole. 26.7 divided by 12.01 is 2.223. The molar mass of hydrogen is 1.008
and 2.2 divided by 1.008 gives us 2.183 moles of hydrogen. Similarly, the molar mass of oxygen
is 15.99. So, we have 4.447 moles of oxygen
in our sample. Now that we have the amount of
carbon, oxygen, and hydrogen in our sample in moles, we need to figure out how to
express this in the simplest whole number ratio.

The easiest way to do this is by
dividing by the number that’s the smallest amount of moles, which is the moles of
hydrogen, 2.183. Dividing this number into the moles
of carbon gives us 1.02 which is very close to one, but not quite likely due to some
experimental error associated with finding these percentages. 2.183 divided by 2.183 gives us
one. And finally, 4.447 divided by 2.183
gives us 2.04 which is slightly above two, again likely due to some experimental
error. But we can still safely round it
down to two.

So, the ratio of carbon to hydrogen
to oxygen in our sample is one to one to two. Now that we have this ratio, we can
find the empirical formula. Since the empirical formula
expresses the simplest whole number ratio of atoms in a compound, the empirical
formula is going to be CHO2.

Now, we can move on to finding the
molecular formula. We can do this by taking the molar
mass and dividing it by the empirical formula mass. The molar mass of the compound is
given in the problem. It’s 90 grams per mole, so we just
need to calculate the mass of this empirical formula. So, we can calculate the mass of
the empirical formula by summing the molar masses of each atom in the compound,
which gives us a total of 44.998 grams per mole. So now dividing 90 by 44.998 gives
us two, which means that the molecular formula has twice the mass of the empirical
formula. So, we can find the molecular
formula by multiplying the empirical formula by two, giving us C2H2O4.