### Video Transcript

What is the mass of 2.25 times 10
to the negative three moles of ammonium sulfate? Give your answer in grams and to
three decimal places. The molar mass of hydrogen equals
one gram per mole. The molar mass of nitrogen equals
14 grams per mole. The molar mass of oxygen equals 16
grams per mole. And the molar mass of sulfur equals
32 grams per mole.

To convert between a mass in grams
and the amount of a substance in moles, we can use this formula, which tells us the
mass in grams is equal to the amount of substance in moles times the molar mass of
the substance. The problem gave us the amount of
the substance in moles. So we just need to calculate the
molar mass to solve the problem. We can do this using the provided
data.

The substance in this question is
ammonium sulfate, which is made of ammonium and sulfate ions. Since ammonium has a charge of one
plus and sulfate has a charge of two minus, we need two ammonium ions for every one
sulfate ion so that the compound is neutral overall. So ammonium sulfate has the
chemical formula (NH4)2SO4.

Now that we know the formula, let’s
calculate the molar mass of ammonium sulfate. Hydrogen has a molar mass of one
gram per mole. There are four hydrogen atoms in
one ammonium ion. And there are two ammonium ions in
ammonium sulfate. So there are a total of eight
hydrogen atoms in ammonium sulfate. Nitrogen’s molar mass is 14 grams
per mole. There is one nitrogen atom in
ammonium, so there are two nitrogen atoms total in ammonium sulfate. Oxygen has a molar mass of 16 grams
per mole. There are four oxygen atoms in
ammonium sulfate. Finally, sulfur has a molar mass of
32 grams per mole. There’s just one sulfur atom in
ammonium sulfate. If we multiply and add everything
up, we’ll find the molar mass of ammonium sulfate is 132 grams per mole.

Now that we have the molar mass, we
can solve the problem. The amount of ammonium sulfate that
was given in the problem is 2.25 times 10 to the negative three moles. The molar mass that we just
calculated is 132 grams per mole. The units of moles cancel, and we
get 0.297 grams as our final answer, which is already reported to three decimal
places. So the mass of 2.25 times 10 to the
negative three moles of ammonium sulfate is 0.297 grams.