### Video Transcript

How many oxygen atoms are there in
4.0 times 10 to the negative three moles of Al(NO3)3? Give your answer to one decimal
place.

The mole is the SI unit of amount
of substance. One mole of a substance is equal to
6.02214076 times 10 to the 23rd power of entities. This value is known as Avogadro’s
number. We frequently do not need to use
Avogadro’s number to this level of precision and can round the value to 6.022 times
10 to the 23rd power. Entities may refer to any object
which is being counted but in chemistry frequently refers to atoms, molecules,
formula units, or particles.

With this background information in
mind, let’s return to the question. We want to calculate the number of
oxygen atoms there are, given the moles of aluminum nitrate. We know from the definition of the
mole that one mole of aluminum nitrate will contain 6.022 times 10 to the 23rd
formula units of aluminum nitrate. We know we are starting with 4.0
times 10 to the negative third moles of aluminum nitrate. We can multiply this value by our
relationship written as a fraction, with moles of aluminum nitrate in the
denominator, so that the unit moles of aluminum nitrate will cancel. Performing the calculation gives us
a value of 2.4088 times 10 to the 21st formula units of aluminum nitrate.

Looking at the chemical formula of
aluminum nitrate, we see that each formula unit of aluminum nitrate contains three
nitrate ions. And each nitrate ion contains three
oxygen atoms. This means that one formula unit of
aluminum nitrate has nine oxygen atoms. We know that there are 2.4088 times
10 to the 21st formula units of aluminum nitrate in 4.0 times 10 to the negative
third moles of aluminum nitrate. We also know that one formula unit
of aluminum nitrate contains nine atoms of oxygen. We can multiply the number of
formula units of aluminum nitrate by our relationship written as a fraction, with
formula units of aluminum nitrate in the denominator, so that the units cancel. We perform the calculation and
determine that there are 2.168 times 10 to the 22nd atoms of oxygen.

However, the question asks us to
give our answer to one decimal place. With appropriate rounding, we have
determined that 4.0 times 10 to the negative third moles of aluminum nitrate
contains 2.2 times 10 to the 22nd atoms of oxygen.