Stoichiometry - Chemistry - page 200

One mole of water molecules occupies about 18 ml, so 1/3 of a mole of
water molecules occupies just 6 ml. As you should know by now, each mol-
ecule of water (H 2 O) is made up of three atoms. Therefore, 1/3 of a mole of
water molecules will contain a full mole of atoms. So 6 ml of water, which is
really just a small sip, will contain about 602,000,000,000,000,000,000,000
atoms!
Perhaps you still can't picture the size of a 6 ml sample of water. Think,
instead, of a 1-liter bottle of water. Let's calculate the number of moles of
water molecules in 1 liter of water. One liter is equal to 1000 ml. We al-
ready said that one mole of water occupies about 18 ml. We need to divide
1000 ml by 18 ml to determine how many moles of water molecules there
are in one liter of water. Let's solve the problem using the factor-label
method, which you'll remember from Chapter 2.

1000 ml
1 L

1 mole of H 2 O
18.0 ml

×

1 L × = 55.6 moles H 2 O

So, a 1-liter bottle of water contains 55.6 moles of water molecules.
This represents about 33,500,000,000,000,000,000,000,000 molecules (55.6
moles × 602,000,000,000,000,000,000,000 molecules/mole)! Remember: Be-
cause each water molecule contains 3 atoms, one liter of water represents
approximately 100,000,000,000,000,000,000,000,000 atoms
(33,500,000,000,000,000,000,000,000 molecules × 3 atoms/molecule)! If a
liter of water contains this many atoms, could we ever hope to measure the
mass of a dozen, a score, or even a million atoms on our laboratory bal-
ances? The answer is no, and that is why we group them in such large sets.
This discussion should have not only convinced you of the need for
having a very large number represent the mole, but also of the need to use
scientific notation when dealing with such large numbers. Rather than writ-
ing 602,000,000,000,000,000,000,000 every time we have a mole of some-
thing, we will use 6.02 × 10 23 . I didn't mention this earlier, because some
students are more intimidated when they see the number in scientific nota-
tion. Don't let the notation scare you off. We are just writing the large
number in a more convenient format, so that we don't have to write out all
of the zeros. We can also use scientific notation for the calculations in the
next lesson, so you should review this topic.
To add to this convenience, the number 602,000,000,000,000,000,000,000
is also given a name. It is called “Avogadro's number,” in honor of Amedeo
Avogadro, a famous Italian chemist. So, if you are speaking about the total
number of atoms in 1 mole of water molecules, you can simply say “three
times Avogadro's number,” or 3 × (6.02 × 10 23 ), which is 1.81 × 10 4 atoms.