When we count ordinary objects, we have certain words we use to make counting easier. For
instance, when we talk about our shoes and socks, we always talk about them in terms
of PAIRS. I have 4 pairs of shoes and 12 pairs of socks. A “pair” always means 2. We
usually buy eggs by the DOZEN. A dozen means 12. I can buy a REAM of paper, which is 500
sheets.
We use these kinds of “counting words” - pair, dozen, ream - for specific situations.
You wouldn’t ask for a pair of eggs or a ream of eggs. And you wouldn’t ever ask
for a MOLE of eggs. That’s WAY too many eggs. But a mole makes sense if you are talking
about particles in chemistry. A mole is another counting word, like a pair or a dozen, but
it’s used to count a very large number of objects. 6.02 x 10^23 objects.
Now, when I say objects, I mean atoms; or ions; or formula units in the case of ionic
compounds; or molecules in the case of molecular compounds. Those are all what we call “representative
particles” - the smallest unit of that material. 1 mol of helium is 6.02 x 10^23 atoms, because
helium is atomic. Hydrogen is molecular, and it exists in nature as a molecule of H2 - so
when we say 1 mol of hydrogen we mean 6.02 x 10^23 molecules of H2. 1 mol of NaCl means
6.02 x 10^23 formula units, because NaCl is an ionic compound.
6.02 x 10^23 is known as Avogadro’s Number, named for the great Italian chemist, Amedeo
Avogadro. Although Avogadro did fundamental work on atoms and molecules, he didn’t actually
come up with this number. It’s just named in his honour. They must have thought pretty
highly of Avogadro, because Avogadro’s number is HUGE. It’s used in chemistry because
the particles in chemistry - atoms, ions, molecules - are so tiny that there will be
a MASSIVE number of particles in any appreciable amount of a substance. If we’re going to
talk about the number of atoms in the head of a pin or the number of molecules of a liquid
in a beaker - we need a REALLY big number.
But why 6.02 x 10^23? Why this number, and not 20 billion or some other giant number?
6.0221421 x 10^23 is the number of atoms in 12 grams of Carbon-12. Carbon-12 has historically
been used as a standard in chemistry. For instance, we use C-12 as the standard for
atomic mass, so Avogadro’s number is not completely arbitrary. For ease of use, we
typically round Avogadro’s number to 2 decimal places: 6.02 x 10^23.
Let’s see an example of how to use the mole. We have a beaker full of water. If the beaker
has volumetric markings on the side, it’s easy to measure the volume. The beaker contains
400 mL of water. If we have a balance, we can measure the mass of the water. The beaker
contains 400.0 g of water. But what if someone asked you how many molecules of water are
in the beaker? We’d have to do a little calculating, and that’s when we’d use
the term MOLE.
If we want to convert from grams of water to number of moles of water, we’ll use the
molar mass. The molar mass of water tells you how many grams there are per mole of water.
To find the molar mass of water, H2O, sum up the gram atomic masses of the individual
atoms from the Periodic Table. There are 2 atoms of hydrogen and 1 atom of oxygen, so:
2 x 1.008 g/mol + 1 x 15.999 g/mol = 18.015 g/mol.
Rounded to one decimal place, we get
18.0 g/mol for the molar mass of water.
Let’s convert from grams of water to molecules of water, using the molar mass we just calculated
as a conversion factor, and Avogadro’s number as another conversion factor. 1 mole of water
= 6.02 x 10^23 representative particles, in this case, water molecules.
Start with what we know, 400.0 grams of H2O and leave a space for our conversion factors,
and write the units we want to wind up with on the right. molecules of H2O.
400.0 grams of water times ( 1 mole of water/18.0 g of water) times (6.02 x 10^23 molecules
of water/ 1 mole of water) = some number of molecules of water.
Grams of water cancel, and moles of water cancel, leaving us with molecules of water.
400.0 x 6.02x10^23 / 18.0 = 1.3 x 10^25 molecules of water.
For solids and liquids, this is the most common kind of conversion using the mole - between
mass and number of particles. For gases, you can convert between VOLUME and number of particles.
This is because of a peculiar property that is true of gases at STP - standard temperature
and pressure. STP is 0 degrees C and 100 kPa. Under these conditions, 1 mole of gas = 22.4
L. It doesn’t matter if it’s a mole of hydrogen, or helium, or argon - any gas you
want - a mole of gas measures 22.4 L at STP. Weird, but true. Let’s see an example of
a conversion that uses this fact:
A neon sign holds 200 mL of neon gas. How many atoms of neon is that? And how many grams
does the neon weigh? Assume STP.
Start with what we know, 200 mL of neon. Leave a big gap for conversion factors, and
end with what we want: atoms of neon.
We’ll need several conversion factors for this problem. First, we know we need to go
from mL to L, so we’ll use the conversion factor 1000mL per 1 L. Make sure the orientation
of your conversion factor is correct so units cancel. Next we’ll use the strange-but-true
fact that gases are 22.4L per moL of gas at STP. Then we’ll use Avogadro’s number to get
the number of representative particles. Neon is atomic, not molecular, so in this case,
the representative particles are atoms.
(200 mL neon) times (1L/1000 mL) times (1mol neon/22.4 L neon) times (6.02x10^23 atoms
Neon/ 1 mole Neon) = some number of atoms of neon.
Check to make sure our units cancel: mL cancel, L cancel, and moles cancel, leaving atoms
of Neon. (200 x 6.02x10^23)/(1000)(22.4) = 5.4 x 10^21
atoms of Neon.
Now what about the next part of the question? Given this number of atoms of neon, how many
grams is that? We can use the molar mass of Neon from the Periodic Table and Avogadro’s
number as conversion factors.
5.4 x 10^21 atoms of Neon (1 mol Neon/6.02x10^23 atoms Neon) x 20.18 grams Neon/1 mol of Neon
= some number of grams of Neon. Check to see your units cancel...
We get 0.18 grams of Neon.
Based on our experience with these examples, we can draw a map that relates all of these
kinds of conversions: To go from Mass to Moles, or Moles to Mass, use the Molar Mass (grams
per mole). To go from The Number of Particles to Moles, or Moles to Number of Particles,
use Avogadro’s Number: 6.02x10^23 particles per mole. To go from the Volume of a Gas to
Moles, or from Moles to the Volume of a Gas, use 22.4 L/mol. Remember this only works for
a gas at STP. You can see that the mole is
central to solving all these kinds of conversion problems.