The Mole
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Counting Without Counting

If you had to count the number of coffee beans in
this bag how would you do it? How long would it
take?
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Counting Without Counting

If you had to count the number of grains of sand in
this bag how would you do it? How long would it take?
How do scientists count atoms or molecules?
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Let’s try to come up with a way to count the number
of beans in a large bag of beans without actually
counting them all and without taking a long time.
Eventually we want to apply this new method of
counting to counting atoms!
Any IDEAS?
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Counting by Weighing
Weight of 10 beans
Average weight of one bean
Weight of all beans in bag
453 (g)
Weight of beans in bag _____
_____
8.51 g
0.85 g
_____
453
_____ g
1 bean
_____
0.85 (g)
=
533 beans in a
_____
bag
Counting by weighing works when the
items are all about the same size and
mass. The closer the items are to being
exactly the same, the more accurate the
method is.
If the beans were all exactly the
same we would only have to weigh one and
not take the average of ten!
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Counting by Weighing

What was the key information needed to determine
the number of beans in any bag of beans without
counting them all?
 The average mass of ONE bean!
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Applying “Counting by Weighing”
to Atoms



How can we use this idea to determine the number of
atoms per gram of the element carbon?
We need to know the mass of one atom of carbon!
We can’t weigh an atom of carbon directly but we do
know something about the particles that make up a
carbon-12 atom.
proton
= 1.67 x 10-24g

Carbon-12 has 6 protons
neutron = 1.67 x 10-24g

Carbon–12 has 6 neutrons
electron = too small to count

Carbon-12 has 6 electrons (still too small)
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Mass of one Carbon Atom
Particles in
12
6
C atom
6 protons x
6 neutrons x
6 electrons x
Mass(g) of
particle
Total mass(g)
of particles
-24
1.67 x 10
1.67 x 10-24
Negligible
-23
= 1.0 x 10
= 1.0 x 10-23
= Negligible
Total mass of a
Carbon-12 atom
2.0 x 10-23 g
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Applying “Counting by Weighing” to Atoms



So one atom of Carbon-12 weighs about
2.0 x 10-23 g.
How many grams of carbon should we use? (like
the total mass of an beans bag).
Weight for one carbon atom is a result of 12
particles (6p+6n). So let’s use 12 GRAMS of
carbon.
(Who is this guy?)
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How Many Atoms in 12 Grams of
Carbon


How many atoms do you think are in 12 grams of
carbon?
Let’s use dimensional analysis (canceling units) to
figure it out!
12gC


1 atom C
= 6.0 x 1023 atoms of carbon
2.0x10-23 gC
That’s 600,000,000,000,000,000,000,000 atoms!!
OK, Why Carbon?
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Oxygen and Hydrogen Were Also Both
Used as Mass Standards





Physicists used Hydrogen
Chemists used Oxygen
Because oxygen and
hydrogen both have
isotopes the scales didn’t
agree, but the ratio of two
elements was the same.
Physicists and Chemists
compromise to Carbon as
the mass standard in 1961.
Can you believe it took them
that long to agree!!
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The Mole
Now let’s go backwards using oxygen with that 6 x 1023
number of atoms for 12 grams of carbon
Particles in
O atom
8 protons
8 neutrons
8 electrons
Mass(g) of
particle
1.67 x 10-24
1.67 x 10-24
9.108 x 10-28
x
x
x
Total mass of
Oxygen atom
6.0 x 1023 atoms
oxygen
2.68 x 10-23 g
1 atom oxygen
Total mass(g) of
particles
= 1.34 x 10-23
= 1.34 x 10-23
= Negligible
2.68 x 10-23 g
= 16 g oxygen!!
look familiar?
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The Mole

6.0 x 1023 is a pretty special number.

It’s called “a mole”

1 “Mole” represents 6.0 x 1023 of anything.

Like 1 dozen = 12 of anything (Other examples?)

One mole of beans is 6.0 x 1023 beans.

The mole is based on the number of
atoms in 12 grams of carbon-12
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The Mole

Scientists have determined that
One Mole = 6.02 x 1023 atoms.

It’s important in chemistry because its
used to convert grams to atoms.
 Scientists
want to react atoms with
atoms but they can’t count out atoms
directly, they’re too small.
 Using The Mole scientists can weigh out
a number of grams of a chemical and
calculate the number of atoms present in
that mass!
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Loschmidt (1865)

“The Mole” (or mol) may
come from a shortening
of “molecule”.

Also the word “mole” is
Latin for “heap or pile”

Avogadro didn’t coin the
term, he wasn’t even the
first to recognize how to
calculate the number.

Loschmidt, a school
teacher, was the first to
calculate atoms/mole and
his work was based on
Avogadro’s work.
Avogadro (1811)
Avogadro suggested that equal volumes of all gases at the same
temperature and pressure contain the same number of molecules.
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The Mole




6.02 x 1023 atoms of carbon-12 is 12.00 grams,
and
6.02 x 1023 atoms of oxygen-16 weighs 16.00
grams …
So the mole is clearly related to an element’s
atomic mass.
Let’s define one mole of any element as equal
to the atomic mass (weighted average of
isotopes) of that element.
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What is a Mole
atomic mass of
1 mole of atoms
= of any element
element



=
6.02 x 1023 atoms
of any element
1 mole of carbon = 12.01g carbon = 6.02 x 1023 atoms C
1 mole of oxygen = 16.00g oxygen = 6.02 x 1023 atoms O
1 mole of sodium = 23.00g sodium = 6.02 x 1023 atoms Na
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How Big is a Mole (6.02 x 1023) ?



If you count out loud starting with the number
"one" at the rate of one count every second, it
would take you 1,909,577,942,668,696 years
to finish.
Using a 2 GHz CPU, it will still take about
2,243,506 years to “count” to 1 mole.
One mole of beans would cover the earth 25
miles thick!!
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Using “The Mole”


Once you understand the concept of “The Mole” it’s easy
to use. Now that we know the mole REPRESENTS the
number of particles we can use the mole directly.
Calculate the number of moles in 150.0 g of copper:
150.0 g Cu

1 mole Cu = 2.4 moles of Cu
63.55 g Cu
Calculate the number of atoms in 20.4g of carbon:
20.40 g C
1 mole C
12.01 g C
6.02 x 1023 atoms C = 1.02x1024 atoms C
1 mole C
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Bad Mole Jokes
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The Original Wack-a-Mole
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A
small furry mammal walks into a
bar and orders a drink. The
bartender says, "Sorry, our
maximum occupancy is only 5.99 x
1023. We can't serve a mole."
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 "Do
you have mole problems? If so,
call Avogadro at 602-1023."
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More Practice with the Mole

How many moles of Zinc are in 50.0g of Zinc metal?

How many particles of chlorine gas are there in 20
moles of chlorine gas?
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More Practice with the Mole

How many moles of Zinc are in 50.0g of Zinc metal?
50.0 g Zn

1 mole Zn
65.39 g Zn
=
0.765 Moles Zn
How many molecules of chlorine gas are there in 20 moles
of chlorine gas?
20 moles Cl2 6.02 x 1023 molecules Cl2 = 1.2x1025 Molecules Cl2
1 mole Cl2
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Even More Practice!!
How many moles of NaCl are in 50.0g of sodium chloride?
50.0g NaCl
1 mole NaCl
58.45 g NaCl
=
0.855 Moles NaCl
Na = 23.00g/mole (atomic mass)
Cl = 35.45g/mole (atomic mass)
NaCl = 58.45 g/mole (molar mass)
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