The Mole (and M&M’s)
1
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?
2
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?
3
Let’s try to come up with a way to count the number
of M&M’s in a large bag of M&M’s 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?
4
Counting by Weighing
Average weight of one M&M
_____
8.66 g
0.87 g
_____
Weight of M&M’s in bag
357.2 g
_____
Weight of 10 M&M’s
Weight of M&M’s in bag 357.2
_____ (g)
1 M&M
0.87 (g)
____
=
411 M&M’s 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 M&M’s 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 M&M’s in any bag of M&M’s without
counting them all?
 The average mass of ONE M&M
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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 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 has 6 protons
neutron = 1.67 x 10-24g

Carbon – 12 has 6 neutrons
electron = 9.11 x 10-28g

Carbon has 6 electrons
7
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
1.67 x 10-24
1.67 x 10-24
9.11 x 10-28
= 1.00 x 10-23
= 1.00 x 10-23
= Negligible
Total mass of a
Carbon-12 atom
2.00 x 10-23 g
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Applying “Counting by Weighing” to Atoms



So one atom of Carbon-12 weighs 2.0 x 10-23 g.
Now to determine the relationship between mass and # of Carbon
atoms. How many grams of carbon should we use? (like the total
mass of a M&M’s bag).
Weight for one carbon atom is 12 amu (6p+6n). So let’s use 12
GRAMS of carbon.

How many atoms do you think are in 12 grams of carbon?

Let’s use dimensional analysis to figure it out!
12gC

1 atom C
2.0x10-23 gC
= 6.0 x 1023 atoms of carbon
That’s 600,000,000,000,000,000,000,000 atoms!!
(Who is this guy?)
9
The Mole
Now let’s go backwards using oxygen with that 6 x 1023
number of atoms
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.
“Mole” represents 6.0 x 1023 of anything.
Like 1 dozen = 12 of anything
Using other means scientists have determined that
One Mole = 6.022 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 mass of a
chemical and calculate the number of atoms present in
that mass!
One mole of M&M’s is 6.02 x 1023 M&M’s.
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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

6.022 x 1023 atoms of carbon is 12.00 grams, and

6.022 x 1023 atoms oxygen 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 any element.
atomic mass of
element
1 mole of atoms
6.02 x 1023 atoms
= any element
of
of=any element
1 mole of carbon = 12.00g carbon
1 mole of chlorine = 35.45g chlorine
1 mole of barium = 137.3g barium
any
= 6.02 x 1023 atoms of C
= 6.02 x 1023 atoms of Cl
= 6.02 x 1023 atoms of Ba
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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 Pentium 1 GHz CPU, it will still take
about 2,243,506 years to finish this task.
One mole of M&M’s 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 =
63.55 g Cu
2.4 moles of Cu
Calculate the number of atoms in 20.4g of carbon:
20.40 g C
1 mole C 6.02 x 1023 atoms C = 1.02x1024 atoms C
12.01 g 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 6.00 x
1023. We can't serve a mole."
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 "Do
you have mole problems? If so,
call Avogadro at 555 - 602 - 1023."
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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 = 1.7x1023Molecules Cl2
1 mole Cl2

How many grams of oxygen gas are in 0.625 moles of O2 ?
0.625 mol O2
32.00g O2
1 mole O2
=
20.0g O2
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
END
27
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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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 = 1.7x1023Molecules Cl2
1 mole Cl2

How many grams of oxygen gas are in 0.625 moles of O2 ?
0.625 mole O2 32.00g O2 = 20.0g O2
1 mole O2
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