The Mole
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Real World Chem
 Real
chemists don’t realistically work
with individual atoms and molecules.
Even a small sample of a substance
contains BILLIONS or TRILLIONS of
atoms or molecules
 To keep track of how many atoms,
molecules, compounds, etc. they were
working with, scientists came up with
the “mole”
2
What is a Mole?
3
NO!!!
THESE
4
NONE OF
SI Counting Unit in Chemistry
 The
mole is the standard counting
unit in chemistry (abbreviated “mol”)

Just as a dozen eggs equals 12 eggs…
A mole = 602,000,000,000,000,000,000,000

Or 602 billion trillion

Or 6.02 X 1023 (in scientific notation)
5
The Mole
1
1
1
1
6
dozen = 12
gross = 144
ream = 500
mole = 6.02 x 1023
Avogadro’s Number

Not Avocado

6.02 X 1023 is also known as Avogadro’s
Number

Named after Italian chemist Amadeo
Avogadro who determined that at the
same temp and pressure, all gasses
contained the same number of particles
7
Just How Big is a Mole (6.02 x 1023)?



8
Enough soft drink cans to cover the
surface of the earth to a depth of over
200 miles.
If you had Avogadro's number of
unpopped popcorn kernels, and spread
them across the United States of
America, the country would be covered
in popcorn to a depth of over 9 miles.
If we were able to count atoms at the
rate of 10 million per second, it would
take about 2 billion years to count the
atoms in one mole.
What is a mole?

9
It is also the number of atoms in the
atomic mass in g of any element.
Look at your periodic table, the
atomic mass of Oxygen is 16 g.
This is NOT the mass of 1 oxygen
atom.
It is the mass of 1 mole (or 6.02 x
1023) oxygen atoms
Also… What is a mole?
the number of molecules in the
molecular weight, in grams, of any
compound.
the number of molecules in 18 g of
water (H2O – if you add up the masses
of 2 hydrogens and a water it equals
18g)
There are 6.02 x 1023 molecules of water
in 18g of water.
10
What Can Be Expressed Using Moles?

11
A mole can be used to represent 6.02 x 1023:
-atoms
-molecules
-ions
-compounds
-particles
-items
-formula units
The Mole






1 dozen cookies = 12 cookies
1 mole of cookies = 6.02 X 1023 cookies
1 dozen cars = 12 cars
1 mole of cars = 6.02 X 1023 cars
1 dozen Al atoms = 12 Al atoms
1 mole of Al atoms = 6.02 X 1023 atoms
Note that the NUMBER is always the same, but
the MASS is very different!
12
A Mole of Particles
Contains 6.02 x 1023 particles
1 mole C = 6.02 x 1023 C atoms
1 mole H2O = 6.02 x 1023 H2O molecules
1 mole NaCl = 6.02 x 1023 NaCl “formula units”
13
How do we use the mole?
 We’d never use the mole to describe
macroscopic or real world objects.



1 mole (6.02x1023) of watermelon seeds would be
found inside a watermelon the size of the moon.
1 mole (6.02x1023) of donut holes would cover the
earth and would be 5 miles deep.
Since the mole is such a huge number of items, it
is only used to describe the amount of things that
are very, very small.

1 mole (6.02x1023) of water molecules would barely fill
a shot glass
14
Avogadro’s Number as Conversion
Factor
6.02 x 1023 (small unit) = 1 mol
can be used to solve problems
by putting it in ratio form.
6.02 x 1023 (unit)
1 mole
or
1 mole
6.02 x 1023 (unit)
15
Converting
Moles Molecules
16
Converting MolesMolecules

Use Avogadro’s constant (6.02 x 1023 unit)
when converting between moles and
molecules.
EX: How many atoms are in 3.4 moles of
iron atoms?
Follow these steps…
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Calculation
 1. Start with known value divided by 1.
 2. Then line up units so that only the desired
units are not cancelled.
 3. Divide the products of the numerators by
the products of the denominators.
 4. Express answer in correct sig figs and unit.
3.4 moles
1
18
6.02 x 1023 atoms
1 mole
= 2.0 x 1024
atoms
Learning Check
Number of moles of S in 1.8 X 1024
atoms.
1.8 X 1024 atoms S
1
1 mole S
6.02 x 1023 atoms S
3.0 moles S
19
=
Learning Check
Number of atoms in 0.500 mole of Al
23 atoms Al
6.02
x
10
0.500 mole Al
1
1 mole Al
3.01 X 1023 atoms Al
20
=
Last slide
Learning Check
Number of pieces in 2 moles of M&Ms
23 pieces
6.02
x
10
2 moles M&Ms
1
1 mole M&Ms
1 X 1024 pieces
21
=
The Mole
Part 2
22
Calculating
molar Mass
23
How do we measure moles?
Do you know how to measure out 1 mole of
sugar or salt or water?
 The mole is a counting unit, so we would have
to count out 6.02 x 1023 particles of each
substance. (NO THANKS!)
 There are 2 ways to measure out a number of
moles of a substance:
 Measure it in GRAMS ( a mass)
 Or measure it in LITERS ( a volume)

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Using mass to measure moles…
 To be able to measure out 1 mol of a substance…
we would need to know the mass in grams of 1 mol
of the substance in question.
 Since each atom is a different size and has a
different mass, 6.02 x 1023 of each atom would
weigh a different amount.
 Remember, we don’t use Avogadro’s number to
count anything but atoms, molecules, etc.
 So we need a table that provides the mass 1 mole
would weigh for every combination of atoms
known to man.
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Using mass to measure moles…

It just so happens that the periodic
with that information.


table provides us
The masses of each atom on the table is the equivalent
to the mass of 1 mole of that atom.
The mass on the periodic table is called the molar mass
(units of g/mol), because it represents the mass of 1 mol
of that atom


1 mole of Mg atoms weighs 24.31 g
1 mole of C atoms weighs 12.01 g
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Calculating Molar Mass
 Molar
mass is the mass of 1 mole of a
pure substance.
 Unit (label) = g/mol
 Molar
mass may also be referred to as:
-gram formula mass (ionic compounds)
-formula mass (ionic compounds)
-molecular mass (non metals)
27
Calculating Molar Mass
EX: Find the molar masses for the following:
 Silver
 Argon
 Potassium
 Oxygen
 Hydrogen
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107.87 g/mol
39.95 g/mol
39.10 g/mol
16.00 g/mol
1.01 g/mol
Using mass to measure moles…
That works well for atoms off of the periodic table,
but how do we find the molar mass of molecules
and compounds?
 Each of those compounds and molecules are
composed of a combination of atoms.
 We have the molar masses for all of the atoms on
the periodic table.
 We need to be able to add up the total weight of
all of the atoms in the compound or molecule given
its formula.
 For example, what is the molar mass of H2O?

29
Calculating Molar Mass
The molar mass of a molecule or formula can be
determined by adding the molar masses of each of the
elements present.

EX: H2O
Elements Moles of each Atomic mass
H
O
2
1
x
x
1.01
16.00
Molar mass of H20
30
= 2.02
=16.00
 18.02 g/mol
Calculating Formula Mass
Calculate the formula mass of
magnesium carbonate, MgCO3.
24.31 g + 12.01 g
+ (3 x 16.00 g) =
Thus, 6.02 x 1023 MgCO3’s
would weigh 84.3 grams
31
84.31
g/mol
Calculating Molar Mass

Calculate molar mass of the following:
1.
Al2S3
Al (2 x 26.98) = 53.96
S (3 x 32.07) = 96.21
150.17 g/mol
Last slide
32
Converting
Moles Grams (mass)
33
Mole Conversions

We can use these molar masses in calculations
in which we are either




34
Given moles and asked for its mass equivalent
or
Given mass and asked for its mole equivalent.
If we are given an element… we just use the
mass from the periodic table
If we are given a formula instead… we just
calculate the molar mass of the molecule using
the masses from the periodic table.
Mole Conversions
 The
key to converting between any
units is to label numeric values with
appropriate units and work with these
until the only one that will not cancel is
the one you want.
 You now have the conversion bridge
necessary to convert moles  grams.
35
Conversion Steps
Step 1: Identify given (number and unit) and
place it over 1.
 Step 2: Place the unit that needs to cancel in
the denominator and its equivalent in the
numerator.
EX: 1 mol = 6.02 x 1023 molecules
1 mole = molar mass in grams

36
Conversion Steps
Step 3: Cancel units that are in the numerator
and denominator.
 Step 4: Continue conversion steps until the
only unit remaining is the unit you need.
 Step 5: Multiply all numbers in numerator.
 Step 6: Divide all numbers in the denominator.
 Step 7: Express answer with correct unit and
sig figs.

37
Converting Moles and Grams
Ex:
Aluminum is often used for the structure
of light-weight bicycle frames.
How many grams of Al are in 3.00 moles
of Al?
3.00 moles Al
?
g Al
1.
Molar mass of Al
1 mole Al = 26.98 g Al
2. Conversion factors for Al
26.98g Al
or
1 mol Al
1 mol Al
26.98 g Al
3. Setup
3.00 moles Al
1
x
26.98 g Al
1 mole Al
Answer = 80.9 g Al
Last slide
Mole Conversions
#1. What is the mass in grams of 2.5 mol of O2?
2.5 mol O2 x 32.00 g O2 =
1
1 mol O2
80 g of O2
#2. Determine the number of moles in 5.00 g of H2O.
5.00 g H2O x 1 mol H2O = 0.280 mol of H2O
1
18.02 g H2O
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The Mole
Part 3
41
Review:
Converting
Moles Molecules
&
Converting
Moles Grams (mass)
42
The Mole
 Because
the mole measures both a mass
and a number of particles
(6.02 x 1023 = 1 mole = molar mass),
it is the central unit in converting the
amount of a substance from one type of
measurement to another
 Understanding
how to use the mole is
essential to the study of chemistry
43
Sample Problems
MOLES MOLECULES
Use Avogadro’s #
MOLES GRAMS
Use Molar Mass

0.2 mol H2SO4  molecules

10.00 g CuCO3  moles

1.2 x 1024 molecules of O2 moles

2.5 moles of NaCl  grams
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Atoms, Molecules & Grams

Since 6.02 X 1023 particles = 1 mole
AND
1 mole = molar mass (grams)
You can convert atoms/molecules to moles and
then moles to grams! (Two step process)
You can’t go directly from atoms to grams!!!!

You MUST go thru MOLES.


45
Liters
Atoms
or molecules
22.4
L
Atomic
Mass
Mole
Grams
46
Calculations
molar mass
Grams
Avogadro’s number
Moles
Particles
Everything must go
through Moles!!!
Atoms/Molecules and Grams

How many atoms of Cu are present
in 35.4 g of Cu?
35.4 g Cu
1
1 mol Cu
63.5 g Cu
6.02 X 1023 atoms Cu
1 mol Cu
= 3.36 X 1023 atoms Cu
Mole Conversions


Now a challenge:
Determine the number of molecules there are in a 5.45
g sample of CaCl2.
5.45 g CaCl2 x 1 mol CaCl2 x
1
110.98 g CaCl2
6.02 x 1023 molecules CaCl2
1 mol CaCl2
2.96 x 1022 molecules of CaCl2
49
Practice Problems
1. A sample of hydrochloric acid has 8.75 x 1025
molecules, how many grams is this?
Hydrochloric Acid
2. If aluminum hydroxide has a mass of 150 grams,
how many formula units are there?
(a mole is also known as… a formula units for ionic compounds)
50
Aluminum hydroxide