2/1/2015
Unit 9: Math of Chemistry
“Chemical Quantities”
Part I
6.02 X 1023
Yes
, you will need a
calculator for this chapter!
Lesson # 9.1: The Mole
The Mole
Lesson 9.1: The Mole:
A Measurement of Matter
• OBJECTIVES:
–Describe methods of measuring
the amount of something.
–Define Avogadro’s number as it
relates to a mole of a substance.
How do we measure items?
 You can measure
mass ….
 in grams.
 or volume…..
 in liters.
 or you can count
pieces……
 in MOLES.
Lesson 9.1: The Mole:
A Measurement of Matter
• OBJECTIVES:
–Distinguish between the atomic
mass of an element and its
molar mass.
–Describe how the mass of a mole
of a compound is calculated.
What is the mole?
We’re not talking about this
kind of mole!
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Moles (is abbreviated: mol)
 It is an amount (or a counting unit),
defined as the number of carbon
atoms in exactly 12 grams of
carbon-12.
 1 mole = 6.02 x 1023 of the
representative particles.
 Treat it like a very large dozen
 6.02 x 1023 is called: Avogadro’s
number.



Amedeo Avogadro
(1776 – 1856),

The Mole
• 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!
Mole is abbreviated mol (gee, that’s a lot
quicker to write, huh?)
Suppose we invented a new collection unit
called a comet. One comet contains 8 objects.
1. How many paper clips in 1 comet?
c) 8
2. How many oranges in 2.0 comet?
a) 4
b) 8
c) 16
3. How many comets contain 40 gummy bears?
a) 5
b) 10
• 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 are Representative Particles?
Learning Check
b) 4
Pair: 1 pair of shoelaces
= 2 shoelaces
Dozen: 1 dozen oranges
= 12 oranges
Gross: 1 gross of pencils
= 144 pencils
Ream: 1 ream of paper
= 500 sheets of paper
Just How Big is a Mole?
• 1 dozen cookies = 12 cookies
• 1 mole of cookies = 6.02 X 1023 cookies
a) 1
Similar Words for an amount –
Counting Units
c) 20
 The smallest pieces of a substance:
1) For a molecular compound: it is the
molecule.
2) For an ionic compound: it is the
formula unit (made of ions).
3) For an element: it is the atom.
• Remember the 7 diatomic
elements? ( they are the
exception - made of molecules)
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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
(technically, ionics are compounds not molecules so
they are called formula units)
6.02 x
1023
Na+
ions and
6.02 x 1023 Cl– ions
Learning Check
1. How many atoms of Al are in 0.500 mole of Al
a) 500 Al atoms
b) 6.02 x 1023 Al atoms
c) 3.01 x 1023 Al atoms
2.How many moles of S in 1.8 x 1024 S atoms
a) 1.0 mole S atoms
b) 3.0 mole S atoms
c) 1.1 x 1048 mole S atoms
Practice problems (round to 3 sig. figs.)
 How many molecules of CO2 are in
4.56 moles of CO2? 2.75 x 1024 molecules
 How many moles of water is 5.87 x 1022
molecules?
0.0975 mol (or 9.75 x 10-2)
 How many atoms of carbon are in
1.23 moles of C6H12O6? 4.44 x 1024 atoms C
 How many moles is 7.78 x 1024 formulaunits of MgCl2?
12.9 moles
Avogadro’s Number as Conversion
Factor
6.02 x 1023 particles
1 mole
or
1 mole
6.02 x 1023 particles
Note that a particle could be an atom OR a molecule!
Types of questions
• How many oxygen atoms in the
following?
3 atoms of oxygen
CaCO3
Al2(SO4)3
12 (3 x 4) atoms of oxygen
• How many ions in the following?
CaCl2
3 total ions (1 Ca2+ ion and 2 Cl1- ions)
NaOH
2 total ions (1 Na1+ ion and 1 OH1- ion)
Al2(SO4)3 5 total ions (2 Al3+ + 3 SO42- ions)
Measuring Moles
 Remember relative atomic mass?
- The amu was one twelfth the mass of a
carbon-12 atom.
 Since the mole is the number of atoms in
12 grams of carbon-12,
 the decimal number on the periodic table
is also the mass of 1 mole of those atoms
in grams.
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Gram Atomic Mass (GAM)
 Equals the mass of 1 mole of an element in
grams , or, to the numerical value of the
average atomic mass (get from periodic table)
 12.01 grams of C has the same number of
pieces as 1.008 grams of H and 55.85 grams of
iron.
 We can write this as: 12.01 g C = 1 mole C
(this is also the molar mass)
 We can count things by weighing them.
•
1 mole of C atoms
=
12.0 g
1 mole of Mg atoms
=
24.3 g
1 mole of Cu atoms
=
63.5 g
Other Names Related to Molar Mass
Learning Check!
• Molecular Mass/Molecular Weight: If you have a single
molecule, mass is measured in amu’s instead of grams. But, the
molecular mass/weight is the same numerical value as 1 mole of
molecules. Only the units are different. (This is the beauty of
Find the molar mass
(usually we round to the tenths place)
Avogadro’s Number!)
• Gram Formula Mass/Formula Weight: Same goes for
compounds. But again, the numerical value is the same. Only the
A. 1 mole of Br atoms =
B. 1 mole of Sn atoms =
79.9 g/mole
118.7 g/mole
units are different.
• THE POINT: You may hear all of these terms which mean
the SAME NUMBER… just different units
What about compounds?
 in 1 mole of H2O molecules there are two
moles of H atoms and 1 mole of O atoms
(think of a compound as a molar ratio)
 To find the mass of one mole of a
compound
–determine the number of moles of the
elements present
–Multiply the number times their mass
(from the periodic table)
–add them up for the total mass
Calculating Gram Formula Mass (GFM)
Calculate the formula mass of
magnesium carbonate, MgCO3.
24.3 g
+
12 g
+ 3 x (16.00 g) =
84.3 g
Thus, 84.3 grams is the formula mass
for MgCO3.
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Learning Check!
A. Molar Mass of K2O = ? Grams/mole
94.20 g/mol
B. Molar Mass of antacid Al(OH)3 = ?
Grams/mole
78.01 g/mol
Learning Check
Prozac, C17H18F3NO, is a widely used
antidepressant that inhibits the uptake of
serotonin by the brain. Find its molar
mass.
C. Molar Mass of Al2(SO4)3 = ? Grams/mole
309.36 g/mol
342.14 g/mol
Calculations with Molar Mass
The mole road map shows
the conversion factors
needed to interconvert
between mass, number of
particles, and volume of a
gas at STP. The mole is the
at the center of any
calculation involving
molar mass
Grams
Moles
Converting Moles and Grams
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 = 27.0 g Al
2. Conversion factors for Al
27.0g Al
1 mol Al
3. Setup
or
1 mol Al
27.0 g Al
3.00 moles Al
x
27.0 g Al
1
1 mole Al
Answer
= 81.0 g Al
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Learning Check!
The artificial sweetener aspartame (NutraSweet) formula C14H18N2O5 is used to sweeten
diet foods, coffee and soft drinks. How many
moles of aspartame are present in 225 g of
aspartame?
Calculations
use molar mass
use Avogadro’s number
Grams
Moles
particles
Everything must go through
Moles!!!
Learning Check!
How many atoms of K are present in
78.4 g of K?
Atoms/Molecules and 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.
• That’s like asking 2 dozen cookies weigh
how many ounces if 1 cookie weighs 4 oz?
You have to convert to dozen first!
Atoms/Molecules and Grams
How many atoms of Cu are present in
35.4 g of Cu?
35.4 g Cu X
1
1 mol . X 6.02 X 1023 atoms Cu
63.5 g Cu
1 mol Cu
= 3.4 X 1023 atoms Cu
Learning Check!
What is the mass (in grams) of 1.20 X 1024
molecules of glucose (C6H12O6)?
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Examples
Learning Check!
 How much would 2.34 moles of
carbon weigh? 28.1 grams C
 How many moles of magnesium is
24.31 g of Mg? 1 mol Mg
 How many atoms of lithium is 1.00 g
of Li?
8.72 x 1022 atoms of Li
 How much would 3.45 x 1022 atoms of
U weigh?
13.6 grams U
How many atoms of O are present in
78.1 g of oxygen?
78.1 g O2 1 mol O2 6.02 X 1023 molecules O2 2 atoms O
32.0 g O2 1 mol O2
1 molecule O2
Any
Questions?
What now?
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