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Unit 9: Math of Chemistry
“Chemical Quantities”
Part I
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The Mole
Lesson # 9.1: 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.
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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.
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How do we measure items?
 You can measure mass ….
 or volume…..
 or you can count pieces……
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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.
Similar Words for an amount – Counting Units
 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
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!
Mole is abbreviated mol (gee, that’s a lot quicker to write, huh?)
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Mole is abbreviated mol (gee, that’s a lot quicker to write, huh?)
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Just How Big is a Mole?
• 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.
Learning Check
Suppose we invented a new collection unit called a comet. One comet contains 8
objects.
1. How many paper clips in 1 comet?
a) 1
b) 4
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
c) 20
What are Representative Particles?
 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)
A Mole of Particles
Contains 6.02 x 1023 particles
= 6.02 x 1023 C atoms
= 6.02 x 1023 H2O molecules
= 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
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!
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Learning Check
1. How many atoms of Al are in 0.500 mole of Al
a) 500 Al atoms
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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
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Types of questions
• How many oxygen atoms in the following?
CaCO3
Al2(SO4)3
• How many ions in the following?
CaCl2
NaOH
Al2(SO4)3
Practice problems (round to 3 sig. figs.)
 How many molecules of CO2 are in
4.56 moles of CO2?
 How many moles of water is 5.87 x 1022 molecules?
 How many atoms of carbon are in
1.23 moles of C6H12O6?
 How many moles is 7.78 x 1024 formula- units of MgCl2?
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 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.
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.
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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
• 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
Avogadro’s Number!)
• Gram Formula Mass/Formula Weight: Same goes for compounds. But again, the
numerical value is the same. Only the units are different.
• THE POINT: You may hear all of these terms which mean the SAME NUMBER… just
different units
Learning Check!
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Learning Check!
Find the molar mass
(usually we round to the tenths place)
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)
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
C. Molar Mass of Al2(SO4)3 = ? Grams/mole
342.14 g/mol
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Learning Check
Prozac, C17H18F3NO, is a widely used antidepressant that inhibits the uptake of
serotonin by the brain. Find its molar mass.
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Calculations with Molar Mass
molar mass
Grams
Moles
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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
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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
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3.00 moles Al
? g Al
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1. Molar mass of Al
1 mole Al = 27.0 g Al
2. Conversion factors for Al
27.0g Al
1 mol Al
or
1 mol Al
27.0 g Al
3. Setup
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3.00 moles Al
x 27.0 g Al
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1 mole Al
Answer
= 81.0 g Al
Learning Check!
The artificial sweetener aspartame (Nutra-Sweet) formula C14H18N2O5 is used to
sweeten diet foods, coffee and soft drinks. How many moles of aspartame are
present in 225 g of aspartame?
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!
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Calculations
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Grams
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use molar mass
Moles
use Avogadro’s number
particles
Everything must go through Moles!!!
Atoms/Molecules and Grams
How many atoms of Cu are present in 35.4 g of Cu?
Learning Check!
How many atoms of K are present in 78.4 g of K?
Learning Check!
What is the mass (in grams) of 1.20 X 1024 molecules of glucose (C6H12O6)?
Learning Check!
How many atoms of O are present in 78.1 g of oxygen?
Examples
 How much would 2.34 moles of carbon weigh?
 How many moles of magnesium is 24.31 g of Mg?
 How many atoms of lithium is 1.00 g of Li?
 How much would 3.45 x 1022 atoms of U weigh?
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Percent Composition
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