Chemistry I
Mr. Trotts
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The Mole
Summer 2008
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6.02 X 10
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What we’re going to Learn
1. The concept of the mole
2. Given moles calculate number of particles
3. Be able to calculate molecular mass and
gram formula mass and weight
4. Be able to convert moles to mass,
particles, and volume and convert mass to
moles, volume, and particles
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5. Calculate the percent composition of a
compound by mass of each element.
and
6. Calculate both the empirical (simplest)
formula and molecular formula of a
compound.
NOTE: As we encounter Learning Checks
write the answers down for a daily grade
STOICHIOMETRY
- the study of the
quantitative
aspects of
chemical
reactions.
- Combines mole
problems with
balanced
equations
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The Mole
• A counting unit
• Similar to a dozen, except instead
of 12, it’s 602 billion trillion
602,000,000,000,000,000,000,000
• 6.02 X 1023 (in scientific notation)
• This number is named in honor of
Amedeo Avagadro (1776 – 1856),
who studied quantities of gases
and discovered that no matter what
the gas was, there were the same
number of molecules present
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.
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Everybody Has Avogadro’s
Number!
But Where Did it Come From?
• It was NOT just picked!
It was MEASURED.
• One of the better
methods of measuring
this number was the
Millikan Oil Drop
Experiment
• Since then we have
found even better ways
of measuring using xray technology
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Learning Check
Suppose we invented a new collection unit
called a rapp. One rapp contains 8 objects.
1. How many paper clips in 1 rapp?
a) 1
b) 4
c) 8
2. How many oranges in 2.0 rapp?
a) 4
b) 8
c) 16
3. How many rapps contain 40 gummy bears?
a) 5
b) 10
c) 20
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Solution
Suppose we invented a new collection unit called
a mep. One mep contains 8 objects.
A. How many paper clips in 1 mep?
3) 8
B. How many oranges in 2.0 meps?
3) 16
C. How many meps contain 40 gummy bears?
1) 5
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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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 “molecules”
(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
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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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Example: How many moles of Calcium are in
2.408 x 1024 calcium atoms?
2.408 x 1024 Ca atoms x 1 mole Ca/6.02 x 1023 atoms Ca =
4.0 x 101 moles Ca
Example: How many atoms of Calcium are in 40
moles of Calcium
40 moles Ca x 6.02 x 1023 atoms Ca/1 mole Ca = 2.408 x 1024 atoms
Ca
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Learning Check
4. Number of atoms in 0.500 mole of Al
a) 500 Al atoms
b) 6.02 x 1023 Al atoms
c) 3.01 x 1023 Al atoms
5.Number of 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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Solution
1. Number of atoms in 0.500 mol of Al
3) 3.01 x 1023 Al atoms
0.500 mol Al x 6.02 x 1023 Al atoms
1 mol Al
2. Number of moles of S if a sample of S contains 4.50
x 1024 S atoms
2) 3.0 mole S atoms
4.50 x 1024 S atoms x
1 mol S
6.02 x 1023 S atoms
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Molar Mass
• The Mass of 1 mole (in grams)
• Equal to the numerical value of the average
atomic mass (get from periodic table)
1 mole of C atoms
=
12.0 g
1 mole of Mg atoms
=
24.3 g
1 mole of Cu atoms
=
63.5 g
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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!)
• 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
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Learning Check!
Find the molar mass
(usually we round to the tenths place)
6. 1 mole of Br atoms =
7. 1 mole of Sn atoms =
79.9 g/mole
118.7 g/mole
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Molar Mass of Molecules and
Compounds
Mass in grams of 1 mole equal numerically to
the sum of the atomic masses
1 mole of CaCl2
= 111.1 g/mol
1 mole Ca x 40.1 g/mol
+ 2 moles Cl x 35.5 g/mol
1 mole of N2O4
= 111.1 g/mol CaCl2
= 92.0 g/mol
Learning Check!
8. Molar Mass of K2O = ? Grams/mole
9. Molar Mass of antacid Al(OH)3 = ?
Grams/mole
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Solution
A. 1 mole of K2O
= 94.2 g
2 K x 39.1 g/mole + 1 O x 16.0 g/mole
B. 1 mole of antacid Al(OH)3
= 78.0 g
1 Al x 27.0 g/mole + 3 O x 16.0 g/mole
+ 3 x 1.0
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Learning Check
10. Prozac, C17H18F3NO, is a widely used
antidepressant that inhibits the uptake of
serotonin by the brain. Find its molar
mass.
Complete the handout GRAM FORMULA MASS
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Solution
Prozac, C17H18F3NO, is a widely used
antidepressant that inhibits the uptake of serotonin
by the brain. It has a molar mass of
309 g/mole
17C (12.0) + 18H (1.0) + 3F (19.0) + 1N (14.0) + 1 O
(16.0)
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Calculations with Molar Mass
molar mass
Grams
Moles
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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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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 3.00 moles Al
Answer
x
27.0 g Al
1 mole Al
= 81.0 g Al
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Learning Check!
11. 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?
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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
molar mass
Grams
Avogadro’s number
Moles
particles
Everything must go through
Moles!!!
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Atoms/Molecules and Grams
How many atoms of Cu are
present in 35.4 g of Cu?
35.4 g Cu
1 mol Cu
63.5 g Cu
6.02 X 1023 atoms Cu
1 mol Cu
= 3.4 X 1023 atoms Cu
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Molar Mass Factors
Methane CH4 known as natural gas is used in gas
cook tops and gas heaters. Express the molar
mass of methane in the form of conversion factors.
Molar mass of CH4 =
16.0 g CH4
1 mole CH4
and
16.0 g
1 mole CH4
16.0 g CH4
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Molar Mass Factors
Methane CH4 known as natural gas is used in gas
cook tops and gas heaters. Express the molar
mass of methane in the form of conversion factors.
Molar mass of CH4 =
16.0 g CH4
1 mole CH4
and
16.0 g
1 mole CH4
16.0 g CH4
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Learning Check
12. Acetic acid CH3COOH is the acid in vinegar . It
has a molar mass of 60.0 g/mole.
1 mole of acetic acid =
1 mole acetic acid
g acetic acid
or
____________
g acetic acid
1 mole acetic acid
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Solution
Acetic acid CH3COOH is the acid in vinegar . It has
a molar mass of 60.0 g/mole.
1 mole of acetic acid =
1 mole acetic acid
60.0 g acetic acid
or
60.0 g acetic acid
60.0 g acetic acid
1 mole acetic acid
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Learning Check!
13. How many atoms of K are present
in 78.4 g of K?
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Learning Check!
14. What is the mass (in grams) of 1.20 X
1024 molecules of glucose (C6H12O6)?
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More mole equivalents
1 mole of a gas at standard temperature
(0 Celsius) and pressure (1 atmosphere)
occupies 22.4 liters by volume
Example: 2 moles of oxygen at STP would
occupy 2 moles x 22.4L/1 mole or 44.8L
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Learning Check!
15. 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
Complete the handout Mixed Mole Problems
Given 1 mole = 6.02 x 1023 particles = gfm = 22.4L @ STP
Complete Atoms Worksheet #2 (The Mole)
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Percent Composition
16. What is the percent carbon in C5H8NO4
(the glutamic acid used to make MSG
monosodium glutamate), a compound used
to flavor foods and tenderize meats?
a) 8.22 %C
b) 24.3 %C
c) 41.1 %C
Complete Percentage
Composition Worksheet
Chemical Formulas of Compounds
• Formulas give the relative numbers of atoms or
moles of each element in a formula unit - always a
whole number ratio (the law of definite
proportions).
NO2
2 atoms of O for every 1 atom of N
1 mole of NO2 : 2 moles of O atoms to every 1
mole of N atoms
• If we know or can determine the relative number
of moles of each element in a compound, we can
determine a formula for the compound.
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Types of Formulas
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• Empirical Formula
The formula of a compound that
expresses the smallest whole number ratio
of the atoms present.
The Ionic formula is always the empirical
formula
• Molecular Formula
The formula that states the actual number
of each kind of atom found in one molecule
of the compound.
To obtain an Empirical Formula
1. Determine the mass in grams of each
element present, if necessary.
2. Calculate the number of moles of each
element.
3. Divide each by the smallest number of
moles to obtain the simplest whole
number ratio.
4. If whole numbers are not obtained* in
step 3), multiply through by the smallest
number that will give all whole numbers
* Be
careful! Do not round off numbers prematurely
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A sample of a brown gas, a major air pollutant,
is found to contain 2.34 g N and 5.34g O.
Determine a formula for this substance.
require mole ratios so convert grams to moles
moles of N = 2.34g of N = 0.167 moles of N
14.01 g/mole
moles of O = 5.34 g = 0.334 moles of O
16.00 g/mole
N 0.167 O 0.334  NO 2
Formula: N O
0.167
0.334
0.167
0.167
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Empirical Formula from % Composition
A substance has the following composition by
mass: 60.80 % Na ; 28.60 % B ; 10.60 % H
What is the empirical formula of the substance?
Consider a sample size of 100 grams
This will contain 28.60 grams of B and
10.60 grams H
Determine the number of moles of each
Determine the simplest whole number ratio
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Empirical Formulas from Percent Composition
• Given a compound that is 32.4% Na, 22.5%
S, and 45.1% O
• 32.4gNa x 1 mole/23.0g = 1.41 mole Na
• 22.5gS x 1 mole/32g = .70 mole S
• 45.1gO x 1 mole/16g = 2.82 mole O
• Na = 1.41/.70 = 2
• S = .70/.70 = 1
• O = 2.82/.70 = 4 therefore = Na2SO4
• Complete the Determining Empirical
Formula worksheet
Calculation of the Molecular Formula
17. A compound has an empirical
formula of NO2. The colourless liquid,
used in rocket engines has a molar
mass of 92.0 g/mole. What is the
molecular formula of this substance?
N = 14.0g/mole
O2 = 2 x 16 g/mole = 32g
NO2 = 46g
92.0g/46g = 2
2 x (NO2) = N2O4
Complete Determining Molecular
Formulas Worksheet
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