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Mole Calculations
Slide 3 / 158
Table of Contents
Click on the topic to go to that section
· Avogadro's Number
· Molar Mass
· Molar Volume
· Percent Composition
· Emperical Formula
Slide 4 / 158
Avogadro's Number
Return to
Table of
Contents
Slide 5 / 158
Atomic Mass
Recall an atom's atomic mass is equal to the number of
protons plus the number of neutrons in the atom.
Atomic Number
or number of
protons (Z)
Average
Atomic Mass
in amu
6
C
12.01
The unit for atomic mass is amu.
Carbon-12 has 6 protons and 6 neutrons.
One amu is equal to 1/12 the mass of carbon-12 or
approximately the mass of one proton or neutron
mass of 1 proton = 1 amu
mass of 1 neutron = 1 amu
Slide 6 / 158
Atomic Mass
What if you wanted to measure the mass of one atom in the
laboratory? Would it be possible?
A single atom has a very small mass.
One carbon atom has a mass of about 2.0 x 10-23 grams.
Slide 7 / 158
The Mole
It takes a lot of atoms to give us enough material to directly
measure in a lab.
Hydrogen has a mass of 1 amu. How many atoms of hydrogen
would be needed to make a 1 gram sample of hydrogen?
602,200,000,000,000,000,000,000
The amount 6.02x1023 is called Avogadro's number or amole.
How big is a mole?
Slide 8 / 158
Calculating Avogadro's Number
The atomic mass of one carbon atom is 12.01 amu or 2x10-23 g.
How many carbon atoms would it take to get 12.01 grams of
carbon?
Givens:
mass of 1 carbon atom = 2x10-23 g
total mass of carbon atoms = 12.01 g
2x10-23 g x
? of atoms = 12.01 g
? of atoms = 12.01 g
2x10-23 g
? of atoms = 6.02 x 1023 atoms
Slide 9 / 158
Holy Mole-y!
1 mole of pennies could
be distributed to all the
currently-living people of
the world so that they
could spend a million
dollars per hour every
hour (day and night) for
the rest of their lives!
One mole of marbles would cover the
entire Earth (oceans included) for a
depth of two miles!
If you were able to count at the rate
of 1 million numbers a second, it
would take about 20 billion years to
count out one mole!
Slide 10 / 158
The Mole
A mole is just a grouping of numbers...like dozen, ream, etc.
A dozen means 12 of something.
A mole means 6.02 x 1023 of something.
Common Grouping Quantities
1 dozen = 12
1 gross =144
1 ream = 500
1 mole = 6.02 x 1023
Slide 11 / 158
1
How many eggs are in two dozen eggs?
A
12
B
24
C
0.0833
D
2
E
6.02 x 1023
Slide 12 / 158
2
How many eggs are in half a dozen eggs?
A
12
B
24
C
6
D
0.5
E
6.02 x 1023
Slide 13 / 158
3 How many particles of sand are in 0.5 moles of
sand?
A
1.5 x 1023
B
3.01 x 1023
C
6.02 x 1023
D
1.2 x 1024
E
6.02 x 1024
1 mole = 6.02 x 1023
Slide 14 / 158
4 How many pieces of gold dust are in 2 moles of
gold dust?
A
1.5 x 1023
B
3.01 x 1023
C
6.02 x 1023
D
1.2 x 1024
E
6.02 x 1024
1 mole = 6.02 x 1023
Slide 15 / 158
5 How many dozen eggs are in a container of 6 eggs?
A
4
B
0.5
C
1
D
2
E
6.02 x 1023
Slide 16 / 158
6 How many dozen eggs are in a container of 18
eggs?
A
1.5
B
3
C
0.67
D
2
E
6.02 x 1023
Slide 17 / 158
Dimensional Analysis
How many eggs are in 47 dozen eggs?
The number 47 makes this question a bit more difficult to
calculate mentally.
In chemistry, it is common practice to use equalities and
dimensional analysis to solve problems.
Equalities are two quantities that are identical in value but use
different units. Examples of equalities include:
1 dozen = 12
1 mole = 6.02x1023
1 meter = 1000 millimeters
1 hour = 60 minutes
Slide 18 / 158
Dimensional Analysis
How many eggs are in 47 dozen eggs?
To solve the above problem:
1. Choose the equality with the correct dimensions or units:
1 dozen eggs = 12 eggs
2. Turn the equality into a fraction.
Since 1 dozen and 12 are equal quantities 1 dozen = 12
can also be written as a fraction:
1 dozen eggs
12 eggs
=
12 eggs
1 dozen eggs
=
= 1
Slide 19 / 158
Dimensional Analysis
How many eggs are in 47 dozen eggs?
3. Start with your given:
47 dozen
Use dimensional analysis! Choose the fraction that has the
appropriate dimensions or units to convert from your given
dimensions to your unknown dimensions.
1 dozen
12 eggs
or
12 eggs
unknown dimension
is in the numerator
1 dozen
4. Multiply your given by your chosen fraction and cancel out
the units:
47 dozen x 12 eggs = 564 eggs
1 dozen
Slide 20 / 158
7 The Milky Way Galaxy may have up to 400 billion
(4 x 1014 stars). How many moles of stars does it
have?
A
1.5 x 109
B
6.7 x 10-10
C
10
D
0.5
E
6.02 x 1023
1 mole of stars = 6.02 x 1023 stars
6.02 x 1023 stars
1 mole of stars
or
6.02 x 1023 stars
1 mole of stars
Slide 21 / 158
8 Mathematicians estimate Earth's beaches
contain nearly 5.6 x 1021 grains of sand. How
many moles of sand are on Earth's beaches?
A
1.5
B
9.3 x 10-3
C
10.0
D
107.5
E
6.02 x 1023
1 mole = 6.02 x 1023
Slide 22 / 158
Measuring Matter with Moles
The mole is the SI unit for measuring the amount of
particles in a chemical substance.
One mole (mol) of a substance is 6.02 x 1023 representative
particles of that substance.
1 mole of Carbon
Slide 23 / 158
Measuring Matter with Moles
How many moles of Gold are there in a sample
containing 3.01 x 1023 atoms of Gold?
1 mol = 6.02 x1023 atoms
Given quantity: 3.01 x 1023 Au atoms
Equalities:
1 mol Au
6.02 x1023 Au atoms
or
6.02 x1023 Au atoms
1 mol Au
Solve and cancel units:
3.01 x 1023 Au atoms x
1 mol Au
6.02 x1023 Au atoms
= 0.5 mol Au
Slide 24 / 158
9 How many atoms of titanium are in a sample
containing 0.5 mole of titanium?
A
1.5 x 1023
B
3.01 x 1023
C
6.02 x 1023
D
1.2 x 1024
E
6.02 x 1024
1 mol = 6.02 x 1023
Slide 25 / 158
10How many atoms of sodium are in a sample
containing 2.0 moles of sodium?
A
1.5 x 1023
B
3.01 x 1023
C
6.02 x 1023
D
1.2 x 1024
E
6.02 x 1022
1 mol = 6.02 x 1023
Slide 26 / 158
11
How many moles of potassium are in a sample
containing 3.01 x 1023 atoms of potassium?
A
1.0
B
2.0
C
0.5
D
0.75
E
6.02 x 1024
1 mol = 6.02 x 1023
Slide 27 / 158
12 How many moles of potassium are in a sample
containing 1.2 x 1024 atoms of potassium?
A
0.25 mol
B
0.50 mol
1.0 mol
C
D
E
2.0 mol
3.0 mol
1 mol = 6.02 x 1023
Slide 28 / 158
13 How many moles of tungsten atoms are there in a
sample containing 1.8 x 1024 atoms of tungsten?
A
0.33 mol
B
0.50 mol
C
1.0 mol
D
1.5 mol
E
3.0 mol
1 mol = 6.02 x 1023
Slide 29 / 158
14 How many moles of silver are there in a pure
sample containing 1.5 x 1023 atoms of silver?
A
0.10 mol
B
0.25 mol
C
0.50 mol
D
1.0 mol
E
1.5 mol
1 mol = 6.02 x 1023
Slide 30 / 158
15 How many atoms are there in 5.00 mol of hafnium?
A
6.02 x1023 atoms
B
1.20 x 1023 atoms
C
1.20 x 1022 atoms
D
3.43 x 1023 atoms
E
3.01 x 1024 atoms
1 mol = 6.02 x 1023
Slide 31 / 158
Measuring Matter with Moles
A mole of ANY substance contains Avogadro’s number of
representative particles, or 6.02 x 1023 representative particles.
1 mole of C atoms = 6.02 X 1023 atoms of C
1 mole of bicycles = 6.02 x 1023 bicycles
The term representative particle refers to the species or types of
particles in the substance
For Example:
atoms, molecules, formula units, ions
Slide 32 / 158
Measuring Matter with Moles
laboratory sample size
molecule of H2O
H
O
H
18.0 amu
Avagadro's
number of
molecules
(6.02 x1023 )
1 mol H2O
(18.0 g)
23
In 1 mole of carbon there are 6.02 x 10
carbon atoms.
23 water molecules.
In 1 mole of water there are 6.02 x 10
In 1 mole of NaCl there are 6.02 x 1023 formula units.
Slide 33 / 158
16 Formula units refer to particles of __________
compounds and molecules refer to particles of
__________ compounds.
A
molecular/covalent, ionic
B
ionic, molecular/covalent
C
atoms, molecular
D
atoms, ionic
E
ionic, atomic
Slide 34 / 158
17 How many molecules are there in 2.10 mol CO2 ?
A
3.79 x 10 24
B
3.49 x 10-24
C
1.05 x 10 -23
D
2.53 x 1024
E
1.26 x 1024
1 mol CO2 = 6.02 x 1023 CO2 molecules
Slide 35 / 158
18 How many moles of helium atoms are there in a
pure sample containing 6.02 x 1024 atoms of
helium?
A
2.0 mol
B
4.0 mol
C
6.0 mol
D
10.0 mol
E
2.4 x 1024 mol
1 mol He = 6.02 x 1023 He atoms
Slide 36 / 158
19 How many moles of NaCl are there in a pure
sample containing 6.02 x 1023 formula units of
sodium chloride, NaCl?
A
1.0 mol
B
2.0 mol
C
4.0 mol
D
6.0 mol
E
6.02 x 1023 mol
1 mol NaCl = 6.02 x 1023 NaCl formula units
Slide 37 / 158
20 How many formula units of Pb(NO3)2 are there in
0.5 mole of Pb(NO3)2?
A
0.5 formula units
B
2.0 formula units
C
3.01 x 1023 formula units
D
1.2 x 10 24 formula units
E
6.02 x 1023 formula units
1 mol Pb(NO3)2 = 6.02 x 1023 Pb(NO3)2 formula units
Slide 38 / 158
Real World Application
Calcium deficiency can cause osteoporosis
(weakening of the bones). The minimum
amount of calcium in 1 mL of blood should be
around 1.3 x 1018 atoms.
A patient has her blood tested and the lab
finds there are 3 x 10-5 moles of calcium in
the blood. Is this patient at risk for
osteoporosis?
(6.02 x 1023 atoms/mole) x (3 x 10-5 moles) = 1.8 x 1023 atoms Ca
slide for answer
This exceeds the normal range so they are OK!
Slide 39 / 158
Review: Ionic and Molecular Compounds
The total number of atoms or ions in a compound depends on
electronegativity and bonding.
Ionic Compounds
NaCl
1 Na ion
+
1 Cl ion
-
K2CrO4
2 K+ ions
1 CrO42- ion
Sn(OH)2
1 Sn 2+ ion
2 OH- ions
Molecular Compounds
H 2O
2 hydrogen
atoms
1 oxygen
atom
C 6H 6
6 carbon
atoms
6 hydrogen
atoms
Slide 40 / 158
Review: Ionic and Molecular Compounds
Chemicals are composed of more than one molecule or
formula unit.
To indicate more than one molecule or formulat unit, add a
coefficient in front of the compound.
Example: six molecules of carbon dioxide = 6CO2.
How many atoms of carbon and oxygen are in 6CO2?
6 atoms of carbon and 12 atoms of oxygen
Move to reveal answer
Slide 41 / 158
Review: Ionic and Molecular Compounds
Ionic Compounds - Fill in
3NaCl
3 Na+ ions
__
__
3 Cl- ions
2 K2CrO4
__K+ ions
__CrO42- ions
4Sn(OH)2
__Sn 2+ ions
__OH- ions
Molecular Compounds - Fill in
6 H 2O
__hydrogen
atoms
__oxygen
atom
C 6H 6
__carbon
atoms
__hydrogen
atoms
Slide 42 / 158
Converting Moles to Number of Particles
molecule of H2O
laboratory sample size
H
O
H
18.0 amu
Avagadro's
number of
molecules
(6.02 x10 )
23
1 mol H2O
(18.0 g)
In one mole of water molecules there are:
H 2O
2 moles of
hydrogen atoms
2 x 6.02x1023 atoms
of hydrogen
1 mole of
oxygen atoms
1 x 6.02x1023 atoms
of oxygen
Slide 43 / 158
Converting Moles to Number of Particles
In 3 moles of sodium chloride formula units there are:
3NaCl
3 moles of
Na+ ions
3 moles of
Cl- ions
Slide 44 / 158
21
How many hydrogen atoms are in six molecules of
ethylene glycol, the major component in antifreeze?
The formula for ethylene glycol is: HOCH CH OH.
2
A
6 atoms of H
B
36 atoms of H
C
6 x 6.02 x 1023 atoms of H
D
36 x 6.02 x 1023 atoms of H
E
6.02 x 1023 atoms of H
2
Slide 45 / 158
22
How many CO32- ions are in one formula unit of
CaCO3?
A
1 ion
B
3 ions
C
6 x 6.02 x 1023 ions
D
36 x 6.02 x 1023 ions
E
6.02 x 1023 ions
Slide 46 / 158
23 How many K+ ions are there in two formula units of
potassium hydroxide, 2KOH?
A
1 K+ ion
B
2 K+ ions
C
1 x 6.02 x1023 ions of K+
D
2 x 6.02 x 1023 ions of K+
E
3.12 x 1023 ions of K+
Slide 47 / 158
24 How many sulfide ions (S2- ) are there in 2.0
moles of ammonium sulfide,(NH4 )2 S?
A
2.0 ions
B
1.2 x 1024 ions
C
2.4 x 1024 ions
D
6.02 x 1023 ions
E
none
*Use two equalities to solve:
1 mol (NH4)2S = 6.02 x 1023 (NH4)2S formula units
1 (NH4)2S formula unit = 1 S2- ion
Slide 48 / 158
25 How many ammonium ions (NH4 + ) are there in
2.0 moles of ammonium sulfide, (NH4 )2 S?
A
2.0 ions
B
1.2 x 1024 ions
C
2.4 x 1024 ions
D
6.02 x 10 23 ions
E
8.0 ions
*Use two equalities to solve:
1 mol (NH4)2S = 6.02 x 1023 (NH4)2S formula units
1 (NH4)2S formula unit = 2 NH4+ ions
Slide 49 / 158
26
How many moles of O are in 2.4 X 10
molecules of SO ?
24
3
Slide 50 / 158
Real World Application
Hemoglobin is a protein that carries O2
around your body. The formula for it is
approximately
C2800H4800N3200O800S8Fe4.
If a patient has 2 x 1016 atoms of Fe,
how many moles of Hb would be
present?
moles of Fe: n = N/Na --> (2 x 1016 atoms)/(6.02 x 1023 atoms/n)= 3.3 x 10-7 moles Fe
-7
moles of Hb: There are 1 Hb/4 Feslide
--> (3.3
moles Fe)/(4 moles of Fe/Hb)
forx 10
answer
= 8.2 x 10-8 moles Hb
Slide 51 / 158
Molar Mass
Return to
Table of
Contents
Slide 52 / 158
Mass of Compounds
The total mass of a chemical compound can be
calculated by using the masses on the Periodic Table.
Example: Calculate the mass of the compound
Magnesium Chloride (MgCl2)
Mg =
24.305 amu
2Cl = + (2)35.453 amu
Mass of MgCl2
95.211 amu
Slide 53 / 158
Masses of Elements/Compounds
Units
Atomic mass
Formula mass or
Formula weight (FW)
Molecular mass or
Molecular weight
used for elements
(like F, V, etc..) only
amu
used for ionic
compounds (like
NaCl, MgO, etc..) only
amu
used for molecular
compounds (like
CO2, H2O, etc..) only
amu
Slide 54 / 158
27 What is the formula weight of sodium bromide?
A
79.904 amu
B
102.894 amu
C
205.780 amu
D
300.120 amu
E
605.102 amu
Slide 55 / 158
28 What is the formula weight of Pb(NO3)2?
A
79.90 amu
B
102.89 amu
C
205.78 amu
D
331.34 amu
E
605.10 amu
Slide 56 / 158
29 What is the molecular mass of 3H2O2?
A
17 amu
B
34 amu
C
68 amu
D
102 amu
E
204 amu
Slide 57 / 158
Molar Mass (M)
A mole represents the number of
atoms it takes to convert from a
single atomic mass in amu to the
same mass in grams.
The mass in grams of one mole of any substance is its
molar mass (M). Each of the bars shown below equals
one mole of a pure element.
1 mole of Copper
= 63.546 g
1 mole of Aluminum
= 26.982 g
Slide 58 / 158
Molar Mass (M)
One mole of carbon, sulfur and silver are shown.
1 mol of sulfur
atoms 32.0 g of S
1 mol of Carbon
atoms = 12.0 g
1 mol of silver
= 107.9 g of Ag
Slide 59 / 158
How is the atomic mass of an element
related to the molar mass?
Average atomic mass of 1 atom of Kr = 83.8 amu.
1 mole (6.02 x 1023 atoms) of Kr = 83.8 grams.
The atomic mass of an element expressed in grams is
the mass of one mole or molar mass (M) of the element.
1 mole of Kr = 83.8 grams
Molar mass of Kr = 83.8 grams or 83.8 g/mol
1 mol
Slide 60 / 158
Molar Mass
The molar mass of an element or compound can be used to
convert directly from masses in amu to masses in grams.
Units
Gram atomic mass
used for elements
(like F, V, etc..) only
grams
Gram formula mass or
used for ionic
compounds (like
NaCl, MgO, etc..) only
grams
Formula weight (FW)
Gram molecular mass or
Molecular weight
used for molecular
compounds (like
CO2, H2O, etc..) only
grams
Slide 61 / 158
Molar Mass
To convert from moles to mass, or vice versa, use
dimensional analysis.
How many moles of Helium are in 8.0 grams of Helium?
Molar mass of He = 4.0 g/mol
Given quantity: 8.0 g He
Equalities:
1 mol He
4.0 g He
or
4.0 g He
1 mol He
Solve and cancel units:
8.0 g He x
1 mol He
4.0 g He
=
2 mol He
Slide 62 / 158
30
How many moles are in a 64-gram sample of
pure sulfur?
*Molar mass (M) of S = ? g/mol
Slide 63 / 158
31
How many moles are in a 72-gram sample of pure
magnesium?
*Molar mass (M) of Mg = ? g/mol
Slide 64 / 158
32
What is the mass, in grams, of 2 moles of carbon?
Slide 65 / 158
33
What is the mass, in grams, of 5 moles of iron?
Slide 66 / 158
34
How many grams is 2.0 mol neon atoms?
Slide 67 / 158
Diatomic Molecules
(Recall the seven diatomic molecules: HONClBrIF)
The molar mass of these molecules will be twice their
atomic mass.
Examples:
M of hydrogen gas: H = (2 x 1) = 2 g/mol
2
M of bromine liquid: Br = (2 x 79.9) = 159.8 g/mol
2
M of fluorine molecules: F2 = (2 x 19) = 38 g/mol
Slide 68 / 158
35
How many grams is 1.0 mole of hydrogen
molecules?
Slide 69 / 158
36
How many grams is 0.50 mol of oxygen molecules?
Slide 70 / 158
Molar Mass of a Compound
The molar mass of a compound is the sum of the molar
masses of all the elements in the compound.
To calculate the molar mass of a compound, find the number of
grams of each element in one mole of the compound. Then add
the masses of the elements in the compound.
32.065 g/mol + 3(16.000) g/mol = 80.650 g/mol
Molar mass of SO3 = 80.650 g/mol
Slide 71 / 158
Molar Mass of a Compound
Note the different molar masses of these two compounds.
180 g of glucose (C6 H12 O6 )
= 1 mole glucose
18 g of H2 O =
1 mole H2 O
Slide 72 / 158
[*]
37
What is the molar mass of K O, potassium oxide?
2
Slide 73 / 158
38 What is the molar mass of CaCO3 , calcium
carbonate found in eggshells?
A
50 amu
B
50 grams/mol
C
100 amu
D
100 grams/mol
Slide 74 / 158
39 What is the molar mass of carbon dioxide?
A
28 amu
B
28 grams/mol
C
44 amu
D
44 grams/mol
Slide 75 / 158
40 What is the molar mass of ammonia, NH3 ?
A
17 amu
B
17 grams/mol
C
45 amu
D
45 grams/mol
Slide 76 / 158
Summary of Molar Mass
Molar mass is the mass of 1 mole of a substance
(measured in g/mol).
The atomic mass will be the same number as the molar
mass (measured in amu).
The difference is that the atomic mass refers to only one
representative particle and molar mass refers to one mole
(6.02 x 10 ) of representative particles.
23
Slide 77 / 158
41 What is the mass of one formula unit of
NaCl?
A
17 amu
B
17 grams/mol
C
58.5 amu
D
58.5 grams/mol
Slide 78 / 158
42 What is the mass of one molecule of water?
A
18 amu
B
18 grams/mol
C
8 amu
D
8 grams/mol
Slide 79 / 158
43
The chemical formula of aspirin is C H O .
What is the mass of 0.200 moles of aspirin?
9
8
4
Slide 80 / 158
44 The molar mass of oxygen (O2 ) is:
A equal to the mass of one mole of oxygen atoms.
B
16.0 g/mol
C
32.0 g/mol
D none of the above
E equal to the mass of one oxygen atom.
Slide 81 / 158
45 There are more moles of CO2 in a 44 g sample of
carbon dioxide gas than there are moles of helium
atoms in a box containing 2 x 1023 atoms of He.
True
False
Slide 82 / 158
How many grams of iron are in a 68 gram sample of Fe2O3?
M of Fe2O3 = 160 g/mol
M of Fe = 56g/mol
69 g Fe2O3 x 1 mol Fe2O3 x 2 mol Fe x 56g Fe = 48 g Fe
160g Fe2O3
1 mol Fe2O3 1 mol Fe
Move to see answer
Slide 83 / 158
Molar Volume
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Table of
Contents
Slide 84 / 158
The Mole and the Volume of a Gas
The volume of a gas varies with
temperature and pressure. But
comparisons between gases can
be made by designating a standard
temperature and pressure (STP).
Slide 85 / 158
STP (Standard Temperature and Pressure)
Standard Temperature (T) is considered 0°C (273 K), the
temperature at which water freezes.
Standard Pressure (P) is considered 1 atmosphere (101.3 kPa),
or the pressure of the atmosphere at sea level.
At STP, 1 mole of gas occupies a volume of 22.4 liters (L)
V = 22.4 L
m
For the time being, we will treat all gases as if they are at STP.
Slide 86 / 158
The Mole and the Volume of a Gas
The volume occupied by one mole of gas is called the molar
volume and has the symbol, V . It is the same for all gases.
m
At STP; V = 22.4 liters (L).
m
1 mole of gas = 6.02 x 1023 particles = 22.4 L
Notice that this statement does not depend on the type of gas.
It's true of all gases.
Slide 87 / 158
The Mole and the Volume of a Gas
At STP; V = 22.4 liters (L).
m
This is true because in a gas the molecules are so far apart that
they take up almost no space...the volume of a gas is mostly
empty space, regardless of the type of gas.
So when it comes to volume (at STP) all gases are created equal.
1 mole of He gas occupies 22.4 L @STP
1 mole of HCl gas occupies 22.4 L @STP
Slide 88 / 158
46 Which of the following must be true about 2 moles of
H2 gas vs. 2 moles of CO2 gas at the same
temperature and pressure?
A Each sample will have the same density
The same # of atoms will be present in each
sample
C Each sample will have the same mass
D Each sample will occupy the same volume
E None of these are true
B
Slide 89 / 158
The Mole and the Volume of a Gas
At STP, 1 mole or, 6.02x 10 representative particles, of any
gas occupies a volume of 22.4 L. The quantity 22.4 L is called
the molar volume of a gas.
23
At STP, how many moles of CO2 are there in 11.2 L of CO2?
1 mole of gas = 22.4 L gas
Given quantity: 11.2 L of CO2
Equalities:
1 mol CO2
22.4 L CO2
or
22.4 L CO2
1 mol CO2
Solve and cancel units:
11.2 L CO2
x
1 mol CO2
22.4 L CO2
=
0.5 mol CO2
Slide 90 / 158
47
How many moles are there in 44.8 liters (at STP)
of fluorine gas?
* At STP 1 mol = 22.4 L
Slide 91 / 158
48
How many moles of atoms are there in 22.4 liters
(at STP) of Xenon?
Slide 92 / 158
49
What is the volume (in liters at STP) of 1.00 mole
of sulfur dioxide?
Slide 93 / 158
50
What is the volume (in liters at STP) of 2.50 moles
of carbon monoxide?
Slide 94 / 158
51
What is the volume (in liters at STP) of 4.00
moles of Nitrogen?
Slide 95 / 158
Real World Application
An inflated airbag requires 60 L of
nitrogen gas (N2) at STP in order to
protect the occupant of the vehicle.
How many moles of nitrogen gas
would need to be created in 40
milliseconds to inflate the airbag?
Slide 96 / 158
Mole Calculations
Sometimes multiple steps must be used in mole calculations.
To solve these problems use dimensional analysis and the
appropriate mole conversions.
Here's an example:
How many atoms of carbon are present in a 24 g sample
of pure carbon?
To solve convert from:
grams
moles
atoms
Slide 97 / 158
Mole Calculations
How many atoms of carbon are present in a 24 g sample?
Start with your given: 24 g C
Choose the correct equality to convert from grams to moles:
M of C = 12g/mol
1 mol C
12 g C
or
12 g C
1 mol C
Choose the correct equality to convert from moles to atoms:
1 mole = 6.02 x 10
23
6.02 x 1023 atoms C
1 mol C
or
1 mol C
6.02 x 1023 atoms C
Solve and cancel out units:
24 g C x 1 mol C x 6.02 x 1023 atoms C = 1.2 X 1024 atoms C
12 g C
1 mol C
Slide 98 / 158
Mole Road Map
Particles: atoms, ions, molecules, etc.
1 mol = 6.02 x 1023 particles
Molar mass (M)
1 mol = ___ grams
found using the
Periodic Table
m (mass)
moles Molar Volume (V )
1 mol = 22.4 L
V (Volume)
M
Slide 99 / 158
52
How many molecules are there in 44.8 liters
(at STP) of oxygen gas?
1 mol O2 molecules = 6.02 x 1023 O2 molecules
1 mol O2 gas = 22.4 L O2
Slide 100 / 158
53
How many atoms are there in 11.2 liters (at STP)
of molecular oxygen ( oxygen gas)?
Slide 101 / 158
54
What is the mass of 44.8 liters (at STP) of
molecular oxygen?
Slide 102 / 158
55
What is the volume (at STP) of 3.0 x 10
molecules of fluorine?
23
Slide 103 / 158
56
What is the volume (at STP) of 240 g of
nitrogen gas?
Slide 104 / 158
57
How many atoms are present in 30 g of boron ?
M of Boron= 10.8 g/mol or 1 mol = 10.8 g
1 mol B = 6.02 x 1023 atoms B
Slide 105 / 158
58
What is the mass of a pure sample of lead
which contains 3.0 x 10 atoms?
24
Slide 106 / 158
59
How many moles are there in 11.2 liters (at STP)
of chlorine?
Slide 107 / 158
60
What volume will 6.0x1024 molecules of oxygen gas
occupy at STP?
Slide 108 / 158
61
How many molecules are in a 32g sample of SO ?
2
Slide 109 / 158
62
Determine the volume occupied by 216g of N O at STP?
2
5
Slide 110 / 158
63 What volume will 5.0x1024 atoms of krypton occupy at
STP?
Slide 111 / 158
64 What is the mass of 224 L of hexene (C H ) at STP?
6
12
Slide 112 / 158
65 What is the volume occupied by 6.0x1023 atoms of
Hydrogen at STP?
Slide 113 / 158
66 How many atoms of C are in a 30 milligram sample of
calcium cyanide. (Hint: you must remember that milli
means 1/1000 and you must first write the proper
formula for calcium cyanide)
Slide 114 / 158
67 What is the mass of 44.8L of Argon gas at STP?
Slide 115 / 158
Percent Composition
Return to
Table of
Contents
Slide 116 / 158
Identify an Unknown Substance
We have been able to calculate the molar mass of a material if we
know its formula already. However, what if we encounter an
unidentified substance?
Using the tools we already have, we are able to determine the
composition of a substance if we have certain pieces of
information.
Slide 117 / 158
Percent Composition
One such piece of information is the percent composition, or the
percentage of a compound's mass, made up by its various
elements.
Potassium chromate, K2 CrO4
Potassium dichromate, K2 Cr2 O7
Slide 118 / 158
Percent Composition
The percent by mass of an element in a compound is the
number of grams of the element divided by the mass in grams of
the compound, multiplied by 100%.
% element =
(number of atoms)(atomic weight)
(FW of the compound)
x 100
Slide 119 / 158
Percent Composition of Ethane
The percent composition of carbon and hydrogen in ethane, (C H ) is…
2
%C =
(2)(12.0 amu) x 100
=
30.0 amu
80.0%
%H =
(6)(1.0 amu) x 100 =
30.0 amu
20.0%
6
Since ethane is made of only Carbon and Hydrogen, if the
percent composition of Carbon was 80%, the remaining percent
must be Hydrogen. Another method to calculate the %H is:
%H = 100% - %C
%H = 100% - 80%
%H = 20%
Slide 120 / 158
Percent Composition of Ethane
The percent composition of ethane, (C H ) is…
2
6
%H = 20% and %C = 80%
Note that even though there are more ATOMS of hydrogen in
ethane, there is a much less percentage of mass in the
compound than that of carbon.
This is because 1 carbon atom (12 amu) is much more massive
than 1 hydrogen atom (1 amu).
Therefore, carbon accounts for a much greater percentage of the
mass of ethane than hydrogen does.
Slide 121 / 158
68 In water (H2 O), which element do you think
accounts for more mass?
A Hydrogen
B Oxygen
C Hydrogen and Oxygen account for the same
percent of mass
D Carbon
Slide 122 / 158
69
What is the mass percentage of oxygen in water?
Slide 123 / 158
70 What is the percent by mass of carbon in
acetone, C3 H6 O?
Slide 124 / 158
71 What is the percent of Ba in Ba(NO )
3 2
Slide 125 / 158
72 Iron (II) oxide has a smaller % of iron by mass than
iron (III) oxide.
True
False
Slide 126 / 158
Real World Application
Aluminum is used in soda cans,
aircraft frames, and automobile
engines. Worldwide aluminum demand
is increasing. Aluminum is isolated
from an ore called bauxite which is
roughly 12% aluminum by mass.
bauxite ore
How much bauxite ore (in grams)
must be mined to provide enough
aluminum to make a car engine
requiring 100 kg of aluminum?
Al block engine
move for answer
100 kg x (1000 g/kg) x (100 g of ore/12 gram of Al) = 830,000 g Al
Slide 127 / 158
73 A 2.00 sample of a compound containing only
potassium and oxygen is heated. The oxygen
gas leaves and the resulting mass of the
potassium is 1.66 grams. What is the % by
mass of oxygen in the compound?
A 17%
B 70%
C 30%
D 45%
E Cannot be determined from the information
Slide 128 / 158
74 What is the % by mass of water in the
CaSO4*2H2O crystal?
A 10%
B 21%
C 19%
D 50%
E 75%
Slide 129 / 158
Empirical Formula
Return to
Table of
Contents
Slide 130 / 158
Calculating Empirical Formulas
Now that we are able to calculate the percent of a compound by
mass of each element, we can begin to identify unknown
substances. First, we must identify the ratio of the number of
moles of each element in the substance
This formula, based on whole-number ratio, is called an
empirical formula.
Slide 131 / 158
Calculating Empirical Formulas
Empirical formula: The formula that indicates the molar ratio of
elements present in a molecular compound reduced to the least
common denominator.
For instance, the empirical formula for benzene (C H ) is CH.
6
use
molar mass
Assume 100g
sample
Mass %
elements
Grams of
each element
Moles of
each element
6
Calculate
mole ratio
Empirical
formula
Slide 132 / 158
Calculating Empirical Formulas
Empirical formula: There is only one empirical formula for a
substance, but two different substances can have the same
empirical formula.
That is because an empirical formula is always based on the ratio
of the elements given in their lowest common denominator.
Example:
Substance
Hydrogen peroxide
Hydroxide
Molecular
Formula
Emperical
Formula
H2O2
OH
OH
OH
Slide 133 / 158
75 The empirical formula for C6 H4 (NO3 )2 is
C3 H2 N2 O3
True
False
Slide 134 / 158
76 Which of the following has an empirical formula
that is the same as its molecular formula?
(1) NH4 Cl
A 1 and 3 only
(2) (NH4 )2 CO3
B 1, 2 and 4 only
(3) CH2 Cl2
C 1 and 4 only
(4) CHCl2 Br
D all of them
Slide 135 / 158
Calculating Empirical Formulas
Mass %
elements
The compound para-aminobenzoic acid (listed as PABA
in bottles of sunscreen) is composed of the following
elements (by mass):
carbon (61.31%),
hydrogen (5.14%),
nitrogen (10.21%),
and oxygen (23.33%).
Find the empirical formula of PABA.
Slide 136 / 158
Calculating Empirical Formulas
Assume 100g
sample
Mass %
elements
Grams of
each element
Step 1: convert the mass percentages to mole amountsin a
hypothetical 100 g sample. Assume a 100.00 g amount of
PABA to represent the mass of each element:
C: 61.31% x 100g
= 61.31 g
H: 5.14 % x 100g
= 5.14 g
N: 10.21% x 100g
= 10.21 g
O: 23.33 % x 100g
= 23.33 g
Slide 137 / 158
Calculating Empirical Formulas
use
molar mass
Assume 100g
sample
Mass %
elements
Grams of
each element
Moles of
each element
Step 2: Now that we know the representative mass, we can
use the molar mass of each element to calculate the number
of moles that would be present.
C: 61.31 g x
1 mol
12.01 g
= 5.105 mol
H:
1 mol
1.01 g
= 5.09 mol
N: 10.21 g x
1 mol
14.01 g
= 0.7288 mol
O: 23.33 g x
1 mol
16.00 g
= 1.456 mol
5.14 g x
Slide 138 / 158
Calculating Empirical Formulas
use
molar mass
Assume 100g
sample
Mass %
elements
Grams of
each element
Moles of
each element
Calculate
mole ratio
Empirical
formula
Step 3: Calculate the mole ratio by dividing each mole
value by the smallest number of moles. In this case, by
that of nitrogen. Divide them all by 0.7288.
5.105 mol
C: 5.105 mol
= 7.005 # 7
0.7288 mol
H: 5.09 mol
N: 0.7288 mol
O: 1.456 mol
5.09 mol
0.7288 mol
0.7288 mol
0.7288 mol
1.456 mol
0.7288 mol
= 6.984 # 7
= 1.00 = 1
= 2.001 # 2
The empirical formula for PABA is CH NO
7
7
2
Slide 139 / 158
Calculating Empirical Formulas
1,6 - diaminohexane is used in making nylon.
It is 62.1% C, 13.8% H and 24.1% N. What is the empirical formula?
C: 62.1 g x 1 mol = 5.17 mol
12 .0 g
= 5.17 mol = 3.01 # 3
1.72 mol
H: 13.8 g x 1 mol = 13.8 mol
1.0 g
= 13.8 mol = 7.96 # 8
1.72 mol
N: 24.1 g x 1 mol = 1.72 mol
14.01 g
= 1.72 mol = 1.00
1.72 mol
The empirical formula is C H N
3
8
=1
Slide 140 / 158
77
What is the empirical formula for a compound with
the following percent composition?
A C H4
B C2 H5
C C3 H6
D C3 H8
C: 74.9 %
H: 25.1 %
Slide 141 / 158
78
What is the empirical formula for a compound with
the following percent composition?
A C2 H O
B C H2 O
C C H O2
D C2 H3 O2
C: 40.0 %
H: 6.7 %
O: 53.0 %
Slide 142 / 158
Special Cases
The molar ratio works very well for most compounds. However, in
some cases the math leaves us without whole numbers:
For Example: iron (?) oxide
use
molar mass
Assume 100g
sample
Mass %
elements
Grams of
each element
Moles of
each element
Calculate
mole ratio
Fe: 69.92% -> 69.92g
= 1.25 mol = 1
1.25 mol
55.85 g/mol
O: 30.08% -> 30.08g
16.00g/mol
= 1.88 mol = 1.5
1.25 mol
FeO1.5
Slide 143 / 158
Special Cases
In these cases, it is necessary to multiply the results by an
integer to ensure the ratio is a whole number ratio...
x2=2
x2=3
The empirical formula is Fe O3
2
The name of the compound is iron (III) oxide
Slide 144 / 158
79
What is the empirical formula for a compound with
the following percent composition?
A V O1.67
B V2 O5
C V3 O5
D V3 O8
V: 56.02 %
O: 43.98 %
Slide 145 / 158
80 A 4.68 gram sample of a sulfur oxide is heated
releasing oxygen gas and leaving behind solid sulfur.
If the mass of the sulfur left behind was 2.34 grams,
what must be the empirical formula of the
compound?
A SO
B SO2
C S2O
D S2O3
E SO3
Slide 146 / 158
Hydrated Crystals
Many ionic compounds have a fixed quantity of water molecules
bound within their structure.
CuSO4 * 5H2O
The mole ratio of water to the dry CuSO4 crystal is 5:1
Slide 147 / 158
Finding the formula of a hydrate
One can find the formula of a hydrate by heating the crystal to
remove the water. Then find the mole ratio between the dry crystal
and the water just as you would when finding an empirical formula.
g CuSO4 --> n CuSO4
CuSO4 * ? H2O
HEAT
g H2O --> n H2O
Find
mole
ratio!
Slide 148 / 158
Finding the formula of a hydrate
After heating, a hydrate of MgSO4 was found to be roughly 51.3%
water by mass. What is the formula of the hydrate?
Step 1: Find the % of the crystal and water and express in grams.
100 - 51.3% water = 48.7 % MgSO4 =
48.7 g MgSO4 & 51.3 g of water
Step 2: Convert to moles
48.7 g MgSO4 = 0.405 mol MgSO4
51.3 g H2O = 2.85 mol H2O
120 g/mol
18 g/mol
Slide 149 / 158
Finding the formula of a hydrate
Step 3: Find the mole ratio of the water to the dry crystal
0.405 mol MgSO4 = 1
2.85 mol H2O = 7
0.405 mol
0.405 mol
.....the formula is MgSO4*7H2O
Slide 150 / 158
81 When a 2.4 g sample of a hydrated crystal of
BaCl2 is heated, the dry anhydrous crystal has
a mass of 2.08 grams after heating. What is the
formula of the hydrate?
A BaCl2*H2O
B BaCl2*2H2O
C BaCl2*3H2O
D BaCl2*4H2O
E BaCl2*5H2O
Slide 151 / 158
Molecular Formulas
A molecular formula indicates the number of atoms of each
element present in the molecule.
The molecular formula of a compound is either the same as its
experimentally determined empirical formula, or it is a simple
whole-number multiple of its empirical formula
Slide 152 / 158
Molecular Formulas
Formula Name
Type of Formula
Molar Mass
CH
Empirical
13
C2H2 Ethyne
Molecular
(13x2 =) 26
C6H6 Benzene
Molecular
(13x6 =) 78
CH2O Methanal
Empirical & Molecular
30
C2H4O2 Ethanoic Acid
Molecular
(30x2 =) 60
C6H12O6 Glucose
Molecular
(30x6 =) 180
Slide 153 / 158
Molecular Formulas
To find the actual molecular formula you need one other piece of
information...the molecular weight (mass) of the molecule.
If
you know the ratio of the elements in a molecule
and
then
you know the total mass of the molecule
you can determine the molecular formula.
Slide 154 / 158
Molecular Formulas
What is the molecular formula of a compound with an
empirical formula of CH2 O that has a mass of 180 g/mol?
To find the molecular formula:
Step 1: Determine the molar mass of the empirical formula.
Molar mass of CH2O = 30 g/mol
Step 2: Divide the molecular mass by the empirical mass
Molecular mass = 180 g/mol
Empirical mass
= 6
30 g/mol
Step 3: Multiply the Empirical Formula by the resulting integer
6 x CH2O = C6H12O6
Slide 155 / 158
82 The molecular mass of Benzene is 78. If the
empirical formula of benzene is CH, what is its
molecular formula?
A
C2 H2
B
CH
C
C6 H6
D
C2 H4
Slide 156 / 158
Molecular Formulas
Maleic acid is an organic compound composed of 41.39 %
carbon, 3.47% hydrogen, and the rest is oxygen. It has a
molecular mass of 116 g/mole.
Determine the empirical
formula for Maleic acid.
Then determine the
molecular formula for
Maleic acid.
Slide 157 / 158
Real World Application
Clenbuterol is a steroid drug
that is illegally used in cattle
and in sports like cycling to
help the cattle or athlete lose
fat and gain lean muscle
mass. It can be detected by
mass spectroscopy.
What is the empirical and molecular formula for clenbuterol
if when a 10.0 g sample is combusted in air, it is found it
contains 4.60 g of carbon, 0.613 g of H, 0.51 g of oxygen with
the rest being chlorine? The molecular weight is 313 g/mol.
Slide 158 / 158