Calculations Involving the Mole
2.2
When making chocolate chip cookies, it is more convenient to add a particular
mass of chocolate chips to the mix than a particular number of chocolate chips
(Figure 1). You have learned that the number of small objects in a collection
can be calculated if you know the mass of one or a small number of the
objects and the mass of the collection. For example, if you want to make 10
cookies with approximately 10 chocolate chips per cookie, you should add at
least 100 chocolate chips to the mix. Instead of counting out 100 chocolate
chips, you could calculate the mass that contains 100 chocolate chips. If the
mass of one chocolate chip is 0.1 g, how many grams of chocolate chips must
be added to the cookie mix?
Recall that the symbol m represents mass. In this example, the key value is
100 chocolate chips, the conversion factor equation is 1 chocolate chip 0.1 g,
and the required value is the mass of chocolate chips, mchocolate chips.
0.1 g
mchocolate chips 100 chocolate chips 1 chocolate chip
mchocolate chips 10 g
You would need to add 10 g of chocolate chips to the mix.
Calculations Involving Atoms
When chemists need a certain amount of a chemical, they cannot count out
the atoms, ions, molecules, or formula units. Instead, they calculate the mass
of the chemical that contains the required amount, just as you would calculate
the mass of chocolate chips you need to make cookies. Then, using a precise
balance, they measure out the calculated mass of the chemical. The next three
Sample Problems show the relationships among mass, molar mass, and
amount when dealing with elements.
Figure 1
It is more convenient to determine
the number of chocolate chips by
mass than by counting.
SAMPLE problem 1
Calculating Mass from Amount in Moles
Calculate the mass, in grams, of 2.00 mol of calcium atoms.
Step 1: Identify Key Value and Conversion Factor Equation
nCa 2.00 mol Ca (key value)
Information for a conversion factor equation is not given in this problem. You can
use the molar mass of the element, however, to produce the necessary equation.
Look up the molar mass of calcium in the periodic table.
MCa 40.08 g/mol Ca
1 mol Ca 40.08 g Ca (conversion factor equation)
Step 2: Identify Required Value
The required value is the mass of calcium atoms, mCa. (Remember that the
symbol m is used to represent mass.)
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Quantities in Chemistry
93
Step 3: List Possible Conversion Factors
The possible conversion factors are
40.08 g Ca
1 mol Ca
or 40.08 g Ca
1 mol Ca
Step 4: Substitute Values into Solution Equation, and Solve
Remember that the units in the denominator of the conversion factor must be the
same as the units of the key value.
required value key value conversion factor
40.08 g Ca
mCa 2.00 mol Ca 1 mol Ca
mCa 80.2 g Ca
The mass of 2.00 mol of calcium is 80.2 g.
Example
Calculate the mass of 0.200 mol of nitrogen atoms.
Solution
nN 0.200 mol N
MN 14.01 g/mol N
1 mol N 14.01 g N
14.01 g N
mN 0.200 mol N 1 mol N
mN 2.80 g N
The mass of 0.200 mol of nitrogen atoms is 2.80 g.
Practice
Answers
1. 43.2 g
2. 8.0 g
Understanding Concepts
1. Calculate the mass of 1.60 mol of aluminum atoms.
2. Calculate the mass of 0.25 mol of sulfur atoms.
SAMPLE problem 2
Calculating Amount in Moles from Mass
What amount of gold is in a 275.8-g nugget of pure gold (Figure 2)?
You can use the molar mass of an element to calculate the amount of atoms, in
moles, in a sample of known mass.
Figure 2
Gold is a precious metal that can
be mixed with other metals, such as
nickel and platinum, to create
jewellery.
94
Unit 2
Step 1: Identify Key Value and Conversion Factor Equation
mAu 275.8 g Au (key value)
MAu 196.97 g/mol Au (value from periodic table)
1 mol Au 196.97 g Au (conversion factor equation)
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Section 2.2
Step 2: Identify Required Value
The required value is the amount of gold, nAu.
Step 3: List Possible Conversion Factors
The possible conversion factors are
1 mol Au
196.97 g Au
or 196.97 g Au
1 mol Au
Step 4: Substitute Values into Solution Equation, and Solve
required value key value conversion factor
1 mol Au
nAu 275.8 g Au 196.97 g Au
nAu 1.40 mol Au
There is 1.40 mol of gold in a 275.8-g nugget of pure gold.
Example
What amount of helium is in a balloon that contains 1.60 g of helium gas
(Figure 3)?
Solution
mHe 1.60 g He
MHe 4.00 g/mol He
1 mol He 4.00 g He
1 mol He
nHe 1.60 g He 4.00 g He
nHe 0.400 mol He
Figure 3
Helium is less dense than air and
will cause this balloon to float.
There is 0.400 mol of helium in a balloon that contains 1.60 g of helium gas.
Practice
Understanding Concepts
3. What amount of iron is in a 3.30-g iron nail?
4. What amount of silver is in a silver coin that contains 23.6 g of pure silver?
5. What amount of copper is in a bracelet that contains 7.65 g of pure copper?
Answers
3. 0.059 mol Fe
4. 0.219 mol Ag
5. 0.120 mol Cu
So far, you have learned to calculate
•
•
the mass of an element when the amount is known;
the amount (in moles) of an element when the mass is known.
You can also calculate
•
•
NEL
the number of atoms in an element when the mass is known;
the mass of an element when the number of atoms is known.
Quantities in Chemistry
95
In Sample Problem 3, the element (gold) is the same as the element in
Sample Problem 2, and it has the same mass, so you can compare the two
solutions.
SAMPLE problem 3
Calculating the Number of Atoms from Mass
How many atoms of gold are in a 275.8-g nugget of pure gold?
You can divide this problem into two parts to solve it. In the first part, the molar
mass of the element is used to calculate the amount of gold in the nugget, as in
Sample Problem 2. In the second part, the amount of gold is used to calculate
the number of gold atoms in the nugget.
Part 1: Calculate Amount of Gold
Step 1: Identify Key Value and Conversion Factor Equation
mAu 275.8 g Au (key value)
MAu 196.97 g/mol Au
1 mol Au 196.97 g Au (conversion factor equation)
Step 2: Identify Required Value
The required value for this part of the solution is the amount of gold atoms, nAu.
Step 3: List Possible Conversion Factors
The possible conversion factors are
1 mol Au
196.97 g Au
or 196.97 g Au
1 mol Au
Step 4: Substitute Values into Solution Equation, and Solve
required value key value conversion factor
1 mol Au
nAu 275.8 g Au 196.97 g Au
nAu 1.40 mol Au
Part 2: Calculate Number of Gold Atoms
Step 1: Identify Key Value and Conversion Factor Equation
The amount of gold that was calculated in Part 1 is the key value for Part 2.
nAu 1.40 mol Au (key value)
The conversion factor equation for this part is obtained from the fact that one
mole of atoms contains Avogadro’s number of atoms.
1 mol Au 6.02 1023 atoms Au (conversion factor equation)
Step 2: Identify Required Value
The required value is the number of atoms of gold, NAu. (Remember that N
represents the number of entities.)
96
Unit 2
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Section 2.2
Step 3: List Possible Conversion Factors
The possible conversion factors are
6.02 1023 atoms Au
1 mol Au
or
6.02 1023 atoms Au
1 mol Au
Step 4: Substitute Values into Solution Equation, and Solve
6.02 1023 atoms Au
nAu 1.40 mol Au 1 mol Au
nAu 8.43 1023 atoms Au
There are 8.43 1023 atoms of gold in a 275.8-g nugget of pure gold.
Parts 1 and 2 can be combined into a single-line calculation by substituting
the key value given in the problem and the conversion factors from Parts 1 and 2.
Notice that conversion factor 1 (from Part 1) converts the mass of gold into the
amount of gold. Conversion factor 2 (from Part 2) converts the amount of gold
into the number of gold atoms.
required value key value conversion factor 1 conversion factor 2
1 mol Au
6.02 1023 atoms Au
NAu 275.8 g Au 196.97 g Au
1 mol Au
NAu 8.43 1023 atoms Au
There are 8.43 1023 atoms of gold in a 275.8-g nugget of pure gold.
Example
How many atoms of sulfur are in a 230.0-g sample of pure sulfur (Figure 4)?
Solution
Part 1: Calculate Amount of Sulfur
mS 230.0 g S
MS 32.06 g/mol S
1 mol S 32.06 g S
1 mol S
nS 230.0 g S 32.06 g S
nS 7.17 mol S
Figure 4
Sulfur is a component of black
gunpowder, and it is used to
improve the strength of natural
rubber.
Part 2: Calculate Number of Sulfur Atoms
6.02 1023 atoms S
NS 7.17 mol S 1 mol S
NS 4.32 1024 atoms S
There are 4.32 1024 atoms of sulfur in a 230.0-g sample of sulfur.
Alternative single-line solution:
6.02 1023 atoms S
1 mol S
NS 230.0 g S 32.06 g S
1 mol S
NS 4.32 1024 atoms S
There are 4.32 1024 atoms of sulfur in a 230.0-g sample of sulfur.
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Quantities in Chemistry
97
Practice
Answers
6. 1.65 1023 C atoms
7. 2.03 1023 Ne atoms
8. 2.35 1023 Hg atoms
Understanding Concepts
6. How many atoms of carbon are in a 3.30-g diamond (pure carbon)?
7. How many atoms of neon are in a neon sign that contains 6.80 g of neon?
8. How many atoms of mercury are in the bulb of a thermometer, if the mercury
has a mass of 78.2 g?
The Molar Mass of Molecular Elements and
Compounds
molecular element a molecule
that contains two or more atoms of
one type of element
compound a molecule that
contains two or more atoms of
different elements, or is a
combination of oppositely
charged ions
Molecular elements contain two or more atoms of one element only.
Hydrogen, H2(g), fluorine, F2(g), ozone, O3(g), and sulfur, S8(s), are examples of
molecular elements. Compounds are molecules that contain two or more
atoms of different elements, or they are combinations of oppositely charged
ions represented by formula units. Water, H2O(l), carbon dioxide, CO2(g), and
ammonia, NH3(g), are examples of molecular compounds. Sodium chloride,
NaCl(s), is an example of an ionic compound.
The molar mass of a molecule is equal to the sum of the molar masses of all
the atoms in the molecule. The molar mass of an ionic compound is equal to
the sum of the molar masses of all the ions in the formula unit of the ionic
compound. For example, the molar mass of hydrogen chloride, HCl(g), is
equal to the sum of the molar mass of hydrogen and the molar mass of
chlorine. The following Sample Problem shows how to calculate the molar
mass of a compound.
SAMPLE problem 4
Calculating the Molar Mass of a Compound
Calculate the molar mass of water.
In 1 mol of water, there are 2 mol of hydrogen atoms and 1 mol of oxygen atoms.
Add together the molar masses of these atoms to obtain the molar mass of the
compound. Notice that you have to multiply the molar mass of hydrogen by 2
because there are two hydrogen atoms in every water molecule.
2(MH) 1(MO)
2(1.01 g/mol) 1(16.00 g/mol)
2.02 g/mol 16.00 g/mol
MH O 18.02 g/mol
MH
2O
2
The molar mass of water is 18.02 g/mol.
Example
Calculate the molar mass of sodium hydrogen carbonate (baking soda),
NaHCO3(s).
98
Unit 2
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Section 2.2
Solution
MNaHCO 1(MNa) 1(MH) 1(MC) 3(MO)
3
1(22.99 g/mol) 1(1.01 g/mol) 1(12.01 g/mol) 3(16.00 g/mol)
22.99 g/mol 1.01 g/mol 12.01 g/mol 48.00 g/mol
MNaHCO 84.01 g/mol
3
The molar mass of sodium hydrogen carbonate is 84.01 g/mol.
Practice
Understanding Concepts
9. Calculate the molar mass of octane (a component of gasoline), C8H18(l).
10. Calculate the molar mass of acetylsalicylic acid (Aspirin), C9H8O4(s).
11. Calculate the molar mass of calcium sulfate (gypsum), CaSO4(s).
Answers
9. 114.26 g/mol
10. 180.17 g/mol
11. 136.14 g/mol
Calculations Involving Molecules and
Compounds
Earlier in this section, you learned how to perform various calculations
involving elements. The following Sample Problems show how the same
principles can be applied to molecules and ionic compounds.
SAMPLE problem 5
Calculating Mass from Amount in Moles
Sodium fluoride is added to toothpaste and tap water to help prevent
tooth decay. Calculate the mass of 2.00 mol of sodium fluoride, NaF(s).
Step 1: Identify Key Value and Conversion Factor Equation
nNaF 2.00 mol NaF (key value)
Calculate the molar mass of the compound, MNaF, to determine the conversion
factor equation.
MNaF 1(22.99 g/mol) 1(19.00 g/mol)
MNaF 41.99 g/mol NaF
1 mol NaF 41.99 g NaF (conversion factor equation)
Step 2: Identify Required Value
The required value is the mass of sodium fluoride, mNaF.
Step 3: List Possible Conversion Factors
The possible conversion factors are
1 mol NaF
41.99 g NaF
or 41.99 g NaF
1 mol NaF
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Quantities in Chemistry
99
Step 4: Substitute Values into Solution Equation, and Solve
required value key value conversion factor
41.99 g NaF
mNaF 2.00 mol NaF 1 mol NaF
mNaF 84.0 g NaF
The mass of 2.00 mol of sodium fluoride is 84.0 g.
Example
Calculate the mass of 11.7 mol of ozone, O3(g).
Solution
nO 11.7 mol O3
3
MO 3(16.00 g/mol)
3
MO 48.00 g/mol O3
3
1 mol O3 48.00 g O3
48.00 g O
mO 11.7 mol O3 3
3
1 mol O3
mO 562 g O3
3
The mass of 11.7 mol of ozone is 562 g.
Practice
Answers
12. 15.3 g
13. 435 g
Understanding Concepts
12. Calculate the mass of 0.900 mol of ammonia, NH3(g).
13. Calculate the mass of 3.60 mol of freon-12, CCl2F2(g).
SAMPLE problem 6
Calculating Amount in Moles from Mass
Iron(III) oxide, Fe2O3(s), is more commonly known as rust (Figure 5).
What amount of iron(III) oxide is in a 77.2-g sample?
Figure 5
Cars have steel frames and bodies
that rust when exposed to water
and oxygen.
100
Unit 2
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Section 2.2
Step 1: Identify Key Value and Conversion Factor Equation
mFe O 77.2 g Fe2O3 (key value)
2 3
MFe O 2(55.85 g/mol) 3(16.00 g/mol)
2 3
MFe O 159.7 g/mol Fe2O3
2 3
1 mol Fe2O3 159.7 g Fe2O3 (conversion factor equation)
Step 2: Identify Required Value
The required value is the amount of iron(III) oxide, nFe
.
2O3
Step 3: List Possible Conversion Factors
The possible conversion factors are
1 mol Fe2O3
159.7 g Fe2O3
or 159.7 g Fe2O3
1 mol Fe2O3
Step 4: Substitute Values into Solution Equation, and Solve
required value key value conversion factor
nFe
2O3
nFe
2O3
1 mol Fe2O3
77.2 g Fe2O3 159.7 g Fe2O3
0.483 mol Fe2O3
There is 0.483 mol of iron(III) oxide in a 77.2-g sample.
Example
What amount of propane, C3H8(g), is in a tank that is filled with 5.00 kg of
propane?
Solution
mC
1000 g C3H8
5.00 kg C3H8 1 kg C3H8
mC
5.00 103 g C3H8
3H8
3H8
MC H 3(12.01 g/mol) 8(1.01 g/mol)
3 8
MC H 44.11 g/mol C3H8
3 8
1 mol C3H8 44.11 g C3H8
nC
1 mol C3H8
5.00 103 g C3H8 44.11 g C3H8
nC
113 mol C3H8
3H8
3H8
There is 113 mol of propane in a tank with 5.00 kg of propane in it.
Alternative single-line solution:
nC
1000 g C3H8
1 mol C3H8
5.00 kg C3H8 1 kg C3H8
44.11 g C3H8
nC
113 mol C3H8
3H8
3H8
There is 113 mol of propane in a tank with 5.00 kg of propane in it.
NEL
Quantities in Chemistry
101
Practice
Answers
14. 3.497 mol
15. 2.92 mol
Understanding Concepts
14. What amount of magnesium hydroxide, Mg(OH)2(s), is in 204.0 g of
magnesium hydroxide?
15. What amount of sucrose (table sugar), C12H22O11(s), is in a bag that contains
1.00 kg of sucrose?
You can also calculate the number of entities (molecules or formula units)
in a sample of known mass using the factor-label method. Notice that singleline solutions are used in the following Sample Problem and Example.
SAMPLE problem 7
Calculating the Number of Entities from Mass
How many formula units of the ionic compound iron(III) oxide, Fe2O3(s),
are in 77.2 g of iron(III) oxide?
Step 1: Identify Key Value and Conversion Factor Equation
mFe O 77.2 g Fe2O3 (key value)
2 3
MFe O 2(55.85 g/mol) 3(16.00 g/mol)
2 3
MFe O 159.7 g/mol Fe2O3
2 3
The following two conversion factor equations will be used:
• conversion factor equation 1:
1 mol Fe2O3 159.7 g/mol Fe2O3 (from MFe O )
2 3
• conversion factor equation 2:
1 mol Fe2O3 6.02 1023 formula units Fe2O3 (from mole definition)
Step 2: Identify Required Value
The required value is the number of iron(III) oxide formula units, NFe
2O3
.
Step 3: List Possible Conversion Factors
The possible conversion factors from conversion factor equation 1 are
1 mol Fe2O3
159.7 g Fe2O3
or 159.7 g Fe2O3
1 mol Fe2O3
The possible conversion factors from conversion factor equation 2 are
6.02 1023 formula units Fe2O3
1 mol Fe2O3
or 23
6.02 10 formula units Fe2O3
1 mol Fe2O3
Step 4: Substitute Values into Solution Equation, and Solve
Remember to select conversion factors such that the units in the denominator of
conversion factor 1 match the units of the key value, and the units in the
denominator of conversion factor 2 match the units in the numerator of
conversion factor 1.
102
Unit 2
NEL
Section 2.2
required value key value conversion factor 1 conversion factor 2
NFe
2O3
NFe
2O3
6.02 1023 formula units Fe2O3
1 mol Fe2O3
77.2 g Fe2O3 159.7 g Fe2O3
1 mol Fe2O3
2.91 1023 formula units Fe2O3
There are 2.91 1023 formula units of iron(III) oxide in a 77.2-g sample.
Example
Calcium hydroxide, Ca(OH)2(s), is an ionic compound that is used to make slaked
lime, a substance that is used as a top-coat on the walls of many homes. How
many formula units of calcium hydroxide are in a sample of slaked lime that
contains 250.0 g of calcium hydroxide?
Solution
mCa(OH) 250.0 g Ca(OH)2
2
MCa(OH) 1(40.08 g/mol) 2(16.00 g/mol) 2(1.01 g/mol)
2
MCa(OH) 74.1 g/mol Ca(OH)2
2
1 mol Ca(OH)2
6.02 1023 formula units Ca(OH)
2
NCa(OH) 250.0 g Ca(OH)2 2
74.1 g Ca(OH)2
1 mol Ca(OH)2
NCa(OH) 2.03 1024 formula units Ca(OH)2
2
There are 2.03 1024 formula units of calcium hydroxide in a sample that
contains 250.0 g of calcium hydroxide.
Practice
Understanding Concepts
16. How many molecules of water are in a bottle that contains 250.0 g of water?
17. How many formula units of cobalt(III) dichromate, Co2(Cr2O7)3(s), are in a
3.30-kg sample?
Answers
16. 8.35 1024 molecules
17. 2.59 1024 formula units
Calculating the Number of Atoms from the Mass
of Molecules
Calculating the number of atoms in a sample of molecules can be tricky. If the
sample contains a molecular element, then the atoms are all the same. If the
sample contains a compound, however, then there are different atoms to
consider. The following Sample Problem involves a molecular element, and
the Example involves a compound. Note the differences in the two
calculations.
NEL
Quantities in Chemistry
103
SAMPLE problem 8
Calculating the Number of Atoms
Sand is composed of silicon dioxide, SiO2(s). How many atoms of oxygen are in a bag of pure
sand, which contains 1.00 kg of silicon dioxide?
Step 1: Identify Key Value and Conversion Factor Equation
mSiO 1.00 kg SiO2 (key value)
2
MSiO 1(28.09 g/mol) 2(16.00 g/mol)
2
MSiO 60.09 g/mol SiO2
2
The following conversion factor equations will be used in the solution:
1 kg 1000 g (metric equality)
1 mol SiO2 60.09 g SiO2 (from MSiO )
2
1 mol SiO2 6.02 1023 units SiO2 (from mole definition)
2 atoms O 1 unit SiO2 (since there are two oxygen atoms per unit of silicon dioxide)
Step 2: Identify Required Value
The required value is the number of oxygen atoms, NO.
Step 3: List Possible Conversion Factors
See the conversion factor equations in step 1 and the corresponding conversion factors in step 4.
Step 4: Substitute Values into Solution Equation, and Solve
There are four conversion factors in this solution.
NO key value conversion factor 1 conversion factor 2 conversion factor 3 conversion factor 4
1000 g SiO2
1 mol SiO2
6.02 1023 units SiO
2 atoms O
1.00 kg SiO2 2 1 kg SiO2
60.09 g SiO2
1 mol SiO2
1 unit SiO2
NO 2.00 1025 atoms O
There are 2.00 1025 atoms of oxygen in a bag that contains 1.00 kg of pure sand.
Example
One form of solid sulfur is composed of S8(s) molecules. How many atoms of sulfur are in an 18.0-g
chunk of solid sulfur?
Solution
mS 18.0 g S8
8
MS 8(32.06 g/mol)
8
MS 256.5 g/mol S8
8
1 mol S8 256.5 g S8
8 atoms S
1 mol S8
6.02 1023 molecules S
NS 18.0 g S8 8 256.5 g S8
1 mol S8
1 molecule S8
NS 3.38 1023 atoms S
There are 3.38 1023 atoms of sulfur in an 18.0-g chunk of solid sulfur.
104
Unit 2
NEL
Section 2.2
Practice
Answers
Understanding Concepts
18. How many atoms of fluorine are in 4.4 g of fluorine gas?
19. How many atoms of nitrogen are in 1.26 kg of nitrogen gas?
20. How many atoms of hydrogen are in 29.5 g of ethene, C2H4(g)?
21. How many atoms of oxygen are in 0.170 mg of strontium hydroxide,
Sr(OH)2(s)?
SUMMARY
18. 1.4 1023 F atoms
19. 5.41 1025 N atoms
20. 2.53 1024 H atoms
21. 1.68 1018 O atoms
Steps in the Factor-Label Method
Step 1: Identify Key Value and Conversion Factor Equation
Step 2: Identify Required Value
Step 3: List Possible Conversion Factors
Step 4: Substitute Values into Solution Equation, and Solve
Use the following solution equation:
required value key value conversion factor conversion factor
Note: Use as many conversion factors as required.
TRY THIS activity
Counting Atoms, Molecules, and Other Entities
Use the following materials to measure and/or calculate
the quantity described in each step below. Write an
explanation of each calculation.
Materials: balance, graduated cylinder, beaker,
disposable cups, copper pennies, iron nails, granulated
sugar, table salt, chalk, water
1. Determine the mass of a drop of water by measuring
the mass of 50 drops of water.
2. Place a single drop of water on the lab bench, and
record the time the drop takes to evaporate
completely. Calculate how many molecules of water
evaporate per second.
3. Calculate the number of copper atoms in a penny.
Use the number of copper atoms to calculate the
monetary value of each atom of copper in the penny.
Assume that the penny contains pure copper only.
4. Measure half a mole of sucrose molecules,
C12H22O11(s), into a graduated cylinder.
NEL
5. Measure the quantity of sugar that contains two
6.
7.
8.
9.
moles of carbon atoms into a graduated cylinder.
Record the reading on the graduated cylinder.
Measure the mass of a piece of chalk. Use the piece
of chalk to write your full name on the chalkboard.
Measure the mass of the chalk again. Calculate the
number of atoms that you used to write your name.
(Assume that chalk is made entirely of calcium
carbonate.)
Dissolve 3.00 g of table salt (assume NaCl(s)) in
200 mL of water. Calculate the number of sodium
ions in the salt solution.
Calculate the number of iron atoms in an iron nail.
Calculate the number of years in one mole of
seconds.
Quantities in Chemistry
105
Section 2.2 Questions
Understanding Concepts
1. Magnesium hydroxide, Mg(OH)2(s), is a key ingredient
in some antacid tablets. What is the molar mass of
magnesium hydroxide?
2. Ozone, O3(g), is a molecule that protects you from
dangerous solar radiation. What is the molar mass of
ozone in the upper atmosphere?
3. If the molar mass of a substance is 67.2 g/mol, what
is the mass of 8.0 mol of the substance?
4. Calculate the mass of a mole of sucrose, C12H22O11(s).
5. (a) How many atoms of aluminum are in 0.1 mol of
aluminum?
(b) How many formula units of magnesium chloride,
MgCl2(s), are in 3.5 mol of magnesium chloride?
6. Calculate the amount of entities in each of the
following samples of pure substances:
(a) 5.00 kg of table sugar (sucrose), C12H22O11(s)
(b) 250 g of naphthalene moth balls, C10H8(s)
(c) 35.0 g of propane, C3H8(g), in a camp stove
cylinder
(d) 275 mg of acetylsalicylic acid (Aspirin), C9H8O4(s),
in a headache relief tablet
(e) 240 g of 2-propanol (rubbing alcohol), C3H8O(l)
7. Calculate the mass, in grams, of each of the following
substances:
(a) 2.67 mol of ammonia in a window-cleaning
solution
(b) 0.965 mol of sodium hydroxide, NaOH(s), in a
drain-cleaning solution
(c) 19.7 mol of water vapour produced by a Bunsen
burner
(d) 3.85 mol of potassium permanganate (a
fungicide), KMnO4(s)
(e) 0.47 mol of ammonium sulfate (a fertilizer),
(NH4)2SO4(s)
8. Calculate the number of molecules in each of the
following samples:
(a) 2.5 mol of solid carbon dioxide in dry ice
(b) 2.5 g of ammonia gas in household cleaning
solutions
(c) 2.5 g of hydrogen chloride in hydrochloric acid
9. Calculate the mass, in grams, of 0.10 mol of each of
the following substances:
(a) carbon dioxide
(b) glucose, C6H12O6(s)
(c) oxygen gas
10. Calculate the number of oxygen molecules in 2.7 mol
of oxygen gas.
106
Unit 2
11. A daily vitamin tablet contains 90 mg of vitamin C.
The chemical name for vitamin C is ascorbic acid,
C6H8O6(s). If you take one vitamin tablet each day,
how many molecules of vitamin C are you taking?
12. A recipe for a sweet and sour sauce calls for the
following ingredients:
450 g water
100 g sugar, C12H22O11(s)
30 g vinegar (containing 2.4 g acetic acid,
HC2H3O2(aq))
2 g salt, NaCl(s)
Convert the recipe into amounts (in moles). For
vinegar, use 2.4 g of acetic acid.
Applying Inquiry Skills
13. Silver ions in a solution of silver salts can be
recovered by immersing copper metal in the solution
(Figure 6). Crystals of pure silver are deposited on
the copper metal. Design an experiment to determine
the number of moles of silver atoms that form.
Describe the procedure, materials, and safety
procedures. Explain the required calculations.
Making Connections
14. The Academy of Science is giving a prestigious
award to the most significant scientific concept.
Write a brief paper, nominating the mole for this
award. Cite the role and importance of the mole in
the application of chemical reactions in society,
industry, and the environment.
Figure 6
When copper metal is placed in a solution of silver ions, a single
displacement reaction occurs. Copper ions go into solution, and
silver crystals are formed.
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