4.4
Section 4.3 Questions
Understanding Concepts
1. Define Avogadro’s constant, and explain its significance in quantitative analysis.
2. Distinguish between the terms atomic mass and molar mass.
3. Calculate the mass of a molecule of sucrose (sugar, C12H22O11(s))
and the mass of a mole of sucrose.
DID YOU KNOW ?
Mole Day
Mole Day, which is held in recognition of
the mole concept, is celebrated yearly on
October 23 between 6:02 a.m. and 6:02 p.m.
4. What is the molar mass of octane, C8H18(l), a component of gasoline?
Making Connections
5. One mole of any gas at 0°C and 101 kPa occupies the volume
22.4 L. Use this information and your knowledge of molar mass to
determine the density (in grams per litre) of gaseous hydrogen,
helium, nitrogen, oxygen, and carbon dioxide in those conditions.
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Reflecting
6. You are learning how to calculate molar mass. How do you think
this skill will be useful?
4.4
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Calculations Involving the Mole
Concept
In this section, we will apply the mole concept in a number of situations that we
encounter frequently in the study of chemical reactions. Chemical formulas and
equations are expressed using amount in moles. In a laboratory, we measure mass.
So we constantly need to convert amount in moles into mass and vice versa.
Think about the term molar mass. It contains the concepts of both moles and
mass. We always use molar mass in connecting the two measurements of amount
in moles and mass.
Converting Mass to Amount in Moles
To calculate an amount in moles, we take the given mass in grams and divide by
the molar mass. Let’s take an example. Each mole of carbon atoms has a mass of
12 g. If we have 24 g of carbon atoms, what is the amount in moles? Since 24 g is
twice 12 g, we have 2.0 moles of carbon atoms.
Mathematically, when we divide the mass we are given, 24 g, by the molar
mass, 12 g/mol, we get 2.0 mol.
mass (g)
Amount in moles molar mass (g/mol)
24 g
nc 12 g/mol
1 mol
24 g × 12 g
nc 2.0 mol
Quantities in Chemical Formulas 171
In SI symbols, the relationship of amount (n), mass (m), and molar mass
(M) is expressed as
m
n M
Sample Problem 1
Convert a mass of 1.5 kg of calcium carbonate to an amount in moles.
Solution
mCaCO
3(s)
MCaCO
3(s)
1.5 kg
(1 × 40.08) + (1 × 12.01) + (3 × 16.00) 100.09 g/mol
nCaCO
3(s)
1 mol
1.5 kg × 100.09 g
1 mol
1500 g × 100.09 g
nCaCO
3
15 mol
A mass of 1.5 kg of calcium carbonate is equal to 15 mol of calcium carbonate.
Practice
Understanding Concepts
1. 0.043 mol
1. Convert a mass of 2.5 g of table salt (sodium chloride) to an amount
in moles.
2. 5.6 mol
2. Convert a mass of 1.0 kg of glucose, C6H12O6(s), to an amount in moles.
3. 0.781 mol
3. What is the amount in moles of 25.0 g of oxygen gas?
4. (a) 2.00 mol C, 5.94 mol H,
1.00 mol O
4. A clear, colourless liquid when decomposed produced 24.0 g of
carbon atoms, 6.0 g of hydrogen atoms, and 16.0 g of oxygen atoms.
(a) Calculate the amount in moles of each element in the compound.
(b) Determine the ratio of the number of atoms of carbon to
hydrogen to oxygen, that is, the mole ratio of C:H:O.
(c) From your answer in (b), suggest a formula for the clear, colourless liquid.
Answers
(b) 2:6:1
Converting Amount in Moles to Mass
If we know the amount in moles of a reactant or a product, we can calculate the mass
by using the molar mass. Consider the amount of 2.0 mol of sodium hydroxide,
NaOH(s). The molar mass of NaOH(s) is (22.99 + 16.00 + 1.01) g/mol, or 40.00
g/mol. The mass of 2.0 mol of NaOH(s) would be exactly double the mass of 1.0 mol
of NaOH(s). Therefore, the mass of 2.0 mol of NaOH(s) is double 40 g, which is 80 g.
Mathematically, in order to calculate the mass of a substance, we multiply
the amount in moles by its molar mass.
mass
amount in moles (mol) × molar mass (g/mol)
40.00 g
mol × mNaOH 2.0 1
mol
80 g
172 Chapter 4
4.4
This relationship can be represented by
(a)
m nM
which is simply a rearrangement of the relationship we used earlier:
m
n M
(b)
Sample Problem 2
Convert a reacting amount of 0.346 mol of sodium sulfate into mass in grams.
Solution
nNa SO 0.346 mol
2
4
MNa SO 142.04 g/mol
2
4
mNa SO
2
4
mNa SO
2
4
142.04 g
0.346 mol × 1
mol
49.1 g
The mass of 0.346 mol of Na2SO4(s) is 49.1 g.
Practice
Figure 1
Dacron is a type of polyester made from
1,4-benzendioic acid.
(a) Dacron tubes reinforce a damaged artery.
(b) Dacron fibres are used as insulation in
sleeping bags.
Understanding Concepts
5. Magnesium hydroxide is a base that is used in some antacids. What
is the mass in grams of 0.45 mol of magnesium hydroxide?
6. Ammonia is a gas that, dissolved in water, is used as a cleaning
agent. Convert 87 mmol of ammonia, NH3(g), into mass in grams.
7. 1,4-benzenedioic acid, C8H6O4(s), is a raw material used in the manufacture of Dacron, a synthetic fibre (Figure 1). What is the mass in
grams of 63.28 mol of 1,4-benzenedioic acid?
Answers
5. 26 g
6. 1.5 g
7. 10.51 kg
8. 0.18 g
8. If a patient is prescribed 1.0 × 10–3 mol of acetylsalicylic acid (Aspirin,
C9H8O4(s)), what mass of Aspirin should she take?
Calculations Involving Number of Entities
We often need to know the number of entities in a sample of a substance. When
dealing with gases, for example, the number of atoms or molecules in a container
is related to other factors, such as the temperature and the pressure of the gas.
We will first look at how we can convert an amount in moles into the
number of entities. We know there are always 6.02 × 1023 entities in a mole of
substance. If we have 2.0 mol of copper, then there will be 2.0 × 6.02 × 1023
copper atoms. The number of entities, N, in an amount in moles is calculated by
multiplying the amount in moles by 6.02 × 1023, Avogadro’s constant:
N nNA.
In the case of 2.0 mol of copper atoms,
6.02 × 1023 atoms
1
mol
NCu 2.0 mol × 1.2 × 1024
There are 1.2 × 1024 atoms in 2.0 mol of copper metal.
Quantities in Chemical Formulas 173
Now let’s look at calculating the number of entities in a given mass. How
many copper atoms do you think there are in a penny? (We’ll assume our pennies are dated before 1997, since after this time they were no longer made of
copper, but copper-plated zinc.) The calculations are similar to the preceding
example; however, since we are not told the amount in moles, we need to first
convert the mass into amount in moles.
Our strategy is first to measure the mass of the penny (Figure 2). Then we
convert the mass into amount in moles. Finally, we can convert the amount in
moles to number of atoms. Mass and number of entities are both easily converted to amount in moles, so the middle step in these conversions is always to
determine the amount in moles.
Suppose we measured the mass of a penny and found it to be 2.63 g. We will
convert this mass to amount in moles of copper atoms.
MCu(s) 63.55 g/mol
Figure 2
To reduce error in determining the mass of a
single penny, we can find the mass of 150
pennies and divide the total mass by 150.
Therefore,
1 mol
nCu(s) 2.63 g × 63.55 g
nCu(s) 0.0414 mol
We now simply multiply the amount in moles by NA:
6.02 × 1023
NCu(s) 0.0414 mol × 1
mol
NCu(s) 2.49 × 1022
There are 2.49 × 1022 atoms in a copper penny.
Sample Problem 3
Determine the number of chloride ions in 0.563 mol of calcium chloride,
CaCl2(s).
Solution
nCaCl 0.563 mol
2
6.02 × 1023
mol × NCaCl 0.563 2
1
mol
NCaCl 3.39 × 1023
2
There are 3.39 × 1023 formula units in 0.563 mol of CaCl2.
Since each formula unit (CaCl2) contains two chloride ions, there are 2 ×
(3.39 × 1023), 6.78 × 1023, chloride ions in 0.563 mol of calcium chloride.
174 Chapter 4
4.4
Sample Problem 4
How many sugar (sucrose, C12H22O11(s)) molecules are there in a 1.000 kg bag of
sugar?
Solution
MC H O
[(12 12.01) + (22 1.01) + (11 16.00)] 342.34 g/mol
12 22 11(s)
m 1.000 kg
nC
12H22O11
1 mol
1000.0 g 342.34 g
2.9211 mol
NC
12H22O11
NC
12H22O11
6.02 1023
2.9211 mol 1m
ol
1.76 1024
There are 1.76 1024 sugar molecules in a 1.000 kg bag of sucrose.
Sample Problem 5
What is the mass of one water molecule (Figure 3)?
Solution
MH O (2 1.01) + (1 16.00) 18.02 g/mol
2
Figure 3
The mass of one water molecule is an
unimaginable 2.99 x 10–23 g.
Since there are 6.02 1023 molecules/mol,
18.02 g
1m
ol
mH O 2
1
mol
6.02 1023
mH O 2.99 10–23 g
2
The mass of one water molecule is 2.99 10–23 g.
SUMMARY
Calculating Mass, Amounts in Moles,
and Number of Entities
1. n represents the amount in moles, m the mass measured, M the molar
mass, N the number of entities, and NA Avogadro’s constant (Table 1).
m
2. n M
3. m nM
4. N nNA
Table 1: Stoichiometry, Symbols and
Units
Symbol
Quantity
Unit
n
amount in moles
mol
m
mass
mg, g, kg
M
molar mass
g/mol
N
number of entities
atoms, ions,
formula units,
molecules
NA
Avogadro’s constant,
—
6.02 × 1023
Quantities in Chemical Formulas 175
Try This
Activity
Counting Atoms, Molecules, and Other Entities
Using the materials and equipment supplied, calculate and measure the
quantities described in each of the steps below. Write an explanation of
your calculations.
Materials: balance, graduated cylinder, beaker, disposable cups, copper
pennies, iron nails, granulated sugar, table salt, chalk, water
• Determine the mass of a drop of water by measuring the mass of 50
drops of water. Place a single drop of water on the lab bench and
record the time it takes for it to completely evaporate. Calculate how
many molecules of water evaporate per second.
• Calculate the number of copper atoms in a penny and use that
number to calculate the value of each atom of copper in the penny.
• Measure into a graduated cylinder half a mole of sucrose molecules
(C12H22O11(s)). Record the reading on the graduated cylinder.
• Measure into a graduated cylinder the quantity of sugar that contains two moles of carbon atoms. 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 were needed to write
your name (assume 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 the iron nail.
• Calculate the number of years to span a mole of seconds.
Practice
Understanding Concepts
Answers
9. (a) 18.02 g/mol
(b) 44.01 g/mol
(c) 58.44 g/mol
(d) 342.34 g/mol
(e) 252.10 g/mol
10. (a) 29.21 mol
(b) 8.56 mol
(c) 0.907 mol
(d) 1.80 × 103 mol
(e) 2.45 mol
11. (a) 71.9 g
(b) 8.96 g
(c) 1.03 g
(d) 1.49 ×
103
kg
(e) 1.0 × 102 g
12. (a) 9.0 × 1024 molecules
(b) 5.3 × 1023 molecules
9. Calculate the molar mass of each of the following substances:
(a) H2O(l) (water)
(b) CO2(g) (respiration product)
(c) NaCl(s) (pickling salt, sodium chloride)
(d) C12H22O11(s) (table sugar, sucrose)
(e) (NH4)2Cr2O7(s) (ammonium dichromate)
10. Calculate the amount of pure substance present (in moles) in each of
the following samples of pure substances:
(a) a 10.00-kg bag of table sugar
(b) a 500-g box of pickling salt
(c) 40.0 g of propane, C3H8(g), in a camp-stove cylinder
(d) 325 mg of acetylsalicylic acid (Aspirin), HC9H7O4(s), in a headacherelief tablet
(e) 150 g of 2-propanol (rubbing alcohol), CH3CH2OHCH3(l), from a
pharmacy
11. Calculate the mass of each of the following substances:
(a) 4.22 mol of ammonia in a window-cleaning solution
(b) 0.224 mol of sodium hydroxide in a drain-cleaning solution
(c) 57.3 mmol of water vapour produced by a laboratory burner
(d) 9.44 kmol of potassium permanganate fungicide
(e) 0.77 mol of ammonium sulfate fertilizer
12. Calculate the number of entities in each of the following samples:
(a) 15 mol of solid carbon dioxide, in dry ice
(b) 15 g of ammonia gas, in household cleaners
176 Chapter 4
4.4
(c) 15 g of hydrogen chloride gas, in hydrochloric acid
(d) 15 g of sodium chloride, in table salt
13. Calculate the mass, in grams, of the characteristic entity in each of
the following samples:
(a) carbon dioxide from respiration
(b) glucose from photosynthesis
(c) oxygen from photosynthesis
14. How many water molecules are in a 1.000 L bottle of water? (Recall
the density of water is 1.00 g/mL.)
Answers
12. (c) 2.5 × 1023 molecules
(d) 1.5 × 1023 formula units
13. (a) 7.31 × 1023 g
(b) 2.99 × 1022 g
(c) 5.32 × 1023 g
14. 3.34 × 1025 molecules
Section 4.4 Questions
Understanding Concepts
1. (a) Calculate the number of oxygen molecules in 1.5 mol of
oxygen gas, O2(g).
(b) Calculate the number of atoms in 1.5 mol of O2(g).
2. A daily vitamin tablet contains 90 mg of vitamin C. The chemical
name for vitamin C is ascorbic acid, H2C6H6O6. How many molecules of vitamin C are you taking each day if you take a daily
vitamin tablet?
3. A thyroid condition called goitre can be treated by increasing
iodine in the diet. Iodized salt contains calcium iodate, Ca(IO3)2(s),
which is added to table salt.
(a) How many atoms of iodine are in 1.00 × 10–2 mol of calcium
iodate?
(b) What is the mass of calcium iodate that contains that many
atoms of iodine?
4. A recipe for a sweet-and-sour sauce calls for
500 g water
200 g sugar (C12H22O11(s))
25 g vinegar (assume acetic acid), HC2H3O2(l)
15 g citric acid (C6H8O7(s))
5 g salt (NaCl(s))
Convert the recipe into amounts in moles.
5. If necessary, use density as a conversion factor to answer the following questions. (The density of elements can be referenced on
the periodic table.)
(a) If the density of pure ethanol is 0.789 g/mL, how many
ethanol molecules are there in a 17-mL sample of ethanol,
the approximate quantity of ethanol in a bottle of beer?
(b) How many nickel atoms are there in 0.72 cm3 of a nickel
sample, the approximate volume of a Canadian quarter?
(c) How many water molecules are there in a 100-mL sample of
pure water?
Applying Inquiry Skills
6. Silver ions in waste solutions can be recovered by immersing
copper metal in the solution (Figure 4). The solid copper loses
mass as copper goes into solution as ions. Crystals of silver are
deposited on the copper metal. Design an experiment to determine the ratio of the amount in moles of copper ions dissolved to
Figure 4
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.
(continued)
Quantities in Chemical Formulas 177
the amount in moles of silver atoms formed. Describe the procedure, materials, and equipment used, safety procedures, and
explain the calculations needed.
Making Connections
7. Suppose that there is a prestigious award given by the Academy
of Science each year to the most significant scientific concept.
Write a paper nominating the mole concept for this award, citing
the mole’s role and importance in the application of chemical
reactions in society, industry, and the environment.
Percentage Composition
4.5
Figure 1
This experimental car burns hydrogen as a
fuel, producing water vapour as an exhaust.
The dish collects solar energy, which is used
to dissociate water into hydrogen and
oxygen.
Using molar mass values from a periodic table, we can calculate the mass of reactants and products in chemical reactions—if we already know the chemical formulas. However, when a new substance is produced, we first need to determine its
chemical formula. To do this, we need to determine the chemical composition of the
compound, that is, what elements it is made of and the quantities of each element.
In this section, we will experimentally determine the composition by mass of
a substance and then convert the mass amounts to percentages, to give us the
percentage composition. We can then use atomic mass and molar mass to determine the correct chemical formula.
Before we begin, we will practise the mathematical steps in the calculation of
percentage composition from mass measurements of reactants and products.
Let’s consider 20 g of red jelly beans mixed with 30 g of green jelly beans. What
is the percentage composition of the mixture, by mass? The percentage of red
jelly beans by mass would be 20 g of the total 50 g, which is 20 g/50 g × 100%, or
40%. Similarly, the percentage of green jelly beans would be 30 g of the total 50 g,
which is 60%.
Now let’s look at the percentage composition of water. Water is formed when
hydrogen is allowed to react with oxygen, a reaction that gives off large amounts
of energy (Figure 1). The results of an experiment revealed that 2.5 g of
hydrogen, when completely reacted, produced 22.5 g of water. What is the percentage composition of water by mass?
Since 2.5 g of hydrogen combined with an amount of oxygen to produce
22.5 g of water, we can calculate the mass of oxygen by subtraction:
2.5 g
mH
mH O 22.5 g
2
mO
(22.5 – 2.5) g 20.0 g
mH
× 100%
%H mH
O
2
2.5 g
% H × 100% 11.1%
22.5 g
Similarly,
20.0 g
% O × 100%
22.5 g
% O 88.9%
178 Chapter 4