10
Chemical Q
Quantities
Planning G
Guide
Introducing the
BIGIDEA:
THE MOLE AND QUANTIFYING MATTER
The mole
Th
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i the
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h i t’ invaluable
i l bl unitit ffor specifying
if
the amount of material.
Lessons and Objectives
NSES
Print Resources
For the Student
For the Teacher
A-1, A-2, B-1,
B-2
10.1
The Mole: A Measurement of Matter
p 306–315
10.1.1 Convert among the count, mass, and
volume of something.
10.1.2 Explain how chemists count the number
of atoms, molecules, or formula units in a
substance.
10.1.3 Determine the molar mass of an element
and of a compound.
Reading and Study
Workbook Lesson 10.1
Lesson Assessment 10.1
p 315
Teaching Resources,
Lesson 10.1 Review
Teacher Demo, p 313: Moles
and Mass
Class Activity, p 314:
Calculating Molar Mass
A-1, A-2, B-2
10.2
Mole–Mass and Mole–Volume
Relationships p 317–323
10.2.1 Describe how to convert the mass of a
substance to the number of moles of a
substance, and moles to mass.
10.2.2 Convert the volume of a gas at STP to the
number of moles of the gas.
Reading and Study
Workbook Lesson 10.2
Lesson Assessment 10.2
p 323
Small-Scale Lab: Counting
by Measuring Mass,
p 324
Teaching Resources,
Lesson 10.2 Review
Teacher Demo, p 321: Molar
Volume
A-1, A-2, B-2,
E-2
10.3
Reading and Study
Workbook Lesson 10.3
Lesson Assessment 10.3
p 333
Quick Lab: Percent
Composition p 328
Teaching Resources,
Lesson 10.3 Review
Class Activity, p 330: Empirical
Formulas from Percent
Composition
Percent Composition and Chemical
Formulas p 325–333
10.3.1 Calculate the percent composition of a
compound.
10.3.2 Calculate the empirical formula of a
compound.
10.3.3 Distinguish between empirical and
molecular formulas.
Assessing the
BIGIDEA:
THE MOLE AND QUANTIFYING MATTER
Essential Questions
1. Why is the mole an important measurement in
chemistry?
2. How can the molecular formula of a compound
be determined experimentally?
304A Chapter 10
Study Guide p 336
Math Tune-Up p 337
STP p 343
Reading and Study
Workbook Self-Check
and Vocabulary Review
Chapter 10
Materials List
FFor the
h S
d
Student
Digital Resources
Editable Worksheets
L
W
OV
Small-Scale Lab Manual Lab 13:
Measuring Mass: A Means
of Counting
PearsonChem.com
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Lab 12: The Masses of Equal
Volumes of Gases
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Exam View Assessment Suite
Classroom Resources Disc
(includes editable worksheets)
• Lesson Reviews
• Practice Problems
• Interpret Graphs
• Vocabulary Review
• Chapter Quizzes and Tests
• Lab Record Sheets
O
TU
MATH
TU
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MATH
TU
Converting Atoms to
Moles and Vice Versa
Molar Masses of
Compounds
Finding the Molar Mass
of a Compound
10.2 Lesson Overview
Converting Moles to
Mass and Mass to
Moles
The Mole Roadmap
Quick Lab, p 328
• centigram balance
• burner
• 3 medium-sized test tubes
• test-tube holder
• test-tube rack
• spatula
• 2–3 g each of hydrated salts of copper(II) sulfate, calcium
chloride, and sodium sulfate
For the Teacher
Teacher Demo, p 313
• 1 mol of each of several
different substances
• 1 sealed container per
sample
ESSON
OV
Lab 13: Empirical Formula
Determination
Lab 3 Practical 10-1: Empirical
Formulas
10.1 Lesson Overview
Small-Scale Lab, p 324
• 1 teaspoon each of water, sodium chloride, and calcium
carbonate
• plastic spoon
• weighing paper
• watchglass or small beaker
• balance
• paper
• pencil
• ruler
TOR
10.3 Lesson Overview
Calculating Percent
Composition From
Mass Data and From a
Formula
Percent Composition
Determining the
Empirical Formula of a
Compound
Chapter 10 Problem Set
Class Activity, p 314
• display from the Teacher
Demo on p 313
Teacher Demo, p 321
• 50 g dry ice
• towel
• hammer
• large plastic bag
• duct tape
• tongs
• beaker
• balance
Class Activity, p 330
• 3 red marbles
• 6 green marbles
• 3 black marbles
• 12 blue marbles
Additional Digital Resources
Online Student Edition
Online Teacher’s Edition
10.2 Virtual Chem Lab 3: Counting by Measuring Mass
Unit Conversion
Circle Graphs
Chemical Quantities 304B
CHEM
TOR
NLIN
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CHEM TUTOR Students access guided
step-by-step tutorials for solving various
calculations involving moles.
ONLINE PROBLEMS Students can practice
key problem-solving skills in an online
problem set.
MATH
MATH HELP Identify the students who
T
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PR
UTOR
L
V
IRTUA
struggle with math by assigning an online
math skills diagnostic test. These students
can then improve and practice math skills
using the MathXL tutorial system.
VIRTUAL LAB Students go on an animated
virtual lab tour in which chemical quantities
are studied in a simulated laboratory
environment.
LAB
10
Chemical
Quantities
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CHAPTER 10
What’s Online
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overview of a key chapter concept using
real-world contexts and concrete examples
and analogies. Each activity includes an
interactive animation followed by analysis
questions.
National Science Education Standards
When you shop at the grocery store or farmers’
market, you usually buy blueberries by the pint,
not by the berry. Similarly, chemists use a unit
called the mole to count atoms and molecules.
304
A-1, A-2, B-2, E-2, G-1, G-3
Focus on ELL
1 CONTENT AND LANGUAGE Clarify for students that the word mole has various
common meanings and scientific meanings. The common meanings have several
different origins, but the chemistry meaning is derived from the German word
molekulargewicht, which means “molecular weight.” In chemistry, a mole is a unit
of measurement for particles of matter, such as atoms, molecules, and ions.
BEGINNING: LOW/HIGH Make a non-linguistic representation of the chemistry
meaning of mole and present it to the class. Have students use a bilingual dictionary
to find the definition of mole, and write the definition in their notebooks.
INTERMEDIATE: LOW/HIGH Ask students to brainstorm and write a list of other units
of SI measures of matter.
ADVANCED: LOW/HIGH Predict the meaning of molar mass. Create an analogy
304
Chapter 10
between a grouping unit of measure, such as a pair or dozen, and a chemist’s unit of
measure, the mole.
THE MOLE AND
QUANTIFYING MATTER
Essential Questions:
1. Why is the mole an important
measurement in chemistry?
2. How can the molecular formula
of a compound be determined
experimentally?
CHEMYSTERY
A Formula
for Cheating
Anabolic steroids are compounds that are developed
to increase muscle size and
strength. Stories are often in
n the
news about professional athletes,
such
basehl
h as b
ball players, cyclists, and track stars, who have
used steroids to enhance their performance.
More than 100 different types of anabolic
steroids have been developed, and each of
these substances is illegal in the United States
without a prescription. Steroids have also been
banned by many sports organizations because
of their dangerous side effects and because
they give the user an unfair advantage.
Therefore, athletes are often tested for steroid
use. So, how can the presence of steroids in the
body be detected?
ɀ Connect to the BIGIDEA As you read
about the mole and chemical quantities, think
about how the molar mass and molecular
formula of a compound can be determined
and used to identify the presence of steroids in
the body.
NATIONAL SCIENCE EDUCATION STANDARDS
A-1, A-2, B-2, E-2, G-1, G-3
Understanding by Design
Students are building toward measuring chemical
quantities using the relationships of the mole and
quantifying matter.
PERFORMANCE GOALS At the end of Chapter 10,
students will be able to answer the essential questions
by applying their knowledge of chemical quantities.
Students will also be able to make calculations related
to mole-mass, mole-volume, and percent composition
relationships.
ESSENTIAL QUESTIONS Read the essential questions
aloud. Ask When is it more convenient to count items
in groups (when you are working with large numbers
of very small items) Ask What information does a
molecular formula tell you? (the types of atoms and the
ratio of each type in a compound)
Use the photo of baskets of
blueberries to help students connect
to the concepts they will learn in this chapter.
Activate prior knowledge by asking whether they
usually count berries individually or in groups. Point
out that even a small basket holds a large number
of blueberries. Ask How might grouping the
blueberries make it easier to count them? (grouping
makes the number more manageable)
BIGIDEA
Have students read over the
CHEMystery. Connect the
CHEMystery to the Big Idea of The Mole and
Quantifying Matter by discussing how a molecular
formula helps quantify matter, or describe it using
numbers. Ask What was the laboratory technician
looking for in the urine? (chemicals that indicated
drug use) As a hint to how the mystery could be
solved, encourage students to think about what
information the technician would be able to
determine once the name of any chemical in the
urine is known. (the chemical formula)
CHEMYSTERY
Introduce the Chapter
IDENTIFYING PRECONCEPTIONS Students may not realize that quantifying particles
of matter is even possible. Use this activity to introduce the idea of using mass to
quantify large numbers of items.
Activity Divide students into groups and provide each group with a small cup,
15 pennies,15 dimes, and access to a balance. Alternatively, students can use any
two types of small items. Write the mass of a penny (2.500 g) and a dime (2.268 g)
on the board. Ask How many pennies and dimes would a mass of 7.268 g
indicate? (2 pennies and 1 dime) Give each group of students a cup with a mixture
of pennies and dimes. Have them randomly remove some pennies and dimes
and measure the total mass. Then have them count the coins and calculate the
mass. Point out that in this chapter they will learn about a similar method, using
molecular formulas, to calculate numbers of atoms in a substance.
Chemical Quantities
305
CHAPTER 10
BIGIDEA
LESSON 10.1
Key Objectives
10.1.1 CONVERT among the count, mass, and
volume of something.
10.1
The Mole:
A Measurement of Matter
10.1.2 EXPLAIN how chemists count the
number of atoms, molecules, or formula units in
a substance.
10.1.3 DETERMINE the molar mass of an
element and of a compound.
CHEMISTRY
Y
&YOU
Q: How can you quantify the amount of sand in a sand sculpture? Have you
ever gone to the beach and created a castle or sculpture out of sand? You
could measure the amount of sand in a sculpture by counting the grains of
sand. Is there an easier way to measure the amount of sand? Chemists measure the amount of a substance using a unit called the mole.
Additional Resources
Reading and Study Workbook, Lesson 10.1
Available Online or on Digital Media:
• Teaching Resources, Lesson 10.1 Review
• Small-Scale Laboratory Manual, Lab 13
Key Questions
How can you convert among
the count, mass, and volume of
something?
How do chemists count the
number of atoms, molecules, or
formula units in a substance?
How do you determine the
molar mass of an element and of
a compound ?
Engage
&
CHEMISTRY
Y
YO
YOU
U Have students read the
opening paragraph. Ask Is it practical to count each
grain of sand? (Students should realize that it is not
practical to measure sand by counting individual
grains.) Ask How else might you measure, or
quantify, the sand? (Find its mass or volume.) Lead
students to see that just as a small amount of sand
contains millions of smaller particles, so also small
amounts of chemical substances contain very large
numbers of particles.
Vocabulary
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Measuring Matter
How can you convert among the count, mass, and volume
of something?
Chemistry is a quantitative science. In your study of chemistry, you will analyze the composition of samples of matter and perform chemical calculations
that relate quantities of the reactants in a chemical reaction to quantities of
the products. To solve these and other problems, you will have to be able to
measure the amount of matter you have.
One way to measure matter is to count how many of something you have.
For example, you can count the mp3s in your collection. Another way to
measure matter is to determine its mass. You can buy apples by the kilogram
or pound, as shown in Figure 10.1. You can also measure matter by volume.
For instance, people buy gasoline by the liter or the gallon.
Some of the units used for measuring indicate a specific number of items.
For example, a pair always means two. A pair of shoes is two shoes, and a
pair of aces is two aces. Similarly, a dozen always means 12. A dozen eggs is
12 eggs, and a dozen pens is 12 pens.
Apples can be measured in three different ways. At a fruit stand, they are
often sold by the count. In a supermarket, you usually buy apples by weight
or mass. At an orchard, you can buy apples by volume. Each of these different
ways to measure apples can be equated to a dozen apples.
By count: 1 dozen apples â 12 apples
For average-sized apples, the following approximations can be used.
By mass: 1 dozen apples â 2.0 kg apples
Activate Prior Knowledge
By volume: 1 dozen apples â 0.20 bushel apples
Remind students that a conversion factor is a ratio
equal to one. Ask What method is used to change
one unit of measure to another unit of measure using
conversion factors? (dimensional analysis)
National Science Education Standards
Figure 10.1 Measuring by Mass
A dozen apples has a mass
of about 2.0 kg.
306 $IBQUFSt-FTTPO
A-1, A-2, B-1, B-2
Focus on ELL
1 CONTENT AND LANGUAGE Review common conversion factors like feet to inches,
meters to centimeters, hours to minutes, etc.
2 FRONTLOAD THE LESSON Ask students to share unique terms for grouped items
from their native culture, and explain the quantity and size of the items in the group
that each term represents. Distinguish between groupings in which the number
of items varies and those with set numbers of items as a prelude to discussing
Avogadro’s number.
306
Chapter 10 • Lesson 1
3 COMPREHENSIBLE INPUT Use a model to introduce the concept of molar mass.
Display cartons of small, medium, large, and extra-large eggs as representations of
moles of different elements. Tell students to think of the eggs as atoms, with each size
being a different element. Explain that one carton of small eggs contains the same
number of eggs as a carton of extra-large eggs, but the two cartons of eggs each have
different masses because their individual eggs are different sizes (and masses).
1 dozen apples
12 apples
Foundations for Reading
BUILD VOCABULARY Have students write two or
three sentences, each of which relates a mole to at
least one other vocabulary term, such as: a mole
contains Avogadro’s number of particles; the mass
of one mole of a substance is its molar mass, which
is found by determining the mass in grams of its
representative particles.
1 dozen apples
0.20 bushel apples
2.0 kg apples
1 dozen apples
Sample Problem 10.1
READING STRATEGY Students may more easily
Finding Mass From a Count
What is the mass of 90 average-sized apples if 1 dozen of the apples has
a mass of 2.0 kg?
— Analyze List the knowns and the unknown. Use dimensional
analysis to convert the number of apples to the mass of apples.
˜ Calculate
KNOWNS
number of apples ä 90 apples
12 apples ä1 dozen apples
1 dozen apples ä2.0 kg apples
UNKNOWN
mass of 90 applesä? kg
grasp the meaning of the mole by developing
their own mental picture. For instance, suggest
visualizing a giant egg carton with 6.02 × 1023
depressions for particles, or a giant sack bulging
with Avogadro’s number of particles.
Explain
Solve for the unknown.
First, identify the sequence of
conversions needed to perform the
calculation.
number of apples
Write the conversion factor to
convert from number of apples to
dozens of apples.
1 dozen apples
12 apples
Write the conversion factor to
convert from dozens of apples to
mass of apples.
2.0 kg apples
1 dozen apples
dozens of apples
mass of apples
Measuring Matter
USE MODELS Pass around numerous bags, each of
Multiply the number of apples by
these two conversion factors to get
the answer in kilograms.
90 apples ò
The units apples and dozen
apples cancel, so the answer
has the unit kg.
1 dozen apples
2.0 kg apples
12 apples ò 1 dozen apples ä15 kg apples
™ Evaluate Does the result make sense? A dozen apples has a mass of 2.0 kg, and 90 apples is less
than 10 dozen apples, so the mass should be less than 20 kg of apples (10 dozen ñ 2.0 kg/dozen).
1. If 0.20 bushel is 1 dozen apples and a dozen
apples has a mass of 2.0 kg, what is the mass of
0.50 bushel of apples?
In Problem 1, the desired conversion
dozens of
is bushels of apples
mass of apples.
apples
2. Assume 2.0 kg of apples is 1 dozen and that
each apple has 8 seeds. How many apple seeds
are in 14 kg of apples?
which contains a multiple of 12 beans. Ask How
can you express the quantities of beans in the bags?
(Sample answers: You can count, weigh, or find
the volume of the beans.) Discuss how the word
“dozen” can be used as a unit for the quantity of
beans in each bag.
START A CONVERSATION Remind students that
mass is a measure of the amount of matter that
an object contains. Ask How are mass and weight
related? (Weight is a force that measures the pull of
gravity on a given mass.)
Sample Practice Problem
Assume 1 dozen oranges has a mass of 1.5 kg and
that there are 14 orange slices in each orange. How
many slices are in 6 kg of oranges? (672 slices)
In Problem 2, the desired conversion is
dozens of apples
mass of apples
number of apples
number of seeds.
Chemical Quantities 307
Foundations for Math
WRITING CONVERSIONS Work thorough some conversions that students likely
encounter in their daily lives. For example: If a recipe calls for six eggs, this quantity
can be considered a half-dozen eggs: 6 eggs × (1 dozen/12 eggs) = 0.5 dozen.
As a class, write other familiar relationships, such as 3 feet = 1 yard, 50 cents =
½ dollar, 60 min = 1 h, 30 min = ½ h, etc. Point out that these equalities can be
written in either direction, so 60 min = 1 h can also be written as 1 h = 60 min.
In Sample Problem 10.1, the mass of a large number of apples is determined by
using the mass of a smaller number of apples by means of a conversion factor created
from the subset of apples. (Note that, for this example, the mass of one dozen apples
is an approximation. In reality, the masses of similar-sized apples vary from one apple
to the next.)
Answers
1.
2.
0.50 bushel × (1 dozen/0.20 bushel) ×
(2.0 kg/1 dozen) = 5.0 kg
14 kg × (1 dozen/2.0 kg) × (12 apples/1 dozen) ×
(8 seeds/1 apple) = 670 seeds
Chemical Quantities
307
LESSON 10.1
Knowing how the count, mass, and volume of an item relate to a
common unit allows you to convert among these units. For example, based
on the unit relationships given on the previous page, you could calculate the
mass of a bushel of apples or the mass of 90 average-sized apples using conversion factors such as the following:
LESSON 10.1
What Is a Mole?
How do chemists count the number of atoms, molecules, or
formula units in a substance?
Explain
Counting objects as big as apples is a reasonable way to measure how much of
the object you have. Picture trying to count the grains of sand in a sand sculpture. It would be an endless job. Recall that matter is composed of atoms,
molecules, and ions. These particles are much, much smaller than grains of
sand, and an extremely large number of them are in a small sample of a substance. Obviously, counting particles one by one is not practical. However,
think about counting eggs. It’s easier when the eggs are grouped into dozens,
as shown in Figure 10.2. A dozen is a specified number (12) of things.
What Is a Mole?
USE VISUALS Read aloud the caption to Figure 10.2.
Then have the class read the text that discusses
the number of particles in a mole. Guide students
to understand that a mole represents a number of
items just as dozen, gross, and ream all represent
a quantity of items. Ask If you are counting the
number of an extremely small item, should the
number of items in a unit be small or large? (For
a small item, a large number per counting unit
is more convenient.) Ask How does your answer
apply to a mole? (A mole = 6.02 × 1023 items and is
used to measure extremely small objects.)
&
CHEMISTRY
Y
YO
YOU
U You could measure the
mass of 1 grain of sand. Then you could measure
the mass of the sand castle. If you divide the mass
of the sand castle by the mass of 1 grain of sand,
you can determine the total amount of sand in the
castle.
Figure 10.2 Grouping Objects
Words other than mole are
used to describe a number of
something—for example, a dozen
eggs is 12 eggs.
CHEMISTRY
&YYOU
Q: What are the different
ways you can measure the
amount of sand in a sand
sculpture?
MAKING CONNECTIONS Have students spend 2
minutes writing down what they remember about
scientific notation and properties of exponents.
As a class, share information and create a
summary sheet of the important rules for these
two concepts. Ask student volunteers to write
several large numbers and small numbers on the
board in standard form. Then use the summary
sheet to guide students in rewriting the numbers
using proper scientific notation. Ask When do you
typically see measurements written in scientific
notation? (Sample answers: When a quantity is
extremely small or extremely large, such as the
diameter of a virus or distances in space.) Ask How
might scientific notation be useful in calculating
the amount of atoms in a given number of moles?
(6.02 × 1023 is an extremely long number when
it is not written in scientific notation.)
Counting With Moles Chemists also use a unit that is a specified number of particles. The unit is called the mole. A mole (mol) of a substance is
6.02 ñ 1023 representative particles of that substance and is the SI unit for
measuring the amount of a substance. The number of representative particles
in a mole, 6.02 ñ 1023, is called Avogadro’s number. It was named in honor
of the Italian scientist Amedeo Avogadro di Quaregna (1776–1856), who
helped clarify the difference between atoms and molecules.
The term representative particle refers to the species present in a substance, usually atoms, molecules, or formula units. The representative particle
of most elements is the atom. Iron is composed of iron atoms. Helium is composed of helium atoms. Seven elements, however, normally exist as diatomic
molecules (H2, N2, O2, F2, Cl2, Br2, and I2). The representative particle of these
elements and of all molecular compounds is the molecule. The molecular
compounds water (H2O) and sulfur dioxide (SO2) are composed of H2O and
SO2 molecules, respectively. For ionic compounds, such as calcium chloride,
The mole allows
the representative particle is the formula unit CaCl2.
chemists to count the number of representative particles in a substance.
A mole of any substance contains Avogadro’s number of representative particles, or 6.02 ñ 1023 representative particles. Table 10.1 summarizes the relationship between representative particles and moles of substances.
Table 10.1
Representative Particles and Moles
Substance
Representative
particle
Chemical formula
Representative
particles in
1.00 mol
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Cu
6.02 ñ 1023
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6.02 ñ 1023
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N2
6.02 ñ 1023
Water
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H2O
6.02 ñ 1023
4VDSPTF
.PMFDVMF
C12H22O11
6.02 ñ 1023
$BMDJVNJPO
*PO
Ca
6.02 ñ 1023
$BMDJVNGMVPSJEF
'PSNVMBVOJU
CaF2
6.02 ñ 1023
2à
308 $IBQUFSt-FTTPO
Differentiated Instruction
ELL ENGLISH LANGUAGE LEARNERS Pair each student with limited English
proficiency with a student who has strong mathematical skills. Encourage the
English learners to ask their partners for help with any difficulty they are having
understanding the terms and how to solve the problems.
L1 STRUGGLING STUDENTS Review the use of parentheses and the fraction bar as
ways of grouping symbols to indicate the order of operations. Stress the importance
of writing units for each measure in a calculation. Provide additional simple conversion
problems for practice before students begin solving problems involving the mole.
L3 ADVANCED STUDENTS Have students create a clever way for their classmates to
avoid confusing the concepts of mass and moles.
308
Chapter 10 • Lesson 1
Explain
1 mol
6.02 ñ 1023 representative particles
and
6.02 ñ 1023 representative particles
1 mol
CHEM
TU
TOR
Sample Problem 10.2
Converting Number of Atoms to Moles
Magnesium is a light metal used in the manufacture
of aircraft, automobile wheels, and tools. How
many moles of magnesium is 1.25 ñ 1023 atoms
of magnesium?
— Analyze
List the known and the unknown.
moles.
The desired conversion is atoms
˜ Calculate
KNOWN
number of atoms ä 1.25 ò1023 atoms Mg
UNKNOWN
molesä? mol Mg
APPLY CONCEPTS Explain that the mole is defined
as the amount of substance that contains as many
molecules or particles as there are atoms in 12 g of
carbon-12 (12C). Tell students that when the mole
is used, the representative particles need to be
specified as either atoms, molecules, ions, electrons,
or formula units. Tell students to pay particular
attention to the information given in a problem.
Encourage students to underline or highlight the
type of representative particle stated in a problem.
Sample Practice Problems
A.
Solve for the unknown.
B.
First, state the relationship between moles
and number of representative particles.
1 mol Mg ä 6.02 ò 1023 atoms Mg
Write the conversion factors you get
based on this relationship.
1 mol Mg
6.02ò1023 atoms Mg
Identify the conversion factor needed
to convert from atoms to moles.
1 mol Mg
6.02ò1023 atoms Mg
Multiply the number of atoms of Mg
by the conversion factor.
1.25ò1023 atoms Mg ò
and
6.02 ò 1023 atoms Mg
1 mol Mg
1 mol Mg
6.02ò1023 atoms Mg
ä0.208 mol Mg
How many moles are equal to 3.61 × 1024
representative particles of potassium chloride,
KCl? (6.00 moles)
About how many atoms are equal to 5.82 ×
1023 atoms of tungsten (W)? (0.967 moles)
Extend
Connect to HISTORY Ask students to use
the Internet to examine the history of the idea of
chemical equivalency. Compare and contrast the
ideas of the past with the modern accepted theory.
Students should provide a timeline as well as the
names of any noted scientists involved with this theory.
™ Evaluate
23
Does the result make sense? The given number of atoms
(1.25 ñ 10 ) is less than one fourth of Avogadro’s number (6.02 ñ 1023),
so the answer should be less than one fourth (0.25) mol of atoms.
s. The
answer should have three significant figures.
3. How many moles is 2.80 ñ 1024
atoms of silicon?
Bromine is a diatomic molecule, so
the representative particle is Br2.
4.
4 How
H many moles
l iis 2.17
2 17 ñ 1023 representative particles of bromine?
Chemical Quantities 309
Foundations for Math
DIVIDING POWERS OF 10 Tell students that the rules for dividing powers of 10 are
the same as those for dividing variables with exponents: as long as the base is the
1027
same, you subtract the exponents. For example, 23 5 1027–23 5 10 4. Point out
10
that each term is a power with the same base; caution students not to divide 10 by 10.
In Sample Problem 10.2 have students group the “like” numbers and divide accordingly:
10 23
1.25
Use a calculator to divide the decimal numbers and use the rules of
3
6.02
10 23
exponents to divide the powers. In this case, 1023–23 = 100, which is equal to 1.
Answers
3.
4.
2.80 × 1024 atoms Si × (1 mol/6.02 × 1023
atoms) = 4.65 mol Si
2.17 × 1023 representative particles ×
(1 mol/6.02 × 1023 representative particles) =
0.360 mol Br2
Chemical Quantities
309
LESSON 10.1
Converting Between Number of Particles and Moles The relationship,
1 mol â 6.02 ñ 1023 representative particles, is the basis for the following conversion factors that you can use to convert number of representative particles
to moles and moles to number of representative particles.
LESSON 10.1
Explain
USE VISUALS Direct students’ attention to
Figure 10.3. Have students examine the
photograph. Note that each cup contains six
marbles. Ask How much would a dozen cups of
marbles hold? (72 marbles) Ask What are some
everyday items that come in a package containing
more than one? (Sample answers: tennis balls, 3;
shoes, 2; batteries, 2, 4, 8) Point out that a dozen
packages of tennis balls would be three dozen
tennis balls or 36 tennis balls. Point out that this
idea can be applied to molecules. For example, a
mole of water, H2O, consists of 2 mol H atoms and
1 mol O atoms. Thus a mole of water contains 3 ×
6.02 × 1023 atoms or 1.8 × 1024 atoms.
Figure 10.3 Counting Marbles
A dozen cups of marbles contain more
than a dozen marbles. Similarly, a
mole of molecules contains more than
a mole of atoms.
Calculate How many atoms are
in one mole of molecules if each
molecule consists of six atoms?
Figure 10.4 A Mole of Moles
An average animal-mole has a mass
of 145 g. The mass of 6.02 ñ 1023
animal-moles is 8.73 ñ 1022 kg.
Suppose you want to determine how many atoms are in a mole
of a compound. To do this, you must know how many atoms are in
a representative particle of the compound. This number is determined from the chemical formula. Figure 10.3 illustrates this idea
with marbles (atoms) in cups (molecules). The number of marbles in a
dozen cups is (6 ñ 12), or 72 marbles. In the formula for carbon dioxide (CO2), the subscripts show that one molecule of carbon dioxide is
composed of three atoms: one carbon atom and two oxygen atoms.
A mole of carbon dioxide contains Avogadro’s number of CO2 molecules. Each molecule contains three atoms, so a mole of carbon dioxide contains three times Avogadro’s number of atoms. A molecule of
carbon monoxide (CO) consists of two atoms, so a mole of carbon
monoxide contains two times Avogadro’s number of atoms.
To find the number of atoms in a given number of moles of a
compound, you must first determine the number of representative
particles. To convert the number of moles of a compound to the number of representative particles (molecules or formula units), multiply
the number of moles by 6.02 ñ 1023 representative particles/1 mol.
Then, multiply the number of representative particles by the number
of atoms in each molecule or formula unit.
The Size of a Mole Perhaps you are wondering just how large a
mole is. The SI unit, the mole, is not related to the small burrowing
animal of the same name, shown in Figure 10.4. However, this little
animal can help you appreciate the size of the number 6.02 ñ 1023.
Assume that an average animal-mole is 15 cm long, 5 cm tall, and has
a mass of 145 g. Based on this information, the mass of 6.02 ñ 1023
animal-moles is 8.73 ñ 1022 kg. That means that the mass of
Avogadro’s number of animal-moles is equal to more than 60 times
the combined mass of Earth’s oceans. If spread over the entire surface of Earth, Avogadro’s number of animal-moles would form a layer
more than 8 million animal-moles thick. What about the length of
6.02 ñ 1023 animal-moles? If lined up end-to-end, 6.02 ñ 1023 animalmoles would stretch from Earth to the nearest star, Alpha Centauri,
more than two million times. Are you beginning to understand how
enormous Avogadro’s number is?
310 $IBQUFSt-FTTPO
Check for Understanding
BIGIDEA Assess students’ knowledge about the Big Idea of The Mole and
Quantifying Matter by projecting Table 10.1 on an overhead. Ask students to briefly
state why all the substances in the table have the same number of representative
particles per mole. (One mole of any type of substance is 6.02 × 1023 atoms,
molecules, ions, formula units, etc. The type of particle does not affect the number
of particles in one mole.)
ADJUST INSTRUCTION If students are having difficulty with this concept, have them
review the text preceding Table 10.1. Then repeat the activity.
310
Chapter 10 • Lesson 1
TU
TOR
Sample Problem 10.3
Explain
Converting Moles to Number of Atoms
Propane is a gas used for cooking and heating. How many atoms are in 2.12 mol
of propane (C3H8)?
— Analyze List the knowns and the unknown.
molecules
The desired conversion is moles
atoms.
KNOWNS
number of moles ä2.12 mol C3H8
1 mol C3H8 ä6.02 ò1023 molecules C3H8
1 molecule C3H8 ä11 atoms
(3 carbon atoms and 8 hydrogen atoms)
UNKNOWN
number of atomsä? atoms
˜ Calculate
Solve for the unknown.
First, write the conversion factor to
convert from moles to molecules.
6.02 ò 1023 molecules C3H8
1 mol C3H8
Write the conversion factor to
convert from molecules to atoms.
11 atoms
1 molecule C3H8
Multiply the moles of C3H8 by the
conversion factors.
2.12 mol C3H8 ò
Remember to write the conversion
factors so that the unit in the
denominator cancels the unit in the
numerator of the previous factor.
Misconception Alert
6.02ò1023 molecules C3H8
11 atoms
ò
1 mol C3H8
1 molecule C3H8
ä1.40ò1025 atoms
™ Evaluate Does the result make sense? There are 11 atoms in each molecule of propane and more than 2 mol of propane, so the answer should be
more than 20 times Avogadro’s number of propane molecules. The answer
has three significant figures based on the three significant figures in the
given measurement.
There are 3 atoms of carbon
and 8 atoms of hydrogen in
1 molecule of propane.
5. How many atoms are in 1.14 mol of
sulfur trioxide (SO3)?
CRITICAL THINKING Have students examine the
problem solving process for Sample Problems 10.2
and 10.3. Ask Why do you divide by Avogadro’s
number in Sample Problem 10.2, but multiply by
it in Sample Problem 10.3? (In Sample Problem
10.2, the problem asks for the number of moles;
in Sample Problem 10.3, the problem asks for the
number of atoms.) Have students write a note to
themselves explaining when and how they should
use this conversion factor. Ask Do the identities
of the substances in the problems have any effect
on the way you use Avogadro’s number in the
conversion process? (no) Why? (The number of
representative particles in a mole is a constant. The
only information supplied by the substance is the
number of atoms that makes up one representative
particle of the substance. In Sample Problem 10.2,
the representative particle is a single atom of Mg.
In Sample Problem 10.3, the representative particle
contains 11 atoms.)
6. How many carbon atoms are in 2.12 mol
of propane? How many hydrogen atoms
are in 2.12 mol of propane?
Some students may think they are finished when the
calculator displays the result of the last calculation.
Explain that not all calculators automatically convert
the final answer to proper scientific notation, or use
the proper number of significant figures. Make sure
students know how to make the correct conversion
to scientific notation with their particular calculator.
Sample Practice Problems
A.
B.
C.
D.
Chemical Quantities 311
How many atoms are in 1.00 mole of glucose,
C6H12O6? (1.44 × 1025 atoms)
How many atoms of C are in 2.00 moles of
C6H12O6? (7.22 × 1024 atoms)
How many atoms of H are in 3.00 moles of
C6H12O6? (2.17 × 10 25 atoms)
How many atoms of O are in 1.25 moles of
C6H12O6? (4.52 × 1024 atoms)
Foundations for Math
CONVERTING PRODUCTS TO SCIENTIFIC NOTATION Point out that if a calculation
results in a product that has a power of 10, it may not necessarily be written in
proper scientific notation. The coefficient must be a number greater than or equal
to 1 and less than 10. Have students write a rule in their own words for converting
products in which the coefficient is greater than 10, and in which the coefficient
is less than 0. (Move the decimal to the left and adjust the exponent up; Move the
decimal to the right and adjust the exponent down.)
In Sample Problem 10.3, students might opt to multiply 2.12, 6.02, and 11 together
first, then multiply the result by 1023. This would give an answer of 140 × 1023, which
is not in proper scientific notation. Point out that an additional conversion must be
made by moving the decimal 2 places to the left and adjusting the exponent up by 2
to convert the answer to proper scientific notation.
Answers
FIGURE 10.3 3.61 × 1024 atoms
5.
1.14 mol × (6.02 × 1023 molecules/mol) ×
6.
(4 atoms/molecule) = 2.75 × 1024 atoms
2.12 mol C3H6 × (6.02 × 1023 molecule/mol) ×
(3 atoms/molecule) = 3.83 × 1024 C atoms
2.12 mol C3H6 × (6.02 × 1023 molecule/mol) ×
(8 atoms/molecule) = 1.02 × 1025 H atoms
Chemical Quantities
311
LESSON 10.1
CHEM
LESSON 10.1
Interpret Data
Explain
Molar Mass
Carbon Atoms
Number
Hydrogen Atoms
Mass (amu)
USE MODELS Provide students with tactile counting
MAKING CONNECTIONS Point out that the mass
APPLY CONCEPTS Explain that the molar masses
of all elements contain the same number of atoms
because the atomic masses of the elements are
relative values. Present this idea by telling the class
that the mass of an atom of element X is twice as
great as the mass of an atom of element Y. Ask
If you have 10 grams of element X and 10 grams
of element Y, would you expect both samples to
contain the same number of atoms? Why? (No,
because atoms of element X are twice as massive
as atoms of element Y. The sample of X would
contain only half as many atoms as the sample
of Y.) Ask What would you have to do to get the
same number of atoms in both samples? (Double
the mass of element X so that it is twice the mass
of element Y.)
12 amu
1
24
(2
Mass carbon
Mass hydrogen
Mass (amu)
12
objects to model the carbon and hydrogen
relationship in Table 10.2. Guide students to use
the objects to discover the mass ratio of carbon to
hydrogen.
of a single atom can be expressed in atomic mass
units, but it is not realistic to work with single
atoms. Explain that chemists work with large
numbers of atoms for which the mass can be
expressed in grams. In this text, the atomic masses
are rounded to one place after the decimal point.
Have students solve a given problem multiple times,
using a different rounding rule each time, so they
can see how rounding the atomic masses affects
the answer.
Number
Mass Ratio
1 amu
24 amu
2
ñ 12)
(2
ñ 1)
120
(10 ñ 12)
(10
600
(50 ñ 12)
(50
Avogadro’s
(6.02 ñ 1023) ñ (12)
number
2 amu
120 amu
10
ñ 1)
10 amu
600 amu
50
ñ 1)
Avogadro’s
(6.02 ñ 1023) ñ (1)
number
Table 10.2 An average carbon atom is 12 times heavier than an
average hydrogen atom.
a. Read Tables What is the mass of 50 carbon atoms? What is the
mass of 50 hydrogen atoms?
b. Apply Concepts What is the ratio of the mass of 500 carbon
atoms to the mass of 500 hydrogen atoms?
c. Infer Do 36.0 kg of carbon atoms and 3.0 kg of hydrogen atoms
contain the same number of atoms? Explain.
50 amu
â
â
â
â
12
1
12
1
12
1
12
1
ñ 1023) ñ (12)
12
â
(6.02 ñ 1023) ñ (1)
1
(6.02
Hint: To answer part c,
determine the mass ratio of
carbon to hydrogen.
Molar Mass
How do you determine the molar mass of an element and of
a compound?
Remember that the atomic mass of an element (the mass of a single atom) is
expressed in atomic mass units (amu). The atomic masses are relative values
based on the mass of the most common isotope of carbon (carbon-12).
Table 10.2 shows that an average carbon atom (C) with an atomic mass of
12.0 amu is 12 times heavier than an average hydrogen atom (H) with an
atomic mass of 1.0 amu. Therefore, 100 carbon atoms are 12 times heavier
than 100 hydrogen atoms. In fact, any number of carbon atoms is 12 times
heavier than the same number of hydrogen atoms. So 12.0 g of carbon atoms
and 1.0 g of hydrogen atoms must contain the same number of atoms.
If you look at the atomic masses of the elements in the periodic table, you
will notice that they are not whole numbers. For example, the atomic mass of
carbon is not exactly 12 times the mass of hydrogen. Recall from Chapter 4
that this is because atomic masses are weighted average masses of the isotopes
of each element.
312 $IBQUFSt-FTTPO
History of Avogadro’s Number
Avogadro’s number was not actually developed by Avogadro. In the early 1900s,
a French scientist by the name of J. Perrin first used the term “Avogadro’s number”
to describe the number of particles in a mole. Perrin used Brownian motion to
determine the number.
312
Chapter 10 • Lesson 1
1 mol of sulfur atoms â 32.1 g
1 mol of carbon atoms â 12.0 g
READING SUPPORT
Build Comprehension:
Analogies You can buy
small, medium, and large
eggs. The size of the eggs
doesn’t affect how many
eggs are in one dozen.
Similarly, the size of the
representative particles
doesn’t affect how many
are in one mole. Can you
think of another analogy
to show the relationship
between moles and the size
of representative particles?
Figure 10.5 Molar Mass of an Element
One mole of carbon, sulfur, and iron are
shown.
Apply Concepts How many atoms of
each element are present in each beaker?
Explore
Teacher Demo
PURPOSE Students will observe the difference in the
mass and volume of 1 mol of different substances.
MATERIALS 1 mol each of a variety of common
chemicals, 1 sealed container per sample
PROCEDURE Place 1 mol of at least two substances
from each of the following categories in containers
and seal them: molecular compounds—sucrose,
water, paradichlorobenzene; ionic compounds—
cobalt(II) chloride, potassium hydroxide, potassium
dichromate; elements—sulfur, iron, carbon,
mercury. On each container, mark the mass of
each substance. Point out that each container
holds 1 mol of a substance, no matter whether
the representative particles are molecules, formula
units, or atoms.
EXPECTED OUTCOME Students observe that a
mole of one substance has a different mass from a
mole of another substance, even though the same
number of representative particles, 6.02 × 1023, are
present.
1 mol of iron atoms â 55.8 g
Chemical Quantities 313
Differentiated Instruction
L1 SPECIAL NEEDS STUDENTS For the Teacher Demo, mark the levels of the filled
containers with tape on the outside of the containers so that sight-impaired
students can tell by handling the displays that moles of different substances occupy
different volumes and have different masses.
ELL
INTERPRET DATA
a.
ENGLISH LANGUAGE LEARNERS The differences in the terms mass, atomic
mass, atomic mass unit, and molar mass may be confusing to English learners. Have
students compile a glossary in which they define each term in English and in their
native language. Encourage students to then write the word meanings or synonyms
on sticky notes to be placed in the text.
L1
Answers
STRUGGLING STUDENTS If students are having difficulty with multi-step
problems, break the problem into simple parts. For instance, for Sample Problem
10.4, insert the following after the first sentence: Part a: Find the number of grams
of hydrogen in H2O2. Part b: Find the number of grams of oxygen in H2O2. Part c:
Find the molar mass of H2O2.
b.
c.
mass of 50 carbon atoms = 600 amu,
mass of 50 hydrogen atoms = 50 amu
12/1
Yes, the mass ratio for carbon to hydrogen is 12
to 1.
READING SUPPORT Answers will vary. The size of
the donuts doesn’t affect how many are in
one dozen.
FIGURE 10.5 6.02 × 1023 atoms
Chemical Quantities
313
LESSON 10.1
The Mass of a Mole of an Element Quantities measured in grams are
convenient for working in the laboratory, so chemists have converted the
relative scale of masses of the elements in amu to a relative scale of masses
The atomic mass of an element expressed in grams is
in grams.
the mass of a mole of the element. The mass of a mole of an element is
its molar mass. For carbon, the molar mass is 12.0 g. For atomic hydrogen,
the molar mass is 1.0 g. Figure 10.5 shows one mole of carbon, sulfur, and
iron. Compare the molar masses in the figure to the atomic masses in your
periodic table. Notice that the molar masses are rounded off to one place
after the decimal point. All the examples and problems in this text use
molar masses that are rounded off in this way. If your teacher uses a different rounding rule for molar masses, your answers to problems may differ
slightly from the answers given in the text.
If you were to compare 12.0 g of carbon atoms with 16.0 g of oxygen
atoms, you would find they contain the same number of atoms. The molar
masses of any two elements must contain the same number of atoms. How
many atoms are contained in the molar mass of an element? You already
know. The molar mass of any element contains 1 mol or 6.02 ñ 1023 atoms
of that element.
The mole can now be further defined as the amount of substance that
contains the same number of representative particles as the number of
atoms in 12.0 g of carbon-12. You know that 12.0 g is the molar mass of
carbon-12, so 12.0 g of carbon is 1 mol of carbon atoms. The same relationship applies to hydrogen: 1.0 g of hydrogen is 1 mol of hydrogen atoms.
Similarly, 24.3 g is the molar mass of magnesium, so 1 mol of magnesium
(or 6.02 ñ 1023 atoms of magnesium) has a mass of 24.3 g. Molar mass is
the mass of 1 mol of atoms of any element.
LESSON 10.1
Explore
1 mol of glucose (C6H12O6)
molecules (blood sugar) â 180.0 g
1 mol of paradichlorobenzene (C6H4Cl2)
molecules (moth crystals) â 147.0 g
Class Activity
PURPOSE Students learn to calculate the molar
mass of a compound.
MATERIALS the display prepared for the Teacher
Demo on p. 313
PROCEDURE Select a compound and show students
how to calculate the mass of 1 mol using the
atomic masses of the constituent elements from
the periodic table. Have them calculate the molar
masses of other compounds in the display. Lead
students to see they have determined the mass of
6.02 × 1023 representative particles.
1 mol of water (H2O)
molecules â 18.0 g
Figure 10.6 Molar Mass
of a Compound
One mole is shown for each of
three molecular compounds.
Infer How do you know that
each sample contains Avogadro’s
number of molecules?
ET
KIN IC
ART
See the molar
masses of compounds
animated online.
The Mass of a Mole of a Compound To find the mass of a mole of a compound, you must know the formula of the compound. The formula of sulfur trioxide is SO3. A molecule of SO3 is composed of one atom of sulfur and
three atoms of oxygen.
ã
à
1 SO3 molecule ã 1 S atom à 3 O atoms
You can calculate the mass of a molecule of SO3 by adding the atomic
masses of the atoms making up the molecule. From the periodic table, the
atomic mass of sulfur (S) is 32.1 amu. The mass of three atoms of oxygen is
three times the atomic mass of a single oxygen atom (O): 3 ñ 16.0 amu â
48.0 amu. So, the molecular mass of SO3 is 32.1 amu à 48.0 amu â 80.1 amu.
ã
à
1 S atom à
3 O atoms
ã 1 SO3 molecule
32.1 amu à 16.0 amu à16.0 amu à16.0 amu ã 80.1 amu
Now substitute the unit grams for atomic mass units to find the molar
mass of SO3. The molar mass (g/mol) of any compound is the mass in grams
of 1 mol of that compound. Thus, 1 mol of SO3 has a mass of 80.1 g. This is
the mass of 6.02 ñ 1023 molecules of SO3.
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. This method for calculating molar mass
applies to any compound, molecular or ionic. The molar masses of paradichlorobenzene (C6H4Cl2, 147.0 g), water (H2O, 18.0 g), and glucose (C6H12O6 ,
180.0 g) in Figure 10.6 were obtained in this way.
314 $IBQUFSt-FTTPO
Check for Understanding
The Essential Question Why is the mole an important measurement
in chemistry?
Assess students’ knowledge about the mole by asking them write a one-minute
response that answers this Essential Question. (Sample answer: The mole is an
important measurement in chemistry because it lets scientists turn a very large
number into one that is small enough to use easily in calculations.)
ADJUST INSTRUCTION If students are having trouble answering, have them
re-read the sections What Is a Mole? and Molar Mass. Then allow them to revise
their responses.
314
Chapter 10 • Lesson 1
TU
Sample Problem 10.4
TOR
Explain
Finding the Molar Mass of a Compound
KNOWNS
molecular formula äH2O2
mass of 1 mol Hä1.0 g H
mass of 1 mol O ä16.0 g O
The decomposition of hydrogen peroxide (H2O2) provides
sufficient energy to launch a rocket. What is the molar mass
of hydrogen peroxide?
— Analyze
List the knowns and the unknown. Convert
moles of atoms to grams by using conversion factors (g/mol)
based on the molar mass of each element. The sum of the
masses of the elements is the molar mass.
˜ Calculate
B.
2 mol Hò
2 mol Oò
Add the results.
1.0 g H
ä2.0 g H
1 mol H
One mole of H2O2 has 2 mol of
H atoms and 2 mol of O atoms,
so multiply the molar mass of
each element by 2.
16.0 g O
ä32.0 g O
1 mol O
mass of 1 mol H2O2 ä2.0 g Há32.0 g O ä34.0 g
molar mass of H2O2 ä34.0 g/mol
™ Evaluate Does the result make sense? The answer is the sum of two times the
molar mass of hydrogen and oxygen (17.0 g/mol). The answer is expressed to the
tenths place because the numbers being added are expressed to the tenths place.
One mole of PCl3 has 1 mol of P
atoms and 3 mol of Cl atoms.
8. What is the mass of 1.00 mol of sodium
hydrogen carbonate?
PR
S
E
O
7. Find the molar mass of PCl3.
NLIN
M
OBLE
Determine the mass of one mole of each of
the following compounds: CO2 (44.0 g), SO3
(80.1 g), Br2 (159.8 g), H2 (2.0 g), N2 (28.0 g),
NaOH (40.0 g), Al2(SO4)3 (342.3 g), and
Ba(NO3)2 (261.3 g).
What is the mass, in grams, of 1.72 mol CaCl2?
(191 g)
Evaluate
Informal Assessment
Assess students’ understanding of chemical
quantities by writing the following three questions
on the board and asking students to answer the
questions quantitatively or qualitatively.
1. How many particles does one mole of
any substance represent? (6.02 × 1023
representative particles of that substance)
2. How can you convert the number of atoms of
any substance to moles? (Multiply the number
of atoms by the conversion factor 1 mole
equals 6.02 × 1023 representative particles.)
3. What is the molar mass of Al2(CO3)3? (234.0 g;
also accept qualitative description of calculation)
Then have students complete the 10.1 Lesson Check.
10.1 LessonCheck
Reteach
Review What do you need to know to
convert among the count, mass, and volume of
something?
12. Calculate If a dozen apples has a mass of 2.0 kg
and 0.20 bushel is 1 dozen apples, how many
bushels of apples are in 1.0 kg of apples?
10.
Describe How do chemists count the number of representative particles in a substance?
13. Calculate How many moles is 1.50 ñ 1023 molecules of NH3?
11.
Explain How do you determine the molar
mass of an element? How do you determine the
molar mass of a compound?
14. Calculate How many atoms are in 1.75 mol of
CHCl3?
9.
A.
UNKNOWN
molar massä? g/mol
Solve for the unknown.
Convert moles of hydrogen and
oxygen to grams of hydrogen
and oxygen.
Sample Practice Problems
Set up cooperative learning groups of three or four
students with one student who is proficient in this
topic. Have students review each sample problem in
the lesson and create a list of parameters to follow
for solving each type of question. Then provide the
group with problems related to Lesson 10.1.
15. Calculate What is the molar mass of CaSO4?
Chemical Quantities 315
Lesson Check Answers
9. You need a common unit.
10. Chemists use the mole to count the
number of representative particles in
a substance.
11. The molar mass of an element is
the mass of a mole of the element.
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.
12.
13.
14.
15.
0.10 bushel
2.49 × 10 –1 mol NH3
5.27 × 1024 atoms
136.2 g/mol
Answers
7. 1 mol P × (31.0 g P/1 mol P) = 31.0 g P
3 mol Cl × (35.5 g Cl/1 mol Cl )= 106.5 g Cl
31.0 g P + 106.5 g Cl = 138 g/mol
8. 1 mol Na × (23.0 g Na/1 mol Na) = 23.0 g Na
1 mol H × (1.0 g H/1 mol H) = 1.0 g H
1 mol C × (12.0 g C/1 mol C) = 12.0 g C
3 mol O ×(16.0 g O/1 mol O) = 48.0 g O
23.0 g Na + 1.0 g H + 12.0 g C + 48.0 g O =
84.0 g
Chemical Quantities
315
LESSON 10.1
CHEM
CHEMISTRY & YOU
CHEMISTRY
Y
&
CHEMISTRY
Y
YO
YOU
U Have students read the
text and study the figures. Help students understand
the nature of a mole by posing the following
question: Why is the statement “a mole of carbon
has the same number of particles as a mole of
carbon dioxide” true? You may need to assist
students in the following ways:
• The number of particles in a mole is independent
of mass.
• A particle of a substance may be a single atom or
many atoms joined by covalent bonds, or it may
even be a subatomic particle.
Y U: EVERYDAY
YO
E
MATTER
&YOU:
How Big Is a Mole?
The mole is an especially useful tool to chemists, because it allows them to
express the number of representative particles of a substance in grams. For
example, a 1 mol sample of carbon, which contains Avogadro’s number of
carbon atoms (6.02 ñ 1023), has a mass of 12.0 g.
The mole is a huge quantity. Written out, Avogadro’s number is
602,000,000,000,000,000,000,000. However, it may be difficult for you to
comprehend exactly how big a mole is. Here are some interesting ways to
visualize the size of a mole.
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Explain
CRITICAL THINKING Students may wonder why a
number such as a mole is used. Explain that there
are certain numbers in science, called fundamental
constants, each of which explains some property
of nature. Challenge students to name other
fundamental constants. Examples include the speed
of light in a vacuum, c = 3.00 × 108 m/s, and the
elementary charge, e = 1.602 × 10–19 coulombs.
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Take It Further
1. Calculate Show how to calculate the number of
years it would take to count to Avogadro’s number if you
could count at the rate of 1 million numbers per second.
2. Use Models Develop your own concept to illustrate
the size of Avogadro’s number. Show your calculations.
3. Draw Conclusions At home, using a food scale,
measure out a mole of table sugar (sucrose, C12H22O11)
or a mole of table salt (sodium chloride, NaCl). What
does this measurement tell you about the size of atoms
and molecules?
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Answers
TAKE IT FURTHER
1.
2.
3.
6.02 × 1023 numbers/(1 × 106 numbers/sec) =
6.02 × 1017 sec,
6.02 × 1017 sec × (1year/3.15 × 107 sec) =
1.91 × 1010 years
Answers will vary but students should show the
conversion factors in each calculation.
The masses of atoms and molecules are not all
the same.
316
Chapter 10 • Chemistry & You
21st Century Skills To be successful in the 21st century, students need
skills and learning experiences that extend beyond subject matter mastery. The
following project helps students build these 21st Century Skills: Critical Thinking
and Problem Solving, Creativity and Innovation, Communication & Collaboration,
Information Literacy, Initiative and Self-Direction, and Productivity and Accountability.
MODELING THE MOLE Divide students into small groups of 4–6 students. Pose the
following challenge to students. An intermediate school teacher has requested your
group’s assistance in explaining the mole to her eighth grade science class, using
a creative and entertaining five-minute animation or a computerized slide show
with audio. The presentation should include multiple examples and demonstrate
step-by-step calculations that support the examples. Students should submit their
presentations on CD or DVD-ROM.