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13.1
13.1
The Nature of Gases
1
Connecting to Your World
You are walking your dog in
the woods. Suddenly your dog begins to bark
and run toward what you think is a black cat.
But before you realize that the “cat” is not a
cat, the damage is done. The skunk has
released its spray! Within seconds you
smell that all-too-familiar foul odor. In this
section, you will discover some general
characteristics of gases that help explain
how odors travel through the air, even on
a windless day.
Kinetic Theory and a Model for Gases
The word kinetic refers to motion. The energy an object has because of its
motion is called kinetic energy. According to the kinetic theory, all matter
consists of tiny particles that are in constant motion. The particles in a gas
are usually molecules or atoms. The kinetic theory as it applies to gases
includes the following fundamental assumptions about gases.
The particles in a gas are considered to be small, hard spheres with
an insignificant volume. Within a gas, the particles are relatively far apart
compared with the distance between particles in a liquid or solid. Between the
particles, there is empty space. No attractive or repulsive forces exist between
the particles. The motion of one particle in a gas is independent of the motion
of all the other particles.
The motion of the particles in a gas is rapid, constant, and
random. As a result, gases fill their containers regardless of the shape
and volume of the containers. An uncontained gas can spread out into
space without limit. The particles travel in straight-line paths until they
collide with another particle, or another object, such as the wall of their
container. The particles change direction only when they rebound from
collisions with one another or with other objects.
Measurements indicate that the average speed of oxygen molecules in air
at 20°C is an amazing 1700 km/h! At these high speeds, the odor from a hot
cheese pizza in Washington, D.C., should reach Mexico City in about
115 minutes. That does not happen, however, because the molecules responsible for the odor are constantly striking molecules in air and rebounding in
other directions. Their path of uninterrupted travel in a straight line is very
short. The aimless path the molecules take is called a random walk.
All collisions between particles in a gas are perfectly elastic. During an elastic collision, kinetic energy is transferred without loss from one
particle to another, and the total kinetic energy remains constant. The diagrams in Figure 13.1 on the next page illustrate the assumptions of kinetic
theory as applied to gases.
Guide for Reading
Key Concepts
• What are the three assumptions
of the kinetic theory as it
applies to gases?
• How does kinetic theory
explain gas pressure?
• What is the relationship
between the temperature in
kelvins and the average kinetic
energy of particles?
Vocabulary
kinetic energy
kinetic theory
gas pressure
vacuum
atmospheric pressure
barometer
pascal (Pa)
standard atmosphere (atm)
Reading Strategy
Relating Text and Visuals
As you read, look closely at
Figure 13.3. Explain how this
illustration helps you understand
how kinetic energy is distributed
among the particles of a gas at
two different temperatures.
Word Origins
Kinetic comes from the
Greek word kinetos, meaning
“to move.” Kinetic energy
is the energy an object
has because of its motion.
Some sculptures are
kinetic. What characteristic
do they share?
Section 13.1 The Nature of Gases 385
FOCUS
Objectives
13.1.1 Describe the assumptions of
the kinetic theory as it applies
to gases.
13.1.2 Interpret gas pressure in terms
of kinetic theory.
13.1.3 Define the relationship
between Kelvin temperature
and average kinetic energy.
Guide for Reading
Build Vocabulary
Word Forms The word vacuum comes
from the Latin vacare, meaning “to be
empty.” Discuss what happens in a
vacuum cleaner (Suction occurs as
matter rushes in to fill a vacuum.)
Reading Strategy
Print
• Guided Reading and Study Workbook,
Technology
• Interactive Textbook with ChemASAP,
Section 13.1
• Core Teaching Resources,
Section 13.1 Review
• Transparencies, T139–T141
Problem-Solving 13.1, Animation 14,
Assessment 13.1
• Go Online, Section 13.1
L2
Active Comprehension Read the first
paragraph of Kinetic Energy and Temperature. Ask students what more they
would like to know about this topic.
Students can look for answers to their
questions as they read the rest of
Kinetic Energy and Temperature.
2
INSTRUCT
Ask, How can you smell a skunk’s odor?
(Molecules emitted by the skunk travel
through the air to receptors in your nose.)
Kinetic Theory and a
Model for Gases
L2
Discuss
Section Resources
L2
Because multiple units are introduced
for pressure, you many want to review
the use of conversion factors.
Word Origins
L2
A kinetic sculpture has moving parts.
Some are free-hanging mobiles; some
are stabiles with motors.
States of Matter
385
chem_TE_ch13_IPL.fm Page 386 Wednesday, August 4, 2004 12:58 PM
Section 13.1 (continued)
a
c
b
Gas Pressure
Bromine
molecule
TEACHER
Demo
Elastic Collisions
Br2
vapor
L2
Purpose Students will differentiate
elastic colllisions from perfectly elastic
collisions.
Materials Newtonian cradle (a device
in which small steel balls are suspended by thin nylon tethers to horizontal wooden sticks)
Procedure Explain that in an elastic
collision, kinetic energy is transferred
between the objects that collide. In a
perfectly elastic collision, the total
amount of kinetic energy remains constant. Then pull back one of the balls
and let it fall into the other balls. After
the balls come to rest, ask, Were the
collisions between the balls elastic?
(Yes, because kinetic energy was transferred with each collision.) Why did the
balls eventually stop moving? (The
collisions were not perfectly elastic; some
kinetic energy was lost as heat during
each collision.)
Remind students that the kinetic theory assumes that all collisions between
particles in a gas are perfectly elastic.
(In Chapter 14, students will learn that
the assumptions of the kinetic theory
do not hold true for real gases under all
conditions.)
Use Visuals
Figure 13.1 Gases share some general characteristics.
a The rapid, constant motion of particles in a gas causes them to
collide with one another and with the walls of their container.
b The particles travel in straight-line paths between collisions.
c A gas fills all the available space in its container.
Gas Pressure
Vacuum
760 mm Hg
(barometric
pressure)
Atmospheric
pressure
A helium-filled balloon maintains its shape because of the pressure of the
gas within it. Gas pressure results from the force exerted by a gas per unit
surface area of an object. What causes this force? Moving bodies exert a
force when they collide with other bodies. Although a single particle in a
gas is a moving body, the force it exerts is extremely small. Yet it is not hard
to imagine that simultaneous collisions involving many particles would
produce a measurable force on an object.
Gas pressure is the result
of simultaneous collisions of billions of rapidly moving particles in a
gas with an object. If there are no particles, there cannot be collisions.
Consequently, there is no pressure. An empty space with no particles and
no pressure is called a vacuum.
A gas pressure that you are familiar with is that caused by a mixture of
gases—air. Air exerts pressure on Earth because gravity holds the particles
in air in Earth’s atmosphere. Atmospheric pressure results from the collisions of atoms and molecules in air with objects. Atmospheric pressure
decreases as you climb a mountain because the density of Earth’s atmosphere decreases as the elevation increases.
A barometer is a device that is used to measure
atmospheric pressure. Figure 13.2 shows an early
type of mercury barometer. The height of the mercury column in the tube depends on the pressure
exerted by particles in air colliding with the surface
of the mercury in the dish. Atmospheric pressure
depends on weather and on altitude. In fair weather
at sea level, the atmospheric pressure is sufficient to
support a mercury column about 760 mm high.
253 mm Hg
L1
Figure 13.2 Point out the parts of the
barometer and explain how the barometer is used to measure atmospheric pressure. Ask,What is the air pressure on
top of Mount Everest in kPa? (33.7 kPa)
Sea level
On top of Mount Everest
Figure 13.2 At sea level, air exerts enough
pressure to support a 760-mm column of
mercury. On top of Mount Everest, at 9000 m,
the air exerts only enough pressure to support
a 253-mm column of mercury.
Calculating What is the decrease in pressure
from sea level to the top of Mount Everest?
386 Chapter 13
FYI
In Chapter 14, students will study factors
that affect gas pressure—amount of gas,
temperature, and volume.
Differentiated Instruction
L3
Gifted and Talented
Encourage students to examine critically
how barometric pressure is reported in local
newspapers and on television. Ask, What
units are commonly used in weather
reports to express barometric pressure?
(Unfortunately, units are rarely stated in the
reports. Pressure is usually reported in inches of
386 Chapter 13
mercury. Students may infer the unit based on
the numerical values of the stated pressures.)
Bring in the weather sections of newspapers
and have students determine today’s pressure in mm Hg, in kPa, and in atm. Students
may wish to track the daily pressure and display the changes on a graph.
chem_TE_ch13_IPL.fm Page 387 Wednesday, August 4, 2004 12:58 PM
The SI unit of pressure is the pascal (Pa). It represents a very small amount
of pressure. For example, normal atmospheric pressure is about 100,000 Pa,
that is, 100 kilopascals (kPa). Two older units of pressure are still commonly
used. These units are millimeters of mercury (mm Hg) and atmospheres.
One standard atmosphere (atm) is the pressure required to support 760 mm
of mercury in a mercury barometer at 25°C. The numerical relationship
among the three units is given below.
Sample Problem 13.1
Answers
1. 51.3 kPa, 0.507 atm
2. 33.7 kPa is greater than 0.25 atm
L2
Practice Problems Plus
1 atm 760 mm Hg 101.3 kPa
What pressure, in mm Hg and atm,
does a sample of neon gas exert at
75.0 kPa? (563 mm Hg, 0.740 atm)
In the case of gases, it is important to be able to relate measured values to
standards. Recall that the standard temperature and pressure (STP) are
defined as a temperature of 0°C and a pressure of 101.3 kPa, or 1 atm.
SAMPLE PROBLEM 13.1
Converting Between Units of Pressure
Using a Calculator
A pressure gauge records a pressure of 450 kPa. What is this measurement expressed in atmospheres and millimeters of mercury?
After you analyze a sample
problem, you can use a calculator to solve for the unknown.
A calculator provides the four
basic arithmetic functions of
addition (), subtraction (),
multiplication (), and division
(). You can also raise to a
power (x2), take the square
root (兹x ), and take the logarithm (log). You will need to be
able to enter measurements
written in scientific notation.
On many calculators, you will
use the EE key or EXP key to
enter such measurements.
Analyze List the knowns and the unknowns.
Knowns
• pressure 450 kPa
• 1 atm 101.3 kPa
• 1 atm 760 mm Hg
Unknowns
• pressure ? atm
• pressure ? mm Hg
For converting kPa ¡ atm, the appropriate conversion factor is
1 atm
101.3 kPa
For converting kPa ¡ mm Hg, the appropriate conversion factor is
760 mm Hg
101.3 kPa
Calculate Solve for the unknowns.
Math
1 atm 4.4 atm
101.3 kPa
760 mm Hg
450 kPa 3400 mm Hg 3.4 103 mm Hg
101.3 kPa
450 kPa Practice Problems
2. The pressure at the top of
Mount Everest is 33.7 kPa. Is
that pressure greater or less
than 0.25 atm?
Problem-Solving 13.1 Solve
Problem 1 with the help of an
interactive guided tutorial.
with ChemASAP
Section 13.1 The Nature of Gases 387
Facts and Figures
Aneroid Barometers
Unlike traditional barometers, aneroid
barometers do not balance atmospheric
pressure against a liquid of known density. In
fact, they contain no liquid and are independent of gravity. If possible, bring one to class
and explain its components. Have interested
Math
Handbook
For a math refresher and practice, direct students to using a
calculator, page R62.
TEACHER
Demo
L2
Air Pressure
Because the first conversion factor is much less than 1 and the second
much greater than 1, it makes sense that the values expressed in atm
and mm Hg are respectively smaller and larger than the value expressed
in kPa.
and in atmospheres, does a gas
exert at 385 mm Hg?
When students use a calculator to
convert between units, they
should evaluate the answer to
make sure that they entered the
data correctly and that they used
an appropriate conversion factor.
Handbook
For help using a calculator,
go to page R62.
Evaluate Do the results make sense?
1. What pressure, in kilopascals
Using a Calculator
students research the advantages of aneroid
barometers. (They are compact, self enclosed,
and easily transported. They can operate under
conditions not suited to mercury barometers.)
Interested students may wish to construct an
aneroid barometer and demonstrate its use.
Purpose Students will become aware
of the tremendous pressure exerted by
Earth’s atmosphere.
Materials empty aluminum beverage
can, water, hot plate, foil or other material for sealing opening of can
Procedure Explain to students that they
live at the bottom of a very deep “ocean”
of air. Fill an empty aluminum beverage
container with water to a depth of about
1 to 2 cm. Set the can on a hot plate and
bring the water to a boil. Allow the water
to boil vigorously for several minutes.
Remove the can from the heat source,
seal the opening, and allow the can to
cool at room temperature or invert the
can in a pan of cool water.
Expected Outcome Once the water
vapor inside the can condenses, the
atmospheric pressure will crush the
can. Ask students to interpret their
observations.
Answers to...
Figure 13.2 507 mm Hg
States of Matter
387
chem_TE_ch13_IPL.fm Page 388 Thursday, August 5, 2004 10:33 AM
Section 13.1 (continued)
Kinetic Energy and Temperature
Kinetic Energy and
Temperature
As a substance is heated, its particles absorb energy, some of which is stored
within the particles. This stored portion of the energy, or potential energy,
does not raise the temperature of the substance. The remaining absorbed
energy speeds up the particles—that is, increases their kinetic energy. This
increase in kinetic energy results in an increase in temperature.
L2
a. a point near the peak of the curve
b. The curves have the same overall
shape, but the curve for hot water is
wider with a lower peak. c. At an even
higher temperature, the graph would
be wider than the red curve with a
lower peak; at an even lower temperature, the graph would be narrower
than the blue curve with a higher peak.
Enrichment Question
For: Links on Kinetic Theory
Visit: www.SciLinks.org
Web Code: cdn-1131
molecules at a given temperature have a wide range of kinetic energies.
Most of the particles have kinetic energies somewhere in the middle of this
range. Therefore, average kinetic energy is used when discussing the kinetic
energy of a collection of particles in a substance. At any given temperature
the particles of all substances, regardless of physical state, have the same
average kinetic energy. For example, the ions in table salt, the molecules
in water, and the atoms in helium all have the same average kinetic energy
at room temperature even though the three substances are in different
physical states.
Figure 13.3 shows the distribution of kinetic energies of water molecules at two different temperatures. The blue curve shows the distribution
of kinetic energy among the water molecules in cold water. The red curve
shows the distribution of kinetic energy among the water molecules in hot
water. In both cases, most of the molecules have intermediate kinetic energies, which are close to the average value. Notice that at the higher temperature there is a wider range of kinetic energies.
There is a relationship between the average kinetic energy of the particles in a substance and the substance’s temperature. An increase in the
average kinetic energy of the particles causes the temperature of a substance to rise. As a substance cools, the particles tend to move more slowly,
and their average kinetic energy declines.
L3
Compare the kinetic energy of the
particles represented by the points
on the red and blue curves where
the curves intersect. (The particles
have the same kinetic energy.)
CLASS
Activity
Kinetic Energy and Frequency
L2
of Collisions
Purpose Students will be able to visualize what is happening in a gas as the
average kinetic energy increases.
Materials cardboard containers (e.g.,
half-pint milk cartons), ball bearings
Procedure Give students cardboard
boxes containing the same number of
ball bearings. Have students shake the
boxes slowly at first. Then have them
gradually increase the rate of shaking
and observe what happens. Tell students that the shaking is analogous to
adding energy to the particles in a gas.
The greater the rate of the shaking, the
more energy is added. Then ask how an
increase in energy affects the frequency
of collisions.
Expected Outcome Student should
hear and feel the increase in number of
collisions as the rate of shaking (or the
amount of energy added) increases.
Download a worksheet on Kinetic
Theory for students to complete,
and find additional teacher support
from NSTA SciLinks.
388
Chapter 13
Average Kinetic Energy The particles in any collection of atoms or
Figure 13.3 The red and blue
curves show the kinetic energy
distributions of a typical
collection of molecules at two
different temperatures.
Distribution of Molecular Kinetic Energy
Many molecules
have an intermediate
kinetic energy
INTERPRETING GRAPHS
a. Inferring Which point
on each curve represents the
average kinetic energy?
b. Analyzing Data
Compare the shapes of the
curves for cold water and
hot water.
c. Predicting What would
happen to the shape of the
curve if the water temperature
were even higher? Even lower?
Percent of molecules
Interpreting Graphs
Higher temperature
(hot water)
Few molecules
have a very high
kinetic energy
Kinetic energy
388 Chapter 13
Lower temperature
(cold water)
chem_TE_ch13.fm Page 389 Monday, April 17, 2006 11:34 AM
Figure 13.4 In this vacuum
chamber, scientists cooled
sodium vapor to nearly absolute
zero. To keep the atoms from
sticking to the walls of the
chamber, the scientists used
magnetism and gravity to trap
the atoms 0.5 cm above the coil
in the center of the chamber. The
coil is shown at about two times
its actual size.
You could reasonably expect the particles of all substances to stop moving at some very low temperature. The particles would have no kinetic energy
at that temperature because they would have no motion. Absolute zero (0 K,
or 273.15°C) is the temperature at which the motion of particles theoretically ceases. There is no temperature lower than absolute zero. Absolute zero
has never been produced in the laboratory. However, near-zero temperatures of about 0.0000000005 K (0.5 109 K), which is 0.5 nanokelvin, have
been achieved in the vacuum chamber shown in Figure 13.4.
ASSESS
L2
Evaluate Understanding
To assess students’ comprehension of
kinetic theory as it applies to gases,
ask, What is kinetic energy? (energy
due to the motion of an object) How is
the average kinetic energy of a
collection of particles related to
temperature? (Average kinetic energy
is directly proportional to the Kelvin temperature. Higher temperatures reflect a
greater average kinetic energy.)
L1
Reteach
Average Kinetic Energy and Kelvin Temperature The Kelvin temperature scale reflects the relationship between temperature and average
kinetic energy.
The Kelvin temperature of a substance is directly proportional to the average kinetic energy of the particles of the substance.
For example, the particles in helium gas at 200 K have twice the average
kinetic energy as the particles in helium gas at 100 K. The effects of temperature on particle motion in liquids and solids are more complex than in gases.
3
Animation 14 Observe
particles in motion and
discover the connection
between temperature and
kinetic energy.
Have students look at Figure 13.3. Ask,
What does the blue curve represent?
(The distribution of kinetic energy in cold
water.) What does the red curve represent? (The distribution of kinetic
energy in hot water.) In which sample
is the average kinetic energy of the
particles higher? (hot water).
with ChemASAP
Checkpoint What happens to the temperature of a substance when the
average kinetic energy of its particles decreases?
Student paragraphs should
describe straight-line, random
motion until particles collide with
each other and with the sides of the
container. After a collision, the
direction of motion changes.
13.1 Section Assessment
3.
Key Concept Briefly describe the assumptions of kinetic theory as applied to gases.
4.
Key Concept Use kinetic theory to explain
what causes gas pressure.
5.
Key Concept How is the Kelvin temperature
of a substance related to the average kinetic
energy of its particles?
Describing Motion in a Gas Write a paragraph
describing the behavior of an oxygen molecule in a
sealed container of air. Include what happens when
the molecule collides with another molecule or the
walls of the container.
6. Convert the following pressures to kilopascals.
a. 0.95 atm
b. 45 mm Hg
7. A cylinder of oxygen gas is cooled from 300 K
(27°C) to 150 K (123°C). By what factor does the
average kinetic energy of the oxygen molecules in
the cylinder decrease?
Assessment 13.1 Test yourself
on the concepts in Section 13.1.
with ChemASAP
If your class subscribes to the
Interactive Textbook, use it to
review key concepts in Section 13.1.
with ChemASAP
Section 13.1 The Nature of Gases 389
Section 13.1 Assessment
3. A gas is composed of tiny particles
whose motion is rapid, constant, and
random. Collisions between particles are
perfectly elastic.
4. Gas pressure is the result of simultaneous collisions of billions of rapidly
moving particles with an object.
5. The Kelvin temperature is directly proportional to the average kinetic energy
of the particles.
6. a. 96 kPa
b. 6.0 kPa
7. by one-half
Answers to...
Checkpoint
The tempera-
ture decreases.
States of Matter
389