Chemistry

The Kinetic-Molecular SECTION 1
Theory of Matter
OBJECTIVES
I n Chapter 1, you read that matter exists on Earth in the forms of
State the kinetic-molecular
solids, liquids, and gases. Although it is not usually possible to observe theory of matter, and describe
individual particles directly, scientists have studied large groups of these how it explains certain prop-
particles as they occur in solids, liquids, and gases. erties of matter.
List the five assumptions of
In the late nineteenth century, scientists developed the kinetic- the kinetic-molecular theory
molecular theory of matter to account for the behavior of the atoms and of gases. Define the terms
molecules that make up matter. The kinetic-molecular theory is based ideal gas and real gas.
on the idea that particles of matter are always in motion. The theory can Describe each of the following
be used to explain the properties of solids, liquids, and gases in terms of characteristic properties of
the energy of particles and the forces that act between them. In this sec- gases: expansion, density, flu-
tion, you will study the theory as it applies to gas molecules. idity, compressibility, diffusion,
and effusion.
The Kinetic-Molecular Describe the conditions under
Theory of Gases which a real gas deviates
from “ideal” behavior.
The kinetic-molecular theory can help you understand the behavior of
gas molecules and the physical properties of gases. The theory provides www.scilinks.org
a model of what is called an ideal gas. An ideal gas is a hypothetical gas Topic: Gases
that perfectly fits all the assumptions of the kinetic-molecular theory. Code: HC60638

The kinetic-molecular theory of gases is based on the following five S T A T E S O F M A T T E R 329
assumptions:
1. Gases consist of large numbers of tiny particles that are far apart rela-

tive to their size. These particles, usually molecules or atoms, typically
occupy a volume that is about 1000 times greater than the volume
occupied by an equal number of particles in the liquid or solid state.
Thus, molecules of gases are much farther apart than molecules of liq-
uids or solids. Most of the volume occupied by a gas is empty space,
which is the reason that gases have a lower density than liquids and
solids do. This also explains the fact that gases are easily compressed.
2. Collisions between gas particles and between particles and container
walls are elastic collisions. An elastic collision is one in which there is
no net loss of total kinetic energy. Kinetic energy is transferred
between two particles during collisions. However, the total kinetic
energy of the two particles remains the same as long as temperature
is constant.

FIGURE 1 Gas particles travel in 3. Gas particles are in continuous, rapid, random motion. They there-
a straight-line motion until they col- fore possess kinetic energy, which is energy of motion. Gas particles
lide with each other or the walls of move in all directions, as shown in Figure 1. The kinetic energy of
their container. the particles overcomes the attractive forces between them, except
near the temperature at which the gas condenses and becomes a
Chemical Content liquid.

Go to go.hrw.com for another ver- 4. There are no forces of attraction between gas particles. You can think
sion of this content. See the chapters of ideal gas molecules as behaving like small billiard balls. When they
“Physical Characteristics of Gases,” collide, they do not stick together but immediately bounce apart.
“Molecular Composition of Gases,”
and “Liquids and Solids.” 5. The temperature of a gas depends on the average kinetic energy of the
particles of the gas. The kinetic energy of any moving object, includ-
Keyword: HC6STMX ing a particle, is given by the following equation:

KE = ⎯1 mv2
2

In the equation, m is the mass of the particle and v is its speed. Because
all the particles of a specific gas have the same mass, their kinetic energies
depend only on their speeds. The average speeds and kinetic energies of
gas particles increase with an increase in temperature and decrease with
a decrease in temperature.

All gases at the same temperature have the same average kinetic
energy. Therefore, at the same temperature, lighter gas particles, such
as hydrogen molecules, have higher average speeds than do heavier
gas particles, such as oxygen molecules.

The Kinetic-Molecular Theory
and the Nature of Gases

The kinetic-molecular theory applies only to ideal gases. Although ideal
gases do not actually exist, many gases behave nearly ideally if pressure
is not very high and temperature is not very low. In the following sec-
tions, you will see how the kinetic-molecular theory accounts for the
physical properties of gases.

Expansion

Gases do not have a definite shape or a definite volume. They com-
pletely fill any container in which they are enclosed, and they take its
shape. A gas transferred from a one-liter vessel to a two-liter vessel will
quickly expand to fill the entire two-liter volume. The kinetic-molecular
theory explains these facts. According to the theory, gas particles move
rapidly in all directions (assumption 3) without significant attraction
between them (assumption 4).

Fluidity

Because the attractive forces between gas particles are insignificant
(assumption 4), gas particles glide easily past one another. This ability to

330 C H A P T E R 1 0

flow causes gases to behave as liquids do. Because liquids and gases www.scilinks.org
flow, they are both referred to as fluids. Topic: Diffusion/Effusion
Code: HC60407
Low Density

The density of a gaseous substance at atmospheric pressure is about
1/1000 the density of the same substance in the liquid or solid state. The
reason is that the particles are so much farther apart in the gaseous state
(assumption 1).

Compressibility

During compression, the gas particles, which are initially very far apart
(assumption 1), are crowded closer together. The volume of a given
sample of a gas can be greatly decreased. Steel cylinders containing
gases under pressure are widely used in industry. When they are full,
such cylinders may contain more than 100 times as many particles of gas
as nonpressurized containers of the same size could contain.

Diffusion and Effusion

Gases spread out and mix with one another, even without being stirred.
If the stopper is removed from a container of ammonia in a room,
ammonia gas will mix uniformly with the air and spread throughout the
room. The random and continuous motion of the ammonia molecules
(assumption 3) carries them throughout the available space. Such spon-
taneous mixing of the particles of two substances caused by their random
motion is called diffusion.

Gases diffuse readily into one another and mix together due to the
rapid motion of the molecules and the empty space between the mole-
cules. The gas molecules in each of the two flasks in Figure 2a continu-
ously move about in separate flasks because the stopcock is closed.
When the stopcock is open, the gas molecules continuously diffuse back
and forth from one flask to the other through the opening in the stop-
cock, as shown in Figure 2b.

H2 N2 Stopcock
Stopcock open

closed

(a) (b)

FIGURE 2 Gases diffuse readily into one another. The space between the
molecules allows different gases to mix together easily.

S T A T E S O F M A T T E R 331

Diffusion is a process by which particles of a gas spread out sponta-
neously and mix with other gases. In contrast, effusion is a process by
which gas particles pass through a tiny opening. The rates of effusion of
different gases are directly proportional to the velocities of their parti-
cles. Because of this proportionality, molecules of low mass effuse faster
than molecules of high mass.

(a) Deviations of Real Gases
from Ideal Behavior
(b)
FIGURE 3 (a) Gas molecules in a Because particles of gases occupy space and exert attractive forces on
car engine cylinder expand to fill the each other, all real gases deviate to some degree from ideal gas behav-
cylinder. (b) As pressure is exerted ior. A real gas is a gas that does not behave completely according to the
on them, the gas molecules move assumptions of the kinetic-molecular theory. At very high pressures and
closer together, reducing their low temperatures, the gas particles will be closer together and their
volume. kinetic energy will be insufficient to overcome completely the attractive
forces. At such conditions, the gas is most likely to behave like a non-
ideal gas. These conditions are illustrated in Figure 3.

The kinetic-molecular theory is more likely to hold true for gases
whose particles have little attraction for each other. The noble gases,
such as helium, He, and neon, Ne, show essentially ideal gas behavior
over a wide range of temperatures and pressures. The particles of these
gases are monatomic and thus nonpolar. The particles of gases, such as
nitrogen, N2, and hydrogen, H2, are nonpolar diatomic molecules. The
behavior of these gases most closely approximates that of the ideal gas
under certain conditions. The more polar the molecules of a gas are, the
greater the attractive forces between them and the more the gas will
deviate from ideal gas behavior. For example, highly polar gases, such as
ammonia, NH3, and water vapor, deviate from ideal behavior to a larger
degree than nonpolar gases.

SECTION REVIEW 5. What happens to gas particles when a gas is
compressed?
1. Use the kinetic-molecular theory to explain each
of the following properties of gases: expansion, 6. What happens to gas particles when a gas is
fluidity, low density, compressibility, and diffusion. heated?

2. Describe the conditions under which a real gas is Critical Thinking
most likely to behave ideally.
7. DRAWING CONCLUSIONS Molecules of hydrogen
3. Which of the following gases would you expect to escape from Earth, but molecules of oxygen and
deviate significantly from ideal behavior: He, O2, nitrogen are held to the surface and remain in the
H2, H2O, N2, HCl, or NH3? atmosphere. Explain.

4. How does the kinetic-molecular theory explain the
pressure exerted by gases?

332 C H A P T E R 1 0

Liquids SECTION 2

T he water in the waves crashing on a beach and the molten lava OBJECTIVES

rushing down the sides of a volcano are examples of matter in the liq- Describe the motion of
uid state. When you think of Earth’s oceans, lakes, and rivers and the particles in liquids and the
many liquids you use every day, it is hard to believe that liquids are the properties of liquids according
least common state of matter in the universe. Liquids are less common to the kinetic-molecular theory.
than solids and gases because a substance can exist in the liquid state
only within a relatively narrow range of temperatures and pressures. Discuss the process by which
liquids can change into a gas.
In this section, you will examine the properties of the liquid state. Define vaporization.
You will also compare them with those of the solid state and the
gas state. These properties will be discussed in terms of the kinetic- Discuss the process by which
molecular theory. liquids can change into a
solid. Define freezing.

Properties of Liquids and the www.scilinks.org
Kinetic-Molecular Theory Topic: Properties of Liquids
Code: HC61228
A liquid can be described as a form of matter that has a definite vol-
ume and takes the shape of its container. The properties of liquids can S T A T E S O F M A T T E R 333
be understood by applying the kinetic-molecular theory, considering
the motion and arrangement of molecules and the attractive forces
between them.

As in a gas, particles in a liquid are in constant motion. However, the
particles in a liquid are closer together than the particles in a gas are.
Therefore, the attractive forces between particles in a liquid are more
effective than those between particles in a gas. This attraction between
liquid particles is caused by the intermolecular forces discussed in
Chapter 6: dipole-dipole forces, London dispersion forces, and hydro-
gen bonding. Some molecules at the surface of a liquid can have enough
kinetic energy to overcome these forces, and enter the gas state.

Liquids are more ordered than gases because of the stronger inter-
molecular forces and the lower mobility of the liquid particles.
According to the kinetic-molecular theory of liquids, the particles are
not bound together in fixed positions. Instead, they move about con-
stantly. This particle mobility explains why liquids and gases are
referred to as fluids. A fluid is a substance that can flow and therefore
take the shape of its container. Most liquids naturally flow downhill
because of gravity. However, some liquids can flow in other directions
as well. For example, liquid helium near absolute zero has the unusual
property of being able to flow uphill.

Solid cork Increasing density Relatively High Density

Liquid alcohol At normal atmospheric pressure, most substances are hundreds of times
denser in a liquid state than in a gaseous state. This higher density is a
Solid paraffin result of the close arrangement of liquid particles. Most substances are
only slightly less dense (about 10%) in a liquid state than in a solid state,
Liquid oil however. Water is one of the few substances that becomes less dense
when it solidifies, as will be discussed further in Section 5.
Liquid water
At the same temperature and pressure, different liquids can differ
Solid rubber greatly in density. Figure 4 shows some liquids and solids with different
densities. The densities differ to such an extent that the liquids form
Liquid glycerin layers.

FIGURE 4 Solids and liquids of Relative Incompressibility
different densities are shown. The
densest materials are at the bottom. When liquid water at 20°C is compressed by a pressure of 1000 atm, its
The least dense are at the top. (Dyes volume decreases by only 4%. Such behavior is typical of all liquids and
have been added to the liquids to is similar to the behavior of solids. In contrast, a gas under a pressure of
make the layers more visible.) 1000 atm would have only about 1/1000 of its volume at normal atmos-
pheric pressure. Liquids are much less compressible than gases because
FIGURE 5 Like gases, the two liq- liquid particles are more closely packed together. Like gases, liquids can
uids in this beaker diffuse over time. transmit pressure equally in all directions.
The green liquid food coloring from
the drop will eventually form Ability to Diffuse
a uniform solution with the water.
As described in Section 1, gases diffuse and mix with other gas particles.
Water Liquids also diffuse and mix with other liquids, as shown in Figure 5.
molecule Any liquid gradually diffuses throughout any other liquid in which it
can dissolve. The constant, random motion of particles causes diffusion
in liquids, as it does in gases. Yet diffusion is much slower in liquids than
in gases because liquid particles are closer together. Also, the attractive
forces between the particles of a liquid slow their movement. As the
temperature of a liquid is increased, diffusion occurs more rapidly. The
reason is that the average kinetic energy, and therefore the average
speed of the particles, is increased.

Dye
molecule

334 C H A P T E R 1 0

Surface Tension Attractions on a Attractions on a
typical molecule surface molecule
A property common to all liquids is surface tension, a force that tends to in a liquid
pull adjacent parts of a liquid’s surface together, thereby decreasing surface
area to the smallest possible size. Surface tension results from the attrac- FIGURE 6 As a result of surface
tive forces between particles of a liquid.The higher the force of attraction, tension, liquids form roughly spheri-
the higher the surface tension. Water has a higher surface tension than cal drops. The net attractive forces
most liquids. This is due in large part to the hydrogen bonds water mole- between the particles pull the mole-
cules can form with each other. The molecules at the surface of the water cules on the surface of the drop
are a special case. They can form hydrogen bonds with the other water inward. The molecules are pulled
molecules beneath them and beside them, but not with the molecules in very close together, which minimizes
the air above them. As a result, the surface water molecules are drawn the surface area.
together and toward the body of the liquid, creating a high surface ten-
sion. Surface tension causes liquid droplets to take on a spherical shape
because a sphere has the smallest possible surface area for a given vol-
ume. An example of this phenomenon is shown in Figure 6.

Capillary action, the attraction of the surface of a liquid to the surface
of a solid, is a property closely related to surface tension. A liquid will
rise quite high in a very narrow tube and will wet the tube if a strong
attraction exists between the liquid molecules and the molecules that
make up the surface of the tube. This attraction tends to pull the liquid
molecules upward along the surface and against the pull of gravity. This
process continues until the attractive forces between the liquid mol-
ecules and the surface of the tube are balanced by the weight of the liq-
uid. Capillary action can occur between water molecules and paper
fibers, as shown in Figure 7. Capillary action is at least partly responsi-
ble for the transportation of water from the roots of a plant to its leaves.
The same process is responsible for the concave liquid surface, called a
meniscus, that forms in a test tube or graduated cylinder.

Evaporation and Boiling

The process by which a liquid or solid changes to a gas is vaporization.
Evaporation is a form of vaporization. Evaporation is the process by
which particles escape from the surface of a nonboiling liquid and enter
the gas state.

(a) (b) FIGURE 7 The attraction between polar
water molecules and polar cellulose molecules
in paper fibers causes the water to move up in
the paper. The water-soluble ink placed near
the bottom of the paper in (a) rises up the
paper along with the water, as seen in (b). As
the ink moves up the paper, it is separated into
its various components, producing the different
bands of color. This separation occurs because
the water and the paper attract the molecules
of the ink components differently. These phe-
nomena are used in the separation process of
paper chromatography seen here.

S T A T E S O F M A T T E R 335

Evaporated Br2(g) A small amount of liquid bromine was added to the bottle shown in
molecule diffusing into air Figure 8. Within a few minutes, the air above the liquid bromine turned
brownish-red because some bromine molecules escaped from the sur-
N2(g) molecule O2(g) molecule face of the liquid. These molecules became gas molecules, or bromine
vapor, which mixed with the air. A similar phenomenon occurs if you
Br2(l) apply perfume to your wrist. Within seconds, you become aware of the
molecule perfume’s fragrance. Scent molecules evaporate from your skin and dif-
fuse through the air, where your nose detects them.
FIGURE 8 Liquid bromine, Br2,
evaporates near room temperature. Evaporation occurs because the particles of a liquid have different
The resulting brownish red gas kinetic energies. Particles with higher-than-average energies move
diffuses into the air above the faster. Some surface particles with higher-than-average energies can
surface of the liquid. overcome the intermolecular forces that bind them to the liquid. They
can then escape into the gas state.

Evaporation is a crucial process in nature. Evaporation removes
fresh water from the surface of the ocean, leaving behind a higher con-
centration of salts. In tropical areas, evaporation occurs at a higher rate,
causing the surface water to be saltier. All water that falls to Earth in
the form of rain and snow previously evaporated from oceans, lakes,
and rivers. Evaporation of perspiration plays an important role in keep-
ing you cool. Perspiration, which is mostly water, cools you by absorb-
ing body heat when it evaporates. Energy as heat is absorbed from the
skin, causing the cooling effect.

Boiling is the change of a liquid to bubbles of vapor that appear
throughout the liquid. Boiling differs from evaporation, as you will see
in Section 4.

Formation of Solids

When a liquid is cooled, the average energy of its particles decreases.
If the energy is low enough, attractive forces pull the particles into an
even more orderly arrangement. The substance then becomes a solid.
The physical change of a liquid to a solid by removal of energy as heat
is called freezing or solidification. Perhaps the best-known example of
freezing is the change of liquid water to solid water, or ice, at 0°C.
Another familiar example is the solidification of paraffin at room tem-
perature. All liquids freeze, although not necessarily at temperatures
you normally encounter. Ethanol, for example, freezes near −114°C.

SECTION REVIEW 4. Explain why liquids in a test tube form a meniscus.

1. Describe the liquid state according to the kinetic- 5. Compare vaporization and evaporation.
molecular theory.
Critical Thinking
2. List the properties of liquids.
6. INTERPRETING CONCEPTS The evaporation of
3. How does the kinetic-molecular theory explain the liquid water from the surface of Earth is an impor-
following properties of liquids: (a) relatively high tant step in the water cycle. How do water mol-
density, (b) ability to diffuse, and (c) ability to ecules obtain enough kinetic energy to escape
evaporate? into the gas state?

336 C H A P T E R 1 0

Solids SECTION 3

T he common expression “solid as a rock” suggests that something is OBJECTIVES

hard or unyielding and has a definite shape and volume. In this section Describe the motion of
you will examine the properties of solids and compare them with those particles in solids and the
of liquids and gases. The properties of solids are explained in terms of properties of solids according
the kinetic-molecular theory, as the other states of matter are. to the kinetic-molecular theory.

Properties of Solids and the Distinguish between the two
Kinetic-Molecular Theory types of solids.

The particles of a solid are more closely packed than those of a liquid or Describe the different types
gas. Intermolecular forces between particles are therefore much more of crystal symmetry. Define
effective in solids. All interparticle attractions such as dipole-dipole crystal structure and unit cell.
attractions, London dispersion forces, and hydrogen bonding exert
stronger effects in solids than in the corresponding liquids or gases. FIGURE 9 Particles of sodium
Attractive forces tend to hold the particles of a solid in relatively fixed metal in three different states are
positions, with only vibrational movement around fixed points. Because shown. Sodium exists in a gaseous
the motions of the particles are restricted in this way, solids are more state in a sodium-vapor lamp.
ordered than liquids and are much more ordered than gases. The impor-
tance of order and disorder in physical and chemical changes will be dis- Arrangement of
cussed in Chapter 16. Compare the physical appearance and molecular particles in a gas
arrangement of the element in Figure 9 in solid, liquid, and gas form.

Arrangement of Arrangement of
particles in a solid particles in a liquid

S T A T E S O F M A T T E R 337

(a) Chloride ion, There are two types of solids: crystalline solids and amorphous solids.
Sodium ion, Cl− Most solids are crystalline solids—they consist of crystals. A crystal is a
Na+ substance in which the particles are arranged in an orderly, geometric,
repeating pattern. Noncrystalline solids, including glass and plastics, are
(b) called amorphous solids. An amorphous solid is one in which the parti-
cles are arranged randomly. The two types of solids will be discussed in
FIGURE 10 (a) This is a scanning more detail later in this section.
electron micrograph (SEM) of a
sodium chloride crystal. A sodium Definite Shape and Volume
chloride crystal can be represented
by its crystal structure (b), which is Unlike liquids and gases, solids can maintain a definite shape without a
made up of individual unit cells container. In addition, crystalline solids are geometrically regular. Even
represented regularly in three the fragments of a shattered crystalline solid have distinct geometric
dimensions. Here, one unit cell is shapes that reflect their internal structure. Amorphous solids maintain
outlined in red. a definite shape, but they do not have the distinct geometric shapes of
crystalline solids. For example, glass can be molded into any shape. If it
338 C H A P T E R 1 0 is shattered, glass fragments can have a wide variety of irregular shapes.

The volume of a solid changes only slightly with a change in tempera-
ture or pressure. Solids have definite volume because their particles are
packed closely together. There is very little empty space into which the
particles can be compressed. Crystalline solids generally do not flow
because their particles are held in relatively fixed positions.

Definite Melting Point

Melting is the physical change of a solid to a liquid by the addition of
energy as heat. The temperature at which a solid becomes a liquid is its
melting point. At this temperature, the kinetic energies of the particles
within the solid overcome the attractive forces holding them together.
The particles can then break out of their positions in crystalline solids,
which have definite melting points. In contrast, amorphous solids, such
as glass and plastics, have no definite melting point. They have the abil-
ity to flow over a range of temperatures. Therefore, amorphous solids
are sometimes classified as supercooled liquids, which are substances
that retain certain liquid properties even at temperatures at which they
appear to be solid. These properties exist because the particles in amor-
phous solids are arranged randomly, much like the particles in a liquid.
Unlike the particles in a true liquid, however, the particles in amor-
phous solids are not constantly changing their positions.

High Density and Incompressibility

In general, substances are most dense in the solid state. Solids tend to be
slightly denser than liquids and much denser than gases. The higher den-
sity results from the fact that the particles of a solid are more closely
packed than those of a liquid or a gas. Solid hydrogen is the least dense
solid; it has a density of about 1/320 of the densest element, osmium, Os.

Solids are generally less compressible than liquids. For practical pur-
poses, solids can be considered incompressible. Some solids, such as
wood and cork, may seem compressible, but they are not. They contain
pores that are filled with air. When subjected to intense pressure, the
pores are compressed, not the solid matter in the wood or cork itself.

Fluorite Chalcopyrite Emerald
Cubic Tetragonal Hexagonal

Calcite Aragonite Azurite
Trigonal Orthorhombic Monoclinic

Low Rate of Diffusion

If a zinc plate and a copper plate are clamped together for a long time,
a few atoms of each metal will diffuse into the other. This observation
shows that diffusion does occur in solids. The rate of diffusion is millions
of times slower in solids than in liquids, however.

Crystalline Solids Rhodonite
Triclinic
Crystalline solids exist either as single crystals or as groups of crystals
fused together. The total three-dimensional arrangement of particles of FIGURE 11 Shown are the seven
a crystal is called a crystal structure. The arrangement of particles in the basic crystalline systems and repre-
crystal can be represented by a coordinate system called a lattice. The sentative minerals of each.
smallest portion of a crystal lattice that shows the three-dimensional pat-
tern of the entire lattice is called a unit cell. Each crystal lattice contains S T A T E S O F M A T T E R 339
many unit cells packed together. Figure 10 shows the relationship
between a crystal lattice and its unit cell. A crystal and its unit cells can
have any one of seven types of symmetry. This fact enables scientists to
classify crystals by their shape. Diagrams and examples of each type of
crystal symmetry are shown in Figure 11.

Binding Forces in Crystals

Crystal structures can also be described in terms of the types of parti-
cles in them and the types of chemical bonding between the particles.

TABLE 1 Melting and Boiling Points of
Representative Crystalline Solids

Type of Formula Melting Boiling point
substance point (°C) at 1 atm (°C)

Ionic NaCl 801 1413
Covalent network MgF2 1266 2239
Metallic
(SiO2)x 1610 2230
Cx (diamond) 3500 3930

Hg −39 357
Cu 1083 2567
Fe 1535 2750
W 3410 5660

Covalent molecular H2 −259 −253
(nonpolar) O2 −218 −183
CH4 −182 −164
Covalent molecular CCl4 −23
(polar) C6H6 77
6 80
NH3
H2O −78 −33
0 100

www.scilinks.org According to this method of classification, there are four types of crys-
Topic: Crystalline Solids tals. These types are listed in Table 1. Refer to this table as you read the
Code: HC60369 following discussion.

340 C H A P T E R 1 0 1. Ionic crystals. The ionic crystal structure consists of positive and neg-
ative ions arranged in a regular pattern. The ions can be monatomic
or polyatomic. Generally, ionic crystals form when Group 1 or
Group 2 metals combine with Group 16 or Group 17 nonmetals or
nonmetallic polyatomic ions. The strong binding forces between the
positive and negative ions in the crystal structure give the ionic crys-
tals certain properties. For example, these crystals are hard and brit-
tle, have high melting points, and are good insulators.

2. Covalent network crystals. In covalent network crystals, each atom is
covalently bonded to its nearest neighboring atoms. The covalent
bonding extends throughout a network that includes a very large num-
ber of atoms. Three-dimensional covalent network solids include dia-
mond, Cx, quartz, (SiO2)x—shown in Figure 12—silicon carbide,
(SiC)x, and many oxides of transition metals. Such solids are essential-
ly giant molecules. The subscript x in these formulas indicates that the
component within the parentheses extends indefinitely. The network
solids are nearly always very hard and brittle. They have rather high
melting points and are usually nonconductors or semiconductors.

3. Metallic crystals. The metallic crystal structure consists of metal
cations surrounded by a sea of delocalized valence electrons. The
electrons come from the metal atoms and belong to the crystal as a
whole. The freedom of these delocalized electrons to move through-
out the crystal explains the high electric conductivity of metals.

4. Covalent molecular crystals. The crystal structure of a covalent mo-
lecular substance consists of covalently bonded molecules held
together by intermolecular forces. If the molecules are nonpolar—
for example, hydrogen, H2, methane, CH4, and benzene, C6H6—then
there are only weak London dispersion forces between molecules.
In a polar covalent molecular crystal—for example, water, H2O, and
ammonia, NH3—molecules are held together by dispersion forces,
by somewhat stronger dipole-dipole forces, and sometimes by even
stronger hydrogen bonding. The forces that hold polar or nonpolar
molecules together in the structure are much weaker than the
covalent chemical bonds between the atoms within each molecule.
Covalent molecular crystals thus have low melting points. They are
easily vaporized, are relatively soft, and are good insulators.
Ice crystals, the most familiar molecular crystals, are discussed in
Section 5.

Amorphous Solids FIGURE 12 Covalent network
crystals include three-dimensional
The word amorphous comes from the Greek for “without shape.” network solids, such as this quartz,
Unlike the atoms that form crystals, the atoms that make up amorphous (SiO2)x, shown here with its three-
solids, such as glasses and plastics, are not arranged in a regular pattern. dimensional atomic structure.

Glasses are made by cooling certain molten materials in a way that
prevents them from crystallizing. The properties that result make
glasses suitable for many uses, including windows, light bulbs, trans-
former cores, and optical fibers that carry telephone conversations.

Plastics, another type of amorphous solid, are easily molded at high
temperatures and pressures. They are used in many structural materials.

Other, more recently created amorphous solids have been placed in
many important applications. Amorphous semiconductors are used in
electronic devices, including solar cells, copiers, laser printers, and flat-
panel displays for computer monitors and television screens.

SECTION REVIEW 4. Compare and contrast the four types of crystals.

1. Describe the solid state according to the kinetic- 5. Why do crystalline solids shatter into regularly
molecular theory. shaped fragments when broken?

2. What is the difference between an amorphous Critical Thinking
solid and a crystalline solid?
6. RELATING IDEAS Explain why ionic crystals melt
3. Account for each of the following properties at much higher temperatures than typical covalent
of solids: (a) the definite volume, (b) the relatively molecular crystals?
high density of solids, (c) the extremely low rate
of diffusion.

S T A T E S O F M A T T E R 341

SECTION 4 Changes of State

OBJECTIVES M atter on Earth can exist in any of these states—gas, liquid, or solid—

Explain the relationship and can change from one state to another. Table 2 lists the possible
between equilibrium and changes of state. In this section, you will examine these changes of state
changes of state. and the factors that determine them.
Interpret phase diagrams.
Explain what is meant by Changes of State and Equilibrium
equilibrium vapor pressure.
Describe the processes of Some liquid chemical substances, such as rubbing alcohol, have an odor
boiling, freezing, melting, and that is very easily detected. This is because some molecules at the upper
sublimation. surface of the liquid have enough energy to overcome the attraction of
neighboring molecules. These molecules leave the liquid phase and
www.scilinks.org evaporate. A phase is any part of a system that has uniform composition
Topic: Factors Affecting and properties. In a closed bottle of rubbing alcohol, the gas molecules
are confined to the area under the cap. Some of the gas molecules strike
Equilibrium the liquid surface and reenter the liquid phase through condensation.
Code: HC60561 Condensation is the process by which a gas changes to a liquid. A gas in
contact with its liquid or solid phase is often called a vapor.
342 C H A P T E R 1 0
If the temperature of the liquid remains constant and the cap
remains closed, the rate at which molecules move from the liquid phase
to the vapor phase remains constant. Near the beginning of the evapo-
ration process, very few molecules are in the gas phase, so the rate of
condensation is very low. But as more liquid evaporates, the increasing
number of gas molecules causes the rate of condensation to increase.
Eventually, the rate of condensation equals the rate of evaporation, and
a state of equilibrium is established, as shown in Figure 13. Equilibrium
is a dynamic condition in which two opposing changes occur at equal
rates in a closed system. Even though molecules are constantly moving

TABLE 2 Possible Changes of State

Change of state Process Example

Solid ⎯→ liquid melting ice ⎯→ water
Solid ⎯→ gas sublimation dry ice ⎯→ CO2 gas
Liquid ⎯→ solid freezing water ⎯→ ice
Liquid ⎯→ gas vaporization liquid bromine ⎯→ bromine vapor
Gas ⎯→ liquid condensation water vapor⎯→ water
Gas ⎯→ solid deposition water vapor ⎯→ ice

(a) (b) (c) Chemical Content

FIGURE 13 A liquid-vapor equilibrium develops in a closed system. (a) At Go to go.hrw.com for more infor-
first there is only liquid present, but molecules are beginning to evaporate. mation on equilibrium and changes
(b) Evaporation continues at a constant rate. Some vapor molecules are of state.
beginning to condense to liquid. (c) Equilibrium has been reached between
the rate of condensation and the rate of evaporation. Keyword: HC6STMX

between liquid and gas phases, there is no net change in the amount of S T A T E S O F M A T T E R 343
substance in either phase.

Equilibrium Vapor Pressure of a Liquid

Vapor molecules in equilibrium with a liquid in a closed system exert a
pressure proportional to the concentration of molecules in the vapor
phase. The pressure exerted by a vapor in equilibrium with its corre-
sponding liquid at a given temperature is called the equilibrium vapor
pressure of the liquid.

The increase in equilibrium vapor pressure with increasing tempera-
ture can be explained in terms of the kinetic-molecular theory for the
liquid and gaseous states. Increasing the temperature of a liquid increas-
es the average kinetic energy of the liquid’s molecules. This energy
change increases the number of molecules that have enough energy to
escape from the liquid phase into the vapor phase. The resulting
increased evaporation rate increases the number of molecules in the
vapor phase, which in turn increases the equilibrium vapor pressure.

Because all liquids have characteristic forces of attraction between
their particles, every liquid has a specific equilibrium vapor pressure at a
given temperature. The stronger these attractive forces are, the smaller
the percentage of liquid particles that can evaporate at any given tem-
perature is. A low percentage of evaporation results in a low equilibrium
vapor pressure is. Volatile liquids, which are liquids that evaporate readi-
ly, have relatively weak forces of attraction between their particles.
Ether is a typical volatile liquid. Nonvolatile liquids do not evaporate
readily, and have relatively strong attractive forces between their parti-
cles. Molten ionic compounds are examples of nonvolatile liquids.

Boiling

Equilibrium vapor pressures can be used to explain and define the con-

cept of boiling, which you read about in Section 3. Boiling is the con-

version of a liquid to a vapor within the liquid as well as at its surface.

If the temperature of the liquid is increased, the equilibrium vapor

pressure also increases. The boiling point of a liquid is the temperature at

which the equilibrium vapor pressure of the liquid equals the atmospheric

pressure. The lower the atmospheric pressure is, the lower the boiling

point is.

Vapor Pressures of Diethyl Ether, Ethanol, At the boiling point, all of the ener-
and Water at Various Temperatures gy absorbed is used to evaporate the
liquid, and the temperature remains

760 torr = 101.3 kPa constant as long as the pressure does
= 1 atm not change. If the pressure above the
800 liquid being heated is increased, the

temperature of the liquid will rise

Pressure (torr) 600 Water until the vapor pressure equals the
Diethyl ether Ethanol new pressure and the liquid boils once
Normal again. This is the principle behind the
Normal Normal b.p. 100.oC operation of a pressure cooker. The

b.p. 34.6oC b.p. 78.5oC

400

cooker is sealed so that steam pres-

sure builds up over the surface of the
200 boiling water inside. The pressure

increases the boiling temperature of

0 the water, resulting in shorter cooking
–20 0 20 40 60 80 100 120 140 160 times. Conversely, a device called a

Temperature (oC) vacuum evaporator causes boiling
at lower-than-normal temperatures.

FIGURE 14 The vapor pressure of Vacuum evaporators are used to remove water from milk and sugar solu-
any liquid increases as its tempera- tions. Under reduced pressure, the water boils away at a temperature low
ture increases. A liquid boils when enough to avoid scorching the milk or sugar. This process is used to pre-
its vapor pressure equals the pres- pare evaporated milk and sweetened condensed milk.
sure of the atmosphere.
At normal atmospheric pressure (1 atm, 760 torr, or 101.3 kPa), the

boiling point of water is exactly 100°C. This temperature is known as the

normal boiling point of water. Figure 14 shows that the normal boiling

point of each liquid is the temperature at which the liquid’s equilibrium

vapor pressure equals 760 torr.

Energy and Boiling

Energy must be added continuously in order to keep a liquid boiling. A
pot of boiling water stops boiling almost immediately after it is removed
from the stove. If you were to carefully measure the temperature of a
boiling liquid and its vapor you would find that they are at the same con-
stant temperature. The temperature at the boiling point remains constant
despite the continuous addition of energy. The added energy is used to
overcome the attractive forces between molecules of the liquid during the
liquid-to-gas change and is stored in the vapor as potential energy.

344 C H A P T E R 1 0

Number of moleculesEnergy Distribution of Molecules in a Liquid FIGURE 15 The number of mol-
at Different Temperatures ecules in a liquid with various kinetic
energies is represented at two differ-
Lower temperature ent temperatures. Notice the shaded
area, which shows the fraction of the
Higher temperature molecules that have at least the mini-
mum amount of kinetic energy
Minimum kinetic energy required for evaporation to take
required for escape of place.
molecules from surface
of liquid

Kinetic energy

Molar Enthalpy of Vaporization

The amount of energy as heat that is needed to vaporize one mole of liq-
uid at the liquid’s boiling point at constant pressure is called the liquid’s
molar enthalpy of vaporization, ΔHv. The magnitude of the molar
enthalpy of vaporization is a measure of the attraction between parti-
cles of the liquid. The stronger this attraction is, the more energy that is
required to overcome it, which results in a higher molar enthalpy of
vaporization. Each liquid has a characteristic molar enthalpy of vapor-
ization. Compared with other liquids, water has an unusually high molar
enthalpy of vaporization due to the extensive hydrogen bonding in liq-
uid water. This property makes water a very effective cooling agent.
When water evaporates from your skin, the escaping molecules carry a
great deal of energy as heat away with them. Figure 15 shows the dis-
tribution of the kinetic energies of molecules in a liquid at two different
temperatures. You can see that at the higher temperature, a greater por-
tion of the molecules have the kinetic energy required to escape from
the liquid surface and become vapor.

Freezing and Melting

As you learned in Section 2, the physical change of a liquid to a solid is
called freezing. Freezing involves a loss of energy in the form of heat by
the liquid and can be represented by the following reaction.

liquid ⎯→ solid + energy

In the case of a pure crystalline substance, this change occurs at constant
temperature. The normal freezing point is the temperature at which the
solid and liquid are in equilibrium at 1 atm (760 torr, or 101.3 kPa) pres-
sure. At the freezing point, particles of the liquid and the solid have the
same average kinetic energy. Therefore, the energy loss during freezing

S T A T E S O F M A T T E R 345

Surface Melting is a loss of potential energy that was present in the liquid. At the same
time energy decreases, there is a significant increase in particle order
Freezing of water and melting of ice because the solid state of a substance is much more ordered than the liq-
are phase changes that are familiar to uid state, even at the same temperature.
all of us. Yet physicists and chemists
have only recently begun to understand Melting, the reverse of freezing, also occurs at constant temperature.
the basic aspects of these phase As a solid melts, it continuously absorbs energy as heat, as represented
changes, with experimental and theo- by the following equation.
retical studies of a phenomenon known
as surface melting. Experimental stud- solid + energy ⎯→ liquid
ies in the mid-1980s confirmed that the
rigid surface arrangements of metals For pure crystalline solids, the melting point and freezing point are
can become increasingly disordered the same. At equilibrium, melting and freezing proceed at equal rates.
several degrees below the melting The following general equilibrium equation can be used to represent
point of the metal, forming a “quasi- these states.
liquid layer.” Many different techniques
have now shown that ice also has such solid + energy ←⎯⎯→ liquid
a fluid surface layer just a few mole-
cules thick. This surface melting of ice At normal atmospheric pressure, the temperature of a system contain-
might explain observations as diverse ing ice and liquid water will remain at 0.°C as long as both ice and
as the origin of lightning, the unique water are present. That temperature will persist no matter what the
shapes of snowflakes, and ice skating. surrounding temperature. Adding energy in the form of heat to such a
system shifts the equilibrium to the right. That shift increases the pro-
346 C H A P T E R 1 0 portion of liquid water and decreases that of ice. Only after all the ice
has melted will the addition of energy increase the temperature of the
system.

Molar Enthalpy of Fusion

The amount of energy as heat required to melt one mole of solid at the
solid’s melting point is the solid’s molar enthalpy of fusion, ΔHf. The
energy absorbed increases the solid’s potential energy as its particles
are pulled apart, overcoming the attractive forces holding them togeth-
er. At the same time, there is a significant decrease in particle order as
the substance makes the transformation from solid to liquid. Similar to
the molar enthalpy of vaporization, the magnitude of the molar
enthalpy of fusion depends on the attraction between the solid particles.

Sublimation and Deposition

At sufficiently low temperature and pressure conditions, a liquid cannot
exist. Under such conditions, a solid substance exists in equilibrium with
its vapor instead of its liquid, as represented by the following equation.

solid + energy ←⎯⎯→ vapor

The change of state from a solid directly to a gas is known as sublima-
tion. The reverse process is called deposition, the change of state from a
gas directly to a solid. Among the common substances that sublime at
ordinary temperatures are dry ice (solid CO2) and iodine. Ordinary ice
sublimes slowly at temperatures lower than its melting point (0.°C).
This explains how a thin layer of snow can eventually disappear, even
if the temperature remains below 0.°C. Sublimation occurs in frost-free

refrigerators when the temperature in the freezer compartment is peri-
odically raised to cause any ice that has formed to sublime. A blower
then removes the water vapor that has formed. The formation of frost
on a cold surface is a familiar example of deposition.

Phase Diagrams CROSS-DISCIPLINARY

A phase diagram is a graph of pressure versus temperature that shows the Go to go.hrw.com for a full-length
conditions under which the phases of a substance exist. A phase diagram article on how cloud seeding is used
also reveals how the states of a system change with changing tempera- to produce precipitation.
ture or pressure.
Keyword: HC6STMX
Figure 16 shows the phase diagram for water over a range of tem-
peratures and pressures. Note the three curves, AB, AC, and AD. Curve
AB indicates the temperature and pressure conditions at which ice and
water vapor can coexist at equilibrium. Curve AC indicates the temper-
ature and pressure conditions at which liquid water and water vapor
coexist at equilibrium. Similarly, curve AD indicates the temperature
and pressure conditions at which ice and liquid water coexist at equilib-
rium. Because ice is less dense than liquid water, an increase in pressure
lowers the melting point. (Most substances have a positive slope for this
curve.) Point A is the triple point of water. The triple point of a sub-
stance indicates the temperature and pressure conditions at which the
solid, liquid, and vapor of the substance can coexist at equilibrium. Point
C is the critical point of water. The critical point of a substance indicates
the critical temperature and critical pressure. The critical temperature
(tc) is the temperature above which the substance cannot exist in the liq-
uid state. The critical temperature of water is 373.99°C. Above this

Phase Diagram for H2O

D Critical point C

217.75
Critical
pressure

Pressure (atm) Liquid

1.00 Normal
freezing
point

Solid Normal
boiling
point

0.0060 A Vapor
B
Triple FIGURE 16 This phase
point diagram shows the relationships
between the physical states of water
0.00 0.01 100.00 373.99 and its pressure and temperature.
Temperature (oC) Critical
temperature S T A T E S O F M A T T E R 347

FIGURE 17 Solids, liquids, and DeposSituibolnimation Gas EvapoCroantidoennsation
gases can undergo various changes Solid Liquid
of state. The changes shown in green Melting
are exothermic, and those shown in Freezing
blue are endothermic.

Chemistry in Action temperature, water cannot be liquefied, no matter how much pressure
is applied. The critical pressure (Pc ) is the lowest pressure at which the
Go to go.hrw.com for a full-length substance can exist as a liquid at the critical temperature. The critical
article on phase-change materials. pressure of water is 217.75 atm.

Keyword: HC6STMX The phase diagram in Figure 16 indicates the normal boiling point and
the normal freezing point of water. It also shows how boiling point and
freezing point change with pressure.As shown by the slope of line AD, ice
melts at a higher temperature with decreasing pressure. Below the triple
point, the temperature of sublimation decreases with decreasing pressure.
Foods are freeze-dried by freezing the food and then lowering the pres-
sure to cause the ice in the food to sublime rather than melt. Figure 17
summarizes the changes of state of solids, liquids, and gases.

SECTION REVIEW Critical Thinking

1. What is equilibrium? 7. INTERPRETING GRAPHICS Refer to the phase dia-
gram for water on page 347 to answer the follow-
2. What happens when a liquid-vapor system at ing questions.
equilibrium experiences an increase in tempera-
ture? What happens when it experiences a a. Describe all the changes a sample of solid water
decrease in temperature? would undergo when heated from −10°C to its
critical temperature at a pressure of 1.00 atm.
3. What would be an example of deposition?
b. Describe all the changes a sample of water
4. What is the equilibrium vapor pressure of a liquid? vapor would undergo when cooled from 110°C
How is it measured? to 5°C at a pressure of 1.00 atm.

5. What is the boiling point of a liquid? c. At approximately what pressure will water
be a vapor at 0°C?
6. In the phase diagram for water, what is meant
by the triple point and the critical point? d. Within what range of pressures will water
be a liquid at temperatures above its normal
boiling point?

348 C H A P T E R 1 0

Water SECTION 5

W ater is a familiar substance in all three physical states: solid, liquid, OBJECTIVES

and gas. On Earth, water is by far the most abundant liquid. Oceans, Describe the structure of a
rivers, and lakes cover about 75% of Earth’s surface. Significant quanti- water molecule.
ties of water are also frozen in glaciers. Water is an essential component Discuss the physical properties
of all organisms; 70% to 90% of the mass of living things is water. The of water. Explain how they
chemical reactions of most life processes take place in water, and water are determined by the
is frequently a reactant or product in such reactions. In order to better structure of water.
understand the importance of water, let us take a closer look at its struc- Calculate the amount of
ture and its properties. energy absorbed or released
when a quantity of water
Structure of Water changes state.

As discussed in Chapter 6, water molecules consist of two atoms of Hydrogen
hydrogen and one atom of oxygen united by polar-covalent bonds. bond
Research shows that a water molecule is bent. The structure can be rep-
resented as follows. Liquid water
FIGURE 18 The structure of
O liquid water shows that within the
HH water molecule, oxygen and hydro-
gen are covalently bonded to each
105° other, while the molecules are held
together in groups by hydrogen
The angle between the two hydrogen-oxygen bonds is about 105°. This bonds.
is close to the angle expected for sp3 hybridization of the oxygen-atom
orbitals. S T A T E S O F M A T T E R 349

The molecules in solid or liquid water are linked by hydrogen bond-
ing. The number of linked molecules decreases with increasing tempera-
ture because increases in kinetic energy make hydrogen bond
formation difficult. Nevertheless, there are usually from four to eight
molecules per group in liquid water, as shown in Figure 18. If it were not
for these molecular groups, water would be a gas at room temperature.
Nonpolar molecules, such as methane, CH4, that are similar in size and
mass to water molecules do not undergo hydrogen bonding. Such sub-
stances are gases at room temperature.

Ice consists of water molecules in the hexagonal arrangement shown
in Figure 19. The empty spaces between molecules in this pattern
account for the relatively low density of ice. As ice is heated, the
increased energy of the molecules causes them to move and vibrate
more vigorously. When the melting point is reached, the energy of the

Hydrogen molecules is so great that the rigid open structure of the ice crystals
bond breaks down, and ice turns into liquid water.

Figures 18 and 19 also show that the hydrogen bonds between mole-
cules of liquid water at 0.°C are fewer and more disordered than those
between molecules of ice at the same temperature. Because the rigid
open structure of ice has broken down, water molecules can crowd clos-
er together. Thus, liquid water is denser than ice.

As the liquid water is warmed from 0.°C, the water molecules crowd
still closer together. Water molecules are as tightly packed as possible at
3.98°C. At temperatures above 3.98°C, the increasing kinetic energy of
the water molecules causes them to overcome molecular attractions.
The molecules move farther apart as the temperature continues to rise.
As the temperature approaches the boiling point, groups of liquid water
molecules absorb enough energy to break up into separate molecules.
Because of hydrogen bonding between water molecules, a high kinetic
energy is needed, causing water’s boiling point to be relatively high
(100.°C) compared to other liquids that have similar molar masses.

Ice Physical Properties of Water
FIGURE 19 Ice contains the same
types of bonding as liquid water. At room temperature, pure liquid water is transparent, odorless, taste-
However, the structure of the hydro- less, and almost colorless. Any observable odor or taste is caused by
gen bonding is much more rigid and impurities, such as dissolved minerals, liquids, or gases.
open than it is in liquid water.
As shown by its phase diagram in Figure 16, water freezes and ice
350 C H A P T E R 1 0 melts at 0.°C at a pressure of 1 atm (101.3 kPa). The molar enthalpy of
fusion of ice is 6.009 kJ/mol.That value is relatively large compared with
the molar enthalpy of fusion of other solids. As you have read, water has
the unusual property of expanding in volume as it freezes, because its
molecules form an open rigid structure. As a result, ice at 0.°C has a den-
sity of only about 0.917 g/cm3, but liquid water at 0.°C has a density of
0.999 84 g/cm3.

This lower density explains why ice floats in liquid water. The insu-
lating effect of floating ice is particularly important in the case of large
bodies of water. If ice were more dense than liquid water, it would sink
to the bottom of lakes and ponds, where it would be less likely to melt
completely. The water of such bodies of water in temperate climates
would eventually freeze solid, killing nearly all the living things in it.

Under a pressure of 1 atm (101.3 kPa), water boils at 100.°C. At this
temperature, water’s molar enthalpy of vaporization is 40.79 kJ/mol.
Both the boiling point and the molar enthalpy of vaporization of water
are quite high compared with those of nonpolar substances of compa-
rable molecular mass, such as methane. The values are high because of
the strong hydrogen bonding that must be overcome for boiling to
occur. The high molar enthalpy of vaporization makes water useful for
household steam-heating systems. The steam (vaporized water) stores
a great deal of energy as heat. When the steam condenses in radiators,
great quantities of energy are released.

SAMPLE PROBLEM A For more help, go to the Math Tutor at the end of this chapter.

How much energy is absorbed when 47.0 g of ice melts at STP? How much energy is absorbed when this
same mass of liquid water boils?

SOLUTION

1 ANALYZE Given: mass of H2O(s) = 47.0 g; mass of H2O(l) = 47.0 g; molar enthalpy of fusion of
ice = 6.009 kJ/mol; molar enthalpy of vaporization = 40.79 kJ/mol

Unknown: energy absorbed when ice melts; energy absorbed when liquid water boils

2 PLAN First, convert the mass of water from grams to moles.

47.0 g H2O × ⎯1 mol⎯H2O = 2.61 mol H2O
18.02 g H2O

Then, use the molar enthalpy of fusion of a solid to calculate the amount of energy
absorbed when the solid melts. Multiply the number of moles by the amount of energy
needed to melt one mole of ice at its melting point (the molar enthalpy of fusion of ice).
Using the same method, calculate the amount of energy absorbed when water boils by
using the molar enthalpy of vaporization.

amount of substance (mol) × molar enthalpy of fusion or vaporization (kJ/mol) = energy (kJ)

3 COMPUTE 2.61 mol × 6.009 kJ/mol = 15.7 kJ (on melting)
2.61 mol × 40.79 kJ/mol = 106 kJ (on vaporizing or boiling)

4 EVALUATE Units have canceled correctly. The answers have the proper number of significant digits and
are reasonably close to estimated values of 18 (3 × 6) and 120 (3 × 40), respectively.

PRACTICE Answers in Appendix E

1. What quantity of energy is released when 506 g of liquid water Go to go.hrw.com for
freezes? more practice problems
that ask you to use
2. What mass of steam is required to release 4.97 × 105 kJ of energy enthalpies to calculate
on condensation? energies absorbed or
released.

Keyword: HC6STMX

SECTION REVIEW 5. Why is ice less dense than liquid water?

1. Why is a water molecule polar? 6. Is more energy required to melt one gram of ice at
0°C or to boil one gram of water at 100°C? How
2. How is the structure of water responsible for do you know?
some of water’s unique characteristics?
Critical Thinking
3. Describe the arrangement of molecules in
liquid water and in ice. 7. RELATING IDEAS Why is exposure to steam
dangerous?
4. Why does ice float? Why is this phenomenon
important?

S T A T E S O F M A T T E R 351

CHAPTER HIGHLIGHTS

The Kinetic-Molecular Theory of Matter

Vocabulary diffusion • The kinetic-molecular theory of matter can be used to explain
kinetic-molecular effusion
real gas the properties of gases, liquids, and solids.
theory
• The kinetic-molecular theory of gases describes a model of an
ideal gas
ideal gas.
elastic collision
• Gases consist of large numbers of tiny, fast-moving particles that

are far apart relative to their size.

Liquids vaporization • The particles of a liquid are closer together and more ordered
evaporation
Vocabulary freezing than those of a gas and are less ordered than those of a solid.
fluid
surface tension • Liquids have a definite volume and a fairly high density, and
capillary action
they are relatively incompressible. Like gases, liquids can flow
and thus are considered to be fluids.

Solids melting point • The particles of a solid are not nearly as free to move about as
supercooled liquids
Vocabulary crystal structure those of a liquid or a gas are.
crystalline solids unit cell
crystal • Solids have a definite shape and may be crystalline or amor-
amorphous solids
melting phous. They have a definite volume and are generally nonfluid.

• A crystal structure is the total three-dimensional array of points

that describes the arrangement of the particles of a crystal.

• Unlike crystalline solids, amorphous solids do not have a highly

ordered structure or a regular shape.

Changes of State

Vocabulary freezing point • A liquid in a closed system will gradually reach a liquid-vapor
phase molar enthalpy of
condensation equilibrium as the rate at which molecules condense equals the
equilibrium fusion rate at which they evaporate.
equilibrium vapor sublimation
deposition • When two opposing changes occur at equal rates in the same
pressure phase diagram
volatile liquids triple point closed system, the system is said to be in dynamic equilibrium.
boiling critical point
boiling point critical temperature
molar enthalpy of critical pressure

vaporization

Water

• Water is a polar covalent compound.
• The structure and the hydrogen bonding in water are responsi-

ble for its relatively high melting point, molar enthalpy of

fusion, boiling point, and molar enthalpy of vaporization.

352 C H A P T E R 1 0

CHAPTER REVIEW

The Kinetic-Molecular Changes of State
Theory of Matter
SECTION 4 REVIEW
SECTION 1 REVIEW
1. What idea is the kinetic-molecular theory 13. Using Figure 14, estimate the approximate
based on? equilibrium vapor pressure of each of the fol-
2. What is an ideal gas? lowing at the specified temperature.
3. State the five basic assumptions of the kinetic- a. water at 80°C
molecular theory. b. diethyl ether at 20°C
4. How do gases compare with liquids and solids in c. ethanol at 60°C
terms of the distance between their molecules?
5. What is the relationship between the tem- 14. a. What is sublimation?
perature, speed, and kinetic energy of gas b. Give two examples of common substances
molecules? that sublime at ordinary temperatures.
6. a. What is diffusion?
b. What factors affect the rate of diffusion of 15. What is meant by the normal freezing point of a
one gas through another? substance?

Liquids 16. Explain how the attractive forces between the
particles in a liquid are related to the equilibri-
SECTION 2 REVIEW um vapor pressure of that liquid.
7. What is a fluid?
8. What is surface tension? 17. Explain the relationship between atmospheric
9. Give two reasons why evaporation is a crucial pressure and the actual boiling point of a liquid.
process in nature.
18. Explain the relationship between the molar
Solids enthalpy of fusion of a solid and the strength of
attraction between that solid’s particles.
SECTION 3 REVIEW
10. List six properties of solids, and explain each in PRACTICE PROBLEMS

terms of the kinetic-molecular theory of solids. 19. a. The molar enthalpy of vaporization for water
11. List four common examples of amorphous is 40.79 kJ/mol. Express this enthalpy of
vaporization in joules per gram.
solids.
12. List and describe the four types of crystals in b. The molar enthalpy of fusion for water is
6.009 kJ/mol. Express this enthalpy of fusion
terms of the nature of their component particles in joules per gram.
and the type of bonding between them.
20. Calculate the molar enthalpy of vaporization of a
substance given that 0.433 mol of the substance
absorbs 36.5 kJ of energy when it is vaporized.

21. Given that a substance has a molar mass of
259.0 g/mol and a 71.8 g sample of the sub-
stance absorbs 4.307 kJ when it melts,
a. calculate the number of moles in the sample.
b. calculate the molar enthalpy of fusion.

22. a. Calculate the number of moles in a liquid
sample of a substance that has a molar
enthalpy of fusion of 3.811 kJ/mol, given that
the sample releases 83.2 kJ when it freezes.

b. Calculate the molar mass of this substance if
the mass of the sample is 5519 g.

S T A T E S O F M A T T E R 353

CHAPTER REVIEW

Water 32. What volume and mass of steam at 100.°C and
760. torr would release the same amount of
SECTION 5 REVIEW energy as heat during condensation as 65.5 cm3
of liquid water would release during freezing?
23. Describe the structure of a water molecule.
24. List at least eight physical properties of water. 33. The following liquid-vapor system is at equilib-
rium at a given temperature in a closed system.
PRACTICE PROBLEMS liquid + energy ←⎯⎯→ vapor
Suppose the temperature is increased and equi-
25. Which contains more molecules of water: librium is established at the higher temperature.
5.00 cm3 of ice at 0°C or 5.00 cm3 of liquid How does the final value of each of the follow-
water at 0.°C? How many more? What is the ing compare with its initial value? (In each case,
ratio of the numbers of molecules in these two answer either higher, lower, or the same.)
samples? a. the rate of evaporation
b. the rate of condensation
26. a. What volume and mass of steam at 100.°C c. the final concentration of vapor molecules
and 1.00 atm would release the same amount d. the final number of liquid molecules
of energy during condensation as 100. cm3 of
liquid water would release during freezing? 34. Given a sample of water at any point on curve
AB in Figure 16, what effect would each of the
b. What do you note, qualitatively, about the rel- following changes have on that sample?
ative volumes and masses of steam and liquid a. adding energy at constant pressure
water required to release the same amount of b. decreasing the volume at constant temperature
heat? (Hint: See Sample Problem A) c. removing energy at constant pressure
d. increasing the volume at constant temperature
MIXED REVIEW
35. Using the phase diagram for CO2, describe all
27. Find the molar enthalpy of vaporization for a the phase changes that would occur when CO2
substance, given that 3.21 mol of the substance is heated from −100°C to −10°C at a constant
absorbs 28.4 kJ of energy as heat when the sub- pressure of 6 atm.
stance changes from a liquid to a gas.
CO2 Phase Diagram
28. Water’s molar enthalpy of fusion is 6.009 kJ/mol.
Calculate the amount of energy as heat required 16 Liquid
to melt 7.95 × 105 g of ice.
Pressure (atm) 14
29. A certain substance has a molar enthalpy of Solid
vaporization of 31.6 kJ/mol. How much of the
substance is in a sample that requires 57.0 kJ to 12
vaporize?
10
30. Given that water has a molar enthalpy of vapor-
ization of 40.79 kJ/mol, how many grams of 8
water could be vaporized by 0.545 kJ?
Gas
31. Calculate the amount of energy released as heat 6
by the freezing of 13.3 g of a liquid substance,
given that the substance has a molar mass of 4
82.9 g/mol and a molar enthalpy of fusion of
4.60 kJ/mol. 2

0
–100 – 80 – 60 – 40 – 20 0 +20 +40 +60

Temperature (oC)

354 C H A P T E R 1 0

CHAPTER REVIEW

CRITICAL THINKING c. The body-centered cubic lattice is the least-
efficient packing structure of the metals.
36. Interpreting Concepts During the freezing of a What elements in Groups 1 and 2 show this
substance, energy is being removed from that sub- arrangement?
stance. Yet the temperature of the liquid-solid sys-
tem remains constant. Explain this phenomenon. RESEARCH & WRITING

37. Applying Models At normal atmospheric pres- 41. Ceramics are formed from silicates found in the
sure, the temperature of an ice-water system soil. Artists use them to create pottery, but engi-
remains at 0°C as long as both ice and liquid neers and scientists have created ceramics with
water are present, regardless of the surrounding superconductive properties. Investigate the
temperature. Explain why this occurs. growing field of superconductive ceramics.

38. Predicting Outcomes Given a sample of water 42. Liquid crystals are substances that possess the
at any point on curve AD in Figure 16, how combined properties of both liquids and crys-
could more of the liquid water in that sample be tals. Write a report on these substances and the
converted into a solid without changing the various uses we are finding for them.
temperature? Explain your reasoning.
ALTERNATIVE ASSESSMENT
39. Interpreting Diagrams Refer to the phase dia-
gram in question 44. 43. Compile separate lists of crystalline and amor-
a. Explain what happens when solid CO2 (“dry phous solids found in your home. Compare your
ice”) warms up to room temperature at nor- lists with those of your classmates.
mal atmospheric pressure.
b. Is there a pressure below which liquid CO2 44. Design an experiment to grow crystals of vari-
cannot exist? Estimate that pressure from ous safe, common household materials. Record
the graph. the conditions under which each type of crystal
is best grown.
USING THE HANDBOOK
Graphing Calculator
40. The Elements Handbook contains a table of Vapor Pressure
properties for each group that includes informa- Go to go.hrw.com for a graphing calculator
tion on the crystal structures of the elements. exercise that asks you to create a graph of
Most metals crystallize in one of three lattice the vapor pressure of water as a function
arrangements: body-centered cubic, face- of temperature.
centered cubic, or hexagonal close-packed.
Figure 10 shows a model of the face-centered Keyword: HC6STMX
cubic lattice for sodium chloride. Use this figure
and the information in the Elements Handbook
to answer the following.
a. What elements in Group 2 have the same lat-
tice structure as sodium chloride?
b. How would the model of an element in a
face-centered cubic lattice differ from the
compound shown in Figure 10?

S T A T E S O F M A T T E R 355

Math Tutor CALCULATIONS USING ENTHALPIES OF FUSION

When one mole of a liquid freezes to a solid, energy is released as attractive forces
between particles pull the disordered particles of the liquid into a more orderly crys-
talline solid. When the solid melts to a liquid, the solid must absorb the same quantity
of energy in order to separate the particles of the crystal and overcome the attractive
forces opposing separation. This quantity of energy used to melt or freeze one mole of
a substance at its melting point is called its molar enthalpy of fusion, ΔHf.

Problem-Solving S

• The enthalpy of fusion of a substance can be given as either joules per gram
or kilojoules per mole.

• Molar enthalpy of fusion is most commonly used in calculations.

• The enthalpy of fusion is the energy absorbed or given off as heat when a
substance melts or freezes at the melting point of the substance.

• No net change in temperature occurs as the state change occurs.

SAMPLE 1 SAMPLE 2

7.30 kJ of energy is required to melt 0.650 mol of Determine the quantity of energy that will be
ethylene glycol (C2H6O2) at its melting point. needed to melt 2.50 ؋ 105 kg of iron at its melting
Calculate the molar enthalpy of fusion, ΔHf , of eth- point, 1536°C. The ΔHf of iron is 13.807 kJ/mol.
ylene glycol and the energy absorbed.
To calculate the number of moles of iron, use
molar enthalpy of fusion = ΔHf = the equation below.

⎯energy a⎯bsorbed moles of substance = ⎯mass⎯of subst⎯ance
moles of substance molar mass of substance

⎯7.30⎯kJ ⎯kJ Next, use the following equation for energy as
0.065 mol mol heat absorbed.

ΔHf ,ethylene glycol = = 11.2 energy absorbed = ΔHf × moles of substance

Now, substitute the calculation for moles of
substance, and solve.

energy absorbed =

ΔHf × ⎯gram⎯s of s⎯ubsta⎯nce =
molar mass of substance

13.807 ⎯kJ × ⎯2.50 × 1⎯08 g Fe
mol 55.847 g Fe/mol Fe

energy absorbed = 6.18 × 107 kJ

PRACTICE PROBLEMS 2. What quantity of energy in kJ must be

1. Calculate the molar enthalpy of fusion of sil- absorbed by 6.47 mol of solid acetic acid,
ver if 1.940 mol of silver requires 22.60 kJ of
energy to change from a solid to a liquid at its C2H4O2, to melt it at its melting point, 16.7°C?
melting point, 961°C. The ΔHf for acetic acid is 11.54 kJ/mol.

356 C H A P T E R 1 0

Standardized Test Prep

Answer the following items on a separate piece of paper. 7.The kinetic-molecular theory states that ideal
gas molecules
MULTIPLE CHOICE A. are in constant, rapid, random motion.
B. have mass and take up space.
1.Surface tension is C. exert forces of attraction and repulsion on
A. skin on the surface of a liquid. each other.
B. the tendency of the surface of liquids to D. have high densities compared with liquids
decrease the area. and solids.
C. the spontaneous mixing of two substances.
D. the same as vapor pressure. SHORT ANSWER

2.Pure liquids boil at higher temperatures under 8.Using this graph of vapor pressures of sub-
high pressures than they do under low pres- stances at various temperatures, estimate the
sures, because boiling point of ethanol at an applied (external)
A. the molecules of liquid are closer together pressure of 300 torr.
under higher pressures.
B. it takes a higher temperature for the vapor 800
pressure to equal the higher external pressure.
C. the molecules of vapor are farther apart Pressure (torr) 600 Diethyl ether Ethanol
under higher pressures.
D. the vapor diffuses more rapidly at higher 400
pressures. Water

3.The formation of frost is an example of 200
A. condensation.
B. evaporation. 0
C. deposition. –20 0 20 40 60 80 100
D. melting point.
Temperature (oC)
4.The graph that shows the pressure and temper-
ature conditions under which the phases of a 9.It is found that 60.0 J of energy are required to
substance exist is called melt 15 g of a substance. The molar mass of the
A. a phase diagram. substance is 120 g/mol. Calculate the enthalpy of
B. a vapor pressure curve. fusion of the substance in kilojoules per mole.
C. a unit cell.
D. the kinetic-molecular theory of matter. EXTENDED RESPONSE

5.Water boils at 100°C. Ethanol boils at 78.5°C. 10.Describe how a pressure cooker works.
Which of the following statements is true?
A. Water has the higher vapor pressure at 78.5°C. 11.What is meant by the statement that a liquid
B. Ethanol has the higher vapor pressure at and its vapor in a closed container are in a state
78.5°C. of dynamic equilibrium?
C. Both have the same vapor pressure at 78.5°C.
D. Vapor pressure is not related to boiling point. Test questions are not necessari-
ly arranged in order of increasing difficulty. If you are
6.Which of the following is not a property of typi- unable to answer a question, mark it and move on to
cal solids? other questions.
A. definite melting point
B. high density S T A T E S O F M A T T E R 357
C. easily compressible
D. low rate of diffusion

CHAPTER LAB MICRO-

“Wet” Dry Ice LAB

OBJECTIVES Pressure (atm) of CO2 Solid Liquid
• Interpret a phase diagram.
• Observe the melting of CO2 while varying X Triple Gas
Normal point
pressure. boiling
• Relate observations of CO2 to its phase point

diagram. 1.0
MATERIALS
• 4–5 g CO2 as dry ice, broken into –78 –56

rice-sized pieces Temperature (oC) of CO2
• forceps
• metric ruler FIGURE A The phase diagram for CO2 shows the temperatures and
• plastic pipets, 5 mL, shatterproof pressures at which CO2 can undergo phase changes.
• pliers
• scissors BACKGROUND
• transparent plastic cup The phase diagram for carbon dioxide in Figure A
shows that CO2 can exist only as a gas at ordinary
358 C H A P T E R 1 0 room temperature and pressure. To observe the tran-
sition of solid CO2 to liquid CO2, you must increase
the pressure until it is at or above the triple point
pressure, which is labeled X in the diagram.

SAFETY

For review of safety, please see Safety in the
Chemistry Laboratory in the front of your book.

PREPARATION
1. Organize a place in your lab notebook for
recording your observations.

PROCEDURE
1. Use forceps to place 2−3 very small pieces of dry
ice on the table, and observe them until they
have completely sublimed. Caution: Dry ice will
freeze skin very quickly. Do not attempt to pick
up the dry ice with your fingers.

2. Fill a plastic cup with tap water to a depth of CLEANUP AND DISPOSAL
4−5 cm. 9. Clean all apparatus and your lab station.
Return equipment to its proper place.
3. Cut the tapered end (tip) off the graduated pipet. Dispose of chemicals and solutions in
4. Use forceps to carefully slide 8−10 pieces of dry the containers designated by your teacher. Do
not pour any chemicals down the drain or place
ice down the stem and into the bulb of the pipet. them in the trash unless your teacher directs you
5. Use a pair of pliers to clamp the opening of to do so. Wash your hands thoroughly before you
leave the lab and after all work is finished.
the pipet stem securely shut so that no gas can
escape. Use the pliers to hold the tube and to ANALYSIS AND INTERPRETATION
lower the pipet into the cup just until the bulb is 1. Analyzing Results: What differences did you
submerged, as shown in Figure B. From the side observe between the subliming and the
of the cup, observe the behavior of the dry ice. melting of CO2?
6. As soon as the dry ice has begun to melt, quick-
ly loosen the pliers while still holding the bulb 2. Analyzing Methods: As you melted the CO2
in the water. Observe the CO2. sample over and over, why did it eventually
7. Tighten the pliers again, and observe. disappear? What could you have done to make
8. Repeat Procedure steps 6 and 7 as many times the sample last longer?
as possible.
3. Analyzing Methods: What purpose(s) do you
Pliers suppose the water in the cup served?

Water EXTENSIONS
1. Predicting Outcomes: What would have hap-
Dry ice pened if fewer pieces of dry ice (only 1 or 2)
had been placed inside the pipet bulb? If time
permits, test your prediction.

2. Predicting Outcomes: What might have hap-
pened if too much dry ice (20 or 30 pieces, for
example) had been placed inside the pipet bulb?
How quickly would the process have occurred?
If time permits, test your prediction.

3. Predicting Outcomes: What would have
happened if the pliers had not been released
once the dry ice melted? If time permits, test
your prediction.

FIGURE B Clamp the end of the pipet shut with the pliers.
Submerge the bulb in water in a transparent cup.

S T A T E S O F M A T T E R 359

CHAPTER 11

Gases

The density of a gas decreases
as the temperature of the gas increases.

Hot-Air Balloons

Gases and Pressure SECTION 1

I n the chapter “States of Matter,” you read about the kinetic- OBJECTIVES

molecular theory, which is based on the idea that particles of matter are Define pressure, give units of
always in motion. In this section, you will study the implications of the pressure, and describe how
kinetic-molecular theory of gases. pressure is measured.

You have learned that the temperature of a gas is related to the State the standard conditions
kinetic energy of the gas molecules. In this chapter, you will learn about of temperature and pressure
other properties of gases, including pressure, volume, and amount of gas and convert units of pressure.
present, and the relationship between these properties.
Use Dalton’s law of partial
Pressure and Force pressures to calculate partial
pressures and total pressures.
If you pump air into an automobile tire, the pressure in the tire will
increase. The pressure increase is caused by the increase in the number FIGURE 1 The pressure the bal-
of collisions of molecules of air with the inside walls of the tire. The col- let dancer exerts against the floor
lisions cause an outward push, or force, against the inside walls. Gas depends on the area of contact.
molecules exert pressure on any surface with which they collide. The The smaller the area of contact, the
pressure exerted by a gas depends on volume, temperature, and the greater the pressure.
number of molecules present. Pressure (P) is defined as the force per
unit area on a surface. The equation defining pressure is shown in
Figure 1.

Force = 500 N Force = 500 N Force = 500 N

(a) Area of contact = 325 cm2 (b) Area of contact = 13 cm2 (c) Area of contact = 6.5 cm2
Pressure = force Pressure = force Pressure = force
area area area
= 500 N = 1.5 N/cm2 = 500 N = 38 N/cm2 = 500 N = 77 N/cm2
325 cm2 13 cm2 6.5 cm2

G A S E S 361

www.scilinks.org The SI unit for force is the newton, (N). It is the force that will
Topic: Gases
Code: HC60638 increase the speed of a one-kilogram mass by one meter per second each

FIGURE 2 Air molecules—most second that the force is applied. At Earth’s surface, gravity has an accel-
of which are nitrogen or oxygen— eration of 9.8 m/s2. Consider a ballet dancer with a mass of 51 kg, as
collide with Earth’s surface, creating shown in Figure 1. A mass of 51 kg exerts a force of 500 N (51 kg ×
a pressure of 10.1 N/cm2. 9.8 m/s2) on Earth’s surface. No matter how the dancer stands, she

exerts that much force against the floor. But the pressure exerted

against the floor depends on the area of contact. When the dancer rests

her weight on the soles of both feet, as shown in Figure 1a, the area of
contact with the floor is about 325 cm2. The pressure, or force per unit
area, when she stands in this manner is 500 N/325 cm2, or roughly
1.5 N/cm2. When she stands on her toes, as in Figure 1b, the total area of
contact with the floor is only 13 cm2. The pressure exerted is then equal
to 500 N/13 cm2—roughly 38 N/cm2. And when she stands on one toe, as
in Figure 1c, the pressure exerted is twice that, or about 77 N/cm2. Thus,

the same force applied to a smaller area results in a greater pressure.

The atmosphere—the shell of air surrounding Earth—exerts pres-

sure. Figure 2 shows that atmospheric pressure at sea level is about

equal to the weight of a 1.03 kg mass per square centimeter of surface,
or 10.1 N/cm2. The pressure of the atmosphere can be thought of as

caused by the weight of the gases that compose the atmosphere. The

atmosphere contains about 78% nitrogen, 21% oxygen, and 1% other

gases, including argon and carbon dioxide. Atmospheric pressure is the

sum of the individual pressures of the various gases in the atmosphere.

Your ears “pop” when you fly in an airplane because the density—

and therefore the pressure—of the air is lower at higher altitudes. The

popping happens when the air pressure inside your ears changes to

reach the same pressure as the air inside the cabin.

Force Oxygen molecule, O2 Nitrogen molecule, N2

1 atm of

pressure is

the force of

10.1 N
on 1 cm2

Pressure

362 C H A P T E R 1 1

Measuring Pressure Vacuum Nitrogen molecule, N2
Oxygen molecule, O2
A barometer is a device used to measure atmospheric
760 mm
pressure. The first type of barometer, illustrated in Pressure exerted
Figure 3, was introduced by Evangelista Torricelli during by the column
the early 1600s. Torricelli wondered why water pumps
of mercury

could raise water to a maximum height of only about

34 feet. He thought that the height must depend some-

how on the weight of water compared with the weight of

air. He reasoned that liquid mercury, which is about Atmospheric
14 times as dense as water, could be raised only 1/14 as pressure

high as water. To test this idea, Torricelli sealed a long

glass tube at one end and filled it with mercury. Holding

the open end with his thumb, he inverted the tube into a

dish of mercury without allowing any air to enter the

tube. When he removed his thumb, the mercury column

in the tube dropped to a height of about 30 in. (760 mm) Surface of
mercury
above the surface of the mercury in the dish. He repeat-
FIGURE 3 Torricelli discovered
ed the experiment with tubes of different diameters and that the pressure of the atmosphere
supports a column of mercury about
lengths longer than 760 mm. In every case, the mercury 760 mm above the surface of the
mercury in the dish.
dropped to a height of about 760 mm.

The space above the mercury in such a tube is nearly a vacuum. The

mercury in the tube pushes downward because of gravitational force.

The column of mercury in the tube is stopped from falling beyond a cer-

tain point because the atmosphere exerts a pressure on the surface of

the mercury outside the tube. This pressure is transmitted through the

fluid mercury and is exerted upward on the column of mercury. The

mercury in the tube falls only until the pressure exerted by its weight is

equal to the pressure exerted by the atmosphere.

The exact height of the mercury in the tube depends on the atmos- Vacuum

pheric pressure, or force per unit area. The pressure is measured in Pressure
of oxygen
terms of the mercury column’s height in the barometer tube. gas in
mm Hg
From experiments like Torricelli’s, it is known that at sea level and at

0°C, the average pressure of the atmosphere can support a 760 mm col-

umn of mercury. The atmospheric pressure at any given place depends

on the elevation and the weather conditions. If the atmospheric pressure Oxygen gas
molecules exert
is greater than the average at sea level, the height of the mercury column a force

in a barometer will be greater than 760 mm. If the atmospheric pressure

is less, the height of the mercury column will be less than 760 mm.

All gases, not only those in the atmosphere, exert pressure. A device

called a manometer can be used to measure the pressure of an enclosed Oxygen
molecules
gas sample, as shown in Figure 4. The difference in the height of mer-
Mercury
cury in the two arms of the U-tube is a measure of the oxygen gas pres-
FIGURE 4 In the manometer
sure in the container. above, the pressure of the oxygen
gas in the flask pushes on the mer-
To understand gas pressure, consider a can that is filled with air. The cury column. The difference in the
height of the mercury in the two
atmosphere exerts a pressure against the outside of the can. The air arms of the U-tube indicates the
oxygen gas pressure.
inside the can pushes outward and balances the atmosphere’s inward-

pushing force. If a vacuum pump is used to remove the air from the can,

the balancing outward force is removed. As a result, the unbalanced

force due to atmospheric pressure immediately crushes the can.

G A S E S 363

Chemical Content Units of Pressure

Go to go.hrw.com for another A number of different units are used to measure pressure. Because
version of this content. See the atmospheric pressure is often measured by a mercury barometer, pres-
chapters “Physical Characteristics of sure can be expressed in terms of the height of a mercury column. Thus,
Gases” and “Molecular Composition the common unit of pressure is millimeters of mercury, symbolized
of Gases.” mm Hg. A pressure of 1 mm Hg is also called 1 torr in honor of Torricelli
for his invention of the barometer. The average atmospheric pressure at
Keyword: HC6GASX sea level at 0°C is 760 mm Hg.

Pressures are often measured in units of atmospheres. One atmosphere
of pressure (atm) is defined as being exactly equivalent to 760 mm Hg.

In SI, pressure is expressed in derived units called pascals. The unit is
named for Blaise Pascal, a French mathematician and philosopher who
studied pressure during the seventeenth century. One pascal (Pa) is
defined as the pressure exerted by a force of one newton (1 N) acting on
an area of one square meter.

In many cases, it is more convenient to express pressure in kilopascals
(kPa). The standard atmosphere (1 atm) is equal to 1.013 25 × 105 Pa, or
101.325 kPa. The pressure units used in this book are summarized in
Table 1.

Standard Temperature and Pressure

To compare volumes of gases, one must know the temperature and
pressure at which the volumes are measured. For purposes of compari-
son, scientists have agreed on standard conditions of exactly 1 atm pres-
sure and 0°C. These conditions are called standard temperature and
pressure and are commonly abbreviated STP.

TABLE 1 Units of Pressure

Unit Symbol Definition/relationship

pascal Pa SI pressure unit
1 Pa = ⎯1mN⎯2
millimeter of mercury mm Hg
pressure that supports a
torr torr 1 mm mercury column in a
atmosphere atm barometer

pounds per psi 1 torr = 1 mm Hg
square inch
average atmospheric
pressure at sea level and 0°C

1 atm = 760 mm Hg
= 760 torr
= 1.013 25 × 105 Pa
= 101.325 kPa

1 psi = 6.892 86 × 103 Pa
1 atm = 14.700 psi

364 C H A P T E R 1 1

SAMPLE PROBLEM A

The average atmospheric pressure in Denver, Colorado, is 0.830 atm. Express this pressure
in (a) millimeters of mercury (mm Hg) and (b) kilopascals (kPa).

SOLUTION

1 ANALYZE Given: P of atmosphere = 0.830 atm

760 mm Hg = 1 atm (definition); 101.325 kPa = 1 atm (definition)

Unknown: a. P of atmosphere in mm Hg; b. P of atmosphere in kPa

2 PLAN a. atm ⎯→ mm Hg; atm × 7⎯60 m⎯m Hg = mm Hg
atm

b. atm ⎯→ kPa; atm × ⎯101.32⎯5 kPa = kPa
atm

3 COMPUTE a. 0.830 atm × 7⎯60 m⎯m Hg = 631 mm Hg
4 EVALUATE atm

b. 0.830 atm × ⎯101.32⎯5 kPa = 84.1 kPa
atm

Units have canceled to give the desired units, and answers are expressed to the correct
number of significant figures. The known pressure and the calculated pressures are about
80% of the atmospheric pressure, as expressed in the new units.

PRACTICE Answers in Appendix E

1. Convert a pressure of 1.75 atm to kPa and to mm Hg. Go to go.hrw.com
2. The critical pressure of carbon dioxide is 72.7 atm. What is this for more practice
problems that ask you
value in units of pascals? to convert between
units of pressure.

Keyword: HC6GASX

Dalton’s Law of Partial Pressures

John Dalton, the English chemist who proposed the atomic theory, also
studied gas mixtures. The pressure exerted by each gas in an unreactive
mixture is independent of that exerted by other gases present. The pres-
sure of each gas in a mixture is called the partial pressure of that gas.
Dalton’s law of partial pressures states that the total pressure of a gas
mixture is the sum of the partial pressures of the component gases. The
law is true regardless of the number of different gases that are present.
Dalton’s law may be expressed as follows.

PT = P1 + P2 + P3 + . . .

PT is the total pressure of the mixture. P1, P2, P3, and so on are the
partial pressures of component gases 1, 2, 3, and so on.

G A S E S 365

FIGURE 5 Hydrogen can be Water vapor,
collected by water displacement by molecule, H2O
reacting zinc with sulfuric acid. The
hydrogen gas produced displaces
the water in the gas collecting
bottle. It now contains some
water vapor.

Hydrogen gas
molecule, H2

You can understand Dalton’s law in terms of the kinetic-molecular
theory. Each of the rapidly moving particles of gases in a mixture has an
equal chance to collide with the container walls. Therefore, each gas
exerts a pressure independent of that exerted by the other gases pre-
sent. The total pressure is the result of the total number of collisions per
unit of wall area in a given time.

Gases Collected by Water Displacement

Gases produced in the laboratory are often collected over water, as
shown in Figure 5. The gas produced by the reaction displaces the water,
which is more dense, in the collection bottle. You can apply Dalton’s law
of partial pressures in calculating the pressures of gases collected in this
way. A gas collected by water displacement is not pure but is always
mixed with water vapor. That is because water molecules at the liquid
surface evaporate and mix with the gas molecules. Water vapor, like
other gases, exerts a pressure known as vapor pressure.

Suppose you wished to determine the total pressure of the gas and
water vapor inside a collection bottle. You would raise the bottle until
the water levels inside and outside the bottle were the same. At that
point, the total pressure inside the bottle would be the same as the
atmospheric pressure, Patm. According to Dalton’s law of partial pres-
sures, the following is true.

Patm = Pgas + PH2O
Suppose you then needed to calculate the partial pressure of the dry
gas collected. You would read the atmospheric pressure, Patm, from a
barometer in the laboratory. To make the calculation, subtract the vapor
pressure of the water at the given temperature from the total pressure.
The vapor pressure of water varies with temperature. You need to look
up the value of PH2O at the temperature of the experiment in a standard
reference table, such as Table A-8 in Appendix A of this book.

366 C H A P T E R 1 1

SAMPLE PROBLEM B

Oxygen gas from the decomposition of potassium chlorate, KClO3, was collected by water
displacement. The barometric pressure and the temperature during the experiment were
731.0 torr and 20.0°C, respectively. What was the partial pressure of the oxygen collected?

SOLUTION

1 ANALYZE Given: PT = Patm = 731.0 torr
PH2O = 17.5 torr (vapor pressure of water at 20.0°C, from Table A-8)
Patm = PO2 + PH2O

Unknown: PO2 in torr

2 PLAN The partial pressure of the collected oxygen is found by subtracting the partial pressure of
water vapor from the atmospheric pressure, according to Dalton’s law of partial pressures.

3 COMPUTE PO2 = Patm − PH2O
4 EVALUATE
Substituting values for Patm and PH2O gives PO2.

PO2 = 731.0 torr − 17.5 torr = 713.5 torr

As expected, the oxygen partial pressure is less than atmospheric pressure. It is reasonably
close to an estimated value of 713, calculated as 730 − 17.

PRACTICE Answers in Appendix E

1. Some hydrogen gas is collected over water at 20.0°C. The levels of Go to go.hrw.com
water inside and outside the gas-collection bottle are the same. for more practice
The partial pressure of hydrogen is 742.5 torr. What is the baro- problems that ask you
metric pressure at the time the gas is collected? to calculate partial
pressure.

Keyword: HC6GASX

SECTION REVIEW 6. Why can you calculate the total pressure of a mix-
ture of gases by adding together the partial pres-
1. Define pressure. sures of the component gases?

2. What units are used to express pressure Critical Thinking
measurements?
7. EVALUATING METHODS Clean rooms used for
3. What are standard conditions for gas sterile biological research are sealed and operate
measurements? at slightly above atmospheric pressure. Explain
why.
4. Convert the following pressures to pressures in
standard atmospheres: 8. INFERRING RELATIONSHIPS Explain why helium-
filled balloons deflate over time faster than air-
a. 151.98 kPa b. 456 torr filled balloons do.

5. A sample of nitrogen gas is collected over water
at a temperature of 23.0°C. What is the pressure
of the nitrogen gas if atmospheric pressure is
785 mm Hg?

G A S E S 367

The Gas Laws and Scuba Diving

An understanding of Dalton’s law and increase in the air pressure leads to the excess nitrogen is discharged
Henry’s law is essential to safe scuba an increase in the partial pressures through the lungs. However, if the
diving. Dalton’s law states that the of the nitrogen and oxygen in air, as diver comes up too rapidly, the nitro-
total pressure of a gas mixture is predicted by Dalton’s law. Henry’s gen will form bubbles in the tissues
equal to the sum of the partial pres- law predicts that this increase in par- and veins. This condition is known as
sures of the component gases. Henry’s tial pressures will increase the solu- decompression sickness, or “the
law predicts that the solubility of a bility of nitrogen and oxygen in the bends.” If the bubbles block blood
gas in a liquid is a direct function of diver’s bloodstream. flow, a wide range of effects, includ-
the partial pressure of that gas. ing severe joint pain, may occur. For
The increase in the partial pressure this reason, divers are very careful to
For every 33 ft of sea water that a of oxygen is not problematic under ascend slowly after diving.
diver descends, he or she feels one typical diving conditions because a
additional atmosphere of pressure diver’s body can metabolize the extra At extreme depths, even the
because of the increasing weight of oxygen that is present in the blood- increased pressure of oxygen
water overhead. Most divers use stream. The body does not metabolize becomes a problem for scuba divers.
compressed air tanks to breathe nitrogen, however, so it can accumu- Although oxygen is necessary for life,
underwater. The air in these tanks, late in a diver’s body during a dive. extended exposure to large concen-
which contains approximately 78% The extra nitrogen can affect the nerve trations of oxygen can result in oxy-
nitrogen and 21% oxygen, is the cells of the diver, causing nitrogen nar- gen toxicity. This condition can cause
same as the air that we breathe. cosis. Divers suffering from nitrogen damage to the lungs and nervous
Once the compressed air enters the narcosis become disoriented and expe- system. Divers can avoid oxygen toxi-
diver’s lungs, it is subjected to the rience symptoms similar to intoxica- city by breathing gas mixtures that
pressure caused by the water. The tion. This impairment of a diver’s contain more helium and less oxygen
than compressed air does.
judgment can be very danger-
ous. To decrease the probability Questions
of contracting nitrogen narco-
sis, divers can use gas mixtures 1. Why is the concentration of
that contain less nitrogen than helium increased in some gas
compressed air does. mixtures that divers breathe in
order to reduce the partial pres-
Dissolved nitrogen can also sure of oxygen?
be harmful if a diver ascends
too quickly. As Henry’s law 2. Although carbon monoxide, CO,
predicts, nitrogen becomes is normally present in trace
less soluble in the blood as quantities in air, compressed air
the pressure decreases. This scuba tanks that are filled
decrease in solubility causes improperly can contain elevated
nitrogen to leave the diver’s levels of CO. Why is this particu-
tissues and blood. Normally, larly dangerous for divers?

In order to dive safely, scuba divers must be
aware of some of the basic gas laws.

368 C H A P T E R 1 1

The Gas Laws SECTION 2

S cientists have been studying physical properties of gases for hundreds OBJECTIVES

of years. In 1662, Robert Boyle discovered that gas pressure and volume Use the kinetic-molecular the-
are related mathematically.The observations of Boyle and others led to the ory to explain the relation-
development of the gas laws. The gas laws are simple mathematical rela- ships between gas volume,
tionships between the volume, temperature, pressure, and amount of a gas. temperature, and pressure.

Boyle’s Law: Pressure-Volume Use Boyle’s law to calculate
Relationship volume-pressure changes at
constant temperature.
Robert Boyle discovered that doubling the pressure on a sample of gas
at constant temperature reduces its volume by one-half. Reducing the Use Charles’s law to calculate
pressure on a gas by one-half allows the volume of the gas to double. As volume-temperature changes
one variable increases, the other decreases. Figure 6 shows that as the at constant pressure.
volume of gas in the syringe decreases, the pressure of the gas increases.
Use Gay-Lussac’s law to cal-
You can use the kinetic-molecular theory to understand why this culate pressure-temperature
pressure-volume relationship holds. The pressure of a gas is caused by changes at constant volume.
moving molecules hitting the container walls. Suppose the volume of a
container is decreased but the same number of gas molecules is present Use the combined gas law to
at the same temperature. There will be more molecules per unit volume. calculate volume-tempera-
The number of collisions with a given unit of wall area per unit time will ture-pressure changes.
increase as a result. Therefore, pressure will also increase.

Lower pressure Higher pressure

FIGURE 6 The volume of gas in
the syringe shown in the photo is
reduced when the plunger is pushed
down. The gas pressure increases as
the volume is reduced because the
molecules collide more frequently
with the walls of the container in a
smaller volume.

G A S E S 369

Volume Vs. PressureVolume (mL) Plotting the values of volume versus pressure for a gas at constant
for a Gas at Constant temperature gives a curve like that in Figure 7. The general volume-
Temperature pressure relationship that is illustrated is called Boyle’s law. Boyle’s law
states that the volume of a fixed mass of gas varies inversely with the pres-
1200 sure at constant temperature.

900 Mathematically, Boyle’s law can be expressed as follows:

600 PV = k

300 In the equation above, P is the pressure, V is the volume, and k is a
constant. Since P and V vary inversely, their product remains the same.
0 Because two quantities that are equal to the same thing are equal to
0123456 each other, the relationship between changes of pressure and volume
Pressure (atm) can be expressed as shown below.

FIGURE 7 This graph shows that P1V1 = P2V2
there is an inverse relationship
between volume and pressure. P1 and V1 represent initial conditions. P2 and V2 represent a differ-
ent set of conditions. Given three of the four values P1, V1, P2, and V2,
you can use this equation to calculate the fourth value for a system at
constant temperature.

SAMPLE PROBLEM C For more help, go to the Math Tutor at the end of this chapter.

A sample of oxygen gas has a volume of 150.0 mL when its pressure is 0.947 atm. What will
the volume of the gas be at a pressure of 0.987 atm if the temperature remains constant?

SOLUTION

1 ANALYZE Given: V1 of O2 = 150.0 mL; P1 of O2 = 0.947 atm; P2 of O2 = 0.987 atm
Unknown: V2 of O2 in mL

2 PLAN Rearrange the equation for Boyle’s law (P1V1 = P2V2) to obtain V2.
3 COMPUTE
4 EVALUATE V2 = P⎯1V1
P2

Substitute values for P1, V1, and P2 to obtain the new volume, V2.

V2 = P⎯1V1 = (⎯0.947 atm⎯)(150.0⎯mL O2) = 144 mL O2
P2 0.987 atm

When the pressure is increased slightly at constant temperature, the volume decreases
slightly, as expected. Units cancel to give milliliters, a volume unit.

PRACTICE Answers in Appendix E

1. A balloon filled with helium gas has a volume of 500 mL at a Go to go.hrw.com
pressure of 1 atm. The balloon is released and reaches an for more practice
altitude of 6.5 km, where the pressure is 0.5 atm. If the problems that ask you
temperature has remained the same, what volume does the gas to use Boyle’s Law.
occupy at this height?
Keyword: HC6GASX

370 C H A P T E R 1 1

Charles’s Law: Volume- FIGURE 8 As air-filled balloons
Temperature Relationship are exposed to liquid nitrogen, they
shrink greatly in volume because the
Balloonists, such as those in the photo at the beginning of this chapter, air molecules in the balloon get clos-
are making use of a physical property of gases: if pressure is constant, er together. When the balloons are
gases expand when heated. When the temperature increases, the vol- removed from the liquid nitrogen
ume of a fixed number of gas molecules must increase if the pressure is and the air inside them is warmed to
to stay constant. At the higher temperature, the gas molecules move room temperature, they expand to
faster. They collide with the walls of the container more frequently and their original volume.
with more force. The volume of a flexible container must then increase
in order for the pressure to remain the same.

The quantitative relationship between volume and temperature was
discovered by the French scientist Jacques Charles in 1787. Charles’s
experiments showed that all gases expand to the same extent when
heated through the same temperature interval. Charles found that the
volume changes by 1/273 of the original volume for each Celsius degree,
at constant pressure and an initial temperature of 0°C. For example,
raising the temperature to 1°C causes the gas volume to increase by
1/273 of the volume it had at 0°C. If the temperature is increased by
273°C, the volume increases by 273/273 of the original, that is, the vol-
ume doubles. The same regularity of volume change occurs if a gas is
cooled at constant pressure, as the balloons in Figure 8 show.

The Kelvin temperature scale is a scale that starts at a temperature
corresponding to −273.15°C. That temperature is the lowest one possi-
ble. The temperature −273.15°C is referred to as absolute zero and is
given a value of zero in the Kelvin scale. This fact gives the following
relationship between the two temperature scales.

K = 273.15 + °C

For calculations in this book, 273.15 is rounded off to 273.

G A S E S 371

Volume Vs.Volume (mL) Gas volume and Kelvin temperature are directly proportional to
Temperature for a Gas each other at constant pressure as shown in Figure 9.
at Constant Pressure
The relationship between Kelvin temperature and gas volume is
1100 known as Charles’s law. Charles’s law states that the volume of a fixed
mass of gas at constant pressure varies directly with the Kelvin tempera-
900 ture. Charles’s law may be expressed as follows:

700 V = kT or ⎯V = k
T
500
The value of T is the Kelvin temperature, and k is a constant. The
300 ratio V/T for any set of volume-temperature values always equals the
same k. The form of Charles’s law that can be applied directly to most
100 volume-temperature problems involving gases is as follows:
0 200 400 600
Temperature (K) V⎯1 = V⎯2
T1 T2
FIGURE 9 This graph shows the
plot of the volume versus the Kelvin V1 and T1 represent initial conditions. V2 and T2 represent a differ-
temperature data of a sample of gas ent set of conditions. When three of the four values T1, V1, T2, and V2
at constant pressure. are known, you can use this equation to calculate the fourth value for a
system at constant pressure.

SAMPLE PROBLEM D For more help, go to the Math Tutor at the end of this chapter.

A sample of neon gas occupies a volume of 752 mL at 25°C. What volume will the gas
occupy at 50°C if the pressure remains constant?

SOLUTION

1 ANALYZE Given: V1 of Ne = 752 mL; T1 of Ne = 25°C + 273 = 298 K; T2 of Ne = 50°C + 273 = 323 K
Unknown: V2 of Ne in mL

2 PLAN Because the gas remains at constant pressure, an increase in temperature will cause an
increase in volume. To obtain V2, rearrange the equation for Charles’s law.

3 COMPUTE Substitute values for V1, T1, and T2 to obtain the new volume, V2.
4 EVALUATE
V2 = V⎯1T2 = ⎯(752 m⎯L Ne)(⎯323 K) = 815 mL Ne
T1 298 K

As expected, the volume of the gas increases as the temperature increases. Units cancel to
yield milliliters, as desired. The answer contains the appropriate number of significant figures.

PRACTICE Answers in Appendix E

1. A sample of neon gas has a volume of 752 mL at 25.0°C. What will Go to go.hrw.com
the volume at 100.0°C be if pressure is constant? for more practice
problems that ask you
2. A sample of nitrogen gas is contained in a piston with a freely mov- to use Charles’s law.
ing cylinder. At 0.0°C, the volume of the gas is 375 mL. To what tem-
perature must the gas be heated to occupy a volume of 500.0 mL? Keyword: HC6GASX

372 C H A P T E R 1 1

Gay-Lussac’s Law: Pressure- Pressure Vs.
Temperature Relationship Temperature for a Gas
at Constant Volume
You have just learned about the quantitative relationship between vol- Pressure (atm)
ume and temperature at constant pressure.What would you predict about 6.0
the relationship between pressure and temperature at constant volume?
You have seen that pressure is the result of collisions of molecules with 5.0
container walls. The energy and frequency of collisions depend on the
average kinetic energy of molecules. For a fixed quantity of gas at con- 4.0
stant volume, the pressure should be directly proportional to the Kelvin
temperature, which depends directly on average kinetic energy. 3.0

That prediction turns out to be correct. For every kelvin of tempera- 2.0
ture change, the pressure of a confined gas changes by 1/273 of the pres-
sure at 0°C. Joseph Gay-Lussac is given credit for recognizing this in 1802. 1.0
The data plotted in Figure 10 illustrate Gay-Lussac’s law: The pressure of
a fixed mass of gas at constant volume varies directly with the Kelvin tem- 0
perature. Mathematically, Gay-Lussac’s law is expressed as follows. 0 100 200 300 400 500
Temperature (K)
P
P = kT or = k FIGURE 10 A graph of pressure
versus temperature of a sample of
T gas at constant volume is a straight
line, indicating a direct relationship
between pressure and temperature.

The value of T is the temperature in kelvins, and k is a constant that

depends on the quantity of gas and the volume. For a given mass of gas

at constant volume, the ratio P/T is the same for any set of pressure-

temperature values. Unknown values can be found using the following

form of Gay-Lussac’s law.

P1 = P2
T1 T2

P1 and T1 represent initial conditions. P2 and T2 represent a different set
of conditions. When values are known for three of the four quantities,

the fourth value can be calculated for a system at constant volume.

SAMPLE PROBLEM E For more help, go to the Math Tutor at the end of this chapter.

The gas in a container is at a pressure of 3.00 atm at 25°C. Directions on the container warn
the user not to keep it in a place where the temperature exceeds 52°C. What would the gas
pressure in the container be at 52°C?

SOLUTION

1 ANALYZE Given: P1 of gas = 3.00 atm
T1 of gas = 25°C + 273 = 298 K; T2 of gas = 52°C + 273 = 325 K

Unknown: P2 of gas in atm

2 PLAN Because the gaseous contents remain at the constant volume of the container, an increase
in temperature will cause an increase in pressure. Rearrange Gay-Lussac’s law to obtain P2.

P2 = P⎯1T2
T1

G A S E S 373

3 COMPUTE Substitute values for P1, T2, and T1 to obtain the new pressure, P2.
4 EVALUATE
P2 = (⎯3.00 atm⎯)(325 K) = 3.27 atm
298 K

As expected, a temperature increase at constant volume causes the pressure of the contents
in the container to increase. Units cancel correctly. The answer contains the proper number of
significant figures. It is close to an estimated value of 3.25, calculated as (3 × 325)/300.

PRACTICE Answers in Appendix E

1. At 120.0°C, the pressure of a sample of nitrogen is 1.07 atm. What
will the pressure be at 205°C, assuming constant volume?

2. At 122°C the pressure of a sample of nitrogen gas is 1.07 atm. Go to go.hrw.com
What will the pressure be at 205°C, assuming constant volume? for more practice prob-
lems that ask you to
3. A sample of helium gas has a pressure of 1.20 atm at 22°C. At what use Gay-Lussac’s law.
Celsius temperature will the helium reach a pressure of 2.00 atm,
assuming constant volume? Keyword: HC6GASX

www.scilinks.org The Combined Gas Law
Topic: Gas Laws
Code: HC60637 A gas sample often undergoes changes in temperature, pressure, and
volume all at the same time. When this happens, three variables must be
Chemical Content dealt with at once. Boyle’s law, Charles’s law, and Gay-Lussac’s law can
be combined into a single expression that is useful in such situations.
Go to go.hrw.com for more infor- The combined gas law expresses the relationship between pressure, vol-
mation on how the combined ume, and temperature of a fixed amount of gas. The combined gas law
gas law can be derived from can be expressed as follows.
Boyle’s law, Charles’s law, and
Gay-Lussac’s law. P⎯V = k
T
Keyword: HC6GASX
In the equation, k is constant and depends on the amount of gas. The
374 C H A P T E R 1 1 combined gas law can also be written as follows.

P⎯1V1 = P⎯2V2
T1 T2

The subscripts in the equation above indicate two different sets of
conditions, and T represents Kelvin temperature.

From this expression, any value can be calculated if the other five are
known. Note that each of the gas laws can be obtained from the com-
bined gas law when the proper variable is constant. For example,
Boyle’s law is obtained when the temperature is constant. Because
T1 = T2, T1 and T2 will cancel out on both sides of the combined gas law
equation, giving Boyle’s law.

P1V1 = P2V2

SAMPLE PROBLEM F For more help, go to the Math Tutor at the end of this chapter.

A helium-filled balloon has a volume of 50.0 L at 25°C and 1.08 atm. What volume will it
have at 0.855 atm and 10.0°C?

SOLUTION

1 ANALYZE Given: V1 of He = 50.0 L; T1 of He = 25°C + 273 = 298 K; T2 of He = 10°C + 273 = 283 K
P1 of He = 1.08 atm; P2 of He = 0.855 atm

Unknown: V2 of He in L

2 PLAN Because the gas changes in both temperature and pressure, the combined gas law is needed.
3 COMPUTE Rearrange the combined gas law to solve for the final volume, V2.
4 EVALUATE
P⎯1V1 = P⎯2V2 ⎯→ V2 = P⎯1V1T2
T1 T2 P2T1

Substitute the known values into the equation to obtain a value for V2.

V2 = (⎯1.08 atm⎯)(50.0⎯L He)(⎯283 K) = 60.0 L He
(0.855 atm)(298 K)

Here the pressure decreases much more than the temperature decreases. As expected, the
net result of the two changes gives an increase in the volume, from 50.0 L to 60.0 L. Units
cancel appropriately. The answer is correctly expressed to three significant figures. It is also
reasonably close to an estimated value of 50, calculated as (50 × 300)/300.

PRACTICE Answers in Appendix E

1. The volume of a gas is 27.5 mL at 22.0°C and 0.974 atm. What Go to go.hrw.com
will the volume be at 15.0°C and 0.993 atm? for more practice
problems that ask
2. A 700.0 mL gas sample at STP is compressed to a volume of you to use the
200.0 mL, and the temperature is increased to 30.0°C. What is combined gas law.
the new pressure of the gas in Pa?
Keyword: HC6GASX

SECTION REVIEW 4. A gas occupies 2.0 m3 at 100.0 K and exerts a
pressure of 100.0 kPa. What volume will the gas
1. Relate the effect of temperature and pressure on occupy if the temperature is increased to 400.0 K
a gas to the model of a gas given by the kinetic- and the pressure is increased to 200.0 kPa?
molecular theory.
Critical Thinking
2. A sample of helium gas has a volume of 200.0 mL
at 0.960 atm. What pressure, in atmospheres, is 5. ANALYZING RESULTS A student has the following
needed to reduce the volume at constant tempera- data: V1 = 822 mL, T1 = 75°C, and T2 = −25°C. He
ture to 50.0 mL? calculates V2 and gets −274 mL. Is this value cor-
rect? Explain why or why not.
3. A sample of nitrogen gas occupies 1.55 L at
27.0°C and 1.00 atm. What will the volume be at 6. APPLYING MODELS Explain Charles’s law in terms
−100.0°C and the same pressure? of the kinetic-molecular theory.

G A S E S 375

Chemistry’s First Law

Historical Perspective further hypothesized that the air exerted pressure on the mer-
The notion that “nature abhors a vacuum”—meaning that cury in the container and thus supported the mercury in the
there is no such thing as “empty space”—was proposed column.
by the Greek philosopher Aristotle, whose word was
unchallenged for nearly 2000 years. Then, in the Support for the New Theory
mid-1600s, a new breed of thinkers known as natural Although the idea of an atmosphere that has weight and
philosophers—what we now know as “scientists”— exerts a pressure on the objects within it seems obvious
began testing the long-held assumption that all space today, it was a radical theory at the time.
must contain matter. These investigations were some of
the earliest experiments with gases, and they led to the To test the effects of the atmosphere, Robert Boyle, one
discovery of the first empirical principle of chemistry, of the period’s great scientists, had his talented assistant,
Boyle’s law. Robert Hooke, create a piece of equipment that would rev-
olutionize the study of air. The apparatus was
Overturning an Ancient Assumption an improved version of a pump designed by the German
experimenter Otto von Guericke; the pump had a large
The first scientist to demonstrate the existence of a receptacle in which a partial vacuum could be created.

vacuum was Evangelista Torricelli. In 1643, he showed that Boyle placed Torricelli’s setup, known today as a barom-
eter, in the receptacle of the pump and observed the mer-
when a glass tube that was 3 ft. long and about 1 in. in cury column as he reduced the pressure around it. The
height of the mercury decreased as the pressure surround-
diameter was sealed ing the mercury in the container dropped, strongly support-
ing Torricelli’s atmospheric theory.
at one end, filled
Using Hooke’s pump, Boyle performed additional studies
with mercury, and that verified the idea that air exerted pressure and had
weight. Boyle’s experiments also led to the important con-
inverted in a con- clusion that air was elastic: that is, it could expand and con-
tract. Boyle discovered the fundamental law that bears his
tainer full of mer- name during an investigation into air’s elasticity.

cury, the mercury in An Ingenious Experiment
In response to a criticism of his findings, Boyle performed
the tube fell to a an experiment to show that air could be compressed to a
pressure greater than that of the atmosphere. First, he pre-
height of about pared a glass J-tube with the short end sealed off and the
long end left open. Then, he poured mercury into the tube,
30 in. above the making sure that the levels in the two ends were the same
and letting air travel freely between the ends, to ensure
level of mercury in that each column was at atmospheric pressure.

the container. Some Then, by pouring more mercury into the long end of the
tube until it was about 30 in. above the level of mercury in
thinkers remained the short end, Boyle exposed the trapped air to about
twice as much atmospheric pressure. He observed that the
skeptical, but it was

generally accepted

that the space

Evangelista Torricelli invented the between the mercury
mercury barometer. and the sealed end
of the tube was

indeed a vacuum.

Torricelli then turned his attention to how the mercury in

the glass tube of his apparatus was supported. The fact that

liquids exert a pressure on objects immersed in them inspired

him to hypothesize that a “sea of air” surrounded Earth. He

376 C H A P T E R 1 1

We can measure the
difference between the
atmospheric pressure on
a mountaintop and the
atmospheric pressure at
sea level thanks to the
work of Torricelli and
Boyle.

volume of the trapped air was halved. He continued to Questions
add mercury until the total pressure on the trapped air
was about 4 times that of the atmosphere. Noting that the 1. Why was it necessary for Boyle to seal one end of his
air had been compressed to a volume about one-fourth of J-tube?
what it originally was, Boyle discovered the inverse rela-
tionship between air’s pressure and volume. 2. What would have happened if Boyle had allowed the
temperature of the trapped air sample to change as
A Long-Standing Contribution he added mercury to the tube?
Boyle went on to show that the relationship between air
pressure and volume, P ∝ 1/V (at constant temperature), www.scilinks.org
held not only when the gas was compressed but also Topic: Torricelli
when it was allowed to expand. Future investigators Code: HC61539
would show that the law is a principle that applies to Topic: Robert Boyle
gases in general. Along with the findings of other Code: HC61317
researchers, such as Jacques Charles, Joseph Gay-Lussac,
and Amadeo Avogadro, Boyle’s discovery led chemists to
the famous ideal gas law, PV = nRT, which serves as a
starting point in the study of chemistry today.

G A S E S 377

SECTION 3 Gas Volumes and the
Ideal Gas Law
OBJECTIVES
I n this section, you will study the relationships between the volumes
State the law of combining
volumes. of gases that react with each other. You will also learn about the rela-
State Avogadro’s law and tionship between molar amount of gas and volume, and a single gas law
explain its significance. that unifies all the basic gas laws into a single equation.
Define standard molar volume
of a gas and use it to calcu- Measuring and Comparing the
late gas masses and volumes. Volumes of Reacting Gases
State the ideal gas law.
Using the ideal gas law, In the early 1800s, French chemist Joseph Gay-Lussac studied gas vol-
calculate pressure, volume, ume relationships involving a chemical reaction between hydrogen and
temperature, or amount of oxygen. He observed that 2 L of hydrogen can react with 1 L of oxygen
gas when the other three to form 2 L of water vapor at constant temperature and pressure.
quantities are known.
hydrogen gas + oxygen gas ⎯→ water vapor
378 C H A P T E R 1 1 2 L (2 volumes) 1 L (1 volume) 2 L (2 volumes)

In other words, this reaction shows a simple and definite 2:1:2 rela-
tionship between the volumes of the reactants and the product. Two vol-
umes of hydrogen react with 1 volume of oxygen to produce 2 volumes
of water vapor. The 2:1:2 relationship for this reaction applies to any
proportions for volume—for example, 2 mL, 1 mL, and 2 mL; 600 L,
300 L, and 600 L; or 400 cm3, 200 cm3, and 400 cm3.

Gay-Lussac also noticed simple and definite proportions by volume
in other reactions of gases, such as in the reaction between hydrogen gas
and chlorine gas.

hydrogen gas + chlorine gas ⎯→ hydrogen choloride gas

1 L (1 volume) 1 L (1 volume) 2 L (2 volumes)

In 1808, Gay-Lussac summarized the results of his experiments in a
statement known today as Gay-Lussac’s law of combining volumes of
gases. The law states that at constant temperature and pressure, the vol-
umes of gaseous reactants and products can be expressed as ratios of
small whole numbers. This simple observation, combined with the
insight of Avogadro, provided more understanding of how gases react
and combine with each other.