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9
The Kinetic Theory of Gases
549 549
19-1 AVOGADRO’S NUMBER
After reading this module, you should be able to . . .
19.01 Identify Avogadro’s number N A .
19.02 Apply the relationship between the number of moles n,
the number of molecules N, and Avogadro’s number N A .
19.03 Apply the relationships between the mass m of a sample,
the molar mass M of the molecules in the sample, the number of moles n in the sample, and Avogadro’s number N A .
● The kinetic theory of gases relates the macroscopic
properties of gases (for example, pressure and temperature)
to the microscopic properties of gas molecules (for example,
speed and kinetic energy).
● One mole of a substance contains N A (Avogadro’s
number) elementary units (usually atoms or molecules),
where N A is found experimentally to be
N A ϭ 6.02 ϫ 10
23
mol
Ϫ1
(Avogadro’s number).
One molar mass M of any substance is the mass of one mole
of the substance.
● A mole is related to the mass m of the individual molecules
of the substance by
M ϭ mN A .
● The number of moles n contained in a sample of mass
M sam , consisting of N molecules, is related to the molar
mass M of the molecules and to Avogadro’s number N A
as given by
n ϭ
N
N A
ϭ
M sam
M
ϭ
M sam
mN A
.
Learning Objectives
Key Ideas
What Is Physics?
One of the main subjects in thermodynamics is the physics of gases. A gas consists
of atoms (either individually or bound together as molecules) that fill their container’s volume and exert pressure on the container’s walls. We can usually assign
a temperature to such a contained gas. These three variables associated with a
gas—volume, pressure, and temperature—are all a consequence of the motion of
the atoms. The volume is a result of the freedom the atoms have to spread
throughout the container, the pressure is a result of the collisions of the atoms
with the container’s walls, and the temperature has to do with the kinetic energy
of the atoms. The kinetic theory of gases, the focus of this chapter, relates the
motion of the atoms to the volume, pressure, and temperature of the gas.
Applications of the kinetic theory of gases are countless. Automobile engineers are concerned with the combustion of vaporized fuel (a gas) in the automobile engines. Food engineers are concerned with the production rate of the
fermentation gas that causes bread to rise as it bakes. Beverage engineers are
concerned with how gas can produce the head in a glass of beer or shoot a cork
from a champagne bottle. Medical engineers and physiologists are concerned
with calculating how long a scuba diver must pause during ascent to eliminate
nitrogen gas from the bloodstream (to avoid the bends). Environmental scientists
are concerned with how heat exchanges between the oceans and the atmosphere
can affect weather conditions.
The first step in our discussion of the kinetic theory of gases deals with measuring the amount of a gas present in a sample, for which we use Avogadro’s number.
H
A
P
T
E
R
1
9
The Kinetic Theory of Gases
549 549
19-1 AVOGADRO’S NUMBER
After reading this module, you should be able to . . .
19.01 Identify Avogadro’s number N A .
19.02 Apply the relationship between the number of moles n,
the number of molecules N, and Avogadro’s number N A .
19.03 Apply the relationships between the mass m of a sample,
the molar mass M of the molecules in the sample, the number of moles n in the sample, and Avogadro’s number N A .
● The kinetic theory of gases relates the macroscopic
properties of gases (for example, pressure and temperature)
to the microscopic properties of gas molecules (for example,
speed and kinetic energy).
● One mole of a substance contains N A (Avogadro’s
number) elementary units (usually atoms or molecules),
where N A is found experimentally to be
N A ϭ 6.02 ϫ 10
23
mol
Ϫ1
(Avogadro’s number).
One molar mass M of any substance is the mass of one mole
of the substance.
● A mole is related to the mass m of the individual molecules
of the substance by
M ϭ mN A .
● The number of moles n contained in a sample of mass
M sam , consisting of N molecules, is related to the molar
mass M of the molecules and to Avogadro’s number N A
as given by
n ϭ
N
N A
ϭ
M sam
M
ϭ
M sam
mN A
.
Learning Objectives
Key Ideas
What Is Physics?
One of the main subjects in thermodynamics is the physics of gases. A gas consists
of atoms (either individually or bound together as molecules) that fill their container’s volume and exert pressure on the container’s walls. We can usually assign
a temperature to such a contained gas. These three variables associated with a
gas—volume, pressure, and temperature—are all a consequence of the motion of
the atoms. The volume is a result of the freedom the atoms have to spread
throughout the container, the pressure is a result of the collisions of the atoms
with the container’s walls, and the temperature has to do with the kinetic energy
of the atoms. The kinetic theory of gases, the focus of this chapter, relates the
motion of the atoms to the volume, pressure, and temperature of the gas.
Applications of the kinetic theory of gases are countless. Automobile engineers are concerned with the combustion of vaporized fuel (a gas) in the automobile engines. Food engineers are concerned with the production rate of the
fermentation gas that causes bread to rise as it bakes. Beverage engineers are
concerned with how gas can produce the head in a glass of beer or shoot a cork
from a champagne bottle. Medical engineers and physiologists are concerned
with calculating how long a scuba diver must pause during ascent to eliminate
nitrogen gas from the bloodstream (to avoid the bends). Environmental scientists
are concerned with how heat exchanges between the oceans and the atmosphere
can affect weather conditions.
The first step in our discussion of the kinetic theory of gases deals with measuring the amount of a gas present in a sample, for which we use Avogadro’s number.