C H A P T E R

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C H A P T E R   14The Ideal Gas Law and Kinetic
Theory
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14.1 The Mole, Avogadro's Number, and Molecular
Mass
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Atomic Mass Unit, U
By international agreement, the reference element
is chosen to be the most abundant type of carbon,
called carbon-12, and its atomic mass is defined
to be exactly twelve atomic mass units, or 12 u.
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Molecular Mass
The molecular mass of a molecule is the sum of
the atomic masses of its atoms. For instance,
hydrogen and oxygen have atomic masses of 1.007
94 u and 15.9994 u, respectively. The molecular
mass of a water molecule (H2O) is 2(1.007 94 u)
15.9994 u 18.0153 u.
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Avogadro's Number NA
The number of atoms per mole is known as
Avogadro's number NA, after the Italian scientist
Amedeo Avogadro (17761856)
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Number of Moles, n
The number of moles n contained in any sample is
the number of particles N in the sample divided
by the number of particles per mole NA
(Avogadro's number)
The number of moles contained in a sample can
also be found from its mass.
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14.2 The Ideal Gas Law
An ideal gas is an idealized model for real gases
that have sufficiently low densities.
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The Ideal Gas Law
An ideal gas is an idealized model for real gases
that have sufficiently low densities. The
condition of low density means that the molecules
of the gas are so far apart that they do not
interact (except during collisions that are
effectively elastic).
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The Ideal Gas Law
An ideal gas is an idealized model for real gases
that have sufficiently low densities. The
condition of low density means that the molecules
of the gas are so far apart that they do not
interact (except during collisions that are
effectively elastic). The ideal gas law
expresses the relationship between the absolute
pressure (P), the Kelvin temperature (T), the
volume (V), and the number of moles (n) of the
gas.
Where R is the universal gas constant. R 8.31
J/(mol K).
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The Ideal Gas Law
The constant term R/NA is referred to as
Boltzmann's constant, in honor of the Austrian
physicist Ludwig Boltzmann (18441906), and is
represented by the symbol k
PV NkT
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14.3 Kinetic Theory of Gases
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Kinetic Theory of Gases
The pressure that a gas exerts is caused by the
impact of its molecules on the walls of the
container.
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Kinetic Theory of Gases
The pressure that a gas exerts is caused by the
impact of its molecules on the walls of the
container.
It can be shown that the average translational
kinetic energy of a molecule of an ideal gas is
given by,
where k is Boltzmann's constant and T is the
Kelvin temperature.
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Derivation of,
Consider a gas molecule colliding elastically
with the right wall of the container and
rebounding from it.
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The force on the molecule is obtained using
Newtons second law as follows,
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The force on one of the molecule,
According to Newton's law of actionreaction, the
force on the wall is equal in magnitude to this
value, but oppositely directed.
The force exerted on the wall by one molecule,
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If N is the total number of molecules, since
these particles move randomly in three
dimensions, one-third of them on the average
strike the right wall. Therefore, the total force
is
Vrms root-mean-square velocity.
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Pressure is force per unit area, so the pressure
P acting on a wall of area L2 is
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Pressure is force per unit area, so the pressure
P acting on a wall of area L2 is
Since the volume of the box is V L3, the
equation above can be written as,
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PV NkT
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EXAMPLE 6 The Speed of Molecules in Air
Air is primarily a mixture of nitrogen N2
(molecular mass 28.0 u) and oxygen O2
(molecular mass 32.0 u). Assume that each
behaves as an ideal gas and determine the rms
speed of the nitrogen and oxygen molecules when
the temperature of the air is 293 K.
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The Internal Energy of a Monatomic Ideal Gas