Geoscience Reference
In-Depth Information
Ideal Gas Law
In the seventeenth and eighteenth centuries it was discovered that there are simple
relationships between the pressure, volume, and temperature of gases.
Boyle's Law
,
for example, states that at constant temperature, the absolute pressure,
P
, and the
volume,
V
, of a gas are inversely proportional. Similarly,
Charles's Law
states that at
constant pressure, the volume of a given mass of an ideal gas increases or decreases
by the same factor as its temperature increases or decreases, providing the
temperature,
T
, is measured in K. These two laws can be combined to give the
Ideal Gas Law
, which has the form:
PV nRT
=
(2.4)
where
R
is the
universal gas constant
equal to 8.314 J mol
−1
K
−1
, and
n
is the number
of moles of gas considered. One mole of gas is defined as comprising 6.02
10
23
molecules: this number is called
Avogadro's number
. Strictly speaking, Equation
(2.4) only applies for an 'ideal' gas in which the molecules are treated as non-
interacting point particles engaged in a random motion that obeys the conserva-
tion of energy. In practice, however, the real gases that make up the atmosphere
approximate the behavior of an ideal gas closely for the range of temperatures and
pressure found in the troposphere.
The mass of a mole of one specific gas,
M
g
, is called the gram molecular weight
of the gas. If a volume,
V
, contains
n
moles of gas, it therefore has a mass (
nM
g
),
and the sample of gas has a density
×
r
g
=
(
nM
g
)/V. This means Equation (2.4) can be
re-written as:
PRT
=
r
(2.5)
gg
where
R
g
(
R
/
M
g
) is the gas constant for the specific gas. It is convenient to use this
second form of the ideal gas law when describing moist air. The gram molecular
weight of water is 18 grams per mole and if dry air is assumed to comprise
78% nitrogen and 22% oxygen, the gram molecular weight of dry air is 29 grams
per mole. Consequently, the specific gas constants of water vapor and dry air are
461.5 J kg
−1
K
−1
and 286.9 J kg
−1
K
−1
, respectively.
Since the molecules making up a gas are typically separated by about ten
molecular diameters at normal temperatures and pressures, only about one
thousandth of the volume of the gas is actually occupied by gas molecules. Gases
are therefore largely empty space and this means that for a gas that is a mixture of
molecules, the contribution to the pressure made by one constituent gas in the
mixture is independent of the pressure contribution made by the other gases
present. This result is
Dalton's law of partial pressures
, and it means that the ideal
gas law can be applied not only to the mixture of gases but also separately to each
constituent in a gas mixture.
=
