Geoscience Reference
In-Depth Information
is the number concentration of gas molecules (mole-
cules of gas per cubic meter or cubic centimeter of air),
R
*
is the universal gas constant (0.083145 m
3
hPa mol
−
1
K
−
1
10
4
cm
3
hPa mol
−
1
K
−
1
), and
or 8.314
×
R
∗
A
k
B
=
(3.8)
10
−
25
m
3
hPa K
−
1
is Boltzmann's constant (1.3807
×
molec
−
1
or 1.3807
10
−
19
cm
3
hPa K
−
1
molec
−
1
). The
Appendix contains alternative units for
R
*
×
and
k
B
.
Example 3.4
Calculate the number concentration of air
molecules in the atmosphere at standard sea-
level pressure and temperature and at a pressure
of 1 hPa.
Solution
At standard sea level,
p
=
1,013 hPa and
T
=
288 K. Thus, from Equation 3.6,
N
=
2.55
×
10
19
molec cm
−3
.FromFigure 3.2a,
p
1hPaoccurs
at 48 km. At this altitude and pressure,
T
=
270 K,
as shown in Figure 3.3. Under such conditions,
N
=
10
16
molec cm
−3
.
=
2.68
×
Figure 3.9.
John Dalton (1766-1844). Edgar Fahs
Smith Collection, University of Pennsylvania Library.
Equation 3.6 can be used to relate the partial pres-
sure exerted by a gas to its number concentration. In
1803,
John Dalton
(1766-1844), an English chemist
and physicist (Figure 3.9), stated that total atmospheric
pressure equals the sum of the partial pressures of the
individual gases in the air. This is
Dalton's law of par-
tial pressure
.The
partial pressure
exerted byagasin
amixture is the pressure the gas exerts if it alone occu-
pies the same volume as the mixture. Mathematically,
the partial pressure of gas
q
is
99.996 percent of dry air by volume. The partial pres-
sures of all gases aside from these four can be ignored,
without much loss in accuracy, when dry air pressure
is calculated. This assumption is convenient because
the concentrations of most trace gases vary in time and
space.
The partial pressure of dry air is related to the mass
density and number concentration of dry air through the
equation of state for dry air
,
p
q
=
N
q
k
B
T
(3.9)
p
d
=
d
R
T
=
N
d
k
B
T
(3.12)
where
N
q
is the number concentration of the gas
(molec cm
−
3
). Total atmospheric pressure is
d
is the mass density of dry air (kg m
−
3
or g
cm
−
3
) and
R
is the gas constant for dry air (2.8704 m
3
hPa kg
−
1
K
−
1
or 2,870.3 cm
3
hPa g
−
1
K
−
1
;alternative
units are given in the Appendix), and
N
d
is the number
concentration of dry air molecules (molec cm
−
3
). The
dry air mass density, number concentration, and gas
constant are further defined as
where
p
a
=
p
q
.
(3.10)
q
Dalton is also known for proposing the atomic theory
of matter and studying color blindness (Daltonism).
Total atmospheric pressure can also be written as
R
∗
m
d
n
d
m
d
V
n
d
A
V
p
a
=
p
d
+
p
v
(3.11)
R
=
d
=
N
d
=
(3.13)
where
p
d
is the partial pressure exerted by dry air and
p
v
is the partial pressure exerted by water vapor. Dry
air consists of all gases in the air, except water vapor.
Together, N
2
(g), O
2
(g), Ar(g), and CO
2
(g) constitute
respectively, where
n
d
is the number of moles of dry air
and
m
d
is the molecular weight of dry air, which is a
volume-weighted average of the molecular weights of
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