Specifying Gas Concentration
39
A middle range temperature for biophysical calculations is 293 K (20" C),
giving $ = 41.4 mol m-3 at sea level (101.3 Ha).
The relationship between volume, temperature, and pressure for a
perfect gas is
where pi is the partial pressure of gas j, and R is the gas constant, 8.3 143 J
mol-I K-'. Substituting Eq. (3.4) into Eq. (3.2) gives
so the mole fraction of a gas can be calculated as the ratio of its partial
pressure and the total atmospheric pressure.
One more relationship between mole fraction and other measures is
useful. If two gases with initial volumes Vl and V2 are mixed to make
a volume Va and the pressure is the same on all three volumes, then
the volume fraction, Vl/ Va is equal to the mole fraction, nlln,. Gas
concentrations in air are often expressed as percentages, parts per million
(ppm), or parts per billion (ppb) on a volume basis (volume of the pure
gas divided by the volume of air). It can be seen here that these measures
are directly related to the mole fraction.
One more version of the perfect gas law is also useful. The density
of a gas is the molecular mass multiplied by the number of moles, and
divided by the volume occupied by the gas (Eq. (3.1)). Substituting this
into Eq. (3.4) gives the relationship between the partial pressure of a gas
and its concentration:
Example 3.1. In 1985 the average concentration of C02 in the atmosphere ofthe earth was estimated to be 344 ppm. What is the mole fraction,
partial pressure, and density (concentration) of atmospheric C02 in air at
20" C?
Solution. Parts per million (ppm) means volumes of C02 in lo6 volumes
of air. Since the volume ratio is equal to the mole fraction, 344 ppm is
the same as 3.44 x
moles/mole or 344p mol/mol. Using Eq. (329,
pc = Ccpa.Ifp, = 101 kPa,thenpc = 3 . 4 4 ~
x 1.01 x lo5 Pa =
35 Pa. For density Eq. (3.6) is used and rearranged to get
pCMc
35 pa x 44
C -
-
P - - -
g
= 0.63 - .
x 293K
RT
8.31m 3
mol K
To get the units to divide out, you may need to refer to Table I .2. Note that
a Pascal is a Newton per square meter, and that a joule is a Newton-meter.
A Pascal is therefore equivalent to a joule per cubic meter.
39
A middle range temperature for biophysical calculations is 293 K (20" C),
giving $ = 41.4 mol m-3 at sea level (101.3 Ha).
The relationship between volume, temperature, and pressure for a
perfect gas is
where pi is the partial pressure of gas j, and R is the gas constant, 8.3 143 J
mol-I K-'. Substituting Eq. (3.4) into Eq. (3.2) gives
so the mole fraction of a gas can be calculated as the ratio of its partial
pressure and the total atmospheric pressure.
One more relationship between mole fraction and other measures is
useful. If two gases with initial volumes Vl and V2 are mixed to make
a volume Va and the pressure is the same on all three volumes, then
the volume fraction, Vl/ Va is equal to the mole fraction, nlln,. Gas
concentrations in air are often expressed as percentages, parts per million
(ppm), or parts per billion (ppb) on a volume basis (volume of the pure
gas divided by the volume of air). It can be seen here that these measures
are directly related to the mole fraction.
One more version of the perfect gas law is also useful. The density
of a gas is the molecular mass multiplied by the number of moles, and
divided by the volume occupied by the gas (Eq. (3.1)). Substituting this
into Eq. (3.4) gives the relationship between the partial pressure of a gas
and its concentration:
Example 3.1. In 1985 the average concentration of C02 in the atmosphere ofthe earth was estimated to be 344 ppm. What is the mole fraction,
partial pressure, and density (concentration) of atmospheric C02 in air at
20" C?
Solution. Parts per million (ppm) means volumes of C02 in lo6 volumes
of air. Since the volume ratio is equal to the mole fraction, 344 ppm is
the same as 3.44 x
moles/mole or 344p mol/mol. Using Eq. (329,
pc = Ccpa.Ifp, = 101 kPa,thenpc = 3 . 4 4 ~
x 1.01 x lo5 Pa =
35 Pa. For density Eq. (3.6) is used and rearranged to get
pCMc
35 pa x 44
C -
-
P - - -
g
= 0.63 - .
x 293K
RT
8.31m 3
mol K
To get the units to divide out, you may need to refer to Table I .2. Note that
a Pascal is a Newton per square meter, and that a joule is a Newton-meter.
A Pascal is therefore equivalent to a joule per cubic meter.