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2.1 Gas Kinetics 35

For ideal gases under some conditions, mole fraction of any species is equal to
its volume fraction. The molar weight of a mixture of ideal gases can be determined
from the mole fraction of each compound and the corresponding molar weight
using Eq. (2.39):
N
X
M ¼ y i M i ð2:39Þ
i¼1
where M i is the molar weight of each substance in the gas mixture.

Example 2.2: Molar weight of simplified air
Dry air can be approximated as a mixture of nitrogen and oxygen molecules where
oxygen takes 21 % by volume. The approximate molar weights of nitrogen and
oxygen molecules are 28 and 32 g/mol, respectively. Estimate the molar weight of
standard dry air.
Solution
Using Eq. (2.39) we can get

M air ¼ y N 2 M N 2 þ y O 2 M O 2
¼ 0:79 28 þ 0:21 32 ¼ 28:84ðkg/kmolÞ
Assuming the gases are nonreactive, each individual gas in the mixture is also
governed by the ideal gas law:
P i V ¼ n i RT ð2:40Þ

where P i is partial pressure of the gas compound i. Combining Eqs. (2.33) and
(2.40) gives,

n i
P i ¼ P ¼ y i P ð2:41Þ
n
This relationship is also referred to as Dalton’s law. It states that the total
pressure of a mixture of nonreactive gases is equal to the sum of the partial pres-
sures of all individual gases.
The partial pressure of a gas in a mixture is an important property that affects
many engineering practices, for example, the solubility of a gas in liquid depends
on the partial pressure of the gas (see Sect. 2.3).
Example 2.3: Partial pressure of an ideal gas
Table 2.1 shows the compositions of pure dry air at sea level. Using the volume
percentage in this table, determine the partial pressures of nitrogen, oxygen,
methane, and carbon dioxide in Pascal at sea level where the atmospheric pressure
is 101.325 kPa.