Page 56 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

30 2 Basic Properties of Gases

Since A and B are randomly selected and they are independent on each other, the
ð
term ~ c A ~ c B Þ results in a quantity of zero. Meanwhile, since A and B are
ave
randomly selected from the same population, where the molecules behave statis-
tically the same, we also have c A ¼ c B ¼ c. Then Eq. (2.11) becomes
2
2
c 2 ¼ c þ c ¼ 2 c 2 ð2:12Þ
A=B A B
The relation between the magnitudes of the average relative speed and mean
speed is

1=2

p ffiffiffi 16kT
c A=B ¼ 2 c ¼ : ð2:13Þ
pm
2.1.2 Avogadro Constant and Molar Weight
A gas volume contains a large number of molecules, which are treated as particles,
in rapid motions. Mole amount is used to quantify the amount of molecules. In
1 mol of gas there are 6:022 10 23 molecules. This is described using the
Avogadro number or Avogadro constant

N A ¼ 6:022 10 23 ð1=molÞ ð2:14Þ

Any gas can be characterized with its molar weight, which is the mass of 1 mol
of the gas

M ¼ N A m ð2:15Þ

where m is the mass of a single molecule, and M is the molar weight of a gas with a
unit of g/mol or kg/kmol. Molar weights of typical gases with known molecular
formula can be determined by the corresponding number of atoms. For example, the
molar weight of O 2 is 32 because there are two oxygen atoms in one oxygen
molecule and each of the atom weight is 16 g/mol.

2.1.3 Gas Pressure

The pressure of a gas is resulted from the force exerted by gas molecules on the
walls of the container due to the collision between the wall and molecules. Consider
a cubic container having N gas molecules and the length of the container is l.
The linear momentum before and after the impact is m~ c 1 and m~ c 2 , respectively,
when a gas molecule collides with the wall of the container that is normal to the
x coordinate axis and bounces back in the opposite direction. From the principle of
impulse and linear momentum one has,