UNIT 6. GAS LAWS
KINETIC MOLECULAR THEORY:
!
There are five main postulates of the Kinetic Molecular Theory:
(1) Gas is composed of very small particles, either molecules or atoms
(2) The gas particles are tiny in comparison to the distances between them, so
we assume that the volume of the gas particles themselves is negligible
(3) These gas particles are in constant motion, moving in straight lines in a
random fashion and colliding with each other and the inside walls of the
container
" Gas particles colliding with the walls of their container produce
pressure
(4) The gas particles are assumed to neither attract nor repel each other
" They may collide with each other but if they do, the collisions are assumed to be elastic;
that is, no kinetic energy is lost, only transferred from one gas molecule to another
(5) The average kinetic energy of the gas is directly proportional to the temperature measured in
Kelvin (K = °C + 273)
" The higher the temperature, the greater the kinetic energy of the gas particles
" Kinetic energy is defined as the energy of motion and is calculated using the following
equation:
m = mass measured in kg
KE per molecule = ½ mv2
v = velocity measured in m/s
" Any sample of gas contains a normal distribution of energies
The majority of particles possess an intermediate
amount of energy, which represents the
temperature of the sample
A small number of particles possess
a large amount of energy and are
therefore moving extremely quickly
A small number of particles
possess a small amount of
energy and are therefore
barely moving
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" At any given temperature, however the molecules in all gases have the same average
kinetic energy which can be calculated using the following equation:
R = Gas constant
T = temperature measured in K
" The average velocity of the gas particles is called the root mean square (rms) speed and it
is the speed of a gas particle having the average kinetic energy of the gas particle
–
Mathematically it can be represented as:
R = Gas constant
T = temperature measured in K
M = molar mass measured in kg
!
–
You will not be asked to perform calculation of root mean square speed, but you need to
appreciate that it is dependent upon molar mass and temperature
–
That is, heavier particles move more slowly and that particles at higher temperatures
move more quickly
A gas that obeys the five postulates of the Kinetic Molecular Theory is an ideal gas
" However, there are no ideal gases; only gases that approach ideal behaviour
" We know that real gas particles do occupy a certain finite volume and we know that there are
interactions between real gas particles
" These factors cause real gases to deviate a little from the ideal behaviour of the Kinetic
Molecular Theory
" We will examine how to modify our equations to account for non-ideal behaviour later in this
chapter
PRESSURE:
!
Pressure is the exertion of a force by one body on another
!
When we use the word pressure, we may be referring to the pressure of a gas inside a container or
to atmospheric pressure (the pressure due to the weight of the atmosphere above us)
!
These two different types of pressure are measured in slightly different ways
!
Atmospheric pressure is measured using a barometer
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" It consists of an evacuated hollow tube sealed at
one end is filled with mercury, and then the open
end is immersed in a pool of mercury
" Gravity will tend to pull the liquid inside the tube
down, while the weight of the atmospheric gases
on the surface of the mercury pool will tend to
force the liquid up into the tube
" These two opposing forces will quickly balance
each other and the column of mercury inside the
tube will stabilize
" The height of the column of mercury above the
surface of the mercury pool is called the
atmospheric pressure
" At sea level, the column averages 760 mm high or 760 torr (1 mm Hg = 1 torr)
" This pressure is also called 1 atmosphere (atm)
" Pounds per square inch (psi) is sometimes used to represent pressure, so that 1 atm = 14.69 psi
" The SI unit of pressure is the pascal (Pa), so that:
1 atm = 760 mm Hg = 760 torr = 101,300 Pa (101.3 kPa) = 14.69 psi
!
To measure the gas pressure inside a container, a manometer is used
" The principle involved is the same as that of the barometer
" A manometer consists of a U-tube partially filled with mercury
" One side of the U-tube is connected to the gas container and
the other side is open to a region of known pressure, most
often the atmosphere
" The gas in the container exerts a force on the mercury that
tends to push it down while the atmospheric pressure exerts a
downward force on the mercury at the open end of the tube
" The difference between the heights of the two mercury levels
is a direct measure of the difference between the two gas
pressures
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" Three possible results are produced using a manometer:
Pgas = Patm
!
Pgas < Patm
Pgas > Patm
Pgas = Patm – Δh
Pgas = Patm + Δh
Examples:
(1) When a container of gas is connected to a manometer, the mercury in the open end of the U-tube
rises until it is 112 mm higher than the mercury in the container side. If the atmospheric
pressure, measured with a barometer, is 765 mm Hg, what is the gas pressure in the container?
Pgas
>
Palm
Pgas
765+112
=
877
=
mmHg
(2) What is the pressure of the following gas sample attached to a U-tube manometer open to an
atmospheric pressure of 749.5 mm Hg?
Palm
d
Pgas< Palm
57.2-34.6=22
Dh=
mm
22.6cm
=
bcm
!
emmx
1,02
,
Bas
Mmm
226mm
=
Pgas
atm
x
.
=
749.5
-
524mm Hg
=
226
524
=
latm
×
760mm
=
0.689dm
mmHg
Hg
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