Particles in motion: kinetic theory
It is known that particles in solids, liquids & gases are
in a state of constant motion.Movement in solids, liquids and gases
This is called the kinetic theory of matter.
In liquids, particles are moving more freely than in
solids and in gases they move more freely than in
liquids.
Particles in a gas such as ammonia (NH3) spread very
quickly through the air in a classroom. This process –
of a gas spreading through another gas is called
diffusion. This occurs in liquids as well.
Motion of molecules in gases
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Kinetic theory of gases
All matter consists of minute particles in constant,
random motion.
In solids, particles are close together & exhibit
vibratory motion.
In liquids & gases, particles further apart & freer to
move. Particles can vibrate, spin & move from place to
place. Diffusion can take place.
In gases, spaces between particles are large & can
thus be compressed. Molecules bump into each other
& walls of container – thus creating a pressure that
acts in all directions.
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Kinetic theory of gases
Molecules in a sample of gas particles all move at
different speeds.
The average speed of the sample of gas particles
remains constant for a certain temperature.
Average kinetic energy Ek ∝ T.
Particles moving at different speeds,
but having the same average Ek.
Movement of gas particles
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Kinetic theory of gases
Solid –
particles
close
together
with
vibratory
motion
Liquid –
particles further
apart, move
more easily &
move from
point to point in
liquid.
Exert pressure
Gas – particles far apart,
move with higher
velocities & fill the
container with their
movement.
Exert pressure inside
container.
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Ideal gas model
Ideal gases are imaginary gases where the
particles:
Ideal gas always
1. Are identical in all ways obeys gas laws
2. Occupy no volume
under all conditions.
3. Exert no forces on each other (except
during collisions)
4. Collide with perfectly elastic collisions in
which energy is conserved.
Gas laws
As pressure is increased,
volume of an ideal gas can
decrease to 0 volume!
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Ideal vs real gases
Real gases deviate from the behaviour of ideal
gases at very low temperatures and very high
pressures – where they tend to become liquids.
Most of the time, real gases behave like ideal
gases.
The real gases that behave closest to the ideal
gas model are He and H2.
Ideal vs real gases
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elationship between properties of a ga
In order to fully describe and study a gas, we
need to refer to the mass, volume, pressure
and temperature of the gas.
To see how they relate to one another, we
need to keep 2 variables constant and then
see how the one changes as we vary the
other.
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Gas pressure & volume
You are surrounded by millions of air particles all the
time – the atmosphere.
They exert a pressure in all directions – even on you!
This pressure is called the
atmospheric pressure.
In view of the fact that this
pressure has always been
there – you do not notice it
at all.
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Gas pressure & volume
Using a bicycle pump, pull out the plunger, put your
finger over the hole at the bottom & then push the
plunger in as far as you can.
Pressure, volume & temperature
As the pressure increases, so the volume decreases
because the same number of particles are now in a
more confined space & they are bumping each other &
the walls of the container more frequently – resulting in
an increased pressure in the pump.
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Double the pressure is experienced when vol. is halved.
Measuring pressure
The unit of pressure is the pascal (Pa).
1 Pa occurs when 1 N acts on 1 m2 surface area.
This is a small value & we usually use kilopascals
(kPa) instead. 1 kPa = 1000 Pa.
Atmospheric pressure is 100 kPa at sea level.
A Bourdon gauge is used to measure gas pressure.
How gauge works
Bourdon gauge
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Boyle's Law
Robert Boyle
1627 -1691
The apparatus is used to inves- Volume vs pressure
tigate the relationship between
p and V for a fixed number of moles of a gas at a
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constant temperature.
Boyle's Law
Air trapped
in tube A.
Air causes
increased
pressure.
Bourdon
guage.
Air pumped
in.
Oil
reservoir
12
.
Boyle's Law
Vol (V)
in cm3
58,0
48,3
36,3
29,0
24,2
20,7
19,3
Pressure
(p) in kPa
100
120
160
200
240
280
300
1/V
pV
0,017
0,023
0,027
0,034
0,041
0,048
0,107
5800
5800
5800
5800
5800
5800
5800
These are typical values using the Boyle’s law
apparatus
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Boyle's Law
volume
Drawing the graph for
these numbers you get:
Boyle's Law ..
Animated click
here
pressure
The shape of the curve reminds one of a
hyperbola. If this is the case, the equation
would be pV = k. Pressure is inversely
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proportional to volume of a fixed mass of gas.
Boyle's Law
As the curve could be something other than
a hyperbola, we can check as follows:
If pV = k
V = 1/p k
A graph of V vs 1/p would therefore indicate
a straight line through the origin (compare
y = mx).
As a straight line is obtained it means the
original graph was a hyperbola therefore
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pV = k .
Boyle's Law
volume
N.B.
Definition:
Volume is directly
proportional to the
reciprocal of
pressure or
V ∝ i/p
1/
pressure
The volume of a given mass of gas is inversely
proportional to the pressure exerted on it,
provided the temperature is constant.
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Boyle's Law
From the defining relationship between
pressure and volume, we get the equation
derived from this relationship:
Since p1V1 = k and p2V2 = k then:
p1V1 = p2V2
Boyle’s law equation.
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Boyle's Law
Take note that the conditions for Boyle’s law
stated in the previous formulation are:
1. The quantity of gas remains constant.
2. The temperature remains constant.
If pV = k, what would the unit of measurement
for k be?
Explain the answer in terms of the units of
measurement for p and V.
Relationship P, V & T
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Other graphs
As p increases, V decreases
proportionally so that pV = k
constant for real gases at
atmospheric temperatures and
pressures.
pV
p
Boyle’s law graphs for
different temperatures.
high
p
medium
low
1/ V
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Pressure, volume & temperature
What happens when a
cannon is fired?
The exploding gunpowder
causes the gas to expand
rapidly and thrust the cannon
ball into the air at high
velocity.
This principle can be used in rockets, car engines,
power station turbines & hot air balloons.
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Volume-temperature relationship
Drop of Hg in capillary tube
Ruler
Thermometer
Ice cubes
Air trapped
in tube
Record the volume of the air
column below the Hg as the
temperature rises & record the
values.
As the temperature increases, so the volume also
increases & we need to study this relationship
between volume & temperature.
This is known as Charles’ law of volume. 21
Volume-temperature relationship
Volume in cm3
38,0
39,0
39,5
40,0
40,5
43,0
44,5
45,0
45,9
49
Temp. in 0C
-5
0
5
10
12
30
40
45
50
70
Now draw
the graph to
illustrate the
relationship.
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-273 0C
0K
Volume
Volume
Volume-temperature relationship
0 0C
273 K
Drawing the graph
gives a straight line
– but not through
the origin.
100 0C Temperature
373 K
If we now extrapolate the graph, we find it
intersects at -273 0C.
This temperature has been given the value of 0 K and is
called absolute zero. The kelvin temperature scale has
developed from this relationship.
1 K = 1 0C, so a temp of 0 0C = 273 K & 100 0C = 373 k
We can say V ∝ T (in K) V1/T1 =V2/T2
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-273 0C
0K
Pressure
Pressure
Pressure-temperature relationship
0 0C
273 K
Drawing the graph
gives a straight line
– but not through
the origin.
100 0C Temperature
373 K
If we now extrapolate the graph, we find it
also intersects at -273 0C.
p1 p2
=
We can say p ∝ T (in K)& thus
T T
1
2
This is known as Guy Lussac’s law.
Gay Lussac's law
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Volume-temperature relationship
Lord William Thomson Kelvin
1824 -1907
V1
V2
= T
T1
2
From this relationship we get the
above equation.
P T V relationships
Combining the p-V, the p-T and the
V-T relationships, we then get:
p1V1
=
p2V2
PV&T
Charles and Gay-Lussac's Law –
Animated click here
T1
T2
This is known as the general gas equation.
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N. B. v & P may be in any units, but T must be in kelvin.
Temperature conversions
To convert one temperature to the other – or
vice-versa, we use the following equation:
Temp in kelvin = 273 + temp in celsius
T = 273 + t
Conversion of Celcius to Kelvin temperatures
0
A temp of –50 C is thus:
T = 273 + (-50 0C)
= 223 K
Now try converting the following:
20 0C
150 0C
70 K
200 K
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Standard temperature & pressure
When describing a gas, sometimes we refer to S.T.P.
This is standard temperature & pressure.
These standard conditions are:
Standard pressure = 100 kPa & (1 Atm pressure)
Standard temperature = 0 0C or 273 K
Now try some problems & calculations on the gas laws.
Molecular Model for an Ideal Gas
Special processes of an ideal gas
click here
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Ideal gas law equation:
We can combine the 3 gas law equations and
get the following ideal gas law equation:
pV = nRT
Pressure must be in pascals
Volume in m3 &
Temperature in kelvin (K)
The universal gas constant (R) has the
value of 8,31 J∙K-1∙mol-1
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Deviations from the ideal gas model
The behaviour of gases deviates from Boyle’s
law at low temperatures and high pressures.
p
V
1/
V
T
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Explain the deviations in the two graphs.
Deviations from the ideal gas model
p1  T1 and p2  T2
p
p1/T1 = p2/T2
0
T
Explain the deviation above.
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Deviations from the ideal gas model
N2
pV
H2
He
Ideal gas
p
Consider the above graphs and explain
the similarities and the differences.
Deviations for real gases
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