It is known that particles in solids, liquids & gases are in a state of constant motion.

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.

Movement in solids, liquids and gases

Motion of molecules in gases1

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. 2

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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Solid – particles close together with vibratory motion

Gas – particles far apart, move with higher velocities & fill the container with their movement.

Exert pressure inside container.

Liquid – particles further apart, move more easily & move from point to point in liquid.

Exert pressure

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Ideal gases are imaginary gases where the particles: 1.Are identical in all ways2.Occupy no volume 3.Exert no forces on each other (except during collisions)4.Collide with perfectly elastic collisions in which energy is conserved.

As pressure is increased, volume of an ideal gas can decrease to 0 volume!

Ideal gas always obeys gas laws under all conditions.

Gas laws

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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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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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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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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.

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.

Double the pressure is experienced when vol. is halved.

Pressure, volume & temperature

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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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The apparatus is used to inves-tigate the relationship between p and V for a fixed number of moles of a gas at aconstant temperature.

Robert Boyle1627 -1691

Volume vs pressure

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Air trapped in tube A. Bourdon

guage.

Air pumped in.

Oil reservoir.

Air causes increased pressure.

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Vol (V) in cm3

Pressure (p) in kPa

1/V pV

58,0 100 0,017 5800

48,3 120 0,023 5800

36,3 160 0,027 5800

29,0 200 0,034 5800

24,2 240 0,041 5800

20,7 280 0,048 5800

19,3 300 0,107 5800

These are typical values using the Boyle’s law apparatus 13

volume

pressureThe shape of the curve reminds one of a hyperbola. If this is the case, the equationwould be pV = k. Pressure is inversely proportional to volume of a fixed mass of gas.

Drawing the graph for these numbers you get:

Boyle's Law .. Animated click here

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As the curve could be something other thana hyperbola, we can check as follows:

If pV = k V = 1/p k

A graph of V vs 1/p would therefore indicatea straight line through the origin (comparey = mx).

As a straight line is obtained it means the original graph was a hyperbola therefore pV = k .

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volume

1/pressure

The volume of a given mass of gas is inverselyproportional to the pressure exerted on it, provided the temperature is constant.

N.B.

Definition:

Volume is directly proportional to the reciprocal of pressure or

V i/p ∝

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From the defining relationship between pressure and volume, we get the equation derived from this relationship:

p1V1 = p2V2

Since p1V1 = k and p2V2 = k then:

Boyle’s law equation.

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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 measurementfor k be?

Explain the answer in terms of the units of measurement for p and V.

Relationship P, V & T18

pV

p

As p increases, V decreases proportionally so that pV = k constant for real gases at atmospheric temperatures and pressures.

low

medium

highp

1/ V

Boyle’s law graphs for different temperatures.

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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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Ru

ler

Drop of Hg in capillary tube

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 in cm3 Temp. in 0C

38,0 -5

39,0 0

39,5 5

40,0 10

40,5 12

43,0 30

44,5 40

45,0 45

45,9 50

49 70

Now draw the graph to illustrate the relationship.

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Vol

ume

Vol

ume

-273 0C Temperature0 0C 100 0C

Drawing the graph gives a straight line – but not through the origin.

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

0 K 273 K 373 K

If we now extrapolate the graph, we find it intersects at -273 0C.

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Pre

ssur

e

Pre

ssur

e

-273 0C Temperature0 0C 100 0C

Drawing the graph gives a straight line – but not through the origin.

We can say p ∝ T (in K)& thus

0 K 273 K 373 K

If we now extrapolate the graph, we find it also intersects at -273 0C.

2

2

1

1

Tp

Tp

This is known as Guy Lussac’s law. Gay Lussac's law

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Lord William Thomson Kelvin1824 -1907

From this relationship we get the above equation.

V1 T1 V2

T2

=

Combining the p-V, the p-T and the V-T relationships, we then get:

p1V1 p2V2

T1 T2

=

This is known as the general gas equation.

N. B. v & P may be in any units, but T must be in kelvin.

Charles and Gay-Lussac's Law – Animated click here

P T V relationships

P V & T

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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

A temp of –50 0C is thus:

T = 273 + (-50 0C)

= 223 K

Now try converting the following:

20 0C 150 0C 70 K 200 K

Conversion of Celcius to Kelvin temperatures

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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.Special processes of an ideal gas click here

Molecular Model for an Ideal Gas

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We can combine the 3 gas law equations and get the following ideal gas law equation:

pV = nRT Pressure must be in pascalsVolume 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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The behaviour of gases deviates from Boyle’slaw at low temperatures and high pressures.

p

1/V

V

TExplain the deviations in the two graphs.

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30

p

T0

Explain the deviation above.

p1 T1 and p2 T2

p1/T1 = p2/T2

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Ideal gas

He

H2N2

pV

p

Consider the above graphs and explain the similarities and the differences.

Deviations for real gases