physical properties of gases chapter 21. behaviour of gases air is used to inflate vehicle tyres. ...

Physical Properties Physical Properties of Gasesof GasesChapter 21Chapter 21

Behaviour of GasesBehaviour of Gases

Air is used to inflate vehicle tyres.Air is used to inflate vehicle tyres. Aerosol cans carry a warning not to expose them to high Aerosol cans carry a warning not to expose them to high

temperaturestemperatures Helium balloons carry instruments into the upper atmosphere for Helium balloons carry instruments into the upper atmosphere for

scientist observations are only partially inflated when they leave scientist observations are only partially inflated when they leave the ground.the ground.

Balloons for sight-seeing can use heated air.Balloons for sight-seeing can use heated air. If a bottle of strong-smelling liquid, such as perfume, is opened in If a bottle of strong-smelling liquid, such as perfume, is opened in

a room, it doesn’t take long for the smell to spread.a room, it doesn’t take long for the smell to spread. Scuba divers have to be careful when ascending from a dive.Scuba divers have to be careful when ascending from a dive. When travelling in a plane you often experience a ‘popping’ When travelling in a plane you often experience a ‘popping’

sensation in your ears.sensation in your ears.

Behaviour of GasesBehaviour of Gases

Each of these situations can be Each of these situations can be explained in terms of properties of gases. explained in terms of properties of gases.

Properties of GasesProperties of Gases

The properties of gases can be used to develop a The properties of gases can be used to develop a particle model of gas behaviour. particle model of gas behaviour.

The low density of gas, relative to a liquid and solid, The low density of gas, relative to a liquid and solid, suggest that the particles of gas are much more widely suggest that the particles of gas are much more widely spaced.spaced. This is consistent with the observation that gases are easily This is consistent with the observation that gases are easily

compressed.compressed. The observations that gases spread to fill the space The observations that gases spread to fill the space

available suggests that the particles of a gas more available suggests that the particles of a gas more independently of each other.independently of each other.

The wide spacing of particles together with their The wide spacing of particles together with their movement explains why gases mix rapidly.movement explains why gases mix rapidly.

Kinetic Molecular TheoryKinetic Molecular Theory

This is the model used by scientists to This is the model used by scientists to explain gas behaviour is known as the explain gas behaviour is known as the kinetic molecular theory of gases.kinetic molecular theory of gases.

According to this model:According to this model: Gases are composed of small particles. The Gases are composed of small particles. The

total volume of the particles in the sample is total volume of the particles in the sample is very much smaller than the volume occupied very much smaller than the volume occupied by the gas. Most of the volume taken up by by the gas. Most of the volume taken up by a gas is empty space.a gas is empty space.

These particles move rapidly in a random, These particles move rapidly in a random, straight line motion. Particles will collide with straight line motion. Particles will collide with each other and with the walls of the each other and with the walls of the container.container.


The bonding forces between particles are The bonding forces between particles are extremely weak. It is assumed that particles extremely weak. It is assumed that particles move around independently.move around independently.

Collisions between particles are elastic, i.e. Collisions between particles are elastic, i.e. energy is conserved. Kinetic energy can be energy is conserved. Kinetic energy can be transferred from one particle to another, but transferred from one particle to another, but the total kinetic energy will remain constant.the total kinetic energy will remain constant.

The average kinetic energy of the particles The average kinetic energy of the particles increases as the temperature of the gas is increases as the temperature of the gas is increased.increased.


Relationship between Relationship between molecular kinetic energy and molecular kinetic energy and temperaturetemperature The average kinetic energy of gas particles The average kinetic energy of gas particles

is proportional to the temperature of the is proportional to the temperature of the gas sample.gas sample.

Meaning as one increases so does the Meaning as one increases so does the other.other.

Keep in mind that this is the average of all Keep in mind that this is the average of all the gas particles, with each sample there the gas particles, with each sample there will be some high energy particles and will be some high energy particles and some low energy particles.some low energy particles.

Relationship between Relationship between molecular kinetic energy and molecular kinetic energy and temperaturetemperature

This figure shows the distribution of This figure shows the distribution of kinetic energies of particles in a gas at a kinetic energies of particles in a gas at a given temperature.given temperature.

It shows:It shows: Only a small proportion of molecules has a very low Only a small proportion of molecules has a very low

or a very high kinetic energyor a very high kinetic energy At all 3 temps there are some molecules with very At all 3 temps there are some molecules with very

low kinetic energylow kinetic energy The proportion of molecules with high kinetic energy The proportion of molecules with high kinetic energy

increases with temperatureincreases with temperature The average kinetic energy of the sample increases The average kinetic energy of the sample increases

with temperature.with temperature. The area under each graph represents the total The area under each graph represents the total

number of molecules. The area under all 3 graphs is number of molecules. The area under all 3 graphs is the same.the same.

Kinetic molecular theoryKinetic molecular theory

The average kinetic energy of particles in The average kinetic energy of particles in gases is related to their average speed of gases is related to their average speed of movement by the relationship:movement by the relationship:Average kinetic energy = 1/2mvAverage kinetic energy = 1/2mv22

Where m is the mass of the gas particlesWhere m is the mass of the gas particles

And v is the average velocity of the particlesAnd v is the average velocity of the particles

DiffusionDiffusion

Diffusion is the term used to describe the way Diffusion is the term used to describe the way each gas in a mixture of gases spreads itself each gas in a mixture of gases spreads itself evenly to fill the total volume available.evenly to fill the total volume available.

The rate at which diffusion occurs depends on The rate at which diffusion occurs depends on the average velocity of their particles.the average velocity of their particles.

Gases of lower molecular mass will diffuse Gases of lower molecular mass will diffuse more rapidly that gases of higher molecular more rapidly that gases of higher molecular mass.mass.

Diffusion occurs more rapidly at higher Diffusion occurs more rapidly at higher temperature.temperature.

The Kinetic Molecular The Kinetic Molecular Theory can tell us:Theory can tell us:

That gas particles are in constant motion and continue That gas particles are in constant motion and continue to move in all directions.to move in all directions.

Gas particles expand to fill a container.Gas particles expand to fill a container. This means that the volume of a gas can be altered by This means that the volume of a gas can be altered by

changing the size of a container.changing the size of a container. A gas can be compressed by reducing the volume of A gas can be compressed by reducing the volume of

its container because there is so much space between its container because there is so much space between particles.particles. The more a gas is compressed, the greater the number of The more a gas is compressed, the greater the number of

collisions the gas particles will have with each other and the collisions the gas particles will have with each other and the walls of the container. These collisions produce a force on the walls of the container. These collisions produce a force on the walls of the container which we measure as pressure.walls of the container which we measure as pressure.

PressurePressure

Pressure is:Pressure is: The force exerted on a unit area of a surface.The force exerted on a unit area of a surface.

This is done by the particles of a gas as they This is done by the particles of a gas as they collide with each other and the walls of a collide with each other and the walls of a container.container.

The gas pressure exerted depends on the The gas pressure exerted depends on the number of collisions between the molecules number of collisions between the molecules and the walls of the container.and the walls of the container.

PressurePressure

The pressure of a fixed amount of gas is The pressure of a fixed amount of gas is independent of the actual gas.independent of the actual gas.

In a gaseous mixture of air, the nitrogen In a gaseous mixture of air, the nitrogen molecules collide with the walls exerting molecules collide with the walls exerting pressure. As do the oxygen molecules and the pressure. As do the oxygen molecules and the argon molecules and so on for each gas argon molecules and so on for each gas present in air.present in air.

The measured air pressure is the total of these The measured air pressure is the total of these individual gas pressures.individual gas pressures.

Figure 21.5 page 360Figure 21.5 page 360

Partial PressurePartial Pressure

The pressure exerted by the individual The pressure exerted by the individual gases in a mixture.gases in a mixture.

The total pressure is the sum of the The total pressure is the sum of the individual partial pressures of the gases individual partial pressures of the gases in the mixture.in the mixture.

The pressure will increase if the amount The pressure will increase if the amount of gas is increased, the temperature of of gas is increased, the temperature of the gas is increased or the volume of the the gas is increased or the volume of the container is decreased.container is decreased.

Your TurnYour Turn

Page 360Page 360 Question 1Question 1 Question 4Question 4

Measuring Pressure and Measuring Pressure and VolumeVolume

We use a barometer to We use a barometer to forecast weather.forecast weather. It actually measures air It actually measures air

pressure and relates pressure and relates pressure change to the pressure change to the changes in weather.changes in weather.

The first barometer was The first barometer was invented in the 17invented in the 17thth century century and looked a lot like this and looked a lot like this one.one.

Units of pressureUnits of pressure

Pressure is the force exerted on a unit Pressure is the force exerted on a unit area of a surface:area of a surface:

The units of pressure will depend on the The units of pressure will depend on the units used to measure force and area.units used to measure force and area.

Pressure = forcearea

Or P = FA

Units of PressureUnits of Pressure

There are many different units for pressure.There are many different units for pressure. SI unit for force is the newton and for the area SI unit for force is the newton and for the area

the square metre.the square metre. Pressure in SI units is therefore newtons per Pressure in SI units is therefore newtons per

square metre of N msquare metre of N m-2-2.. This is equivalent to a pressure of one pascal This is equivalent to a pressure of one pascal

(1 Pa).(1 Pa). Mercury barometers resulted in pressure being Mercury barometers resulted in pressure being

measured in mmHgmeasured in mmHg Other units are atmosphere (atm) and bar.Other units are atmosphere (atm) and bar.

Units of PressureUnits of Pressure

We generally use pascal to measure pressure.We generally use pascal to measure pressure. At 25At 25°°C atmospheric pressure is:C atmospheric pressure is:

1.000 atm1.000 atm 760 mmHg760 mmHg 1.013 x 101.013 x 1055 Pa Pa 101.3 kPa101.3 kPa 1.013 bar1.013 bar

We will mainly use kPa in chemistryWe will mainly use kPa in chemistry

Worked Example 21.3aWorked Example 21.3a

We can use the relationship to covert pressure We can use the relationship to covert pressure from one unit to another.from one unit to another.

The atmospheric pressure at the top of Mt The atmospheric pressure at the top of Mt Everest is 253mmHg. What is the pressure in:Everest is 253mmHg. What is the pressure in: Atmospheres?Atmospheres? Pascals?Pascals? Kilopascals?Kilopascals? Bars?Bars?

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Page 363Page 363 Question 5Question 5

VolumeVolume

1ml = 1 cm1ml = 1 cm33

1 L = 1 dm1 L = 1 dm33

1L = 1 x 101L = 1 x 1033 ml ml 1 m1 m33 = 1 x 10 = 1 x 1033 dm = 1 x 10 dm = 1 x 1066 cm cm 1 m = 1 x 101 m = 1 x 1033 L = 1 x 10 L = 1 x 1066 ml ml

Your TurnYour Turn

Page 363Page 363 Question 6Question 6 If you get stuck look at worked example If you get stuck look at worked example

21.3b on previous page21.3b on previous page

The gas lawsThe gas laws

Quantify the relationship between Quantify the relationship between volume, pressure, temperature and the volume, pressure, temperature and the number of particles of gas.number of particles of gas.

Boyle’s LawBoyle’s Law

In 1662 Robert Boyle showed In 1662 Robert Boyle showed experimentally that:experimentally that: For a given amount of gas at constant For a given amount of gas at constant

temperature, the volume of the gas is temperature, the volume of the gas is inversely proportional to its pressure.inversely proportional to its pressure.

In other words if the volume decreases In other words if the volume decreases by a set amount the pressure increases by a set amount the pressure increases by that same amount and vice versa.by that same amount and vice versa.


Figure 21.10Figure 21.10 The variation of The variation of volume with pressure for a volume with pressure for a fixedfixed amount of gas at amount of gas at constant temperature.constant temperature.


For a fixed amount of gas at constant For a fixed amount of gas at constant temperature this relationship can be written as:temperature this relationship can be written as: PV = k ( where k is a constant).PV = k ( where k is a constant).

This is very useful because it allows the This is very useful because it allows the calculation of volumes of a fixed amount of gas calculation of volumes of a fixed amount of gas at constant temperature if the pressure is at constant temperature if the pressure is changed:changed: PP11VV11 = P = P22VV22


Page 364Page 364

Your TurnYour Turn

Page 364Page 364 Question 9, 10 and 11Question 9, 10 and 11

Kelvin ScaleKelvin Scale

Kelvin scale is also known as the absolute Kelvin scale is also known as the absolute temperature scale.temperature scale.

It is measured in Kelvin (K).It is measured in Kelvin (K). 0 K is equivalent to -2730 K is equivalent to -273°°C and is known as C and is known as

absolute zero. This is where all molecules absolute zero. This is where all molecules would have zero kinetic energy.would have zero kinetic energy.

The relationship between temperature on the The relationship between temperature on the Celsius scale (t) and temperature on the kelvin Celsius scale (t) and temperature on the kelvin scale (T) is:scale (T) is: T = t + 273T = t + 273

Your TurnYour Turn


Charles’ LawCharles’ Law

The kinetic molecular theory states that The kinetic molecular theory states that an increase in the temperature of a gas an increase in the temperature of a gas increases the average kinetic energy. increases the average kinetic energy. This can cause:This can cause: The volume of gas to increase, if the The volume of gas to increase, if the

pressure on the gas is fixed.pressure on the gas is fixed. The pressure to increase, if the volume of The pressure to increase, if the volume of

the gas container is fixed.the gas container is fixed.


Using the kelvin scale, the relationship Using the kelvin scale, the relationship between volume and temperature can be between volume and temperature can be summarised by the statement:summarised by the statement: The volume of a fixed amount of gas is The volume of a fixed amount of gas is

directly proportional to the kelvin directly proportional to the kelvin temperature provided the pressure remains temperature provided the pressure remains constant.constant.

This is Charles’ LawThis is Charles’ Law


This law can be written as:This law can be written as: V = kT (k is constant) orV = kT (k is constant) or

We can use this relationship to calculate We can use this relationship to calculate changes in volume resulting in changes in volume resulting in temperature changes.temperature changes.

= kVT

V1

T1

V2

T2=

Worked Example 21.4b Worked Example 21.4b and your turnand your turn


Amount of gasAmount of gas

The volume of occupied gas depends The volume of occupied gas depends directly on the amount of gas (in mol) directly on the amount of gas (in mol) present, provided the pressure and present, provided the pressure and temperature remain constant.temperature remain constant.

V = kn (k is constant)V = kn (k is constant)

Worked example 21.4cWorked example 21.4c

V1

n1

V2

n2=

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Page 368Page 368 Question 14 and 15Question 14 and 15

Standard Laboratory Standard Laboratory Conditions (SLC)Conditions (SLC)

These are set conditions that normally These are set conditions that normally exist in a laboratory.exist in a laboratory.

The temperature is 25The temperature is 25°°C (298 K)C (298 K) Pressure is 101.3 kPaPressure is 101.3 kPa

Standard Temperature Standard Temperature and Pressure (STP)and Pressure (STP)

This refers to a set of conditions.This refers to a set of conditions. Temperature at 0Temperature at 0°°CC Pressure of 101.3 kPaPressure of 101.3 kPa

Molar Volume of a GasMolar Volume of a Gas

If we take 1 mole of any gas, the volume If we take 1 mole of any gas, the volume it occupies will depend on temperature it occupies will depend on temperature and pressure only. and pressure only.

We define this volume as the molar We define this volume as the molar volume (Vvolume (Vmm) of a gas.) of a gas.

The volume of 1 mole of gas is equal to The volume of 1 mole of gas is equal to its total volume divided by the amount, in its total volume divided by the amount, in mol, of gas present.mol, of gas present.

Molar VolumeMolar Volume

Molar volume can be represented by the Molar volume can be represented by the relationship:relationship:

For a given temperature and pressureFor a given temperature and pressure

Vm =V

n

n =V

Vm

Molar Volume and Molar Volume and Standard ConditionsStandard Conditions

VVmm at SLC is 24.5 L mol-1 at SLC is 24.5 L mol-1

VVmm at STP is 22.4 L mol-1 at STP is 22.4 L mol-1

From these values we can calculate the From these values we can calculate the amount of a gas given its volume at SLC amount of a gas given its volume at SLC or STP or STP

Worked Examples 21.4d and e page 369Worked Examples 21.4d and e page 369

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Page 370Page 370 Questions 16 and 17Questions 16 and 17

Combined Gas EquationCombined Gas Equation

In most experiments with gases, it is In most experiments with gases, it is inconvenient to hold variables such as inconvenient to hold variables such as temperature and pressure constant. temperature and pressure constant.

It is more common for amount of gas, It is more common for amount of gas, temperature, pressure and volume to all temperature, pressure and volume to all change in the one process. change in the one process.

Combined Gas EquationCombined Gas Equation

The combined gas equation relates The combined gas equation relates changes in pressure, volume, changes in pressure, volume, temperature and amount.temperature and amount.

P1V1 P2V2=n1T1 n2T2


A 0.25 mol sample of gas in a 10.0L A 0.25 mol sample of gas in a 10.0L cylinder exerts a pressure of 100 kPa at cylinder exerts a pressure of 100 kPa at 208208°C. A second cylinder, volume 15L °C. A second cylinder, volume 15L contains gas at a temperature of 100°C contains gas at a temperature of 100°C and a pressure of 120 kPa. What is the and a pressure of 120 kPa. What is the amount of gas in the second container?amount of gas in the second container?

Worked Example 21.5bWorked Example 21.5b

A gas exerts a pressure of 2.0 atm at A gas exerts a pressure of 2.0 atm at 3030°C, in a 10L container. In what size °C, in a 10L container. In what size container would the same amount of fas container would the same amount of fas exert a pressure of 4.0 atm at 20°C?exert a pressure of 4.0 atm at 20°C?

21.5c21.5c

Calculate the molar volume of an ideal Calculate the molar volume of an ideal gas at -10gas at -10°C and 90.0 kPa. Molar volume °C and 90.0 kPa. Molar volume at SLC (25°C and 101.3 kPa) is 24.5 L at SLC (25°C and 101.3 kPa) is 24.5 L molmol-1-1..

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Page 372Page 372 Question 18Question 18 Question 19Question 19 Question 20Question 20 Question 21Question 21

General Gas EquationGeneral Gas Equation

The general gas equation isThe general gas equation is PV = nRTPV = nRT Where P is measured in kilopascalsWhere P is measured in kilopascals V is measured in litresV is measured in litres n is measured in molesn is measured in moles T is measured in kelvinsT is measured in kelvins R is a constant and is 8.31 J KR is a constant and is 8.31 J K-1-1 mol mol-1-1

R is the proportionality constant. R is always R is the proportionality constant. R is always the same number and always has the same the same number and always has the same units. units.

General Gas EquationGeneral Gas Equation

A gas that behaves according to the general A gas that behaves according to the general gas equation is said to be an ideal gas. gas equation is said to be an ideal gas.

In practice, most gases can be considered to In practice, most gases can be considered to obey the general gas equation at low obey the general gas equation at low pressures and high temperatures. pressures and high temperatures.

If you can assume a gas is behaving ideally, If you can assume a gas is behaving ideally, this equation can be used to find the pressure, this equation can be used to find the pressure, temperature, volume or number of moles.temperature, volume or number of moles.

Worked Example 21.6a Worked Example 21.6a and band b

a) Calculate the amount of oxygen gas a) Calculate the amount of oxygen gas (O(O22) in a cylinder of 30 L, if the pressure ) in a cylinder of 30 L, if the pressure

is 20 atm at 30is 20 atm at 30°°CC

b) At what temperature would 3.2 g of b) At what temperature would 3.2 g of helium occupy a volume of 25 L at a helium occupy a volume of 25 L at a pressure of 700 mm Hgpressure of 700 mm Hg

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Page 373Page 373 Question 22, 23 and 25Question 22, 23 and 25

Reacting QuantitiesReacting Quantities

We can now add our new equations to We can now add our new equations to the ones we already know.the ones we already know.

This allows us to use stoichiometry to This allows us to use stoichiometry to solve equations on gasessolve equations on gases

Mass-Volume Stoichiometry Mass-Volume Stoichiometry – Standard Conditions– Standard Conditions

When standard conditions apply (SLC or When standard conditions apply (SLC or STP), once the amount of gas in mol, has STP), once the amount of gas in mol, has been determined, the molar volume can been determined, the molar volume can be used to calculate the required volume be used to calculate the required volume of gas.of gas.


A sample of calcium carbonate, mass A sample of calcium carbonate, mass 1.0g is heated until it has decomposed 1.0g is heated until it has decomposed completely. Calculate.completely. Calculate. a) the mass of carbon dioxide produceda) the mass of carbon dioxide produced b) the volume of carbon dioxide, measured b) the volume of carbon dioxide, measured

at SLCat SLC c) the volume of carbon dioxide, measured c) the volume of carbon dioxide, measured

at STPat STP

Non-Standard ConditionsNon-Standard Conditions

Calculations become more complex if the Calculations become more complex if the gas is not at standard conditions. gas is not at standard conditions.

In such cases, once the amount of gas, In such cases, once the amount of gas, in mol, has been calculated, the general in mol, has been calculated, the general gas equation can be used to calculate gas equation can be used to calculate the volume of gas.the volume of gas.

Worked Example 21.7bWorked Example 21.7b

Hydrogen peroxide decomposes Hydrogen peroxide decomposes according to the following equation:according to the following equation:

2H2H22OO22(aq) (aq) → 2H→ 2H22O(l) + OO(l) + O22(g)(g)

What volume of oxygen, collected at What volume of oxygen, collected at 3030°°C and 91kPa, is produced when C and 91kPa, is produced when 10.0g of hydrogen peroxide 10.0g of hydrogen peroxide decomposes?decomposes?

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Page 378Page 378 Question 27Question 27 Question 29Question 29

Volume-volume Volume-volume StoichiometryStoichiometry

For chemical reactions in the gaseous state it For chemical reactions in the gaseous state it is usually more convenient to measure is usually more convenient to measure volumes rather than masses.volumes rather than masses.

We have already discussed this chapter that We have already discussed this chapter that equal amounts (mol) of gases occupy equal equal amounts (mol) of gases occupy equal volumes, provided they are at the same volumes, provided they are at the same pressure and temperature.pressure and temperature.

We can therefore use the ratios in a balanced We can therefore use the ratios in a balanced equation to calculate the volumes of gaseous equation to calculate the volumes of gaseous reactants or productsreactants or products

Worked Example 21.7cWorked Example 21.7c

Methane is burnt in a gas stove. If 50 mL Methane is burnt in a gas stove. If 50 mL of methane, measured at a pressure of 1 of methane, measured at a pressure of 1 atm, is burnt in air at 500atm, is burnt in air at 500°C, calculate:°C, calculate: The volume of OThe volume of O22, measured at 1 atm and , measured at 1 atm and

500°C, required for complete combustion of 500°C, required for complete combustion of the methanethe methane

The volumes of COThe volumes of CO22 and H and H22O vapour O vapour

produced at 1 atm and 500°Cproduced at 1 atm and 500°C

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Page 378Page 378 Questions 30 and 31Questions 30 and 31