Chapter 21 – Physical Properties of Gases

Week 1, Lesson 1

Behaviour of Gases• Here are some everyday illustrations of the behaviour of gases.

These examples tell us a great deal about their physical properties.– Air is used to inflate tyres. Generally a maximum air pressure is

recommended for tyres.– Aerosol cans carry a warning not to expose them to high

temperatures.– Helium balloons that are used to carry instruments into the upper

atmosphere for scientific observation are only partially inflated when they leave the ground.

– Balloons used for sight-seeing can use heated air.– 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.– Scuba divers need to be very careful when ascending from a dive.– When going for a drive in the mountains or travelling in a plane, you

often experience a popping sensation in your ears.

Properties of Gas

• Low Density• Spread to fill available space• Easily compressed• Mix together rapidly.

Properties of Gas in Detail

• Low density: suggests that the particles of gas are more widely spread.

• Easily Compressed: as above.• Fill Available Space: suggest particles move

independently of one another.• Mix Rapidly: the wide spacing of particles

together with their movement.

Kinetic Molecular Theory• The model used to explain gas behaviour is called the kinetic

molecular theory.• According to this model:

– Gases are composed of small particles. The total volume of the particles in sample is very much smaller than the volume of occupied space. Most of the volume taken up is empty space.

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

– The bonding forces between particles are extremely weak. It is assumed the particles move independently.

– Collisions between particles are elastic, energy is conserved. Kinetic energy (energy of movement) can be transferred from one particle to another but total kinetic energy will remain constant.

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

Relationship between Molecular Kinetic Energy and Temperature

• According to the kinetic molecular theory, the average kinetic energy of gas particles is proportional to the temperature of that gas sample.

• At an given temperature however;– The average kinetic energy of the gas is not dependent on the

particular gas– Within each gas sample, there will be some particles of low

kinetic energy and some of high energy. The temperature merely reflects the average kinetic energy particles in the sample.

Relationship b/w molecular kinetic energy and temperature cont…

• The graph below shows the relative number of oxygen molecules with a given kinetic energy at three different temperatures.

• From the figure, you can see that:– Only a small proportion of molecules has very low or very high

kinetic energy.– At all three temperatures, there are some molecules with very

low kinetic energy– The proportion of molecules with high kinetic energy increases

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

temperature– The area under each graph represents the total number of

oxygen molecules. As the amount of gas is the same at all three temperatures, the area under each graph must be the same.

Average Kinetic Energy = ½ mv2

• The average kinetic energy of particles in gases is related to their average speed of movement by the relationship:

• m = mass of gas particles• v = average velocity of the particles• Therefore the lighter the gas atoms or

molecules in the sample, the greater their average velocity.

Diffusion

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

• The rate at which gases diffuse depends on the average velocity of their particles.

• Therefore gases of lower relative molecular mass will diffuse more rapidly than gases of higher relative molecular mass at the same temperature.

• Diffusion occurs more rapidly at higher temperatures than lower temperatures.

Using the Kinetic Molecular Theory

• The model of gases helps to explain why strong smells spread quickly.

• The particles that make up the gas are in constant motion and continue to move in all directions.

• Because there is so much space between these particles and all other gas particles in the air, all the gas particles rapidly mix with each other.

Using the Kinetic Molecular Theory cont…

• The model also explains why gases expand to fill any container.

• The gas particles continue to move outwards until stopped by walls of the container.

• This means that the amount of space a fixed mass of gas takes up can be altered by changing the size of its container.

Using the Kinetic Molecular Theory cont…

• A gas can be compressed by reducing the volume of its container because there is so much space between the gas particles.

• The more a gas is compressed, the greater the number of collisions the gas particles will have with each other and the wall of its container.

• These collisions produce a force on the walls of the container, such as the inside of a tyre, which can be measured.

• The force on the wall area is measured as pressure.

Pressure

• In terms of the kinetic theory of gases, pressure is defined as the force exerted in a unit area of a surface by the particles of a gas as they collide with each other and the walls of a container.

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

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

Partial Pressure

• The pressure exerted by the individual gases in a mixture is known as partial pressure.

• In a sample of air in a container, the partial pressure of the nitrogen is the pressure that amount of nitrogen would exert if it were the only gas in the container.

• When two gases are mixed together, the molecules of each move independently and collide with the walls as though the other gas were not there.

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

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

Measuring Pressure and Volume

• Since pressure is the force exerted on a unit of area of a surface, we can write the relationship:

Pressure = force/area = F/A• The units of pressure will depend on the units

used to measure the force and area.• Over the years, scientists have used different

units to measure force and area, so there are a number of different units of pressure.

Units of Pressure• The SI unit for force is the newton and for area is square metre. So

pressure for SI units is newtons per square metre or N m-2.• One N m-2 is equivalent to the pressure of one pascal (1 Pa)• In 1982, IUPAC, adopted a standard for pressure equivalent to

100000Pa or 100kPa.• This gave rise to a new unit of pressure, the bar, where 1 bar equals

100kPa.• Mercury barometers resulted in atmospheric pressure being

measured in millimetres of mercury or mmHg.• Another unit is the standard atmosphere (atm).• 1 standard atm is the pressure required to support 760mmHg.• This is the average atmospheric pressure at sea level.

Week 1, Lesson 2

Four Units of Pressure

• Millimetres of Mercury (mmHg)• Atmospheres (atm)• Pascals (Pa or N m-2)• Bars (bar)

1atm = 760mmHg = 1.013 x 105Pa = 101.3kPa = 1.013bar

Volume

• There are also a number of different units used for volume.

• The common units are litre (L), millilitre (mL), cubic metre (m3), cubic decimetre (dm3) and cubic centrimetre (cm3).

1 mL = 1cm3 1L = 1dm3

1L = 1 x 103mL 1m3 = 1 x 103dm3 = 1x 106cm3

1m3 = 1 x 103L = 1x106mL

The Gas Laws

• It is possible to establish some rules or laws that quantify the relationship between volume, temperature, pressure and number of particles of gas.

• These are known as the gas laws.• They are used to describe the behaviour of all

gases, regardless of chemical components.

Week 1, Lesson 3

Boyle’s Law

• Robert Boyle showed that for a given amount of gas at constant temperature, the volume of the gas is inversely proportional to its pressure.

• Or, if the volume of a fixed amount of gas is halved, the pressure will be doubled (at constant temp).

• PV = k – this relationship is useful because it allows the calculation of a fixed amount of gas at a constant temperature if the pressure is changed, OR

• P1V1 = P2V2

Charles’ Law

• To work with Charles’ Law we first need to look at temperature.

• In this case, we do not use the celsius scale, rather the kelvin scale or absolute temperature scale.

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

• Absolute zero is 0K or -273°C

Charles’ Law cont…

• Charles’ law states that the volume of a fixed amount of gas is directly proportional to the kelvin temperature, provided the pressure remains constant.

• This law can be expressed using the relationship, V/T = k, and then:

• V1/T1 = V2/T2

Amount of Gas

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

• The relationship between volume and amount of gas is represented by the equation:

V1/n1 = V2/n2

Molar Volume of Gas

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

• This volume is known as the molar volume (Vm) of a gas.

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

• This can be represented by the rearranged equation:n = V/Vm

STP and SLC• It is convenient to know the molar volume of a gas under

the conditions that normally exist in a laboratory. • The temperature of 25°C (298K) and a pressure of

101.3kPa approximate to lab conditions. These conditions are known as standard laboratory conditions (SLC).

• STP, or standard temperature and pressure refers to a temperature of 0°C (273K) and a pressure of 101.3kPa.

• The molar volume of a gas at SLC is 24.5L mol-1 and at STP is 22.4L mol-1

Combined Gas Equation

• In most experiments with gases it is convenient to hold variables such as temperature and pressure constant, however, this is unrealistic.

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

• To deal with such cases, the gas laws can be combined to give:

V = knT/P, where k is the proportionality constant.

Week 2, Lesson 1

Combined Gas Equation cont…

• P1V1/n1T1 = P2V2/n2T2

• This is the combined gas equation. It allows the calculation of any one of these variables, if the other variables have known values.

• It the amount of gas is fixed (n1 = n2), this relationship becomes:

P1V1/T1 = P2V2/T2

General Gas Equation• The general gas equation is developed from the combined gas

equation by determining a value for the constant k in the expression: V = knT/P

• In the general gas equation, the proportionality constant is given the symbol R.

• So the equation becomes: PV = nRT• Where R is called the general gas constant and is given the value

8.31J K-1 mol-1

• P = measured in kPa• V = measured in L• n = measured in moles• T = measured in K

Week 2, Lesson 2

General Gas Equation cont…

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

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

Reacting Quantities

• The molar volume under standard conditions or the general gas equation can be used to calculate the volume of any gas produced or consumed in a reaction.

Week 2, Lesson 3

Mass-Volume Stoichiometry

• Standard ConditionsWhen standard conditions apply (SLC or STP),

once the amount of gas, in mol, has been determined, the molar volume can be used to calculate the required volume of gas.

Standard Conditions exampleA sample of calcium carbonate, mass 1.0g, is heated until it has decomposed completely. Calculate:a) The mass of carbon dioxide producedb) The volume of carbon dioxide at SLCc) The volume of carbon dioxide at STP

a.Step 1: Write a balanced equation for the reactionStep 2: Calculate the amount (in mol) of the substance with the known massStep 3: Use the mole ratio to calculate the amount of the required substanceStep 4: Calculate the mass required

b.Step 1: Calculate the amount of carbon dioxide.Step 2: Calculate the volume of carbon dioxide at SLC

c.Step 1: Find volume of carbon dioxide at STP

Non-Standard Conditions

• Calculations become more complex if the gas is not at standard conditions. In such cases, once the amount of gas, in mol, has been calculated, the general gas equation can be used to calculate the volume of gas.

Non-Standard Conditions Example

Hydrogen peroxide decomposes according to the following equation:

2H2O2(aq) 2H2O(l) + O2(g)

What volume of oxygen, collected at 30°C and 91kPa, is produced when 10.0g of hydrogen peroxide decomposes.

Step 1: Write a balanced equation.Step 2: Calculate the amount (in mol) of the substance with the

known mass.Step 3: Use the mole ratio to calculate the amount of the

required substance.Step 4: Calculate the volume of O2

Volume-Volume Stoichiometry

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

• At constant temperature and pressure, the mole ratio will be equal to the ratio of gas volumes.

Volume-Volume Stoichiometry Example

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

a) The volume of O2, measured at 1atm and 500°C, required for complete combustion of the methane.

b) The volumes of CO2 and H2O vapour produced at 1atm and 500°C

Solution:CH4(g) + 2O2(g) CO2(g) + 2H2O(l)

Mole Ratio 1mol 2mol 1mol 2molAt constant temp and pressure, the mole ratio will equal the ratio of the gas volumes.Volume Ratio 1vol 2vol 1vol 2volTherfore; 50mL 100mL 50mL 100mL