Physical Properties of Gases Chapter 21

Behaviour of Gases Air is used to inflate vehicle tyres. Aerosol cans carry a warning not to expose them to high temperatures Helium balloons carry instruments into the upper atmosphere for scientist observations are only partially inflated when they leave the ground. Balloons 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 have to be careful when ascending from a dive. When travelling in a plane you often experience a ‘popping’ sensation in your ears.

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

Properties of Gases The properties of gases can be used to develop a particle model of gas behaviour. The low density of gas, relative to a liquid and solid, suggest that the particles of gas are much more widely spaced. This is consistent with the observation that gases are easily compressed. The observations that gases spread to fill the space available suggests that the particles of a gas more independently of each other. The wide spacing of particles together with their movement explains why gases mix rapidly.

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

Kinetic Molecular Theory According to this model: Gases are composed of small particles. The total volume of the particles in the sample is very much smaller than the volume occupied by the gas. Most of the volume taken up by a gas is empty space. These particles move rapidly in a random, straight line motion. Particles will collide with each other and with the walls of the container.

Kinetic Molecular Theory The bonding forces between particles are extremely weak. It is assumed that particles move around independently. Collisions between particles are elastic, i.e. energy is conserved. Kinetic energy can be transferred from one particle to another, but the 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 The average kinetic energy of gas particles is proportional to the temperature of the gas sample. Meaning as one increases so does the other. Keep in mind that this is the average of all the gas particles, with each sample there will be some high energy particles and some low energy particles.

Relationship between molecular kinetic energy and temperature This figure shows the distribution of kinetic energies of particles in a gas at a given temperature.

It shows: Only a small proportion of molecules has a very low or a very high kinetic energy At all 3 temps 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 molecules. The area under all 3 graphs is the same.

Kinetic molecular theory The average kinetic energy of particles in gases is related to their average speed of movement by the relationship: Average kinetic energy = 1/2mv2 Where m is the mass of the gas particles And v is the average velocity of the particles

Diffusion 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 diffusion occurs depends on the average velocity of their particles. Gases of lower molecular mass will diffuse more rapidly that gases of higher molecular mass. Diffusion occurs more rapidly at higher temperature.

The Kinetic Molecular Theory can tell us: That gas particles are in constant motion and continue to move in all directions. Gas particles expand to fill a container. This means that the volume of a gas can be altered by changing the size of a container. A gas can be compressed by reducing the volume of its container because there is so much space between particles. The more a gas is compressed, the greater the number of 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 which we measure as pressure.

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

Pressure The pressure of a fixed amount of gas is independent of the actual gas. In a gaseous mixture of air, the nitrogen molecules collide with the walls exerting pressure. As do the oxygen molecules and the argon molecules and so on for each gas present in air. The measured air pressure is the total of these individual gas pressures. Figure 21.5 page 360

Partial Pressure The pressure exerted by the individual gases in a mixture. The total pressure is the sum of the individual partial pressures of the gases in the mixture. The pressure will increase if the amount of gas is increased, the temperature of the gas is increased or the volume of the container is decreased.

Your Turn Page 360 Question 1 Question 4

Measuring Pressure and Volume We use a barometer to forecast weather. It actually measures air pressure and relates pressure change to the changes in weather. The first barometer was invented in the 17th century and looked a lot like this one.

Units of pressure Pressure is the force exerted on a unit area of a surface: The units of pressure will depend on the units used to measure force and area. force F Or P = Pressure = area A

Units of Pressure There are many different units for pressure. SI unit for force is the newton and for the area the square metre. Pressure in SI units is therefore newtons per square metre of N m-2. This is equivalent to a pressure of one pascal (1 Pa). Mercury barometers resulted in pressure being measured in mmHg Other units are atmosphere (atm) and bar.

Units of Pressure We generally use pascal to measure pressure. At 25°C atmospheric pressure is: 1.000 atm 760 mmHg 1.013 x 105 Pa 101.3 kPa 1.013 bar We will mainly use kPa in chemistry

Worked Example 21.3a We can use the relationship to covert pressure from one unit to another. The atmospheric pressure at the top of Mt Everest is 253mmHg. What is the pressure in: Atmospheres? Pascals? Kilopascals? Bars?

Your Turn Page 363 Question 5

Volume 1ml = 1 cm3 1 L = 1 dm3 1L = 1 x 103 ml 1 m3 = 1 x 103 dm = 1 x 106 cm 1 m = 1 x 103 L = 1 x 106 ml

Your Turn Page 363 Question 6 If you get stuck look at worked example 21.3b on previous page

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

Boyle’s Law In 1662 Robert Boyle showed experimentally that: For a given amount of gas at constant temperature, the volume of the gas is inversely proportional to its pressure. In other words if the volume decreases by a set amount the pressure increases by that same amount and vice versa.

Boyle’s Law Figure 21.10 The variation of volume with pressure for a fixed amount of gas at constant temperature.

Boyle’s Law For a fixed amount of gas at constant temperature this relationship can be written as: PV = k ( where k is a constant). This is very useful because it allows the calculation of volumes of a fixed amount of gas at constant temperature if the pressure is changed: P1V1 = P2V2

Worked Example 21.4a Page 364

Your Turn Page 364 Question 9, 10 and 11

Kelvin Scale Kelvin scale is also known as the absolute temperature scale. It is measured in Kelvin (K). 0 K is equivalent to -273°C and is known as absolute zero. This is where all molecules would have zero kinetic energy. The relationship between temperature on the Celsius scale (t) and temperature on the kelvin scale (T) is: T = t + 273

Your Turn Page 367 Question 12

Charles’ Law The kinetic molecular theory states that an increase in the temperature of a gas increases the average kinetic energy. This can cause: The volume of gas to increase, if the pressure on the gas is fixed. The pressure to increase, if the volume of the gas container is fixed.

Charles’ Law Using the kelvin scale, the relationship between volume and temperature can be summarised by the statement: The volume of a fixed amount of gas is directly proportional to the kelvin temperature provided the pressure remains constant. This is Charles’ Law

Charles’ Law This law can be written as: V = kT (k is constant) or We can use this relationship to calculate changes in volume resulting in temperature changes. V T = k V1 T1 V2 T2 =

Worked Example 21.4b and your turn Page 367 Question 13

Amount of gas The volume of occupied gas depends directly on the amount of gas (in mol) present, provided the pressure and temperature remain constant. V = kn (k is constant) Worked example 21.4c V1 n1 V2 n2 =

Your Turn Page 368 Question 14 and 15

Standard Laboratory Conditions (SLC) These are set conditions that normally exist in a laboratory. The temperature is 25°C (298 K) Pressure is 101.3 kPa

Standard Temperature and Pressure (STP) This refers to a set of conditions. Temperature at 0°C Pressure of 101.3 kPa

Molar Volume of a Gas If we take 1 mole of any gas, the volume it occupies will depend on temperature and pressure only. We define this volume 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.

Molar Volume Molar volume can be represented by the relationship: V For a given temperature and pressure V Vm = n V n = Vm

Molar Volume and Standard Conditions Vm at SLC is 24.5 L mol-1 Vm at STP is 22.4 L mol-1 From these values we can calculate the amount of a gas given its volume at SLC or STP Worked Examples 21.4d and e page 369

Your Turn Page 370 Questions 16 and 17

Combined Gas Equation In most experiments with gases, it is inconvenient to hold variables such as temperature and pressure constant. It is more common for amount of gas, temperature, pressure and volume to all change in the one process.

Combined Gas Equation The combined gas equation relates changes in pressure, volume, temperature and amount. P1V1 P2V2 = n1T1 n2T2

Worked Example 21.5a A 0.25 mol sample of gas in a 10.0L cylinder exerts a pressure of 100 kPa at 208°C. A second cylinder, volume 15L contains gas at a temperature of 100°C and a pressure of 120 kPa. What is the amount of gas in the second container?

Worked Example 21.5b A gas exerts a pressure of 2.0 atm at 30°C, in a 10L container. In what size container would the same amount of fas exert a pressure of 4.0 atm at 20°C?

21.5c Calculate the molar volume of an ideal gas at -10°C and 90.0 kPa. Molar volume at SLC (25°C and 101.3 kPa) is 24.5 L mol-1.

Your Turn Page 372 Question 18 Question 19 Question 20 Question 21

General Gas Equation The general gas equation is PV = nRT Where P is measured in kilopascals V is measured in litres n is measured in moles T is measured in kelvins R is a constant and is 8.31 J K-1 mol-1 R is the proportionality constant. R is always the same number and always has the same units.

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

Worked Example 21.6a and b a) Calculate the amount of oxygen gas (O2) in a cylinder of 30 L, if the pressure is 20 atm at 30°C b) At what temperature would 3.2 g of helium occupy a volume of 25 L at a pressure of 700 mm Hg

Your Turn Page 373 Question 22, 23 and 25

Reacting Quantities We can now add our new equations to the ones we already know. This allows us to use stoichiometry to solve equations on gases

Mass-Volume Stoichiometry – Standard Conditions When 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.

Worked Example 21.7a A sample of calcium carbonate, mass 1.0g is heated until it has decomposed completely. Calculate. a) the mass of carbon dioxide produced b) the volume of carbon dioxide, measured at SLC c) the volume of carbon dioxide, measured 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.

Worked Example 21.7b 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?

Your Turn Page 378 Question 27 Question 29

Volume-volume Stoichiometry For chemical reactions in the gaseous state it is usually more convenient to measure volumes rather than masses. We have already discussed this chapter that equal amounts (mol) of gases occupy equal volumes, provided they are at the same pressure and temperature. We can therefore use the ratios in a balanced equation to calculate the volumes of gaseous reactants or products

Worked Example 21.7c Methane is burnt in a gas stove. If 50 mL of methane, measured at a pressure of 1 atm, is burnt in air at 500°C, calculate: The volume of O2, measured at 1 atm and 500°C, required for complete combustion of the methane The volumes of CO2 and H2O vapour produced at 1 atm and 500°C

Your Turn Page 378 Questions 30 and 31