Physical Properties of Gases

1. Physical Properties of Gases Chapter 21

2. 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.

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

4. 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.

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

6. 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.

7. 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.

8. 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.

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

10. 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.

11. 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

12. 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.

13. 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.

14. 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.

15. 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

16. 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.

17. Your Turn • Page 360 • Question 1 • Question 4

18. 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.

19. 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

20. 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.

21. 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

22. 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?

23. Your Turn • Page 363 • Question 5

24. 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

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

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

27. 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.

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

29. 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

30. Worked Example 21.4a • Page 364

31. Your Turn • Page 364 • Question 9, 10 and 11

32. 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

33. Your Turn • Page 367 • Question 12

34. 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.

35. 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

36. V V1 V2 T T1 T2 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. = k =

37. Worked Example 21.4b and your turn • Page 367 • Question 13

38. V1 V2 n1 n2 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 =

39. Your Turn • Page 368 • Question 14 and 15

40. 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

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

42. 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.

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

44. 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

45. Your Turn • Page 370 • Questions 16 and 17

46. 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.

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

48. 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?

49. 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?

50. 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.