1. Properties of Gases
Chpt. 10

2. Particles slide over each other
A Quick Review
Matter is anything that occupies space and
has mass
There are three states of matter
Particles slide over each other
Particles vibrate about a fixed position
Particles have almost complete freedom of movement

3. In this chapter we will be looking at the third state of matter - GAS.
Gases have distinct properties that distinguish them from solids and liquids. These properties may be explained in terms of the particles (atoms, molecules, ions) of a gas having more freedom of movement than the particles of a solid or liquid.

4. Some Properties of Gases:
Gases DO NOT have a definite shape or size and will spread throughout any container they are placed in – DIFFUSION
Diffusion: is the movement of particles from an area of high concentration to an area of low concentration.
Example:
NH3 and HCl Ammonium Chloride
Smoke particles travelling throughout the air
Example liquids (much slower):
Spreading of ink throughout a beaker of water

5. A gas is defined as a substance that has no well-defined boundaries but diffuses rapidly to fill any container in which it is placed.

6. 2. Gases do not have a fixed volume – they fill any
space into which they are put, therefore the
volume of the gas is the volume of the container
in which they are placed.
The volume of a gas is influenced by two factors:
- temperature
- pressure
Increasing Temperature – gas expands and occupies greater volume
Increasing Pressure – gas becomes compressed and occupies a smaller volume

7. Charles (volume & temperature) Boyle (volume & pressure)
Jacques Charles and Robert Boyle were two scientists who investigated how the volume of a gas changes with temperature and how the volume of a gas changes with pressure respectively.
Charles (volume & temperature)
Boyle (volume & pressure)

8. In this chapter we shall be studying the laws that gases obey and why they obey these laws. This also involves a study of the work of Charles and Boyle

9. 3 Main properties of a fixed amount of gas
Temperature
Pressure
Volume
Note: Before studying the laws that gases obey we must first understand how to measure the above three properties

10. Temperature:
Temperature is a measure of the degree of hotness of an object.
Two Scales
Celsius (centigrade) scale Kelvin (absolute) scale
Two fixed points:
- 0oC – freezing point of
water
- 100OC – boiling point of
- 0 K – absolute zero
(temperature at which a gas would occupy no volume)

11. Relationship between Celsius Scale and Kelvin Scale
O0C
10O0C
-273O C
0 K
273 K
373 K
Absolute Zero

12. Temperature can be converted from the Celsius scale to the Kelvin scale by adding 273
Celsius Kelvin
*0oC = = K
30oC = = K
50oC =
80oC =
100oC =
273oC =

13. *Note:
- size of a degree on the Celsius scale is the same as that on the Kelvin scale i.e. rise in temperature of 10oC is same as rise in temperature of 10 K
- SI unit of temperature – Kelvin*

14. Pressure:
Pressure of a gas is the force it exerts on each unit area of its container
SI unit of pressure is N/m2 (Nm-2) or *Pascal (Pa)
We will be dealing with pressure in terms of
atmospheric pressure:
Normal atmospheric pressure:
1.013 x 105 N/m2
1.013 x 105 Pa
101,325 Pa
101kPa (*1kPa – 1000 Pa)

15. Note:
Old method of expressing pressure of gases used millimetres of mercury or atmospheres:
Normal Atmospheric Pressure:
760 mm Hg = 1 atm = x 105Pa

16. Volume:
The volume of a sample of gas is the same as the volume of the container in which the sample is held
SI unit of volume is m3
Laboratory units:
cm3
Litres (L)
A litre is also called a cubic decimetre (dm3= 1/10 of metre)
1L = 1000cm3 = 1dm3

17. Relationship between m3, cm3 and Litres
1m3 = 1 x 106 cm3
*N.B.
To change cm3 to m3 multiply by 10-6
To change litres to m3 multiply by 10-3

18. Summary of measuring three main properties of gases
Temperature – unit Kelvin ( convert from celsius)
Pressure – unit Pascal
Volume – unit cubic metre (convert from cm and litres)

19. Standard Temperature and Pressure (s.t.p.)
As previously noted the volume of a gas varies with temperature and pressure. Thus in order to compare volumes occupied by gases, it is necessary to measure all volumes at the same temperature and pressure:
Standard Temperature = 273 K (0OC)
Standard Pressure = x 105 Pa or
101,325 Pa
101kPa

20. Five Main Gas Laws Boyles Law Charles Law The Combined Gas Law
Gay-Lussac’s Law of combing Volumes
Avogadro’s Law

21. Boyles Law
Irish scientist Robert Boyle experimented with the relationship between pressure and volume of gases.
He set up a J-shaped tube and added mercury to see what it did to the volume of a trapped gas, kept at a constant temperature

22. As pressure increases, volume decreases

23. Boyles Experimental Results
*This relationship is inversely proportional, when one increases the other decreases.

24. The volume is inversely proportional to the pressure
*Note: see fig. 10.8(a) and fig. 10.8(b) pg. 120

25. Boyles Law:
At a constant temperature , the volume of a fixed mass of gas is inversely proportional to its pressure
V α 1 P
The proportionality symbol can be replaced by a constant k which gives us a mathematical equation:
V = k pV = k
p = pressure
V = volume
k = proportionality
constant

26. Knowing that the pressure of a gas multiplied by its volume is always a constant value gives another way of expressing Boyle’s Law:
p1V1 = p2V2
Thus, it is possible to calculate the volume of a gas at one pressure when its volume at another pressure is known.
*Note: see pg. 120 table 10.1 and fig for further explanation

27. Boyle’s Air Pump

28. Boyles Law Summary V α 1 P pV = k p1V1 = p2V2
Must also be familiar with associated graphs (3)!!!!!
(pg 120 – Fig 10.8 & pg 121 – Fig 10.11)

29. Charles Law
French scientist, Jacques Charles, investigated the relationship between the volume and temperature of a fixed mass of gas at constant pressure

30. Charles Law
French physicist Jacques Charles was the first to fill a balloon with hydrogen gas and make a solo flight.
He showed that the volume of a gas increases when the temperature increases (at a constant pressure)

31. Charles Law Experiment

32. Charles Law Experimental results
*Note: see figure pg. 122

33. In previous graph straight line does not go through the origin therefore one cannot say that the volume of the gas is directly proportional to the temperature measured in O C.
However, if the line is continued backwards, it cuts the x-axis at -273oC i.e. absolute zero in terms of the Kelvin Scale

34. -273oC O K *Note: see figure 10.15 pg. 122
Using the Kelvin scale of temperature a direct relationship between volume and temperature can be seen i.e. volume is directly proportional to temperature

36. Charles Law:
At constant pressure , the volume of a fixed mass of gas is directly proportional to its temperature measured on the Kelvin scale
V α T
V = kt V = k T
The proportionality symbol can be replaced by a constant k which gives us a mathematical equation:
V = volume
k = proportionality
constant
T = temperature
(Kelvin)

37. Knowing that volume divided by temperature always gives a constant value allows the volume of a gas at any given temperature to be calculated provided that its volume at some other temperature is known:
V1 = V2
T1 T2
*Note: see pg. 122 table 10.2 and fig for further explanation

38. Charles Law Summary V α T V = k T
V1 = V2
T1 T2
Must also be familiar with associated graphs (3)!!!!!
(pg – Fig , 10.15, 10.17)

39. T1 T2 The Combined Gas Law (The General Gas Law)
The results of Boyle’s and Charles’ law can be combined into a single expression which takes the form:
p1 V1 = p2 V2
T T2
Using this equation, the volume of a gas at any temperature and pressure can be calculated provided that its volume at some other given temperature and pressure is known.

40. *Points to Note:
Since combined gas law derived from Charle’s law MUST convert all temperatures to the KELVIN SCALE
Units on both sides of equation must be consistent e.g. if using kPa on left side must use kPa on right side

41. Example 1:
A certain mass of gas was found to occupy a volume of 269cm3 when the temperature was 17o C and the pressure 99.7kPa. What volume would the gas occupy at s.t.p.?

42. Example 2:
A sample of hydrogen of volume 100cm3 at a pressure of 1 x 105 Pa is compressed to 55cm3 at constant temperature. What is the new pressure of the gas?

43. Gay-Lussac’s Law of Combining Volumes
Following on from work done by Henry Cavendish on the composition of water (electrolysis), Joesph Gay-Lussac confirmed that when hydrogen reacts with oxygen, 2 volumes of hydrogen always react with 1 volume of oxygen
1808 – Gay-Lussac stated his law of combining volumes

44. *Note: Please read through experiment outline pg’s 123-124
He studied the reactions of other gases to further investigate whether they also reacted in simple ratios
Hydrogen Oxygen Steam
2 volumes volume volumes
Hydrogen Chlorine Hydrogen Chloride
1 volume volume 2 volumes
Nitrogen Oxygen Nitrogen Dioxide
Monoxide
2 volumes volume 2 Volumes
*Note: Please read through experiment outline pg’s

45. Gay-Lussac’s Law of Combining Volumes
In 1808, Gay-Lussac was able to state his law of combining volumes:
Gay-Lussac’s Law of Combining Volumes
In a reaction between gases, the volumes of the reacting gases and the volumes of any gaseous products are in the ratio of small whole numbers provided the volumes are measured at the same temperature and pressure.

46. Avogadro’s Law
An explanation of Gay-Lussac’s law depends on the idea that gases consist of particles. Gay-Lussac’s and Daltons Atomic Theory were published at the same time (1808). However attempts to explain Gay-Lussac’s theory using Dalton’s atomic theory failed.
Amedeo Avogadro, (Professor of Physics in 19th century Italy) put forward a hypothesis, which explained Gay-Lussac’s law, relating molecules and volumes.

47. Avogadro showed experimentally that 100 cm3 of hydrogen react exactly with 100 cm3 of chlorine. This indicates that there must be the same number of molecules of hydrogen and chlorine in each volume:
Hydrogen + Chlorine Hydrogen
Chloride
1 volume 1 volume 2 volumes
Applying Avogadro’s Law:
n molecules + n molecules n molecules
Hydrogen Chlorine Hydrogen
1 molecule molecule molecules
H Cl HCl

48. Two volumes of hydrogen contain twice as many molecules ………
…. as one volume of oxygen
Each oxygen atom bonds with two hydrogen atoms to form a molecule of water

49. Similarly,
2H O H2O
2NO O2 2NO
The ratio in which the volumes of gases combine is the same as the ratio in which the molecules of gases combine. Thus, when dealing with gaseous reactions the words volume and molecule can always be interchanged.

51. Avogadro’s Law
Equal volumes of gases, under the same temperature and pressure contain equal numbers of molecules

52. Molar Volume
Leading on from Avogadro’s study of gaseous reactions and the words volume and molecule being interchangeable a definition of molar volume was formed
Remember:
1 mole = 6 x 1023 particles
By experiment it was found that:
1 mole O2 occupies 22.4L at s.t.p.

53. Since 1 mole of any gas contains 6 x 1023 molecules then according to Avogadro’s Law:
At s.t.p. one mole of any gas occupies a volume of 22.4 L
Molar Volume: the volume occupied by one mole of any gas is called its molar volume
*Note: at r.t.p. (room temperature, pressure) one mole occupies a volume of 24 L

54. Calculations involving Molar Volume
1. Moles → Litres
2. Litres → Moles
3. Litres → Number of particles
4. Litres → Grams
5. General Questions

55. Converting moles to litres
Volume (Litres) = moles x Molar Volume (22.4L)
Example 1: What is the volume of 2 moles of H2 at
s.t.p.?
Litres = 2 x 22.4
Litres = 44.8L

56. 2. Converting litres to moles
Moles = Volume
Molar Volume
Note: 22.4L = 22,400cm3
Example 1:
How many moles of SO2 are there in 3L of the gas at s.t.p.?
Moles = 3
22.4
Moles = 0.13 moles

57. Example 2:
How many moles of NO2 are there in 175cm3 of the gas at s.t.p.?
Moles = Volume
Molar Volume
Moles = 175
22,400
Moles = moles

58. 3. Converting litres to number of particles
(molecules/atoms)
Step 1. Change litres/cm3 to moles
Step 2. Change moles to molecules/atoms
Example 1:
How many molecules are there in 560cm3 of chlorine gas at STP?

59. Example 1 Solution:

60. Example 2:
How many atoms are there in 840cm3 of butane gas,C4H10, at STP?

61. 4. Converting Litres to Grams
Step 1: Change Litres/cm3 to moles
Step 2: Change moles to grams
Example 1:
What is the mass in g of 140cm3 of oxygen gas at STP?

62. Example 1 Solution:

63. 5. General Questions
This section involves taking what you know from the previous chapter on the Mole and incorporating this into answering the question
Example 1:
Calculate the volume occupied by 20g of sulphur dioxide gas at s.t.p.?

64. Example 2:
200 cm3 of a certain gas at s.t.p. Have a mass of 0.25g. Calculate the relative molecular mass of the gas.

65. Example 3:
Calculate the density of carbon dioxide at s.t.p.

66. Try the following question:
What is i) the volume at s.t.p. and ii) the number of molecules in 24g of sulphur dioxide (SO2)

67. Please complete the following questions on the mole and molar volume
Book: 10.5, 10.6, pg
Workbook: W10.4, W10.5 pg. 22

68. Mandatory Experiment:
To measure the relative molecular mass of a volatile liquid
*Note: A volatile liquid is a liquid that is easily vaporised

69. The Kinetic Theory of Gases
This theory was developed to explain the five gas laws discussed previously. It was based on the idea that all matter is made up of tiny particles in constant motion i.e. Solids – particles vibrate
Liquids – particles can move freely around each other
Gases – particles have complete freedom of movement
Robert Brown, a botanist, was the first to find evidence to support the idea of particles in motion.

70. Brownian Motion
Brownian Motion: the random movement of tiny particles suspended in a liquid or gas

71. In order to understand the behaviour of gases a number of assumptions were developed – Kinetic Theory of Gases
Assumptions of the Kinetic Theory of Gases:
Gases are made up of particles that are in constant rapid, random motion, colliding with each other and with the walls of the container.
*There are no attractive or repulsive forces between the molecules of a gas
*Gas molecules are so small and so widely separated that the actual volume of all the molecules is negligible compared with the space they occupy i.e. they take up very little space.

72. 4. When molecules collide all collisions are perfectly
elastic i.e.
- If particle collides with wall of its container with a speed of 450 m/s it rebounds with the same speed
- No loss of kinetic energy but may be transferred
5. The average Kinetic energy of the molecules is
proportional to the Kelvin temperature

73. Limitations to the Kinetic Theory of Gases:
- it is not valid to say that there are no attractive or repulsive forces between the molecules of a gas i.e. dipole-dipole forces between polar molecules and van der Waals forces between non-polar molecules.
- it is not always valid to say that the volume of the gases is negligible compared with the space they occupy i.e. under high pressure, when molecules are crowded close together, it is clear that their volume is not negligible.

74. Ideal Gas
Due to these limitations it can be seen that all of the assumptions of the kinetic theory do not hold for real gases but only hold for imaginary or ideal gases
An ideal gas is one that obeys all the assumptions of the kinetic theory of gases under all ALL conditions of temperature and pressure

75. Ideal Gases DO NOT EXIST!!!!
A real gas behaves like an ideal gas at:
- low pressure – molecules widely spaced
and
- high temperatures – molecules are moving rapidly and forces between the molecules are small

76. Reasons why Gases differ from Ideal Gas behaviour
At low temperatures and high pressures:
- the volume of the particles is not negligible compared with the distances between them
- there are attractive and repulsive forces between the particles i.e. molecules are moving slowly and are packed close together resulting in stronger intermolecular forces

77. *Note:
- Under the same conditions of temperature and pressure non-polar molecules come closer to being ideal gases than polar molecules, since the attractive forces are less in the case of non- polar molecules.

78. Student Question:
State which of the following gases you would expect to come closest to ideal behaviour, and which you would expect to deviate most from ideal behaviour:
H2, HF, F2 . Explain your answers.

79. (Equation of State for an Ideal Gas)
Ideal Gas Equation
(Equation of State for an Ideal Gas)
Boyles Law, Charles Law and Avogadro’s law may be combined to form an equation relating volume (V), temperature(T), pressure(p) and number of moles(n) of a gas:
Boyle V α 1 constant temperature p
Charles V α T constant pressure
Avogadro V α n constant temperature &
pressure

80. Combining all three equations:
V α (1) Tn
(p)
Replacing proportionality symbol with R (constant of proportionality – Universal Gas Constant):
V = R(1) Tn
(p)
Rearranging equation:
pV = nRT Ideal Gas Equation

81. The numerical value for R can be found by simply substituting experimental values into the ideal gas equation i.e. we know at s.t.p. I mole of any gas occupies a volume of 22.4L
T = 273K
P = x 105 N/m2 (Pa)
n = 1
V = 22.4L – 22.4 x = m3
pV = nRT R = pV = x 105 x .0224
nT 1 mole x 273
R = 8.31 J mol-1 K-1

82. Units and the Ideal Gas Equation
Measure
Unit
Volume m3
Pressure Pa
Temperature K
Number of moles
mol
Universal Gas Constant (R)
J mol-1 K-1
(always given to you)

83. Calculations involving the Ideal Gas Equation
Example 1:
Calculate the volume occupied by 10g of oxygen gas at 25O C and a pressure of 200kPa
(R = 8.31 J mol-1 K-1)

84. Example 1 Solution:

85. Example 2:
20g of a gas occupies a volume of 5L at 87OC and 200,000 Pa.
i) How many moles of the gas are present?
ii) What is the relative molecular mass of the gas?

86. Example 2 Solution:

87. Student Question:
2.5kg of carbon dioxide gas are released into the air when a fire extinguisher is discharged. What volume does this gas occupy at a pressure of 100,000 Pa and a temperature of 288K?

88. Please answer the following questions:
Book: 10.9 – 10.12
Workbook: W10.6 – W10.12