The Free High School Science Texts: Textbooks for High School Students Chemistry

The Free High School Science Texts: Textbooks for High School Students Chemistry
FHSST Authors
The Free High School Science Texts:
Textbooks for High School Students
Studying the Sciences
Chemistry
Grades 10 - 12
Version 0
November 9, 2008
ii
Copyright 2007 “Free High School Science Texts”
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FHSST Core Team
Mark Horner ; Samuel Halliday ; Sarah Blyth ; Rory Adams ; Spencer Wheaton
FHSST Editors
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Whitfield
FHSST Contributors
Rory Adams ; Prashant Arora ; Richard Baxter ; Dr. Sarah Blyth ; Sebastian Bodenstein ;
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Daniels ; Sean Dobbs ; Fernando Durrell ; Dr. Dan Dwyer ; Frans van Eeden ; Giovanni
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Andrew Kubik ; Dr. Marco van Leeuwen ; Dr. Anton Machacek ; Dr. Komal Maheshwari ;
Kosma von Maltitz ; Nicole Masureik ; John Mathew ; JoEllen McBride ; Nikolai Meures ;
Riana Meyer ; Jenny Miller ; Abdul Mirza ; Asogan Moodaly ; Jothi Moodley ; Nolene Naidu ;
Tyrone Negus ; Thomas O’Donnell ; Dr. Markus Oldenburg ; Dr. Jaynie Padayachee ;
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iii
iv
Contents
I
II
Introduction
1
Matter and Materials
3
1 Classification of Matter - Grade 10
1.1
1.2
5
Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.1.1
Heterogeneous mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.1.2
Homogeneous mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.1.3
Separating mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
Pure Substances: Elements and Compounds . . . . . . . . . . . . . . . . . . . .
9
1.2.1
Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
1.2.2
Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
1.3
Giving names and formulae to substances . . . . . . . . . . . . . . . . . . . . . 10
1.4
Metals, Semi-metals and Non-metals . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.1
Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.2
Non-metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.3
Semi-metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.5
Electrical conductors, semi-conductors and insulators . . . . . . . . . . . . . . . 14
1.6
Thermal Conductors and Insulators . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.7
Magnetic and Non-magnetic Materials . . . . . . . . . . . . . . . . . . . . . . . 17
1.8
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 What are the objects around us made of? - Grade 10
21
2.1
Introduction: The atom as the building block of matter . . . . . . . . . . . . . . 21
2.2
Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.1
Representing molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3
Intramolecular and intermolecular forces . . . . . . . . . . . . . . . . . . . . . . 25
2.4
The Kinetic Theory of Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5
The Properties of Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.6
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3 The Atom - Grade 10
3.1
35
Models of the Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1.1
The Plum Pudding Model . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1.2
Rutherford’s model of the atom
v
. . . . . . . . . . . . . . . . . . . . . . 36
CONTENTS
3.1.3
3.2
3.3
CONTENTS
The Bohr Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
How big is an atom? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.1
How heavy is an atom? . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.2
How big is an atom? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Atomic structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.1
The Electron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3.2
The Nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4
Atomic number and atomic mass number . . . . . . . . . . . . . . . . . . . . . 40
3.5
Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.6
3.7
3.8
3.9
3.5.1
What is an isotope? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.5.2
Relative atomic mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Energy quantisation and electron configuration . . . . . . . . . . . . . . . . . . 46
3.6.1
The energy of electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.6.2
Energy quantisation and line emission spectra . . . . . . . . . . . . . . . 47
3.6.3
Electron configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.6.4
Core and valence electrons . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.6.5
The importance of understanding electron configuration . . . . . . . . . 51
Ionisation Energy and the Periodic Table . . . . . . . . . . . . . . . . . . . . . . 53
3.7.1
Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.7.2
Ionisation Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
The Arrangement of Atoms in the Periodic Table . . . . . . . . . . . . . . . . . 56
3.8.1
Groups in the periodic table
. . . . . . . . . . . . . . . . . . . . . . . . 56
3.8.2
Periods in the periodic table . . . . . . . . . . . . . . . . . . . . . . . . 58
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4 Atomic Combinations - Grade 11
63
4.1
Why do atoms bond? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2
Energy and bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3
What happens when atoms bond? . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.4
Covalent Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.4.1
The nature of the covalent bond . . . . . . . . . . . . . . . . . . . . . . 65
4.5
Lewis notation and molecular structure . . . . . . . . . . . . . . . . . . . . . . . 69
4.6
Electronegativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.7
4.8
4.6.1
Non-polar and polar covalent bonds . . . . . . . . . . . . . . . . . . . . 73
4.6.2
Polar molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Ionic Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.7.1
The nature of the ionic bond . . . . . . . . . . . . . . . . . . . . . . . . 74
4.7.2
The crystal lattice structure of ionic compounds . . . . . . . . . . . . . . 76
4.7.3
Properties of Ionic Compounds . . . . . . . . . . . . . . . . . . . . . . . 76
Metallic bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.8.1
The nature of the metallic bond . . . . . . . . . . . . . . . . . . . . . . 76
4.8.2
The properties of metals . . . . . . . . . . . . . . . . . . . . . . . . . . 77
vi
CONTENTS
4.9
CONTENTS
Writing chemical formulae
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.9.1
The formulae of covalent compounds . . . . . . . . . . . . . . . . . . . . 78
4.9.2
The formulae of ionic compounds . . . . . . . . . . . . . . . . . . . . . 80
4.10 The Shape of Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.10.1 Valence Shell Electron Pair Repulsion (VSEPR) theory . . . . . . . . . . 82
4.10.2 Determining the shape of a molecule . . . . . . . . . . . . . . . . . . . . 82
4.11 Oxidation numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.12 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5 Intermolecular Forces - Grade 11
91
5.1
Types of Intermolecular Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.2
Understanding intermolecular forces . . . . . . . . . . . . . . . . . . . . . . . . 94
5.3
Intermolecular forces in liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.4
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6 Solutions and solubility - Grade 11
101
6.1
Types of solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2
Forces and solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.3
Solubility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.4
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7 Atomic Nuclei - Grade 11
107
7.1
Nuclear structure and stability . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.2
The Discovery of Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.3
Radioactivity and Types of Radiation . . . . . . . . . . . . . . . . . . . . . . . . 108
7.4
7.3.1
Alpha (α) particles and alpha decay . . . . . . . . . . . . . . . . . . . . 109
7.3.2
Beta (β) particles and beta decay . . . . . . . . . . . . . . . . . . . . . 109
7.3.3
Gamma (γ) rays and gamma decay . . . . . . . . . . . . . . . . . . . . . 110
Sources of radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
7.4.1
Natural background radiation . . . . . . . . . . . . . . . . . . . . . . . . 112
7.4.2
Man-made sources of radiation . . . . . . . . . . . . . . . . . . . . . . . 113
7.5
The ’half-life’ of an element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.6
The Dangers of Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.7
The Uses of Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.8
Nuclear Fission
7.9
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.8.1
The Atomic bomb - an abuse of nuclear fission . . . . . . . . . . . . . . 119
7.8.2
Nuclear power - harnessing energy . . . . . . . . . . . . . . . . . . . . . 120
Nuclear Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.10 Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.10.1 Age of Nucleosynthesis (225 s - 103 s) . . . . . . . . . . . . . . . . . . . 121
7.10.2 Age of Ions (103 s - 1013 s) . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.10.3 Age of Atoms (1013 s - 1015 s) . . . . . . . . . . . . . . . . . . . . . . . 122
7.10.4 Age of Stars and Galaxies (the universe today) . . . . . . . . . . . . . . 122
7.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
vii
CONTENTS
CONTENTS
8 Thermal Properties and Ideal Gases - Grade 11
125
8.1
A review of the kinetic theory of matter . . . . . . . . . . . . . . . . . . . . . . 125
8.2
Boyle’s Law: Pressure and volume of an enclosed gas . . . . . . . . . . . . . . . 126
8.3
Charles’s Law: Volume and Temperature of an enclosed gas . . . . . . . . . . . 132
8.4
The relationship between temperature and pressure . . . . . . . . . . . . . . . . 136
8.5
The general gas equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
8.6
The ideal gas equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
8.7
Molar volume of gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.8
Ideal gases and non-ideal gas behaviour . . . . . . . . . . . . . . . . . . . . . . 146
8.9
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
9 Organic Molecules - Grade 12
151
9.1
What is organic chemistry? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
9.2
Sources of carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
9.3
Unique properties of carbon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
9.4
Representing organic compounds . . . . . . . . . . . . . . . . . . . . . . . . . . 152
9.4.1
Molecular formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
9.4.2
Structural formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
9.4.3
Condensed structural formula . . . . . . . . . . . . . . . . . . . . . . . . 153
9.5
Isomerism in organic compounds . . . . . . . . . . . . . . . . . . . . . . . . . . 154
9.6
Functional groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
9.7
The Hydrocarbons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
9.7.1
The Alkanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
9.7.2
Naming the alkanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
9.7.3
Properties of the alkanes . . . . . . . . . . . . . . . . . . . . . . . . . . 163
9.7.4
Reactions of the alkanes . . . . . . . . . . . . . . . . . . . . . . . . . . 163
9.7.5
The alkenes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
9.7.6
Naming the alkenes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
9.7.7
The properties of the alkenes . . . . . . . . . . . . . . . . . . . . . . . . 169
9.7.8
Reactions of the alkenes
9.7.9
The Alkynes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
. . . . . . . . . . . . . . . . . . . . . . . . . . 169
9.7.10 Naming the alkynes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
9.8
9.9
The Alcohols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
9.8.1
Naming the alcohols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
9.8.2
Physical and chemical properties of the alcohols . . . . . . . . . . . . . . 175
Carboxylic Acids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
9.9.1
Physical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
9.9.2
Derivatives of carboxylic acids: The esters . . . . . . . . . . . . . . . . . 178
9.10 The Amino Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
9.11 The Carbonyl Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
9.12 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
viii
CONTENTS
CONTENTS
10 Organic Macromolecules - Grade 12
185
10.1 Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
10.2 How do polymers form? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
10.2.1 Addition polymerisation . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
10.2.2 Condensation polymerisation . . . . . . . . . . . . . . . . . . . . . . . . 188
10.3 The chemical properties of polymers . . . . . . . . . . . . . . . . . . . . . . . . 190
10.4 Types of polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
10.5 Plastics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
10.5.1 The uses of plastics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
10.5.2 Thermoplastics and thermosetting plastics . . . . . . . . . . . . . . . . . 194
10.5.3 Plastics and the environment . . . . . . . . . . . . . . . . . . . . . . . . 195
10.6 Biological Macromolecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
10.6.1 Carbohydrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
10.6.2 Proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
10.6.3 Nucleic Acids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
10.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
III
Chemical Change
209
11 Physical and Chemical Change - Grade 10
211
11.1 Physical changes in matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
11.2 Chemical Changes in Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
11.2.1 Decomposition reactions . . . . . . . . . . . . . . . . . . . . . . . . . . 213
11.2.2 Synthesis reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
11.3 Energy changes in chemical reactions . . . . . . . . . . . . . . . . . . . . . . . . 217
11.4 Conservation of atoms and mass in reactions . . . . . . . . . . . . . . . . . . . . 217
11.5 Law of constant composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
11.6 Volume relationships in gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
11.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
12 Representing Chemical Change - Grade 10
223
12.1 Chemical symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
12.2 Writing chemical formulae
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
12.3 Balancing chemical equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
12.3.1 The law of conservation of mass . . . . . . . . . . . . . . . . . . . . . . 224
12.3.2 Steps to balance a chemical equation
. . . . . . . . . . . . . . . . . . . 226
12.4 State symbols and other information . . . . . . . . . . . . . . . . . . . . . . . . 230
12.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
13 Quantitative Aspects of Chemical Change - Grade 11
233
13.1 The Mole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
13.2 Molar Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
13.3 An equation to calculate moles and mass in chemical reactions . . . . . . . . . . 237
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13.4 Molecules and compounds
CONTENTS
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
13.5 The Composition of Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
13.6 Molar Volumes of Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
13.7 Molar concentrations in liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
13.8 Stoichiometric calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
13.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
14 Energy Changes In Chemical Reactions - Grade 11
255
14.1 What causes the energy changes in chemical reactions? . . . . . . . . . . . . . . 255
14.2 Exothermic and endothermic reactions . . . . . . . . . . . . . . . . . . . . . . . 255
14.3 The heat of reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
14.4 Examples of endothermic and exothermic reactions . . . . . . . . . . . . . . . . 259
14.5 Spontaneous and non-spontaneous reactions . . . . . . . . . . . . . . . . . . . . 260
14.6 Activation energy and the activated complex . . . . . . . . . . . . . . . . . . . . 261
14.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
15 Types of Reactions - Grade 11
267
15.1 Acid-base reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
15.1.1 What are acids and bases? . . . . . . . . . . . . . . . . . . . . . . . . . 267
15.1.2 Defining acids and bases . . . . . . . . . . . . . . . . . . . . . . . . . . 267
15.1.3 Conjugate acid-base pairs . . . . . . . . . . . . . . . . . . . . . . . . . . 269
15.1.4 Acid-base reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
15.1.5 Acid-carbonate reactions . . . . . . . . . . . . . . . . . . . . . . . . . . 274
15.2 Redox reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
15.2.1 Oxidation and reduction
. . . . . . . . . . . . . . . . . . . . . . . . . . 277
15.2.2 Redox reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
15.3 Addition, substitution and elimination reactions . . . . . . . . . . . . . . . . . . 280
15.3.1 Addition reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
15.3.2 Elimination reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
15.3.3 Substitution reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
15.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
16 Reaction Rates - Grade 12
287
16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
16.2 Factors affecting reaction rates . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
16.3 Reaction rates and collision theory . . . . . . . . . . . . . . . . . . . . . . . . . 293
16.4 Measuring Rates of Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
16.5 Mechanism of reaction and catalysis . . . . . . . . . . . . . . . . . . . . . . . . 297
16.6 Chemical equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
16.6.1 Open and closed systems . . . . . . . . . . . . . . . . . . . . . . . . . . 302
16.6.2 Reversible reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
16.6.3 Chemical equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
16.7 The equilibrium constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
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16.7.1 Calculating the equilibrium constant . . . . . . . . . . . . . . . . . . . . 305
16.7.2 The meaning of kc values . . . . . . . . . . . . . . . . . . . . . . . . . . 306
16.8 Le Chatelier’s principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
16.8.1 The effect of concentration on equilibrium . . . . . . . . . . . . . . . . . 310
16.8.2 The effect of temperature on equilibrium . . . . . . . . . . . . . . . . . . 310
16.8.3 The effect of pressure on equilibrium . . . . . . . . . . . . . . . . . . . . 312
16.9 Industrial applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
16.10Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
17 Electrochemical Reactions - Grade 12
319
17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
17.2 The Galvanic Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
17.2.1 Half-cell reactions in the Zn-Cu cell . . . . . . . . . . . . . . . . . . . . 321
17.2.2 Components of the Zn-Cu cell . . . . . . . . . . . . . . . . . . . . . . . 322
17.2.3 The Galvanic cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
17.2.4 Uses and applications of the galvanic cell . . . . . . . . . . . . . . . . . 324
17.3 The Electrolytic cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
17.3.1 The electrolysis of copper sulphate . . . . . . . . . . . . . . . . . . . . . 326
17.3.2 The electrolysis of water . . . . . . . . . . . . . . . . . . . . . . . . . . 327
17.3.3 A comparison of galvanic and electrolytic cells . . . . . . . . . . . . . . . 328
17.4 Standard Electrode Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
17.4.1 The different reactivities of metals . . . . . . . . . . . . . . . . . . . . . 329
17.4.2 Equilibrium reactions in half cells . . . . . . . . . . . . . . . . . . . . . . 329
17.4.3 Measuring electrode potential . . . . . . . . . . . . . . . . . . . . . . . . 330
17.4.4 The standard hydrogen electrode . . . . . . . . . . . . . . . . . . . . . . 330
17.4.5 Standard electrode potentials . . . . . . . . . . . . . . . . . . . . . . . . 333
17.4.6 Combining half cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
17.4.7 Uses of standard electrode potential . . . . . . . . . . . . . . . . . . . . 338
17.5 Balancing redox reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
17.6 Applications of electrochemistry . . . . . . . . . . . . . . . . . . . . . . . . . . 347
17.6.1 Electroplating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
17.6.2 The production of chlorine . . . . . . . . . . . . . . . . . . . . . . . . . 348
17.6.3 Extraction of aluminium
. . . . . . . . . . . . . . . . . . . . . . . . . . 349
17.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
IV
Chemical Systems
353
18 The Water Cycle - Grade 10
355
18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
18.2 The importance of water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
18.3 The movement of water through the water cycle . . . . . . . . . . . . . . . . . . 356
18.4 The microscopic structure of water . . . . . . . . . . . . . . . . . . . . . . . . . 359
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18.4.1 The polar nature of water . . . . . . . . . . . . . . . . . . . . . . . . . . 359
18.4.2 Hydrogen bonding in water molecules . . . . . . . . . . . . . . . . . . . 359
18.5 The unique properties of water . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
18.6 Water conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
18.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
19 Global Cycles: The Nitrogen Cycle - Grade 10
369
19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
19.2 Nitrogen fixation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
19.3 Nitrification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
19.4 Denitrification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372
19.5 Human Influences on the Nitrogen Cycle . . . . . . . . . . . . . . . . . . . . . . 372
19.6 The industrial fixation of nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . 373
19.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
20 The Hydrosphere - Grade 10
377
20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
20.2 Interactions of the hydrosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
20.3 Exploring the Hydrosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378
20.4 The Importance of the Hydrosphere . . . . . . . . . . . . . . . . . . . . . . . . 379
20.5 Ions in aqueous solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
20.5.1 Dissociation in water . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
20.5.2 Ions and water hardness . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
20.5.3 The pH scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
20.5.4 Acid rain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
20.6 Electrolytes, ionisation and conductivity . . . . . . . . . . . . . . . . . . . . . . 386
20.6.1 Electrolytes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386
20.6.2 Non-electrolytes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
20.6.3 Factors that affect the conductivity of water . . . . . . . . . . . . . . . . 387
20.7 Precipitation reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
20.8 Testing for common anions in solution . . . . . . . . . . . . . . . . . . . . . . . 391
20.8.1 Test for a chloride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
20.8.2 Test for a sulphate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
20.8.3 Test for a carbonate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
20.8.4 Test for bromides and iodides . . . . . . . . . . . . . . . . . . . . . . . . 392
20.9 Threats to the Hydrosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
20.10Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
21 The Lithosphere - Grade 11
397
21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
21.2 The chemistry of the earth’s crust . . . . . . . . . . . . . . . . . . . . . . . . . 398
21.3 A brief history of mineral use . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
21.4 Energy resources and their uses . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
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CONTENTS
21.5 Mining and Mineral Processing: Gold . . . . . . . . . . . . . . . . . . . . . . . . 401
21.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
21.5.2 Mining the Gold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
21.5.3 Processing the gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
21.5.4 Characteristics and uses of gold . . . . . . . . . . . . . . . . . . . . . . . 402
21.5.5 Environmental impacts of gold mining . . . . . . . . . . . . . . . . . . . 404
21.6 Mining and mineral processing: Iron . . . . . . . . . . . . . . . . . . . . . . . . 406
21.6.1 Iron mining and iron ore processing . . . . . . . . . . . . . . . . . . . . . 406
21.6.2 Types of iron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
21.6.3 Iron in South Africa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
21.7 Mining and mineral processing: Phosphates . . . . . . . . . . . . . . . . . . . . 409
21.7.1 Mining phosphates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
21.7.2 Uses of phosphates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
21.8 Energy resources and their uses: Coal . . . . . . . . . . . . . . . . . . . . . . . 411
21.8.1 The formation of coal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
21.8.2 How coal is removed from the ground . . . . . . . . . . . . . . . . . . . 411
21.8.3 The uses of coal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
21.8.4 Coal and the South African economy . . . . . . . . . . . . . . . . . . . . 412
21.8.5 The environmental impacts of coal mining . . . . . . . . . . . . . . . . . 413
21.9 Energy resources and their uses: Oil . . . . . . . . . . . . . . . . . . . . . . . . 414
21.9.1 How oil is formed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
21.9.2 Extracting oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
21.9.3 Other oil products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
21.9.4 The environmental impacts of oil extraction and use . . . . . . . . . . . 415
21.10Alternative energy resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
21.11Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
22 The Atmosphere - Grade 11
421
22.1 The composition of the atmosphere . . . . . . . . . . . . . . . . . . . . . . . . 421
22.2 The structure of the atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . 422
22.2.1 The troposphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
22.2.2 The stratosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
22.2.3 The mesosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424
22.2.4 The thermosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424
22.3 Greenhouse gases and global warming . . . . . . . . . . . . . . . . . . . . . . . 426
22.3.1 The heating of the atmosphere . . . . . . . . . . . . . . . . . . . . . . . 426
22.3.2 The greenhouse gases and global warming . . . . . . . . . . . . . . . . . 426
22.3.3 The consequences of global warming . . . . . . . . . . . . . . . . . . . . 429
22.3.4 Taking action to combat global warming . . . . . . . . . . . . . . . . . . 430
22.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
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CONTENTS
23 The Chemical Industry - Grade 12
435
23.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435
23.2 Sasol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435
23.2.1 Sasol today: Technology and production . . . . . . . . . . . . . . . . . . 436
23.2.2 Sasol and the environment . . . . . . . . . . . . . . . . . . . . . . . . . 440
23.3 The Chloralkali Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
23.3.1 The Industrial Production of Chlorine and Sodium Hydroxide . . . . . . . 442
23.3.2 Soaps and Detergents . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446
23.4 The Fertiliser Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
23.4.1 The value of nutrients . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
23.4.2 The Role of fertilisers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
23.4.3 The Industrial Production of Fertilisers . . . . . . . . . . . . . . . . . . . 451
23.4.4 Fertilisers and the Environment: Eutrophication . . . . . . . . . . . . . . 454
23.5 Electrochemistry and batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
23.5.1 How batteries work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
23.5.2 Battery capacity and energy . . . . . . . . . . . . . . . . . . . . . . . . 457
23.5.3 Lead-acid batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457
23.5.4 The zinc-carbon dry cell . . . . . . . . . . . . . . . . . . . . . . . . . . . 459
23.5.5 Environmental considerations . . . . . . . . . . . . . . . . . . . . . . . . 460
23.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461
A GNU Free Documentation License
467
xiv
Chapter 8
Thermal Properties and Ideal
Gases - Grade 11
We are surrounded by gases in our atmosphere which support and protect life on this planet.
In this chapter, we are going to try to understand more about gases, and learn how to predict
how they will behave under different conditions. The kinetic theory of matter was discussed in
chapter 2. This theory is very important in understanding how gases behave.
8.1
A review of the kinetic theory of matter
The main assumptions of the kinetic theory of matter are as follows:
• Matter is made up of particles (e.g. atoms or molecules)
• These particles are constantly moving because they have kinetic energy. The space in
which the particles move is the volume of the gas.
• There are spaces between the particles
• There are attractive forces between particles and these become stronger as the particles
move closer together.
• All particles have energy. The temperature of a substance is a measure of the average
kinetic energy of the particles.
• A change in phase may occur when the energy of the particles is changed.
The kinetic theory applies to all matter, including gases. In a gas, the particles are far apart and
have a high kinetic energy. They move around freely, colliding with each other or with the sides
of the container if the gas is enclosed. The pressure of a gas is a measure of the frequency
of collisions of the gas particles with each other and with the sides of the container that they
are in. If the gas is heated, the average kinetic energy of the gas particles will increase and
if the temperature is decreased, so does their energy. If the energy of the particles decreases
significantly, the gas liquifies. An ideal gas is one that obeys all the assumptions of the kinetic
theory of matter. A real gas behaves like an ideal gas, except at high pressures and low
temperatures. This will be discussed in more detail later in this chapter.
Definition: Ideal gas
An ideal gas or perfect gas is a hypothetical gas that obeys all the assumptions of the kinetic
theory of matter. In other words, an ideal gas would have identical particles of zero volume,
with no intermolecular forces between them. The atoms or molecules in an ideal gas would
also undergo elastic collisions with the walls of their container.
125
8.2
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
Definition: Real gas
Real gases behave more or less like ideal gases except under certain conditions e.g. high
pressures and low temperatures.
There are a number of laws that describe how gases behave. It will be easy to make sense of
these laws if you understand the kinetic theory of gases that was discussed above.
8.2
Boyle’s Law: Pressure and volume of an enclosed gas
Activity :: Demonstration : Boyle’s Law
If you have ever tried to force in the plunger of a syringe or a bicycle pump while
sealing the opening with a finger, you will have seen Boyle’s Law in action! This will
now be demonstrated using a 10 ml syringe.
Aim:
To demonstrate Boyle’s law.
Apparatus:
You will only need a syringe for this demonstration.
5
10
mℓ
Method:
1. Hold the syringe in one hand, and with the other pull the plunger out towards
you so that the syringe is now full of air.
2. Seal the opening of the syringe with your finger so that no air can escape the
syringe.
3. Slowly push the plunger in, and notice whether it becomes more or less difficult
to push the plunger in.
Results:
What did you notice when you pushed the plunger in? What happens to the
volume of air inside the syringe? Did it become more or less difficult to push the
plunger in as the volume of the air in the syringe decreased? In other words, did
you have to apply more or less pressure to the plunger as the volume of air in the
syringe decreased?
As the volume of air in the syringe decreases, you have to apply more pressure
to the plunger to keep forcing it down. The pressure of the gas inside the syringe
pushing back on the plunger is greater. Another way of saying this is that as the
volume of the gas in the syringe decreases, the pressure of that gas increases.
Conclusion:
If the volume of the gas decreases, the pressure of the gas increases. If the
volume of the gas increases, the pressure decreases. These results support Boyle’s
law.
In the previous demonstration, the volume of the gas decreased when the pressure increased,
and the volume increased when the pressure decreased. This is called an inverse relationship.
The inverse relationship between pressure and volume is shown in figure 8.1.
126
8.2
Pressure
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
Volume
Figure 8.1: Graph showing the inverse relationship between pressure and volume
Can you use the kinetic theory of gases to explain this inverse relationship between the pressure
and volume of a gas? Let’s think about it. If you decrease the volume of a gas, this means that
the same number of gas particles are now going to come into contact with each other and with
the sides of the container much more often. You may remember from earlier that we said that
pressure is a measure of the frequency of collisions of gas particles with each other and with
the sides of the container they are in. So, if the volume decreases, the pressure will naturally
increase. The opposite is true if the volume of the gas is increased. Now, the gas particles collide
less frequently and the pressure will decrease.
Pressure
It was an Englishman named Robert Boyle who was able to take very accurate measurements of
gas pressures and volumes using excellent vacuum pumps. He discovered the startlingly simple
fact that the pressure and volume of a gas are not just vaguely inversely related, but are exactly
inversely proportional. This can be seen when a graph of pressure against the inverse of volume
is plotted. When the values are plotted, the graph is a straight line. This relationship is shown
in figure 8.2.
1/Volume
Figure 8.2: The graph of pressure plotted against the inverse of volume, produces a straight line.
This shows that pressure and volume are exactly inversely proportional.
Definition: Boyle’s Law
The pressure of a fixed quantity of gas is inversely proportional to the volume it occupies
so long as the temperature remains constant.
127
8.2
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
Important: Proportionality
During this chapter, the terms directly proportional and inversely proportional will be
used a lot, and it is important that you understand their meaning. Two quantities are
said to be proportional if they vary in such a way that one of the quantities is a constant
multiple of the other, or if they have a constant ratio. We will look at two examples to
show the difference between directly proportional and inversely proportional.
1. Directly proportional
A car travels at a constant speed of 120 km/h. The time and the distance covered
are shown in the table below.
Time (mins)
10
20
30
40
Distance (km)
20
40
60
80
What you will notice is that the two quantities shown are constant multiples of each
other. If you divide each distance value by the time the car has been driving, you
will always get 2. This shows that the values are proportional to each other. They
are directly proportional because both values are increasing. In other words, as
the driving time increases, so does the distance covered. The same is true if the
values decrease. The shorter the driving time, the smaller the distance covered. This
relationship can be described mathematically as:
y = kx
where y is distance, x is time and k is the proportionality constant, which in this case
is 2. Note that this is the equation for a straight line graph! The symbol ∝ is also
used to show a directly proportional relationship.
2. Inversely proportional
Two variables are inversely proportional if one of the variables is directly proportional
to the multiplicative inverse of the other. In other words,
y∝
1
x
y=
k
x
or
This means that as one value gets bigger, the other value will get smaller. For example,
the time taken for a journey is inversely proportional to the speed of travel. Look at
the table below to check this for yourself. For this example, assume that the distance
of the journey is 100 km.
Speed (km/h)
100
80
60
40
Time (mins)
60
75
100
150
According to our definition, the two variables are inversely proportional is one variable
is directly proportional to the inverse of the other. In other words, if we divide one
of the variables by the inverse of the other, we should always get the same number.
For example,
100
= 6000
1/60
128you will find that the answer is always 6000.
If you repeat this using the other values,
The variables are inversely proportional to each other.
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
8.2
We know now that the pressure of a gas is inversely proportional to the volume of the gas,
provided the temperature stays the same. We can write this relationship symbolically as
p∝
1
V
This equation can also be written as follows:
p=
k
V
where k is a proportionality constant. If we rearrange this equation, we can say that:
pV = k
This equation means that, assuming the temperature is constant, multiplying any pressure and
volume values for a fixed amount of gas will always give the same value. So, for example, p1 V1
= k and p2 V2 = k, where the subscripts 1 and 2 refer to two pairs of pressure and volume
readings for the same mass of gas at the same temperature.
From this, we can then say that:
p1 V1 = p2 V2
Important: Remember that Boyle’s Law requires two conditions. First, the amount of
gas must stay constant. Clearly, if you let a little of the air escape from the container
in which it is enclosed, the pressure of the gas will decrease along with the volume, and
the inverse proportion relationship is broken. Second, the temperature must stay constant.
Cooling or heating matter generally causes it to contract or expand. In our original syringe
demonstration, if you were to heat up the gas in the syringe, it would expand and force you
to apply a greater force to keep the plunger at a given position. Again, the proportionality
would be broken.
Activity :: Investigation : Boyle’s Law
Here are some of Boyle’s original data. Note that pressure would originally have
been measured using a mercury manometer and the units for pressure would have
been millimetres mercury or mm Hg. However, to make things a bit easier for you,
the pressure data have been converted to a unit that is more familiar. Note that the
volume is given in terms of arbitrary marks (evenly made).
Volume
(graduation
mark)
12
14
16
18
20
22
24
26
Pressure
(kPa)
398
340
298
264
239
217
199
184
Volume
(graduation
mark)
28
30
32
34
36
38
40
Pressure
(kPa)
170
159
150
141
133
125
120
1. Plot a graph of pressure (p) against volume (V). Volume will be on the x-axis
and pressure on the y-axis. Describe the relationship that you see.
129
In the gas
equations, k
is a ”variable
constant”.
This means
that k is
constant in a
particular set
of situations,
but in two
different sets
of situations
it has different constant
values.
8.2
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
2. Plot a graph of p against 1/V . Describe the relationship that you see.
3. Do your results support Boyle’s Law? Explain your answer.
teresting Did you know that the mechanisms involved in breathing also relate to Boyle’s
Interesting
Fact
Fact
Law? Just below the lungs is a muscle called the diaphragm. When a person
breathes in, the diaphragm moves down and becomes more ’flattened’ so that the
volume of the lungs can increase. When the lung volume increases, the pressure
in the lungs decreases (Boyle’s law). Since air always moves from areas of high
pressure to areas of lower pressure, air will now be drawn into the lungs because
the air pressure outside the body is higher than the pressure in the lungs. The
opposite process happens when a person breathes out. Now, the diaphragm
moves upwards and causes the volume of the lungs to decrease. The pressure
in the lungs will increase, and the air that was in the lungs will be forced out
towards the lower air pressure outside the body.
Worked Example 26: Boyle’s Law 1
Question: A sample of helium occupies a volume of 160 cm3 at 100 kPa and 25 ◦ C.
What volume will it occupy if the pressure is adjusted to 80 kPa and if the temperature remains unchanged?
Answer
Step 4 : Write down all the information that you know about the gas.
V1 = 160 cm3 and V2 = ?
p1 = 100 kPa and p2 = 80 kPa
Step 1 : Use an appropriate gas law equation to calculate the unknown
variable.
Because the temperature of the gas stays the same, the following equation can be
used:
p1 V1 = p2 V2
If the equation is rearranged, then
V2 =
p1 V1
p2
Step 2 : Substitute the known values into the equation, making sure that
the units for each variable are the same. Calculate the unknown variable.
V2 =
100 × 160
= 200cm3
80
The volume occupied by the gas at a pressure of 80kPa, is 200 cm3
130
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
8.2
Worked Example 27: Boyle’s Law 2
Question: The pressure on a 2.5 l volume of gas is increased from 695 Pa to 755 Pa
while a constant temperature is maintained. What is the volume of the gas under
these pressure conditions?
Answer
Step 1 : Write down all the information that you know about the gas.
V1 = 2.5 l and V2 = ?
p1 = 695 Pa and p2 = 755 Pa
Step 2 : Choose a relevant gas law equation to calculate the unknown variable.
At constant temperature,
p1 V1 = p2 V2
Therefore,
V2 =
p1 V1
p2
Step 3 : Substitute the known values into the equation, making sure that
the units for each variable are the same. Calculate the unknown variable.
V2 =
695 × 2.5
= 2.3l
755
Important:
It is not necessary to convert to Standard International (SI) units in the examples we have
used above. Changing pressure and volume into different units involves multiplication. If
you were to change the units in the above equation, this would involve multiplication on
both sides of the equation, and so the conversions cancel each other out. However, although
SI units don’t have to be used, you must make sure that for each variable you use the same
units throughout the equation. This is not true for some of the calculations we will do at a
later stage, where SI units must be used.
Exercise: Boyle’s Law
1. An unknown gas has an initial pressure of 150 kPa and a volume of 1 L. If the
volume is increased to 1.5 L, what will the pressure now be?
2. A bicycle pump contains 250 cm3 of air at a pressure of 90 kPa. If the air is
compressed, the volume is reduced to 200 cm3 . What is the pressure of the air
inside the pump?
3. The air inside a syringe occupies a volume of 10 cm3 and exerts a pressure of
100 kPa. If the end of the syringe is sealed and the plunger is pushed down, the
pressure increases to 120 kPa. What is the volume of the air in the syringe?
4. During an investigation to find the relationship between the pressure and volume
of an enclosed gas at constant temperature, the following results were obtained.
131
8.3
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
Volume (cm3 )
40
30
25
Pressure (kPa)
125.0
166.7
200.0
(a) For the results given in the above table, plot a graph of pressure (y-axis)
against the inverse of volume (x-axis).
(b) From the graph, deduce the relationship between the pressure and volume
of an enclosed gas at constant temperature.
(c) Use the graph to predict what the volume of the gas would be at a pressure
of 40 kPa. Show on your graph how you arrived at your answer.
(IEB 2004 Paper 2 )
8.3
Charles’s Law: Volume and Temperature of an enclosed
gas
Charles’s law describes the relationship between the volume and temperature of a gas. The
law was first published by Joseph Louis Gay-Lussac in 1802, but he referenced unpublished work
by Jacques Charles from around 1787. This law states that at constant pressure, the volume of
a given mass of an ideal gas increases or decreases by the same factor as its temperature (in
kelvin) increases or decreases. Another way of saying this is that temperature and volume are
directly proportional (figure ??).
Definition: Charles’s Law
The volume of an enclosed sample of gas is directly proportional to its absolute temperature
provided the pressure is kept constant.
teresting Charles’s Law is also known as Gay-Lussac’s Law. This is because Charles
Interesting
Fact
Fact
did not publish his discovery, and it was rediscovered independently by another
French Chemist Joseph Louis Gay-Lussac some years later.
Activity :: Demonstration : Charles’s Law
Aim:
To demonstrate Charles’s Law using simple materials.
Apparatus:
glass bottle (e.g. empty glass coke bottle), balloon, bunsen burner, retort stand
Method:
1. Place the balloon over the opening of the empty bottle.
2. Place the bottle on the retort stand over the bunsen burner and allow it to
heat up. Observe what happens to the balloon. WARNING: Be careful when
handling the heated bottle. You may need to wear gloves for protection.
132
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
8.3
Results:
You should see that the balloon starts to expand. As the air inside the bottle
is heated, the pressure also increases, causing the volume to increase. Since the
volume of the glass bottle can’t increase, the air moves into the balloon, causing it
to expand.
Conclusion:
The temperature and volume of the gas are directly related to each other. As
one increases, so does the other.
Mathematically, the relationship between temperature and pressure can be represented as follows:
V ∝T
or
V = kT
If the equation is rearranged, then...
V
=k
T
and, following the same logic that was used for Boyle’s law:
V2
V1
=
T1
T2
Volume
The equation relating volume and temperature produces a straight line graph (refer back to the
notes on proportionality if this is unclear). This relationship is shown in figure 8.3.
0
Temperature (K)
Figure 8.3: The volume of a gas is directly proportional to its temperature, provided the pressure
of the gas is constant.
However, if this graph is plotted on a celsius temperature scale, the zero point of temperature
doesn’t correspond to the zero point of volume. When the volume is zero, the temperature is
actually -273.150C (figure 8.4.
A new temperature scale, the Kelvin scale must be used instead. Since zero on the Celsius
scale corresponds with a Kelvin temperature of -273.150C, it can be said that:
Kelvin temperature (T) = Celsius temperature (t) + 273.15
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CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
Volume (kPa)
8.3
-273◦ C
0K
0◦ C
273 K
Temperature
Figure 8.4: The relationship between volume and temperature, shown on a Celsius temperature
scale.
At school level, you can simplify this slightly and convert between the two temperature scales as
follows:
T = t + 273
or
t = T - 273
Can you explain Charles’s law in terms of the kinetic theory of gases? When the temperature
of a gas increases, so does the average speed of its molecules. The molecules collide with the
walls of the container more often and with greater impact. These collisions will push back the
walls, so that the gas occupies a greater volume than it did at the start. We saw this in the
first demonstration. Because the glass bottle couldn’t expand, the gas pushed out the balloon
instead.
Exercise: Charles’s law
The table below gives the temperature (in 0 C) of a number of gases under
different volumes at a constant pressure.
Volume (l)
0
0.25
0.5
0.75
1.0
1.5
2
2.5
3.0
3.5
He
-272.4
-245.5
-218.6
-191.8
-164.9
-111.1
-57.4
-3.6
50.2
103.9
H2
-271.8
-192.4
-113.1
-33.7
45.7
204.4
363.1
521.8
680.6
839.3
N2 O
-275.0
-123.5
28.1
179.6
331.1
634.1
937.2
1240.2
1543.2
1846.2
1. On the same set of axes, draw graphs to show the relationship between temperature and volume for each of the gases.
2. Describe the relationship you observe.
3. If you extrapolate the graphs (in other words, extend the graph line even though
you may not have the exact data points), at what temperature do they intersect?
4. What is significant about this temperature?
134
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
8.3
Worked Example 28: Charles’s Law 1
Question: Ammonium chloride and calcium hydroxide are allowed to react. The
ammonia that is released in the reaction is collected in a gas syringe and sealed in.
This gas is allowed to come to room temperature which is 32◦ C. The volume of the
ammonia is found to be 122 ml. It is now placed in a water bath set at 7◦ C. What
will be the volume reading after the syringe has been left in the bath for a good
while (assume the plunger moves completely freely)?
Answer
Step 1 : Write down all the information that you know about the gas.
V1 = 122 ml and V2 = ?
T1 = 320 C and T2 = 70 C
Step 2 : Convert the known values to SI units if necessary.
Here, temperature must be converted into Kelvin, therefore:
T1 = 32 + 273 = 305 K
T2 = 7 + 273 = 280 K
Step 3 : Choose a relevant gas law equation that will allow you to calculate
the unknown variable.
V2
V1
=
T1
T2
Therefore,
V2 =
V1 × T2
T1
Step 4 : Substitute the known values into the equation.
unknown variable.
V2 =
Calculate the
122 × 280
= 112ml
305
Important:
Note that here the temperature must be converted to Kelvin (SI) since the change from
degrees Celcius involves addition, not multiplication by a fixed conversion ratio (as is the
case with pressure and volume.)
Worked Example 29: Charles’s Law 2
Question: At a temperature of 298 K, a certain amount of CO2 gas occupies a
volume of 6 l. What volume will the gas occupy if its temperature is reduced to 273
K?
Answer
135
8.4
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
Step 1 : Write down all the information that you know about the gas.
V1 = 6 l and V2 = ?
T1 = 298 K and T2 = 273 K
Step 2 : Convert the known values to SI units if necessary.
Temperature data is already in Kelvin, and so no conversions are necessary.
Step 3 : Choose a relevant gas law equation that will allow you to calculate
the unknown variable.
V2
V1
=
T1
T2
Therefore,
V2 =
V1 × T2
T1
Step 4 : Substitute the known values into the equation.
unknown variable.
V2 =
8.4
Calculate the
6 × 273
= 5.5l
298
The relationship between temperature and pressure
Pressure
The pressure of a gas is directly proportional to its temperature, if the volume is kept constant
(figure 8.5). When the temperature of a gas increases, so does the energy of the particles.
This causes them to move more rapidly and to collide with each other and with the side of the
container more often. Since pressure is a measure of these collisions, the pressure of the gas
increases with an increase in temperature. The pressure of the gas will decrease if its temperature
decreases.
0
Temperature (K)
Figure 8.5: The relationship between the temperature and pressure of a gas
In the same way that we have done for the other gas laws, we can describe the relationship
between temperature and pressure using symbols, as follows:
T ∝ p, therefore p = kT
We can also say that:
p
=k
T
136
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
8.5
and that, provided the amount of gas stays the same...
p1
p2
=
T1
T2
Exercise: More gas laws
1. A gas of unknown volume has a temperature of 14◦ C. When the temperature
of the gas is increased to 100◦ C, the volume is found to be 5.5 L. What was
the initial volume of the gas?
2. A gas has an initial volume of 2600 mL and a temperature of 350 K.
(a) If the volume is reduced to 1500 mL, what will the temperature of the gas
be in Kelvin?
(b) Has the temperature increased or decreased?
(c) Explain this change, using the kinetic theory of matter.
3. A cylinder of propane gas at a temperature of 20◦ C exerts a pressure of 8 atm.
When a cylinder has been placed in sunlight, its temperature increases to 25◦ C.
What is the pressure of the gas inside the cylinder at this temperature?
8.5
The general gas equation
All the gas laws we have described so far rely on the fact that at least one variable (T, p or V)
remains constant. Since this is unlikely to be the case most times, it is useful to combine the
relationships into one equation. These relationships are as follows:
Boyle’s law: p ∝
1
V
(constant T)
Relationship between p and T: p ∝ T (constant V)
If we combine these relationships, we get p ∝
T
V
If we introduce the proportionality constant k, we get p = k VT
or, rearranging the equation...
pV = kT
We can also rewrite this relationship as follows:
pV
=k
T
Provided the mass of the gas stays the same, we can also say that:
p2 V2
p1 V1
=
T1
T2
In the above equation, the subscripts 1 and 2 refer to two pressure and volume readings for
the same mass of gas under different conditions. This is known as the general gas equation.
137
8.5
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
Temperature is always in kelvin and the units used for pressure and volume must be the same
on both sides of the equation.
Important:
Remember that the general gas equation only applies if the mass of the gas is fixed.
Worked Example 30: General Gas Equation 1
Question: At the beginning of a journey, a truck tyre has a volume of 30 dm3 and
an internal pressure of 170 kPa. The temperature of the tyre is 160 C. By the end
of the trip, the volume of the tyre has increased to 32 dm3 and the temperature
of the air inside the tyre is 350 C. What is the tyre pressure at the end of the journey?
Answer
Step 1 : Write down all the information that you know about the gas.
p1 = 170 kPa and p2 = ?
V1 = 30 dm3 and V2 = 32 dm3
T1 = 160 C and T2 = 400 C
Step 2 : Convert the known values to SI units if necessary.
Here, temperature must be converted into Kelvin, therefore:
T1 = 16 + 273 = 289 K
T2 = 40 + 273 = 313 K
Step 3 : Choose a relevant gas law equation that will allow you to calculate
the unknown variable.
Use the general gas equation to solve this problem:
p1 × V1
p2 × V2
=
T1
T2
Therefore,
p2 =
p1 × V1 × T2
T1 × V2
Step 4 : Substitute the known values into the equation.
unknown variable.
Calculate the
170 × 30 × 313
= 173kP a
289 × 32
The pressure of the tyre at the end of the journey is 173 kPa.
p2 =
Worked Example 31: General Gas Equation 2
Question: A cylinder that contains methane gas is kept at a temperature of 150 C
and exerts a pressure of 7 atm. If the temperature of the cylinder increases to 250 C,
what pressure does the gas now exert? (Refer to table 8.1 to see what an ’atm’ is.
Answer
Step 1 : Write down all the information that you know about the gas.
p1 = 7 atm and p2 = ?
138
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
T1 = 150 C and T2 = 250 C
Step 2 : Convert the known values to SI units if necessary.
Here, temperature must be converted into Kelvin, therefore:
T1 = 15 + 273 = 288 K
T2 = 25 + 273 = 298 K
Step 3 : Choose a relevant gas law equation that will allow you to calculate
the unknown variable.
Since the volume of the cylinder is constant, we can write:
p1
p2
=
T1
T2
Therefore,
p2 =
p1 × T 2
T1
Step 4 : Substitute the known values into the equation.
unknown variable.
Calculate the
7 × 298
= 7.24atm
288
The pressure of the gas is 7.24 atm.
p2 =
Worked Example 32: General Gas Equation 3
Question: A gas container can withstand a pressure of 130 kPa before it will start
to leak. Assuming that the volume of the gas in the container stays the same, at
what temperature will the container start to leak if the gas exerts a pressure of 100
kPa at 150 C?
Answer
Step 1 : Write down all the information that you know about the gas.
p1 = 100 kPa and p2 = 130 kPa
T1 = 150 C and T2 = ?
Step 2 : Convert the known values to SI units if necessary.
Here, temperature must be converted into Kelvin, therefore:
T1 = 15 + 273 = 288 K
Step 3 : Choose a relevant gas law equation that will allow you to calculate
the unknown variable.
Since the volume of the container is constant, we can write:
p1
p2
=
T1
T2
Therefore,
Therefore,
p1
1
=
T2
T 1 × p2
T2 =
T 1 × p2
p1
139
8.5
8.6
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
Step 4 : Substitute the known values into the equation.
unknown variable.
T2 =
Calculate the
288 × 130
= 374.4K = 101.40 C
100
Exercise: The general gas equation
1. A closed gas system initially has a volume of 8 L and a temperature of 100◦ C.
The pressure of the gas is unknown. If the temperature of the gas decreases to
50◦ C, the gas occupies a volume of 5 L. If the pressure of the gas under these
conditions is 1.2 atm, what was the initial pressure of the gas?
2. A balloon is filled with helium gas at 27◦ C and a pressure of 1.0 atm. As the
balloon rises, the volume of the balloon increases by a factor of 1.6 and the
temperature decreases to 15◦ C. What is the final pressure of the gas (assuming
none has escaped)?
3. 25 cm3 of gas at 1 atm has a temperature of 20◦ C. When the gas is compressed
to 20 cm3 , the temperature of the gas increases to 28◦ C. Calculate the final
pressure of the gas.
8.6
The ideal gas equation
In the early 1800’s, Amedeo Avogadro hypothesised that if you have samples of different gases,
of the same volume, at a fixed temperature and pressure, then the samples must contain the
same number of freely moving particles (i.e. atoms or molecules).
Definition: Avogadro’s Law
Equal volumes of gases, at the same temperature and pressure, contain the same number
of molecules.
You will remember from an earlier section, that we combined different gas law equations to get
one that included temperature, volume and pressure. In this equation, pV = kT, the value of k
is different for different masses of gas. If we were to measure the amount of gas in moles, then
k = nR, where n is the number of moles of gas and R is the universal gas constant. The value
of R is 8.3143 J.K−1 , or for most calculations, 8.3 J.K−1 . So, if we replace k in the general gas
equation, we get the following ideal gas equation.
pV = nRT
Important:
1. The value of R is the same for all gases
2. All quantities in the equation pV = nRT must be in the same units as the value of
R. In other words, SI units must be used throughout the equation.
The following table may help you when you convert to SI units.
140
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
8.6
Table 8.1: Conversion table showing different units of measurement for volume, pressure and
temperature.
Variable
Pressure (p)
Volume (V)
moles (n)
SI unit
Other units
and conversions
Pascals (Pa)
760 mm Hg
= 1 atm =
101325 Pa =
101.325 kPa
m3
1
m3
=
1000000 cm3
= 1000 dm3
= 1000 litres
mol
universal gas
constant (R)
J.mol.K−1
temperature
(K)
kelvin (K)
K = 0C +
273
Worked Example 33: Ideal gas equation 1
Question: Two moles of oxygen (O2 ) gas occupy a volume of 25 dm3 at a temperature of 400 C. Calculate the pressure of the gas under these conditions.
Answer
Step 1 : Write down all the information that you know about the gas.
p=?
V = 25 dm3
n=2
T = 400 C
Step 2 : Convert the known values to SI units if necessary.
V =
25
= 0.025m3
1000
T = 40 + 273 = 313K
Step 3 : Choose a relevant gas law equation that will allow you to calculate
the unknown variable.
pV = nRT
Therefore,
p=
nRT
V
Step 4 : Substitute the known values into the equation.
unknown variable.
Calculate the
p = 2 × 8.3 × 3130.025 = 207832P a = 207.8kP a
Worked Example 34: Ideal gas equation 2
Question: Carbon dioxide (CO2 ) gas is produced as a result of the reaction between
calcium carbonate and hydrochloric acid. The gas that is produced is collected in
a 20 dm3 container. The pressure of the gas is 105 kPa at a temperature of 200 C.
141
8.6
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
What mass of carbon dioxide was produced?
Answer
Step 1 : Write down all the information that you know about the gas.
p = 105 kPa
V = 20 dm3
T = 200 C
Step 2 : Convert the known values to SI units if necessary.
p = 105 × 1000 = 105000P a
T = 20 + 273 = 293K
V =
20
= 0.02m3
1000
Step 3 : Choose a relevant gas law equation that will allow you to calculate
the unknown variable.
pV = nRT
Therefore,
n=
pV
RT
Step 4 : Substitute the known values into the equation.
unknown variable.
n=
Calculate the
105000 × 0.02
= 0.86moles
8.3 × 293
Step 5 : Calculate mass from moles
n=
m
M
Therefore,
m=n×M
The molar mass of CO2 is calculated as follows:
M = 12 + (2 × 16) = 44g.mol−1
Therefore,
m = 0.86 × 44 = 37.84g
Worked Example 35: Ideal gas equation 3
Question: 1 mole of nitrogen (N2 ) reacts with hydrogen (H2 ) according to the
following equation:
N2 + 3H2 → 2N H3
142
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
The ammonia (NH3 ) gas is collected in a separate gas cylinder which has a volume
of 25 dm3 . The temperature of the gas is 220 C. Calculate the pressure of the gas
inside the cylinder.
Answer
Step 1 : Write down all the information that you know about the gas.
V = 25 dm3
n = 2 (Calculate this by looking at the mole ratio of nitrogen to ammonia, which is
1:2)
T = 220 C
Step 2 : Convert the known values to SI units if necessary.
V =
25
= 0.025m3
1000
T = 22 + 273 = 295K
Step 3 : Choose a relevant gas law equation that will allow you to calculate
the unknown variable.
pV = nRT
Therefore,
p=
nRT
V
Step 4 : Substitute the known values into the equation.
unknown variable.
p=
Calculate the
2 × 8.3 × 295
= 195880P a = 195.89kP a
0.025
Worked Example 36: Ideal gas equation 4
Question: Calculate the number of air particles in a 10 m by 7 m by 2 m classroom
on a day when the temperature is 23◦ C and the air pressure is 98 kPa.
Answer
Step 1 : Write down all the information that you know about the gas.
V = 10 m × 7 m × 2m = 140 m3
p = 98 kPa
T = 230 C
Step 2 : Convert the known values to SI units if necessary.
p = 98 × 1000 = 98000P a
T = 23 + 273 = 296K
Step 3 : Choose a relevant gas law equation that will allow you to calculate
the unknown variable.
pV = nRT
143
8.6
8.6
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
Therefore,
n=
pV
RT
Step 4 : Substitute the known values into the equation.
unknown variable.
n=
Calculate the
98000 × 140
= 5584.5mol
8.3 × 296
Worked Example 37: Applying the gas laws
Question: Most modern cars are equipped with airbags for both the driver and the
passenger. An airbag will completely inflate in 0,05 s. This is important because a
typical car collision lasts about 0,125 s. The following reaction of sodium azide (a
compound found in airbags) is activated by an electrical signal:
2N aN3 (s) → 2N a(s) + 3N2 (g)
1. Calculate the mass of N2 (g) needed to inflate a sample airbag to a volume of
65 dm3 at 25 ◦ C and 99,3 kPa. Assume the gas temperature remains constant
during the reaction.
2. In reality the above reaction is exothermic. Describe, in terms of the kinetic
molecular theory, how the pressure in the sample airbag will change, if at all,
as the gas temperature returns to 25 ◦ C.
Answer
Step 1 : Look at the information you have been given, and the information
you still need.
Here you are given the volume, temperature and pressure. You are required to work
out the mass of N2 .
Step 2 : Check that all the units are S.I. units
Pressure: 93,3 × 103 Pa
Volume: 65 × 10−3 m3
Temperature: (273 + 25) K
Gas Constant: 8,31
Step 3 : Write out the Ideal Gas formula
pV = nRT
Step 4 : Solve for the required quantity using symbols
n=
pV
RT
Step 5 : Solve by substituting numbers into the equation to solve for ’n’.
n=
99,3 × 103 × 65 × 10−3
8,31 × (273 + 25)
Step 6 : Convert the number of moles to number of grams
144
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
m
=
m
m
=
=
8.7
n×M
2,61 × 28
73,0g
Step 7 : Theory Question
When the temperature decreases the intensity of collisions with the walls of the
airbag and between particles decreases. Therefore pressure decreases.
Exercise: The ideal gas equation
1. An unknown gas has pressure, volume and temperature of 0.9 atm, 8 L and
120◦ C respectively. How many moles of gas are present?
2. 6 g of chlorine (Cl2 ) occupies a volume of 0.002 m3 at a temperature of 26◦ C.
What is the pressure of the gas under these conditions?
3. An average pair of human lungs contains about 3.5 L of air after inhalation
and about 3.0 L after exhalation. Assuming that air in your lungs is at 37◦ C
and 1.0 atm, determine the number of moles of air in a typical breath.
4. A learner is asked to calculate the answer to the problem below:
Calculate the pressure exerted by 1.5 moles of nitrogen gas in a container with
a volume of 20 dm3 at a temperature of 37◦ C.
The learner writes the solution as follows:
V = 20 dm3
n = 1.5 mol
R = 8.3 J.K−1 .mol−1
T = 37 + 273 = 310 K
p = nRT, therefore
p=
=
nRV
T
1.5 × 8.3 × 20
310
= 0.8 kPa
(a) Identify 2 mistakes the learner has made in the calculation.
(b) Are the units of the final answer correct?
(c) Rewrite the solution, correcting the mistakes to arrive at the right answer.
8.7
Molar volume of gases
It is possible to calculate the volume of a mole of gas at STP using what we now know about
gases.
1. Write down the ideal gas equation
145
8.8
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
pV = nRT, therefore V =
nRT
p
2. Record the values that you know, making sure that they are in SI units
You know that the gas is under STP conditions. These are as follows:
p = 101.3 kPa = 101300 Pa
n = 1 mole
R = 8.3 J.K−1 .mol−1
T = 273 K
3. Substitute these values into the original equation.
V =
V =
nRT
p
1mol × 8.3J.K −1 .mol−1 × 273K
101300P a
4. Calculate the volume of 1 mole of gas under these conditions
The volume of 1 mole of gas at STP is 22.4 × 10−3 m3 = 22.4 dm3 .
8.8
Ideal gases and non-ideal gas behaviour
In looking at the behaviour of gases to arrive at the Ideal Gas Law, we have limited our examination to a small range of temperature and pressure. Most gases do obey these laws most
of the time, and are called ideal gases, but there are deviations at high pressures and low
temperatures. So what is happening at these two extremes?
Earlier when we discussed the kinetic theory of gases, we made a number of assumptions about
the behaviour of gases. We now need to look at two of these again because they affect how
gases behave either when pressures are high or when temperatures are low.
1. Molecules do occupy volume
Volume
This means that when pressures are very high and the molecules are compressed, their volume becomes significant. This means that the total volume available for the gas molecules
to move is reduced and collisions become more frequent. This causes the pressure of the
gas to be higher than what would normally have been predicted by Boyle’s law (figure
8.6).
rea
i de
al
ga
lg
as
s
Pressure
Figure 8.6: Gases deviate from ideal gas behaviour at high pressure.
146
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
8.9
2. Forces of attraction do exist between molecules
as
lg
lg
as
ea
id
re
a
Pressure
At low temperatures, when the speed of the molecules decreases and they move closer
together, the intermolecular forces become more apparent. As the attraction between
molecules increases, their movement decreases and there are fewer collisions between them.
The pressure of the gas at low temperatures is therefore lower than what would have been
expected for an ideal gas (figure 8.7. If the temperature is low enough or the pressure high
enough, a real gas will liquify.
Temperature
Figure 8.7: Gases deviate from ideal gas behaviour at low temperatures
8.9
Summary
• The kinetic theory of matter helps to explain the behaviour of gases under different
conditions.
• An ideal gas is one that obeys all the assumptions of the kinetic theory.
• A real gas behaves like an ideal gas, except at high pressures and low temperatures. Under
these conditions, the forces between molecules become significant and the gas will liquify.
• Boyle’s law states that the pressure of a fixed quantity of gas is inversely proportional to
its volume, as long as the temperature stays the same. In other words, pV = k or
p1 V1 = p2 V2 .
• Charles’s law states that the volume of an enclosed sample of gas is directly proportional
to its temperature, as long as the pressure stays the same. In other words,
V1
V2
=
T1
T2
• The temperature of a fixed mass of gas is directly proportional to its pressure, if the
volume is constant. In other words,
p1
p2
=
T1
T2
• In the above equations, temperature must be written in Kelvin. Temperature in degrees
Celsius (temperature = t) can be converted to temperature in Kelvin (temperature = T)
using the following equation:
T = t + 273
147
8.9
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
• Combining Boyle’s law and the relationship between the temperature and pressure of a
gas, gives the general gas equation, which applies as long as the amount of gas remains
constant. The general gas equation is pV = kT, or
p1 V1
p2 V2
=
T1
T2
• Because the mass of gas is not always constant, another equation is needed for these
situations. The ideal gas equation can be written as
pV = nRT
where n is the number of moles of gas and R is the universal gas constant, which is 8.3
J.K−1 .mol−1 . In this equation, SI units must be used. Volume (m3 ), pressure (Pa) and
temperature (K).
• The volume of one mole of gas under STP is 22.4 dm3 . This is called the molar gas
volume.
s
Exercise: Summary exercise
1. For each of the following, say whether the statement is true or false. If the
statement is false, rewrite the statement correctly.
(a) Real gases behave like ideal gases, except at low pressures and low temperatures.
(b) The volume of a given mass of gas is inversely proportional to the pressure
it exerts.
(c) The temperature of a fixed mass of gas is directly proportional to its pressure, regardless of the volume of the gas.
2. For each of the following multiple choice questions, choose the one correct
answer.
(a) Which one of the following properties of a fixed quantity of a gas must be
kept constant during a Boyle’s law investigation?
i. density
ii. pressure
iii. temperature
iv. volume
(IEB 2003 Paper 2 )
(b) Three containers of EQUAL VOLUME are filled with EQUAL MASSES
of helium, nitrogen and carbon dioxide gas respectively. The gases in the
three containers are all at the same TEMPERATURE. Which one of the
following statements is correct regarding the pressure of the gases?
i. All three gases will be at the same pressure
ii. The helium will be at the greatest pressure
iii. The nitrogen will be at the greatest pressure
iv. The carbon dioxide will be at the greatest pressure
(IEB 2004 Paper 2 )
(c) One mole of an ideal gas is stored at a temperature T (in Kelvin) in a rigid
gas tank. If the average speed of the gas particles is doubled, what is the
new Kelvin temperature of the gas?
i. 4T
ii. 2T
√
iii. 2T
148
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
iv. 0.5 T
(IEB 2002 Paper 2 )
(d) The ideal gas equation is given by pV = nRT. Which one of the following
conditions is true according to Avogadro’s hypothesis?
a p ∝ 1/V
(T = constant)
b
V∝T
(p = constant)
c
V∝n
(p, T = constant)
d
p∝T
(n = constant)
(DoE Exemplar paper 2, 2007 )
3. Use your knowledge of the gas laws to explain the following statements.
(a) It is dangerous to put an aerosol can near heat.
(b) A pressure vessel that is poorly designed and made can be a serious safety
hazard (a pressure vessel is a closed, rigi container that is used to hold
gases at a pressure that is higher than the normal air pressure).
(c) The volume of a car tyre increases after a trip on a hot road.
4. Copy the following set of labelled axes and answer the questions that follow:
Volume (m3 )
0
Temperature (K)
(a) On the axes, using a solid line, draw the graph that would be obtained
for a fixed mass of an ideal gas if the pressure is kept constant.
(b) If the gradient of the above graph is measured to be 0.008 m3 .K−1 , calculate the pressure that 0.3 mol of this gas would exert.
(IEB 2002 Paper 2)
5. Two gas cylinders, A and B, have a volume of 0.15 m3 and 0.20 m3 respectively.
Cylinder A contains 1.25 mol He gas at pressure p and cylinder B contains 2.45
mol He gas at standard pressure. The ratio of the Kelvin temperatures A:B is
1.80:1.00. Calculate the pressure of the gas (in kPa) in cylinder A.
(IEB 2002 Paper 2 )
6. A learner investigates the relationship between the Celsius temperature and the
pressure of a fixed amount of helium gas in a 500 cm3 closed container. From
the results of the investigation, she draws the graph below:
pressure
(kPa)
300
10
20 temperature (0 C)
(a) Under the conditions of this investigation, helium gas behaves like an ideal
gas. Explain briefly why this is so.
149
8.9
8.9
CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11
(b) From the shape of the graph, the learner concludes that the pressure of
the helium gas is directly proportional to the Celcius temperature. Is her
conclusion correct? Briefly explain your answer.
(c) Calculate the pressure of the helium gas at 0 ◦ C.
(d) Calculate the mass of helium gas in the container.
(IEB 2003 Paper 2 )
7. One of the cylinders of a motor car engine, before compression contains 450
cm3 of a mixture of air and petrol in the gaseous phase, at a temperature of
30◦ C and a pressure of 100 kPa. If the volume of the cylinder after compression
decreases to one tenth of the original volume, and the temperature of the gas
mixture rises to 140◦C, calculate the pressure now exerted by the gas mixture.
8. In an experiment to determine the relationship between pressure and temperature of a fixed mass of gas, a group of learners obtained the following results:
Pressure (kPa)
Temperature (0 C)
Total gas volume (cm3 )
101
0
250
120
50
250
130.5
80
250
138
100
250
(a) Draw a straight-line graph of pressure (on the dependent, y-axis) versus
temperature (on the independent, x-axis) on a piece of graph paper. Plot
the points. Give your graph a suitable heading.
A straight-line graph passing through the origin is essential to obtain a
mathematical relationship between pressure and temperature.
(b) Extrapolate (extend) your graph and determine the temperature (in 0 C)
at which the graph will pass through the temperature axis.
(c) Write down, in words, the relationship between pressure and Kelvin temperature.
(d) From your graph, determine the pressure (in kPa) at 173 K. Indicate on
your graph how you obtained this value.
(e) How would the gradient of the graph be affected (if at all) if a larger mass
of the gas is used? Write down ONLY increases, decreases or stays the
same.
(DoE Exemplar Paper 2, 2007 )
150
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