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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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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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
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Chapter 13
Quantitative Aspects of Chemical
Change - Grade 11
An equation for a chemical reaction can provide us with a lot of useful information. It tells us
what the reactants and the products are in the reaction, and it also tells us the ratio in which
the reactants combine to form products. Look at the equation below:
F e + S → F eS
In this reaction, every atom of iron (Fe) will react with a single atom of sulfur (S) to form one
molecule of iron sulfide (FeS). However, what the equation doesn’t tell us, is the quantities or
the amount of each substance that is involved. You may for example be given a small sample
of iron for the reaction. How will you know how many atoms of iron are in this sample? And
how many atoms of sulfur will you need for the reaction to use up all the iron you have? Is
there a way of knowing what mass of iron sulfide will be produced at the end of the reaction?
These are all very important questions, especially when the reaction is an industrial one, where
it is important to know the quantities of reactants that are needed, and the quantity of product
that will be formed. This chapter will look at how to quantify the changes that take place in
chemical reactions.
13.1
The Mole
Sometimes it is important to know exactly how many particles (e.g. atoms or molecules) are in
a sample of a substance, or what quantity of a substance is needed for a chemical reaction to
take place.
You will remember from chapter 3 that the relative atomic mass of an element, describes the
mass of an atom of that element relative to the mass of an atom of carbon-12. So the mass of
an atom of carbon (relative atomic mass is 12 u) for example, is twelve times greater than the
mass of an atom of hydrogen, which has a relative atomic mass of 1 u. How can this information
be used to help us to know what mass of each element will be needed if we want to end up with
the same number of atoms of carbon and hydrogen?
Let’s say for example, that we have a sample of 12g carbon. What mass of hydrogen will contain
the same number of atoms as 12 g carbon? We know that each atom of carbon weighs twelve
times more than an atom of hydrogen. Surely then, we will only need 1g of hydrogen for the
number of atoms in the two samples to be the same? You will notice that the number of particles
(in this case, atoms) in the two substances is the same when the ratio of their sample masses
(12g carbon: 1g hydrogen = 12:1) is the same as the ratio of their relative atomic masses (12
u: 1 u = 12:1).
233
13.1
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
To take this a step further, if you were to weigh out samples of a number of elements so that the
mass of the sample was the same as the relative atomic mass of that element, you would find
that the number of particles in each sample is 6.023 x 1023 . These results are shown in table
13.1 below for a number of different elements. So, 24.31 g of magnesium (relative atomic mass
= 24.31 u) for example, has the same number of atoms as 40.08 g of calcium (relative atomic
mass = 40.08 u).
Table 13.1: Table showing the relationship between the sample mass, the relative atomic mass
and the number of atoms in a sample, for a number of elements.
Element
Relative atomic mass (u) Sample mass (g) Atoms in sample
Hydrogen (H)
1.01
1.01
6.023 x 1023
Carbon (C)
12.01
12.01
6.023 x 1023
Magnesium (Mg)
24.31
24.31
6.023 x 1023
Sulfur (S)
32.07
32.07
6.023 x 1023
Calcium (Ca)
40.08
40.08
6.023 x 1023
This result is so important that scientists decided to use a special unit of measurement to define
this quantity: the mole or ’mol’. A mole is defined as being an amount of a substance which
contains the same number of particles as there are atoms in 12 g of carbon. In the examples
that were used earlier, 24.31 g magnesium is one mole of magnesium, while 40.08 g of calcium
is one mole of calcium. A mole of any substance always contains the same number of particles.
Definition: Mole
The mole (abbreviation ’n’) is the SI (Standard International) unit for ’amount of substance’.
It is defined as an amount of substance that contains the same number of particles (atoms,
molecules or other particle units) as there are atoms in 12 g carbon.
In one mole of any substance, there are 6.023 x 1023 particles. This is known as Avogadro’s
number.
Definition: Avogadro constant
The number of particles in a mole, equal to 6.023 x 1023 . It is also sometimes referred to
as the number of atoms in 12 g of carbon-12.
teresting The original hypothesis that was proposed by Amadeo Avogadro was that ’equal
Interesting
Fact
Fact
volumes of gases, at the same temperature and pressure, contain the same number
of molecules’. His ideas were not accepted by the scientific community and it
was only four years after his death, that his original hypothesis was accepted
and that it became known as ’Avogadro’s Law’. In honour of his contribution
to science, the number of particles in one mole was named Avogadro’s number.
Exercise: Moles and mass
1. Complete the following table:
234
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
Element
Hydrogen
Magnesium
Carbon
Chlorine
Nitrogen
Relative
atomic mass
(u)
1.01
24.31
12.01
35.45
Sample mass
(g)
13.2
Number
of
moles in the
sample
1.01
24.31
24.02
70.9
42.08
2. How many atoms are there in...
(a) 1 mole of a substance
(b) 2 moles of calcium
(c) 5 moles of phosphorus
(d) 24.31 g of magnesium
(e) 24.02 g of carbon
13.2
Molar Mass
Definition: Molar mass
Molar mass (M) is the mass of 1 mole of a chemical substance. The unit for molar mass is
grams per mole or g.mol−1 .
Refer to table 13.1. You will remember that when the mass, in grams, of an element is equal to
its relative atomic mass, the sample contains one mole of that element. This mass is called the
molar mass of that element.
It is worth remembering the following: On the Periodic Table, the relative atomic mass that is
shown can be interpreted in two ways.
1. The mass of a single, average atom of that element relative to the mass of an atom of
carbon.
2. The mass of one mole of the element. This second use is the molar mass of the element.
Table 13.2: The relationship between relative atomic mass, molar mass and the mass of one
mole for a number of elements.
Element
Magnesium
Lithium
Oxygen
Nitrogen
Iron
Relative
atomic mass
(u)
24.31
6.94
16
14.01
55.85
Molar mass
(g.mol−1 )
24.31
6.94
16
14.01
55.85
235
Mass of one
mole of the
element (g)
24.31
6.94
16
14.01
55.85
13.2
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
Worked Example 55: Calculating the number of moles from mass
Question: Calculate the number of moles of iron (Fe) in a 111.7 g sample.
Answer
Step 1 : Find the molar mass of iron
If we look at the periodic table, we see that the molar mass of iron is 55.85 g.mol−1 .
This means that 1 mole of iron will have a mass of 55.85 g.
Step 2 : Use the molar mass and sample mass to calculate the number of
moles of iron
If 1 mole of iron has a mass of 55.85 g, then: the number of moles of iron in 111.7
g must be:
111.7g
= 2mol
55.85g.mol−1
There are 2 moles of iron in the sample.
Worked Example 56: Calculating mass from moles
Question: You have a sample that contains 5 moles of zinc.
1. What is the mass of the zinc in the sample?
2. How many atoms of zinc are in the sample?
Answer
Step 1 : Find the molar mass of zinc
Molar mass of zinc is 65.38 g.mol−1 , meaning that 1 mole of zinc has a mass of
65.38 g.
Step 2 : Calculate the mass of zinc, using moles and molar mass.
If 1 mole of zinc has a mass of 65.38 g, then 5 moles of zinc has a mass of:
65.38 g x 5 mol = 326.9 g (answer to a)
Step 3 : Use the number of moles of zinc and Avogadro’s number to calculate
the number of zinc atoms in the sample.
5 × 6.023 × 1023 = 30.115 × 1023
Exercise: Moles and molar mass
1. Give the molar mass of each of the following elements:
(a) hydrogen
(b) nitrogen
(c) bromine
2. Calculate the number of moles in each of the following samples:
(a) 21.62 g of boron (B)
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CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
13.3
(b) 54.94 g of manganese (Mn)
(c) 100.3 g of mercury (Hg)
(d) 50 g of barium (Ba)
(e) 40 g of lead (Pb)
13.3
An equation to calculate moles and mass in chemical
reactions
The calculations that have been used so far, can be made much simpler by using the following
equation:
n (number of moles) =
m (mass of substance in g)
M (molar mass of substance in g · mol−1 )
Important: Remember that when you use the equation n = m/M, the mass is always in
grams (g) and molar mass is in grams per mol (g.mol−1 ).
The equation can also be used to calculate mass and molar mass, using the following equations:
m=n×M
and
M=
m
n
The following diagram may help to remember the relationship between these three variables.
You need to imagine that the horizontal line is like a ’division’ sign and that the vertical line is
like a ’multiplication’ sign. So, for example, if you want to calculate ’M’, then the remaining two
letters in the triangle are ’m’ and ’n’ and ’m’ is above ’n’ with a division sign between them. In
your calculation then, ’m’ will be the numerator and ’n’ will be the denominator.
m
n
M
237
13.3
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
Worked Example 57: Calculating moles from mass
Question: Calculate the number of moles of copper there are in a sample that
weighs 127 g.
Answer
Step 1 : Write the equation to calculate the number of moles
n=
m
M
Step 2 : Substitute numbers into the equation
127
=2
63.55
There are 2 moles of copper in the sample.
n=
Worked Example 58: Calculating mass from moles
Question: You are given a 5 mol sample of sodium. What mass of sodium is in the
sample?
Answer
Step 1 : Write the equation to calculate the sample mass.
m=n×M
Step 2 : Substitute values into the equation.
MN a = 22.99 g.mol−1
Therefore,
m = 5 × 22.99 = 114.95g
The sample of sodium has a mass of 114.95 g.
Worked Example 59: Calculating atoms from mass
Question: Calculate the number of atoms there are in a sample of aluminium that
weighs 80.94 g.
Answer
Step 1 : Calculate the number of moles of aluminium in the sample.
n=
m
80.94
=
= 3moles
M
26.98
Step 2 : Use Avogadro’s number to calculate the number of atoms in the
sample.
Number of atoms in 3 mol aluminium = 3 × 6.023 × 1023
There are 18.069 × 1023 aluminium atoms in a sample of 80.94 g.
238
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
13.4
Exercise: Some simple calculations
1. Calculate the number of moles in each of the following samples:
(a) 5.6 g of calcium
(b) 0.02 g of manganese
(c) 40 g of aluminium
2. A lead sinker has a mass of 5 g.
(a) Calculate the number of moles of lead the sinker contains.
(b) How many lead atoms are in the sinker?
3. Calculate the mass of each of the following samples:
(a) 2.5 mol magnesium
(b) 12 g lithium
(c) 4.5 × 1025 atoms of silica
13.4
Molecules and compounds
So far, we have only discussed moles, mass and molar mass in relation to elements. But what
happens if we are dealing with a molecule or some other chemical compound? Do the same
concepts and rules apply? The answer is ’yes’. However, you need to remember that all your calculations will apply to the whole molecule. So, when you calculate the molar mass of a molecule,
you will need to add the molar mass of each atom in that compound. Also, the number of moles
will also apply to the whole molecule. For example, if you have one mole of nitric acid (HNO3 ),
it means you have 6.023 x 1023 molecules of nitric acid in the sample. This also means that
there are 6.023 × 1023 atoms of hydrogen, 6.023 × 1023 atoms of nitrogen and (3 × 6.023 ×
1023 ) atoms of oxygen in the sample.
In a balanced chemical equation, the number that is written in front of the element or compound,
shows the mole ratio in which the reactants combine to form a product. If there are no numbers
in front of the element symbol, this means the number is ’1’.
e.g. N2 + 3H2 → 2N H3
In this reaction, 1 mole of nitrogen reacts with 3 moles of hydrogen to produce 2 moles of
ammonia.
Worked Example 60: Calculating molar mass
Question: Calculate the molar mass of H2 SO4 .
Answer
Step 1 : Use the periodic table to find the molar mass for each element in
the molecule.
Hydrogen = 1.008 g.mol−1 ; Sulfur = 32.07 g.mol−1 ; Oxygen = 16 g.mol−1
239
13.4
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
Step 2 : Add the molar masses of each atom in the molecule
M(H2 SO4 ) = (2 × 1.008) + (32.07) + (4 × 16) = 98.09g.mol−1
Worked Example 61: Calculating moles from mass
Question: Calculate the number of moles there are in 1kg of MgCl2 .
Answer
Step 1 : Write the equation for calculating the number of moles in the
sample.
n=
m
M
Step 2 : Calculate the values that you will need, to substitute into the
equation
1. Convert mass into grams
m = 1kg × 1000 = 1000g
2. Calculate the molar mass of MgCl2 .
M(MgCl2 ) = 24.31 + (2 × 35.45) = 95.21g.mol−1
Step 3 : Substitute values into the equation
1000
= 10.5mol
95.21
There are 10.5 moles of magnesium chloride in a 1 kg sample.
n=
Worked Example 62: Calculating the mass of reactants and products
Question: Barium chloride and sulfuric acid react according to the following equation to produce barium sulphate and hydrochloric acid.
BaCl2 + H2 SO4 → BaSO4 + 2HCl
If you have 2 g of BaCl2 ...
1. What quantity (in g) of H2 SO4 will you need for the reaction so that all the
barium chloride is used up?
2. What mass of HCl is produced during the reaction?
Answer
Step 1 : Calculate the number of moles of BaCl2 that react.
n=
2
m
=
= 0.0096mol
M
208.24
240
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
Step 2 : Determine how many moles of H2 SO4 are needed for the reaction
According to the balanced equation, 1 mole of BaCl2 will react with 1 mole of
H2 SO4 . Therefore, if 0.0096 moles of BaCl2 react, then there must be the same
number of moles of H2 SO4 that react because their mole ratio is 1:1.
Step 3 : Calculate the mass of H2 SO4 that is needed.
m = n × M = 0.0096 × 98.086 = 0.94g
(answer to 1)
Step 4 : Determine the number of moles of HCl produced.
According to the balanced equation, 2 moles of HCl are produced for every 1 mole of
the two reactants. Therefore the number of moles of HCl produced is (2 × 0.0096),
which equals 0.0192 moles.
Step 5 : Calculate the mass of HCl.
m = n × M = 0.0192 × 35.73 = 0.69g
(answer to 2)
Activity :: Group work : Understanding moles, molecules and Avogadro’s
number
Divide into groups of three and spend about 20 minutes answering the following
questions together:
1. What are the units of the mole? Hint: Check the definition of the mole.
2. You have a 56 g sample of iron sulfide (FeS)
(a) How many moles of FeS are there in the sample?
(b) How many molecules of FeS are there in the sample?
(c) What is the difference between a mole and a molecule?
3. The exact size of Avogadro’s number is sometimes difficult to imagine.
(a) Write down Avogadro’s number without using scientific notation.
(b) How long would it take to count to Avogadro’s number? You can assume
that you can count two numbers in each second.
Exercise: More advanced calculations
1. Calculate the molar mass of the following chemical compounds:
(a) KOH
(b) FeCl3
(c) Mg(OH)2
2. How many moles are present in:
(a) 10 g of Na2 SO4
(b) 34 g of Ca(OH)2
(c) 2.45 x 1023 molecules of CH4 ?
241
13.4
13.5
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
3. For a sample of 0.2 moles of potassium bromide (KBr), calculate...
(a) the number of moles of K+ ions
(b) the number of moles of Br− ions
4. You have a sample containing 3 moles of calcium chloride.
(a) What is the chemical formula of calcium chloride?
(b) How many calcium atoms are in the sample?
5. Calculate the mass of:
(a) 3 moles of NH4 OH
(b) 4.2 moles of Ca(NO3 )2
6. 96.2 g sulfur reacts with an unknown quantity of zinc according to the following
equation:
Zn + S → ZnS
(a) What mass of zinc will you need for the reaction, if all the sulfur is to be
used up?
(b) What mass of zinc sulfide will this reaction produce?
7. Calcium chloride reacts with carbonic acid to produce calcium carbonate and
hydrochloric acid according to the following equation:
CaCl2 + H2 CO3 → CaCO3 + 2HCl
If you want to produce 10 g of calcium carbonate through this chemical reaction,
what quantity (in g) of calcium chloride will you need at the start of the
reaction?
13.5
The Composition of Substances
The empirical formula of a chemical compound is a simple expression of the relative number
of each type of atom in it. In contrast, the molecular formula of a chemical compound gives
the actual number of atoms of each element found in a molecule of that compound.
Definition: Empirical formula
The empirical formula of a chemical compound gives the relative number of each type of
atom in it.
Definition: Molecular formula
The molecular formula of a chemical compound gives the exact number of atoms of each
element in one molecule of that compound.
The compound ethanoic acid for example, has the molecular formula CH3 COOH or simply
C2 H4 O2 . In one molecule of this acid, there are two carbon atoms, four hydrogen atoms and
two oxygen atoms. The ratio of atoms in the compound is 2:4:2, which can be simplified to 1:2:1.
Therefore, the empirical formula for this compound is CH2 O. The empirical formula contains the
smallest whole number ratio of the elements that make up a compound.
Knowing either the empirical or molecular formula of a compound, can help to determine its
composition in more detail. The opposite is also true. Knowing the composition of a substance
can help you to determine its formula. There are three different types of composition problems
that you might come across:
242
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
13.5
1. Problems where you will be given the formula of the substance and asked to calculate the
percentage by mass of each element in the substance.
2. Problems where you will be given the percentage composition and asked to calculate the
formula.
3. Problems where you will be given the products of a chemical reaction and asked to calculate
the formula of one of the reactants. These are usually referred to as combustion analysis
problems.
Worked Example 63: Calculating the percentage by mass of elements in a
compound
Question: Calculate the percentage that each element contributes to the overall
mass of sulfuric acid (H2 SO4 ).
Answer
Step 1 : Write down the relative atomic mass of each element in the compound.
Hydrogen = 1.008 × 2 = 2.016 u
Sulfur = 32.07 u
Oxygen = 4 × 16 = 64 u
Step 2 : Calculate the molecular mass of sulfuric acid.
Use the calculations in the previous step to calculate the molecular mass of sulfuric
acid.
M ass = 2.016 + 32.07 + 64 = 98.09u
Step 3 : Convert the mass of each element to a percentage of the total mass
of the compound
Use the equation:
Percentage by mass = atomic mass / molecular mass of H2 SO4 × 100%
Hydrogen
2.016
× 100% = 2.06%
98.09
Sulfur
32.07
× 100% = 32.69%
98.09
Oxygen
64
× 100% = 65.25%
98.09
(You should check at the end that these percentages add up to 100%!)
In other words, in one molecule of sulfuric acid, hydrogen makes up 2.06% of the
mass of the compound, sulfur makes up 32.69% and oxygen makes up 65.25%.
243
13.5
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
Worked Example 64: Determining the empirical formula of a compound
Question: A compound contains 52.2% carbon (C), 13.0% hydrogen (H) and
34.8% oxygen (O). Determine its empirical formula.
Answer
Step 1 : If we assume that we have 100 g of this substance, then we can
convert each element percentage into a mass in grams.
Carbon = 52.2 g, hydrogen = 13 g and oxygen = 34.8 g
Step 2 : Convert the mass of each element into number of moles
n=
m
M
Therefore,
52.2
= 4.35mol
12.01
n(carbon) =
n(hydrogen) =
13
= 12.90mol
1.008
34.8
= 2.18mol
16
Step 3 : Convert these numbers to the simplest mole ratio by dividing by the
smallest number of moles
In this case, the smallest number of moles is 2.18. Therefore...
Carbon
n(oxygen) =
4.35
=2
2.18
Hydrogen
12.90
=6
2.18
Oxygen
2.18
=1
2.18
Therefore the empirical formula of this substance is: C2 H6 O. Do you recognise this
compound?
Worked Example 65: Determining the formula of a compound
Question: 207 g of lead combines with oxygen to form 239 g of a lead oxide. Use
this information to work out the formula of the lead oxide (Relative atomic masses:
Pb = 207 u and O = 16 u).
Answer
Step 1 : Calculate the mass of oxygen in the reactants
239 − 207 = 32g
244
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
Step 2 : Calculate the number of moles of lead and oxygen in the reactants.
n=
m
M
Lead
207
= 1mol
207
Oxygen
32
= 2mol
16
Step 3 : Deduce the formula of the compound
The mole ratio of Pb:O in the product is 1:2, which means that for every atom of
lead, there will be two atoms of oxygen. The formula of the compound is PbO2 .
Worked Example 66: Empirical and molecular formula
Question: Vinegar, which is used in our homes, is a dilute form of acetic acid. A
sample of acetic acid has the following percentage composition: 39.9% carbon, 6.7%
hyrogen and 53.4% oxygen.
1. Determine the empirical formula of acetic acid.
2. Determine the molecular formula of acetic acid if the molar mass of acetic acid
is 60g/mol.
Answer
Step 1 : Calculate the mass of each element in 100 g of acetic acid.
In 100g of acetic acid, there is 39.9 g C, 6.7 g H and 53.4 g O
Step 2 : Calculate the number of moles of each element in 100 g of acetic
acid.
m
n= M
nC
=
nH
=
nO
=
39.9
= 3.33 mol
12
6.7
= 6.7 mol
1
53.4
= 3.34 mol
16
Step 3 : Divide the number of moles of each element by the lowest number
to get the simplest mole ratio of the elements (i.e. the empirical formula) in
acetic acid.
Empirical formula is CH2 O
Step 4 : Calculate the molecular formula, using the molar mass of acetic
acid.
The molar mass of acetic acid using the empirical formula is 30 g/mol. Therefore the
actual number of moles of each element must be double what it is in the emprical
formula.
The molecular formula is therefore C2 H4 O2 or CH3 COOH
245
13.5
13.6
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
Exercise: Moles and empirical formulae
1. Calcium chloride is produced as the product of a chemical reaction.
(a) What is the formula of calcium chloride?
(b) What percentage does each of the elements contribute to the mass of a
molecule of calcium chloride?
(c) If the sample contains 5 g of calcium chloride, what is the mass of calcium
in the sample?
(d) How many moles of calcium chloride are in the sample?
2. 13g of zinc combines with 6.4g of sulfur.What is the empirical formula of zinc
sulfide?
(a) What mass of zinc sulfide will be produced?
(b) What percentage does each of the elements in zinc sulfide contribute to
its mass?
(c) Determine the formula of zinc sulfide.
3. A calcium mineral consisted of 29.4% calcium, 23.5% sulphur and 47.1% oxygen
by mass. Calculate the empirical formula of the mineral.
4. A chlorinated hydrocarbon compound when analysed, consisted of 24.24% carbon, 4.04% hydrogen, 71.72% chlorine. The molecular mass was found to be
99 from another experiment. Deduce the empirical and molecular formula.
13.6
Molar Volumes 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
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 .
246
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
13.7
Important: The standard units used for this equation are P in Pa, V in m3 and T in K.
Remember also that 1000cm3 = 1dm3 and 1000dm3 = 1m3 .
Worked Example 67: Ideal Gas
Question: A sample of gas occupies a volume of 20 dm3 , has a temperature of
280 K and has a pressure of 105 Pa. Calculate the number of moles of gas that are
present in the sample.
Answer
Step 1 : Convert all values into SI units
The only value that is not in SI units is volume. V = 0.02 m3 .
Step 2 : Write the equation for calculating the number of moles in a gas.
We know that pV = nRT
Therefore,
n=
pV
RT
Step 3 : Substitute values into the equation to calculate the number of moles
of the gas.
n=
105 × 0.02
2.1
=
= 0.0009moles
8.31 × 280
2326.8
Exercise: Using the combined gas law
1. An enclosed gas has a volume of 300 cm3 and a temperature of 300 K. The
pressure of the gas is 50 kPa. Calculate the number of moles of gas that are
present in the container.
2. What pressure will 3 mol gaseous nitrogen exert if it is pumped into a container
that has a volume of 25 dm3 at a temperature of 29 0 C?
3. The volume of air inside a tyre is 19 litres and the temperature is 290 K. You
check the pressure of your tyres and find that the pressure is 190 kPa. How
many moles of air are present in the tyre?
4. Compressed carbon dioxide is contained within a gas cylinder at a pressure of
700 kPa. The temperature of the gas in the cylinder is 310 K and the number
of moles of gas is 13 moles carbon dioxide. What is the volume of the gas
inside?
13.7
Molar concentrations in liquids
A typical solution is made by dissolving some solid substance in a liquid. The amount of substance
that is dissolved in a given volume of liquid is known as the concentration of the liquid.
Mathematically, concentration (C) is defined as moles of solute (n) per unit volume (V) of
solution.
247
13.7
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
C=
n
V
For this equation, the units for volume are dm3 . Therefore, the unit of concentration is mol.dm−3 .
When concentration is expressed in mol.dm−3 it is known as the molarity (M) of the solution.
Molarity is the most common expression for concentration.
Definition: Concentration
Concentration is a measure of the amount of solute that is dissolved in a given volume of
liquid. It is measured in mol.dm−3 . Another term that is used for concentration is molarity
(M)
Worked Example 68: Concentration Calculations 1
Question: If 3.5 g of sodium hydroxide (NaOH) is dissolved in 2.5 dm3 of water,
what is the concentration of the solution in mol.dm−3 ?
Answer
Step 1 : Convert the mass of NaOH into moles
m
3.5
=
= 0.0875mol
M
40
Step 2 : Calculate the concentration of the solution.
n=
C=
n
0.0875
=
= 0.035
V
2.5
The concentration of the solution is 0.035 mol.dm−3 or 0.035 M
Worked Example 69: Concentration Calculations 2
Question: You have a 1 dm3 container in which to prepare a solution of potassium
permanganate (KMnO4 ). What mass of KMnO4 is needed to make a solution with
a concentration of 0.2 M?
Answer
Step 1 : Calculate the number of moles of KMnO4 needed.
C=
n
V
therefore
n = C × V = 0.2 × 1 = 0.2mol
Step 2 : Convert the number of moles of KMnO4 to mass.
m = n × M = 0.2 × 158.04 = 31.61g
The mass of KMnO4 that is needed is 31.61 g.
248
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
13.8
Worked Example 70: Concentration Calculations 3
Question: How much sodium chloride (in g) will one need to prepare 500 cm3 of
solution with a concentration of 0.01 M?
Answer
Step 1 : Convert all quantities into the correct units for this equation.
V =
500
= 0.5dm3
1000
Step 2 : Calculate the number of moles of sodium chloride needed.
n = C × V = 0.01 × 0.5 = 0.005mol
Step 3 : Convert moles of KMnO4 to mass.
m = n × M = 0.005 × 58.45 = 0.29g
The mass of sodium chloride needed is 0.29 g
Exercise: Molarity and the concentration of solutions
1. 5.95g of potassium bromide was dissolved in 400cm3 of water. Calculate its
molarity.
2. 100 g of sodium chloride (NaCl) is dissolved in 450 cm3 of water.
(a)
(b)
(c)
(d)
How many moles of NaCl are present in solution?
What is the volume of water (in dm3 )?
Calculate the concentration of the solution.
What mass of sodium chloride would need to be added for the concentration to become 5.7 mol.dm−3 ?
3. What is the molarity of the solution formed by dissolving 80 g of sodium hydroxide (NaOH) in 500 cm3 of water?
4. What mass (g) of hydrogen chloride (HCl) is needed to make up 1000 cm3 of
a solution of concentration 1 mol.dm−3 ?
5. How many moles of H2 SO4 are there in 250 cm3 of a 0.8M sulphuric acid
solution? What mass of acid is in this solution?
13.8
Stoichiometric calculations
Stoichiometry is the study and calculation of relationships between reactants and products of
chemical reactions. Chapter 12 showed how to write balanced chemical equations. By knowing
the ratios of substances in a reaction, it is possible to use stoichiometry to calculate the amount
of reactants and products that are involved in the reaction. Some examples are shown below.
249
13.8
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
Worked Example 71: Stoichiometric calculation 1
Question: What volume of oxygen at S.T.P. is needed for the complete combustion
of 2dm3 of propane (C3 H8 )? (Hint: CO2 and H2 O are the products in this reaction)
Answer
Step 1 : Write a balanced equation for the reaction.
C3 H8 (g) + 5O2 (g) → 3CO2 (g) + 4H2 O(g)
Step 2 : Determine the ratio of oxygen to propane that is needed for the
reaction.
From the balanced equation, the ratio of oxygen to propane in the reactants is 5:1.
Step 3 : Determine the volume of oxygen needed for the reaction.
1 volume of propane needs 5 volumes of oxygen, therefore 2 dm3 of propane will
need 10 dm3 of oxygen for the reaction to proceed to completion.
Worked Example 72: Stoichiometric calculation 2
Question: What mass of iron (II) sulphide is formed when 5.6 g of iron is completely
reacted with sulfur?
Answer
Step 1 : Write a balanced chemical equation for the reaction.
F e(s) + S(s) → F eS(s)
Step 2 : Calculate the number of moles of iron that react.
n=
5.6
m
=
= 0.1mol
M
55.85
Step 3 : Determine the number of moles of FeS produced.
From the equation 1 mole of Fe gives 1 mole of FeS. Therefore, 0.1 moles of iron in
the reactants will give 0.1 moles of iron sulfide in the product.
Step 4 : Calculate the mass of iron sulfide formed
m = n × M = 0.1 × 87.911 = 8.79g
The mass of iron (II) sulfide that is produced during this reaction is 8.79 g.
Important:
A closer look at the previous worked example shows that 5.6 g of iron is needed to produce
8.79 g of iron (II) sulphide. The amount of sulfur that is needed in the reactants is 3.2
g. What would happen if the amount of sulfur in the reactants was increased to 6.4 g but
the amount of iron was still 5.6 g? Would more FeS be produced? In fact, the amount
of iron(II) sulfide produced remains the same. No matter how much sulfur is added to the
system, the amount of iron (II) sulfide will not increase because there is not enough iron
to react with the additional sulfur in the reactants to produce more FeS. When all the iron
is used up the reaction stops. In this example, the iron is called the limiting reagent.
Because there is more sulfur than can be used up in the reaction, it is called the excess
reagent.
250
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
Worked Example 73: Industrial reaction to produce fertiliser
Question: Sulfuric acid (H2 SO4 ) reacts with ammonia (NH3 ) to produce the fertiliser ammonium sulphate ((NH4 )2 SO4 ) according to the following equation:
H2 SO4 (aq) + 2N H3 (g) → (N H4 )2 SO4 (aq)
What is the maximum mass of ammonium sulphate that can be obtained from 2.0
kg of sulfuric acid and 1.0 kg of ammonia?
Answer
Step 1 : Convert the mass of sulfuric acid and ammonia into moles
n(H2 SO4 ) =
2000g
m
=
= 20.39mol
M
98.078g/mol
n(N H3 ) =
1000g
= 58.72mol
17.03g/mol
Step 2 : Use the balanced equation to determine which of the reactants is
limiting.
From the balanced chemical equation, 1 mole of H2 SO4 reacts with 2 moles of NH3
to give 1 mole of (NH4 )2 SO4 . Therefore 20.39 moles of H2 SO4 need to react with
40.78 moles of NH3 . In this example, NH3 is in excess and H2 SO4 is the limiting
reagent.
Step 3 : Calculate the maximum amount of ammonium sulphate that can be
produced
Again from the equation, the mole ratio of H2 SO4 in the reactants to (NH4 )2 SO4
in the product is 1:1. Therefore, 20.39 moles of H2 SO4 will produce 20.39 moles of
(NH4 )2 SO4 .
The maximum mass of ammonium sulphate that can be produced is calculated as
follows:
m = n × M = 20.41mol × 132g/mol = 2694g
The maximum amount of ammonium sulphate that can be produced is 2.694 kg.
Exercise: Stoichiometry
1. Diborane, B2 H6 , was once considered for use as a rocket fuel. The combustion
reaction for diborane is:
B2 H6 (g) + 3O2 (l) → 2HBO2 (g) + 2H2 O(l)
If we react 2.37 grams of diborane, how many grams of water would we expect
to produce?
2. Sodium azide is a commonly used compound in airbags. When triggered, it
has the following reaction:
2N aN3 (s) → 2N a(s) + 3N2 (g)
If 23.4 grams of sodium azide are reacted, how many moles of nitrogen gas
would we expect to produce?
251
13.8
13.9
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
3. Photosynthesis is a chemical reaction that is vital to the existence of life on
Earth. During photosynthesis, plants and bacteria convert carbon dioxide gas,
liquid water, and light into glucose (C6 H12 O6 ) and oxygen gas.
(a) Write down the equation for the photosynthesis reaction.
(b) Balance the equation.
(c) If 3 moles of carbon dioxide are used up in the photosynthesis reaction,
what mass of glucose will be produced?
13.9
Summary
• It is important to be able to quantify the changes that take place during a chemical
reaction.
• The mole (n) is a SI unit that is used to describe an amount of substance that contains
the same number of particles as there are atoms in 12 g of carbon.
• The number of particles in a mole is called the Avogadro constant and its value is 6.023
× 1023 . These particles could be atoms, molecules or other particle units, depending on
the substance.
• The molar mass (M) is the mass of one mole of a substance and is measured in grams
per mole or g.mol−1 . The numerical value of an element’s molar mass is the same as its
relative atomic mass. For a compound, the molar mass has the same numerical value as
the molecular mass of that compound.
• The relationship between moles (n), mass in grams (m) and molar mass (M) is defined by
the following equation:
m
n=
M
• In a balanced chemical equation, the number in front of the chemical symbols describes
the mole ratio of the reactants and products.
• The empirical formula of a compound is an expression of the relative number of each
type of atom in the compound.
• The molecular formula of a compound describes the actual number of atoms of each
element in a molecule of the compound.
• The formula of a substance can be used to calculate the percentage by mass that each
element contributes to the compound.
• The percentage composition of a substance can be used to deduce its chemical formula.
• One mole of gas occupies a volume of 22.4 dm3 .
• The concentration of a solution can be calculated using the following equation,
C=
n
V
where C is the concentration (in mol.dm−3 ), n is the number of moles of solute dissolved
in the solution and V is the volume of the solution (in dm3 ).
• Molarity is a measure of the concentration of a solution, and its units are mol.dm−3 .
• Stoichiometry, the study of the relationships between reactants and products, can be
used to determine the quantities of reactants and products that are involved in chemical
reactions.
252
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
13.9
• A limiting reagent is the chemical that is used up first in a reaction, and which therefore
determines how far the reaction will go before it has to stop.
• An excess reagent is a chemical that is in greater quantity than the limiting reagent in
the reaction. Once the reaction is complete, there will still be some of this chemical that
has not been used up.
Exercise: Summary Exercise
1. Write only the word/term for each of the following descriptions:
(a) the mass of one mole of a substance
(b) the number of particles in one mole of a substance
2. Multiple choice: Choose the one correct answer from those given.
A 5 g of magnesium chloride is formed as the product of a chemical reaction.
Select the true statement from the answers below:
i. 0.08 moles of magnesium chloride are formed in the reaction
ii. the number of atoms of Cl in the product is approximately 0.6023 ×
1023
iii. the number of atoms of Mg is 0.05
iv. the atomic ratio of Mg atoms to Cl atoms in the product is 1:1
B 2 moles of oxygen gas react with hydrogen. What is the mass of oxygen
in the reactants?
i. 32 g
ii. 0.125 g
iii. 64 g
iv. 0.063 g
C In the compound potassium sulphate (K2 SO4 ), oxygen makes up x% of
the mass of the compound. x = ...
i. 36.8
ii. 9.2
iii. 4
iv. 18.3
D The molarity of a 150 cm3 solution, containing 5 g of NaCl is...
i. 0.09 M
ii. 5.7 × 10−4 M
iii. 0.57 M
iv. 0.03 M
3. 300 cm3 of a 0.1 mol.dm−3 solution of sulfuric acid is added to 200 cm3 of a
0.5 mol.dm−3 solution of sodium hydroxide.
a Write down a balanced equation for the reaction which takes place when
these two solutions are mixed.
b Calculate the number of moles of sulfuric acid which were added to the
sodium hydroxide solution.
c Is the number of moles of sulfuric acid enough to fully neutralise the sodium
hydroxide solution? Support your answer by showing all relevant calculations.
(IEB Paper 2 2004)
4. Ozone (O3 ) reacts with nitrogen monoxide gas (NO) to produce NO2 gas. The
NO gas forms largely as a result of emissions from the exhausts of motor vehicles
and from certain jet planes. The NO2 gas also causes the brown smog (smoke
and fog), which is seen over most urban areas. This gas is also harmful to
humans, as it causes breathing (respiratory) problems. The following equation
indicates the reaction between ozone and nitrogen monoxide:
253
13.9
CHAPTER 13. QUANTITATIVE ASPECTS OF CHEMICAL CHANGE - GRADE 11
O3 (g) + N O(g) → O2 (g) + N O2 (g)
In one such reaction 0.74 g of O3 reacts with 0.67 g NO.
a Calculate the number of moles of O3 and of NO present at the start of the
reaction.
b Identify the limiting reagent in the reaction and justify your answer.
c Calculate the mass of NO2 produced from the reaction.
(DoE Exemplar Paper 2, 2007)
5. A learner is asked to make 200 cm3 of sodium hydroxide (NaOH) solution of
concentration 0.5 mol.dm−3 .
a Determine the mass of sodium hydroxide pellets he needs to use to do this.
b Using an accurate balance the learner accurately measures the correct mass
of the NaOH pellets. To the pellets he now adds exactly 200 cm3 of pure
water. Will his solution have the correct concentration? Explain your
answer.
300 cm3 of a 0.1 mol.dm−3 solution of sulfuric acid (H2 SO4 ) is added to
200 cm3 of a 0.5 mol.dm−3 solution of NaOH at 250 C.
c Write down a balanced equation for the reaction which takes place when
these two solutions are mixed.
d Calculate the number of moles of H2 SO4 which were added to the NaOH
solution.
e Is the number of moles of H2 SO4 calculated in the previous question
enough to fully neutralise the NaOH solution? Support your answer by
showing all the relevant calculations.
(IEB Paper 2, 2004)
254
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