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An Introduction to the Gas Phase is adapted from a set of lecture notes for a core first-year lecture course in physical chemistry taught at the University of Oxford. The book is intended to give a relatively concise introduction to the gas phase at a level suitable for any undergraduate scientist. After defining the gas phase, properties of gases such as temperature, pressure, and volume are discussed. The relationships between these properties are explained at a molecular level, and simple models are introduced that allow the various gas laws to be derived from first principles. Finally, the collisional behaviour of gases is used to explain a number of gas-phase phenomena, such as effusion, diffusion, and thermal conductivity.
1 Introduction 1
1.1 States of matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Characteristics of the gas phase . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Gases and vapours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Phase diagrams and phase transitions: under what conditions is a substance
a gas? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4.1 Constructing a phase diagram: the Clapeyron and Clausius-Clapeyron
equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Pressure and Temperature 7
2.1 Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Measurement of pressure . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 Thermal equilibrium and measurement of temperature . . . . . . . 12
3 Relationships between gas properties: the gas laws 14
3.1 The relationship between pressure and volume . . . . . . . . . . . . . . . . 14
3.2 The effect of temperature on pressure and volume . . . . . . . . . . . . . . 14
3.3 The effect of the amount of gas, n . . . . . . . . . . . . . . . . . . . . . . 15
3.4 Equation of state for an ideal gas . . . . . . . . . . . . . . . . . . . . . . . 16
4 Ideal gases and real gases 17
4.1 The ideal gas model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2 The compression factor, Z . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.3 Equations of state for real (non-ideal) gases . . . . . . . . . . . . . . . . . 19
5 A molecular perspective: the kinetic theory of gases and the molecular speed
distribution 22
5.1 Collisions with the container walls - determining pressure from molecular
speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.2 The Maxwell Boltzmann distribution revisited . . . . . . . . . . . . . . . . 25
5.3 Mean speed, most probable speed and root-mean-square speed of the particles
in a gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
ii
CONTENTS iii
6 Collision rates in gases 29
6.1 Collisions with the container walls . . . . . . . . . . . . . . . . . . . . . . 29
6.2 Collisions with other molecules . . . . . . . . . . . . . . . . . . . . . . . . 30
6.3 Mean free path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
6.4 Effusion and gas leaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
6.5 Molecular beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6.5.1 Effusive sources . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
6.5.2 Supersonic sources . . . . . . . . . . . . . . . . . . . . . . . . . . 35
7 Transport properties of gases 36
7.1 Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
7.2 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
7.3 Thermal conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
7.5 A simple derivation of the equipartition result for translational motion . . . 41
7.6 A more general derivation of the equipartition theorem . . . . . . . . . . . 42
Appendix: The Equipartition theorem