# An Introduction to the Gas Phase

Claire Vallance

### Description

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.

Claire Vallance is a Professor of Physical Chemistry in the Department of Chemistry at the University of Oxford, and Tutorial Fellow in Physical Chemistry at Hertford College, Oxford. She grew up in the UK and New Zealand, and holds a BSc (hons) and PhD from the University of Canterbury (Christchurch, NZ). Her current research interests include chemical reaction dynamics, the use of optical microcavities in chemical sensing applications, and the development of spectroscopic techniques for use during cardiovascular surgery and neurosurgery. She has given lecture courses on chemical kinetics, properties of gases, symmetry and group theory, reaction dynamics, and astrochemistry, as well as numerous outreach and public-engagement lectures, and her tutorial teaching spans the breadth of physical chemistry. She is author of more than 90 journal articles, four book chapters, nine patents, an e-Textbook on Symmetry and Group Theory, the textbooks Astrochemistry: from the Big Bang to the Present Day, and An Introduction to Chemical Kinetics, and also co-edited the textbook Tutorials in Molecular Reaction Dynamics.

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

### Bibliographic

Paperback ISBN: 9780750328876

Ebook ISBN: 9781681746951

DOI: 10.1088/978-1-6817-4692-0

Publisher: Morgan & Claypool Publishers

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