An Introduction to the Gas Phase

By (author) Claire Vallance

Publication date:

23 November 2017

Length of book:

58 pages

Publisher

Morgan & Claypool Publishers

Dimensions:

254x178mm
7x10"

ISBN-13: 9781681747378

BOOK DESCRIPTION
TABLE OF CONTENTS

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

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