- Title Pages
- Foreword
- Epigraph
- Preface
- Index of symbols
- Index of units-of-measure
- List of Tables
- 1 Systems and states
- 2 Work and energy
- 3 Temperature and heat
- 4 Thermodynamics and mathematics
- 5 The First Law of Thermodynamics
- 6 Enthalpy and thermochemistry
- 7 Ideal gas processes – and two ideal gas case studies too
- 8 Spontaneous changes
- 9 The Second Law of Thermodynamics
- 10 Clausius, Kelvin, Planck, Carathéodory and Carnot
- 11 Order, information and time
- 12 The Third Law of Thermodynamics
- 13 Free energy
- 14 Chemical equilibrium and chemical kinetics
- 15 Phase equilibria
- 16 Reactions in solution
- 17 Acids, bases and buffer solutions
- 18 Boiling points and melting points
- 19 Mixing and osmosis
- 20 Electrochemistry
- 21 Mathematical round up
- 22 From ideal to real
- 23 The biochemical standard state
- 24 The bioenergetics of living cells
- 25 Macromolecular conformations and interactions
- 26 Thermodynamics today – and tomorrow
- Glossary
- Bibliography
- Index

# Phase equilibria

# Phase equilibria

- Chapter:
- (p.467) 15 Phase equilibria
- Source:
- Modern Thermodynamics for Chemists and Biochemists
- Author(s):
### Dennis Sherwood

### Paul Dalby

- Publisher:
- Oxford University Press

This chapter extends the discussion of gas phase equilibria to phase equilibria. The central concept is the vapour pressure, and the key proof is that the criterion for phase equilibrium is the equality of the molar Gibbs free energies, or chemical potentials, of each phase. This then leads to the Clapeyron and Clausius-Clapeyron equations. A notable feature of this chapter is the discussion of non-ideal gases, answering the question “Given that, by definition, an ideal gas can never liquefy, what is it about a real gas that enables the gas to change phase into a liquid?”. A unique feature of this discussion is the rigorous analysis of the Gibbs free energy of a van der Waals gas under compression, and the proof of the ‘Maxwell construction’.

*Keywords:*
vapour pressure, phase change, solid, liquid, vapour, vaporisation, liquefaction, sublimation, melting, Clapeyron equation, Clausius-Clapeyron equation, ideal gas, real gas, van der Waals equation, critical temperature, Maxwell construction

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- Title Pages
- Foreword
- Epigraph
- Preface
- Index of symbols
- Index of units-of-measure
- List of Tables
- 1 Systems and states
- 2 Work and energy
- 3 Temperature and heat
- 4 Thermodynamics and mathematics
- 5 The First Law of Thermodynamics
- 6 Enthalpy and thermochemistry
- 7 Ideal gas processes – and two ideal gas case studies too
- 8 Spontaneous changes
- 9 The Second Law of Thermodynamics
- 10 Clausius, Kelvin, Planck, Carathéodory and Carnot
- 11 Order, information and time
- 12 The Third Law of Thermodynamics
- 13 Free energy
- 14 Chemical equilibrium and chemical kinetics
- 15 Phase equilibria
- 16 Reactions in solution
- 17 Acids, bases and buffer solutions
- 18 Boiling points and melting points
- 19 Mixing and osmosis
- 20 Electrochemistry
- 21 Mathematical round up
- 22 From ideal to real
- 23 The biochemical standard state
- 24 The bioenergetics of living cells
- 25 Macromolecular conformations and interactions
- 26 Thermodynamics today – and tomorrow
- Glossary
- Bibliography
- Index