Energetics and Equilibria

1 Introduction 1
1.1 Books 2
2 The Second Law 3
2.1 Spontaneous processes 3
2.2 Energy minimization 4
2.3 The Second Law 5
2.4 Molecular basis of entropy 5
2.4.1 Energy levels 6
2.4.2 Ways of arranging things 6
2.4.3 The most probable distribution 7
2.4.4 The Boltzmann distribution 7
2.4.5 Entropy and distributions 8
2.4.6 Entropy as a microscopic property: summary 9
2.5 Classical view of entropy 10
2.6 The Second Law in action: how to make ice 10
2.6.1 Separating the Universe into the system and the surroundings 11
2.6.2 Water freezing 12
3 The First Law of Thermodynamics 15
3.1 What is heat? 15
3.2 What is work? 15
3.3 What is internal energy? 15
3.4 State functions and path functions 16
3.4.1 State functions 16
3.4.2 Path functions 17
3.5 Sign conventions 17
4 Gas expansions 19
4.1 Gas laws 19
4.2 How to think about a gas expansion 19
4.3 Expansion against constant external pressure 20
4.4 Expansion doing maximum work 21
4.4.1 Reversible and irreversible processes 21
4.4.2 Reversible isothermal expansion of an ideal gas 22
4.5 Heat changes in gas expansions 22
4.6 Entropy and the reversible heat 23
4.6.1 Entropy change in an isothermal expansion of an ideal
gas 23
5 Internal energy, enthalpy and heat capacity 25
5.1 Differential forms 25
5.2 Constant volume processes 25
5.2.1 Heat capacities 26
5.3 Constant pressure processes – enthalpy 27
5.3.1 Heat capacity at constant pressure 28
5.3.2 Variation of enthalpy with temperature 28
5.4 Measurement and tabulation of heat capacities 29
6 Measuring entropy 31
6.1 Absolute entropies 31
6.1.1 Practical evaluation of entropies 31
6.1.2 Converting entropies from one temperature to another 32
7 Gibbs energy 34
7.1 Gibbs energy and the Universal entropy 34
7.2 How the Gibbs energy varies with pressure and temperature 35
7.2.1 The Master Equations 35
7.2.2 Variation of G with p (and V), at constant T 36
7.2.3 Variation of G with T, at constant p 38
8 Chemical changes 39
8.1 The ∆
r symbol 39
8.2 Standard states and standard changes 39
8.3 Enthalpies of formation 40
8.4 Standard entropy and Gibbs energy changes for reactions 41
8.5 Variation of ∆
rH◦ with temperature 41
8.6 Variation of ∆
rS ◦ with temperature 42
9 Mixtures 43
9.1 The mixing of ideal gases 43
9.1.1 Partial pressures 43
9.1.2 Gibbs energy of the components in a mixture 44
9.2 Reacting mixtures 44
9.3 Chemical potential 45
9.3.1 The chemical potential of gases, solutions and solids 46
10 Equilibrium 48
10.1 Equilibrium constants 48
10.2 Condition for chemical equilibrium 49
10.3 Relation between ∆
rG◦ and the equilibrium constant 50
10.3.1 Equilibria involving solids 51
10.4 Interpretation of ∆rG◦ = −RT ln K 52
10.5 Influencing equilibrium 53
10.5.1 Le Chatelier’s principle 53
10.5.2 Changing concentration 54
10.5.3 Effect of temperature 54
10.5.4 Variation of equilibrium with pressure 57
11 Applications in biology 59
12 Electrochemistry 61
12.1 Cell conventions 62
12.1.1 Half-cell reactions and couples 62
12.1.2 The cell conventions 62
12.1.3 Shorthand for cells 62
12.1.4 Examples of using the cell conventions 63
12.2 Thermodynamic parameters from cell potentials 64
12.3 The Nernst equation 64
12.3.1 Chemical potentials and activities 64
12.3.2 Derivation of the Nernst equation 65
12.3.3 Nernst equation for half cells 66
12.4 Standard half-cell potentials 67
12.4.1 Tabulation of standard half-cell potentials 67
12.5 The spontaneous cell reaction 67
12.6 Types of half cells 68
12.6.1 Metal/metal ion 68
12.6.2 Gas/ion 69
12.6.3 Redox 69
12.6.4 Metal/insoluble salt/anion 69
12.6.5 Liquid junctions 70
12.7 Redox stability 70
12.8 Applications 72
12.8.1 Solubility product of AgI 72
12.8.2 Thermodynamic parameters of ions 72
12.8.3 Concentration cells 73
13 Appendix: available on www-teach.ch.cam.ac.uk 74
13.1 Partial derivatives 74
13.1.1 The Master Equations 74
13.1.2 Maxwell’s relations 76
13.2 More about ∆
r quantities 77
13.2.1 Variation of ∆
rH with temperature 77
13.2.2 Variation of ∆
rS with temperature 78
13.3 Relationship between ∆rG for the cell reaction and the cell EMF 78
13.3.1 Electrical work from a cell 78
13.3.2 Relation of the cell potential to ∆rGcell 79