PHYSICAL CHEMISTRY IN BRIEF

466 Pages·02.445 MB·English

by  Anatol Malijevsk,Josef P. Nov´ak,Stanislav Lab´ık

PHYSICAL CHEMISTRY
IN BRIEF
Prof. Ing. Anatol Malijevsk´y, CSc., et al.
(September 30, 2005)
Institute of Chemical Technology, Prague
Faculty of Chemical Engineering
Annotation
The Physical Chemistry In Brief offers a digest of all major formulas, terms and definitions
needed for an understanding of the subject. They are illustrated by schematic figures, simple
worked-out examples, and a short accompanying text. The concept of the book makes it
different from common university or physical chemistry textbooks. In terms of contents, the
Physical Chemistry In Brief embraces the fundamental course in physical chemistry as taught
at the Institute of Chemical Technology, Prague, i.e. the state behaviour of gases, liquids,
solid substances and their mixtures, the fundamentals of chemical thermodynamics, phase
equilibrium, chemical equilibrium, the fundamentals of electrochemistry, chemical kinetics and
thekinetics of transportprocesses, colloidchemistry, and partlyalsothe structureofsubstances
and spectra. The reader is assumed to have a reasonable knowledge of mathematics at the level
of secondary school, and of the fundamentals of mathematics as taught at the university level.
3
Authors
Prof. Ing. Josef P. Nov´ak, CSc.
Prof. Ing. Stanislav Lab´ık, CSc.
Ing. Ivona Malijevsk´a, CSc.
4
Introduction
Dear students,
Physical Chemistry is generally considered to be a difficult subject. We thought long and
hard about ways to make its study easier, and this text is the result of our endeavors. The
book provides accurate definitions of terms, definitions of major quantities, and a number of
relations including specification of the conditions under which they are valid. It also contains
a number of schematic figures and examples that clarify the accompanying text. The reader
will not find any derivations in this book, although frequent references are made to the initial
formulas from which the respective relations are obtained.
In terms of contents, we followed the syllabi of “Physical Chemistry I” and “Physical Chem-
istry II” as taught at the Institute of Chemical Technology (ICT), Prague up to 2005. However
the extent of this work is a little broader as our objective was to cover all the major fields of
Physical Chemistry.
This publication is not intended to substitute for any textbooks or books of examples. Yet
we believe that it will prove useful during revision lessons leading up to an exam in Physical
Chemistry or prior to the final (state) examination, as well as during postgraduate studies.
Even experts in Physical Chemistry and related fields may find this work to be useful as a
reference.
Physical Chemistry In Brief has two predecessors, “Breviary of Physical Chemistry I” and
“Breviary of Physical Chemistry II”. Since the first issue in 1993, the texts have been revised
and re-published many times, always selling out. Over the course of time we have thus striven
to eliminate both factual and formal errors, as well as to review and rewrite the less accessible
passages pointed out to us by both students and colleagues in the Department of Physical
Chemistry. Finally, asthenumberofforeignstudentscomingtostudyatourinstitutecontinues
to grow, we decided to give them a proven tool written in the English language. This text is the
result of these efforts. A number of changes have been made to the text and the contents have
been partially extended. We will be grateful to any reader able to detect and inform us of any
errors in our work. Finally, the authors would like to express their thanks to Mrs. Flemrov´a
for her substantial investment in translating this text.
CONTENTS [CONTENTS] 5
Contents
1 Basic terms 24
1.1 Thermodynamic system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.1.1 Isolated system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.1.2 Closed system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.1.3 Open system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.1.4 Phase, homogeneous and heterogeneous systems . . . . . . . . . . . . . . 25
1.2 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.2.1 Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.2.2 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.3 Thermodynamic quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.3.1 Intensive and extensive thermodynamic quantities . . . . . . . . . . . . . 28
1.4 The state of a system and its changes . . . . . . . . . . . . . . . . . . . . . . . . 29
1.4.1 The state of thermodynamic equilibrium . . . . . . . . . . . . . . . . . . 29
1.4.2 System’s transition to the state of equilibrium . . . . . . . . . . . . . . . 30
1.4.3 Thermodynamic process . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.4.4 Reversible and irreversible processes . . . . . . . . . . . . . . . . . . . . . 31
1.4.5 Processes at a constant quantity . . . . . . . . . . . . . . . . . . . . . . . 31
1.4.6 Cyclic process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.5 Some basic and derived quantities . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.5.1 Mass m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.5.2 Amount of substance n . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.5.3 Molar mass M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
CONTENTS [CONTENTS] 6
1.5.4 Absolute temperature T . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.5.5 Pressure p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.5.6 Volume V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.6 Pure substance and mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1.6.1 Mole fraction of the ith component x . . . . . . . . . . . . . . . . . . . . 36
i
1.6.2 Mass fraction w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
i
1.6.3 Volume fraction φ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
i
1.6.4 Amount-of-substance concentration c . . . . . . . . . . . . . . . . . . . . 40
i
1.6.5 Molality m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
i
2 State behaviour 42
2.1 Major terms, quantities and symbols . . . . . . . . . . . . . . . . . . . . . . . . 43
2.1.1 Molar volume V and amount-of-substance (or amount) density c . . . . 43
m
2.1.2 Specific volume v and density ρ . . . . . . . . . . . . . . . . . . . . . . . 43
2.1.3 Compressibility factor z . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.1.4 Critical point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.1.5 Reduced quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.1.6 Coefficient of thermal expansion α . . . . . . . . . . . . . . . . . . . . . 45
p
2.1.7 Coefficient of isothermal compressibility β . . . . . . . . . . . . . . . . . 47
T
2.1.8 Partial pressure p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
i
2.2 Equations of state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.1 Concept of the equation of state . . . . . . . . . . . . . . . . . . . . . . . 48
2.2.2 Equation of state of an ideal gas . . . . . . . . . . . . . . . . . . . . . . 48
2.2.3 Virial expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.2.4 Boyle temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.2.5 Pressure virial expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.2.6 Van der Waals equation of state . . . . . . . . . . . . . . . . . . . . . . . 51
2.2.7 Redlich-Kwong equation of state . . . . . . . . . . . . . . . . . . . . . . 52
2.2.8 Benedict, Webb and Rubin equation of state . . . . . . . . . . . . . . . . 53
2.2.9 Theorem of corresponding states . . . . . . . . . . . . . . . . . . . . . . 53
2.2.10 Application of equations of state . . . . . . . . . . . . . . . . . . . . . . 54
2.3 State behaviour of liquids and solids . . . . . . . . . . . . . . . . . . . . . . . . 56
CONTENTS [CONTENTS] 7
2.3.1 Description of state behaviour using the coefficients of thermal expansion
α and isothermal compressibility β . . . . . . . . . . . . . . . . . . . . . 56
p T
2.3.2 Rackett equation of state . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.3.3 Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.4 State behaviour of mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.4.1 Dalton’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.4.2 Amagat’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.4.3 Ideal mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.4.4 Pseudocritical quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.4.5 Equations of state for mixtures . . . . . . . . . . . . . . . . . . . . . . . 61
2.4.6 Liquid and solid mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3 Fundamentals of thermodynamics 63
3.1 Basic postulates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.1.1 The zeroth law of thermodynamics . . . . . . . . . . . . . . . . . . . . . 63
3.1.2 The first law of thermodynamics . . . . . . . . . . . . . . . . . . . . . . 64
3.1.3 Second law of thermodynamics . . . . . . . . . . . . . . . . . . . . . . . 65
3.1.4 The third law of thermodynamics . . . . . . . . . . . . . . . . . . . . . . 66
3.1.4.1 Impossibility to attain a temperature of 0K . . . . . . . . . . . 67
3.2 Definition of fundamental thermodynamic quantities . . . . . . . . . . . . . . . 68
3.2.1 Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2.2 Helmholtz energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2.3 Gibbs energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.2.4 Heat capacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.2.5 Molar thermodynamic functions . . . . . . . . . . . . . . . . . . . . . . . 74
3.2.6 Fugacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.2.7 Fugacity coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.2.8 Absolute and relative thermodynamic quantities . . . . . . . . . . . . . 75
3.3 Some properties of the total differential . . . . . . . . . . . . . . . . . . . . . . . 77
3.3.1 Total differential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.3.2 Total differential and state functions . . . . . . . . . . . . . . . . . . . . 79
3.3.3 Total differential of the product and ratio of two functions . . . . . . . . 81
3.3.4 Integration of the total differential . . . . . . . . . . . . . . . . . . . . . 81
CONTENTS [CONTENTS] 8
3.4 Combined formulations of the first and second laws of thermodynamics . . . . . 83
3.4.1 Gibbs equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.4.2 Derivatives of U, H, F, and G with respect to natural variables . . . . . 83
3.4.3 Maxwell relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.4.4 Total differential of entropy as a function of T, V and T, p . . . . . . . . 85
3.4.5 Conversion from natural variables to variables T, V or T, p . . . . . . . . 85
3.4.6 Conditions of thermodynamic equilibrium . . . . . . . . . . . . . . . . . 87
3.5 Changes of thermodynamic quantities . . . . . . . . . . . . . . . . . . . . . . . . 90
3.5.1 Heat capacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.5.1.1 Temperature dependence . . . . . . . . . . . . . . . . . . . . . . 90
3.5.1.2 C dependence on pressure . . . . . . . . . . . . . . . . . . . . 91
p
3.5.1.3 C dependence on volume . . . . . . . . . . . . . . . . . . . . . 91
V
3.5.1.4 Relations between heat capacities . . . . . . . . . . . . . . . . . 91
3.5.1.5 Ideal gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.5.2 Internal energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.5.2.1 Temperature and volume dependence for a homogeneous system 92
3.5.2.2 Ideal gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.5.2.3 Changes at phase transitions . . . . . . . . . . . . . . . . . . . 93
3.5.3 Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.5.3.1 Temperature and pressure dependence for a homogeneous system 94
3.5.3.2 Ideal gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.5.3.3 Changes at phase transitions . . . . . . . . . . . . . . . . . . . 95
3.5.4 Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.5.4.1 Temperature and volume dependence for a homogeneous system 96
3.5.4.2 Temperature and pressure dependence for a homogeneous system 97
3.5.4.3 Ideal gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.5.4.4 Changes at phase transitions . . . . . . . . . . . . . . . . . . . 98
3.5.5 Absolute entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.5.6 Helmholtz energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.5.6.1 Dependence on temperature and volume . . . . . . . . . . . . . 101
3.5.6.2 Changes at phase transitions . . . . . . . . . . . . . . . . . . . 102
3.5.7 Gibbs energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.5.7.1 Temperature and pressure dependence . . . . . . . . . . . . . . 103
CONTENTS [CONTENTS] 9
3.5.7.2 Changes at phase transitions . . . . . . . . . . . . . . . . . . . 103
3.5.8 Fugacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.5.8.1 Ideal gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.5.8.2 Changes at phase transitions . . . . . . . . . . . . . . . . . . . 104
3.5.9 Changes of thermodynamic quantities during irreversible processes . . . . 104
4 Application of thermodynamics 107
4.1 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.1.1 Reversible volume work . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.1.2 Irreversible volume work . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.1.3 Other kinds of work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.1.4 Shaft work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.2 Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.2.1 Adiabatic process—Poisson’s equations . . . . . . . . . . . . . . . . . . . 112
4.2.2 Irreversible adiabatic process . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.3 Heat engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.3.1 The Carnot heat engine . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.3.2 Cooling engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.3.3 Heat engine with steady flow of substance . . . . . . . . . . . . . . . . . 120
4.3.4 The Joule-Thomson effect . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.3.5 The Joule-Thomson coefficient . . . . . . . . . . . . . . . . . . . . . . . . 123
4.3.6 Inversion temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5 Thermochemistry 127
5.1 Heat of reaction and thermodynamic quantities of reaction . . . . . . . . . . . . 128
5.1.1 Linear combination of chemical reactions . . . . . . . . . . . . . . . . . . 129
5.1.2 Hess’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.2 Standard reaction enthalpy ∆ H◦ . . . . . . . . . . . . . . . . . . . . . . . . . . 131
r
5.2.1 Standard enthalpy of formation ∆ H◦ . . . . . . . . . . . . . . . . . . . . 131
f
5.2.2 Standard enthalpy of combustion ∆ H◦ . . . . . . . . . . . . . . . . . . . 132
c
5.3 Kirchhoff’s law—dependence of the reaction enthalpy on temperature . . . . . . 134
5.4 Enthalpy balances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
5.4.1 Adiabatic temperature of reaction . . . . . . . . . . . . . . . . . . . . . . 137
CONTENTS [CONTENTS] 10
6 Thermodynamics of homogeneous mixtures 139
6.1 Ideal mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.1.1 General ideal mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.1.2 Ideal mixture of ideal gases . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.2 Integral quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.2.1 Mixing quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.2.2 Excess quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6.2.3 Heat of solution (integral) . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.2.3.1 Relations between the heat of solution and the enthalpy of mix-
ing for a binary mixture . . . . . . . . . . . . . . . . . . . . . . 146
6.3 Differential quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.3.1 Partial molar quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.3.2 Properties of partial molar quantities . . . . . . . . . . . . . . . . . . . . 148
6.3.2.1 Relations between system and partial molar quantities . . . . . 148
6.3.2.2 Relations between partial molar quantities . . . . . . . . . . . . 149
6.3.2.3 Partial molar quantities of an ideal mixture . . . . . . . . . . . 149
6.3.3 Determination of partial molar quantities . . . . . . . . . . . . . . . . . . 150
6.3.4 Excess partial molar quantities . . . . . . . . . . . . . . . . . . . . . . . 152
6.3.5 Differential heat of solution and dilution . . . . . . . . . . . . . . . . . . 153
6.4 Thermodynamics of an open system and the chemical potential . . . . . . . . . 155
6.4.1 Thermodynamic quantities in an open system . . . . . . . . . . . . . . . 155
6.4.2 Chemical potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.5 Fugacity and activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.5.1 Fugacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.5.2 Fugacity coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.5.3 Standard states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.5.4 Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
6.5.5 Activity coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6.5.5.1 Relation between γ[x] and γ . . . . . . . . . . . . . . . . . . . . 168
i i
6.5.5.2 Relation between the activity coefficient and the osmotic coef-
ficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.5.6 Dependence of the excess Gibbs energy and of the activity coefficients on
composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169