Liquid-State Physical Chemistry E-Book

Gijsbertus de With

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 951

Veröffentlichungsjahr: 2013

Beschreibung

For many processes and applications in science and technology a basic knowledge of liquids and solutions is a must. Gaining a better understanding of the behavior and properties of pure liquids and solutions will help to improve many processes and to advance research in many different areas. This book provides a comprehensive, self-contained and integrated survey of this topic and is a must-have for many chemists, chemical engineers and material scientists, ranging from newcomers in the field to more experienced researchers. The author offers a clear, well-structured didactic approach and provides an overview of the most important types of liquids and solutions. Special topics include chemical reactions, surfaces and phase transitions. Suitable both for introductory as well as intermediate level as more advanced parts are clearly marked. Includes also problems and solutions.

Leseprobe

Table of Contents

Related Titles

Title page

Copyright page

Epigraph

Preface

Acknowledgments

List of Important Symbols and Abbreviations

1: Introduction

1.1 The Importance of Liquids

1.2 Solids, Gases, and Liquids

1.3 Outline and Approach

1.4 Notation

2: Basic Macroscopic and Microscopic Concepts: Thermodynamics, Classical, and Quantum Mechanics

2.1 Thermodynamics

2.2 Classical Mechanics

2.3 Quantum Concepts

2.4 Approximate Solutions

3: Basic Energetics: Intermolecular Interactions

3.1 Preliminaries

3.2 Electrostatic Interaction

3.3 Induction Interaction

3.4 Dispersion Interaction

3.5 The total Interaction

3.6 Model Potentials

3.7 Refinements

3.8 The Virial Theorem

4: Describing Liquids: Phenomenological Behavior

4.1 Phase Behavior

4.2 Equations of State

4.3 Corresponding States

5: The Transition from Microscopic to Macroscopic: Statistical Thermodynamics

5.1 Statistical Thermodynamics

5.2 Perfect Gases

5.3 The Semi-Classical Approximation

5.4 A Few General Aspects

5.5 Internal Contributions

5.6 Real Gases

6: Describing Liquids: Structure and Energetics

6.1 The Structure of Solids

6.2 The Meaning of Structure for Liquids

6.3 The Experimental Determination of g(r)

6.4 The Structure of Liquids

6.5 Energetics

6.6 The Potential of Mean Force

7: Modeling the Structure of Liquids: The Integral Equation Approach

7.1 The Vital Role of the Correlation Function

7.2 Integral Equations

7.3 Hard-Sphere Results

7.4 Perturbation Theory

7.5 Molecular Fluids

7.6 Final Remarks

8: Modeling the Structure of Liquids: The Physical Model Approach

8.1 Preliminaries

8.2 Cell Models

8.3 Hole Models

8.4 Significant Liquid Structures

8.5 Scaled-Particle Theory

9: Modeling the Structure of Liquids: The Simulation Approach

9.1 Preliminaries

9.2 Molecular Dynamics

9.3 The Monte Carlo Method

9.4 An Example: Ammonia

10: Describing the Behavior of Liquids: Polar Liquids

10.1 Basic Aspects

10.2 Towards a Microscopic Interpretation

10.3 Dielectric Behavior of Gases

10.4 Dielectric Behavior of Liquids

10.5 Water

11: Mixing Liquids: Molecular Solutions

11.1 Basic Aspects

11.2 Ideal and Real Solutions

11.3 Colligative Properties

11.4 Ideal Behavior in Statistical Terms

11.5 The Regular Solution Model

11.6 A Slightly Different Approach

11.7 The Activity Coefficient for Other Composition Measures

11.8 Empirical Improvements

11.9 Theoretical Improvements

12: Mixing Liquids: Ionic Solutions

12.1 Ions in Solution

12.2 The Born Model and Some Extensions

12.3 Hydration Structure

12.4 Strong and Weak Electrolytes

12.5 Debye–Hückel Theory

12.6 Structure and Thermodynamics

12.7 Conductivity

12.8 Conductivity Continued

12.9 Final Remarks

13: Mixing Liquids: Polymeric Solutions

13.1 Polymer Configurations

13.2 Real Chains in Solution

13.3 The Flory–Huggins Model

13.4 Solubility Theory

13.5 EoS Theories

13.6 The SAFT Approach

14: Some Special Topics: Reactions in Solutions

14.1 Kinetics Basics

14.2 Transition State Theory

14.3 Solvent Effects

14.4 Diffusion Control

14.5 Reaction Control

14.6 Neutral Molecules

14.7 Ionic Solutions

14.8 Final Remarks

15: Some Special Topics: Surfaces of Liquids and Solutions

15.1 Thermodynamics of Surfaces

15.2 One-Component Liquid Surfaces

15.3 Gradient Theory

15.4 Two-Component Liquid Surfaces

15.5 Statistics of Adsorption

15.6 Characteristic Adsorption Behavior

15.7 Final Remarks

16: Some Special Topics: Phase Transitions

16.1 Some General Considerations

16.2 Discontinuous Transitions

16.3 Continuous Transitions and the Critical Point

16.4 Scaling

16.5 Renormalization

16.6 Final Remarks

Appendix A: Units, Physical Constants, and Conversion Factors

Basic and Derived SI Units

Physical Constants

Conversion Factors for Non-SI Units

Prefixes

Greek Alphabet

Standard Values

Appendix B: Some Useful Mathematics

B.1 Symbols and Conventions

B.2 Partial Derivatives

B.3 Composite, Implicit, and Homogeneous Functions

B.4 Extremes and Lagrange Multipliers

B.5 Legendre Transforms

B.6 Matrices and Determinants

B.7 Change of Variables

B.8 Scalars, Vectors, and Tensors

B.9 Tensor Analysis

B.10 Calculus of Variations

B.11 Gamma Function

B.12 Dirac and Heaviside Function

B.13 Laplace and Fourier Transforms

B.14 Some Useful Integrals and Expansions

Appendix C: The Lattice Gas Model

C.1 The Lattice Gas Model

C.2 The Zeroth Approximation or Mean Field Solution

C.3 The First Approximation or Quasi-Chemical Solution

C.4 Final Remarks

Appendix D: Elements of Electrostatics

D.1 Coulomb, Gauss, Poisson, and Laplace

D.2 A Dielectric Sphere in a Dielectric Matrix

D.3 A Dipole in a Spherical Cavity

Appendix E: Data

Appendix F: Numerical Answers to Selected Problems

Index

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Author

Gijsbertus de With

Eindhoven Univ. of Technology

Dept. of Chemical Engineering and Chemistry

Den Dolech 2

5612AZ Eindhoven

The Netherlands

Cover: Martijn de With: Disordered order: an artist's impression of liquids, 2013.

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There are two quite different approaches to a theory of the liquid state which in fact complement each other.

Henry Eyring, page 141 in Liquids: Structure, Properties, Solid Interactions, T.J. Hughel ed., Elsevier Publ. Comp. Amsterdam, 1965.

Preface

For many processes and applications in science and technology a basic knowledge of liquids and solutions is a must. However, the usual curriculum in chemistry, physics, and materials science pays little or no attention to this subject. It must be said that many books have been written on liquids and solutions. However, only a few of them are suitable as an introduction (many of them are far too elaborate), and most of them have been published quite some time ago, apart from the relatively recent book by Barrat and Hansen (2005). In spite of my admiration for that book I feel that it is not suitable as an introduction for chemical engineers and chemists.

In the present book a basic but as far as possible self-contained and integrated treatment of the behavior of liquids and solutions and a few of their simplest applications is presented. After introducing the fundamentals required, we try to present an overview of models of liquids giving an approximately equal weight to pure liquids, simple solutions, be it non-electrolyte, electrolyte, or polymeric solutions. Thereafter, we deal with a few special topics: reactions in solutions, surfaces, and phase transitions. Obviously, not all topics can be treated and a certain initial acquaintance with several aspects of physical chemistry is probably an advantage for the reader.

A particular feature of this book is the attempt to provide a basic but balanced presentation of the various aspects relevant to liquids and solutions, using the regular solution concept as a guide. That does not imply that we “forget” more modern approaches, but the concept is useful as a guide, in particular for engineering applications. To clarify the authors' view on the subject a bit further, it may be useful to quote Henry Eyrings' statement, as printed on the title page, more fully:

There are two quite different approaches to a theory of the liquid state which in fact complement each other. In the deductive approach one proceeds as far as possible strictly mathematically, and when the complications cause this logical procedure to bog down, one resorts to some more or less defensible assumption such as Kirkwood's superposition principle. In the other approach one struggles to find a physical model of the liquid state which is as faithful to reality as can be devised and yet be solvable. The solution of the model may then proceed with considerable rigor. There are advantages and disadvantages to both procedures. In fact, either method expertly enough executed will solve the problem.

Although rigorous approaches have advanced considerably since the time this statement was made, the essence of this remark is still to the point in our view, in spite of the rebuttal by Stuart Rice:

The second approach mentioned by professor Eyring depends on our ability to make a very accurate guess about the structure and proper parameterization of the model or models chosen. It is the adequacy of our guesses as representations of the real liquid which I question.

There is no doubt that rigorous approaches are important, much more so than in the time Eyring made his remark but, in our opinion, understanding is still very much served by using as simple as possible models.

The whole of topics the presented is conveniently described as physical chemistry or the chemical physics1) of liquids and solutions: it describes the physico-chemical behavior of liquids and solutions with applications to engineering problems and processes. Unfortunately, this description is wide, in fact too wide, and we have to limit ourselves to those topics that are most relevant to chemical engineers and chemists. This implies that we do not deal systematically with quantum liquids, molten salts, or liquid metals. Obviously, it is impossible to reflect these considerations exactly in any title so that we have chosen for a brief one, trusting that potential users will read this preface (and the introduction) so that they know what to expect. For brevity, therefore, we refer to the field as liquid-state physical chemistry.

We pay quite some attention to physical models since, despite all developments in simulations, they are rather useful for providing a qualitative understanding of molecular liquids and solutions. Moreover, they form the basis for a description of the behavior of polymer solutions as presently researched, and last – but not least – they provide to a considerable extent solvable models and therefore have a substantial pedagogical value. Whilst, admittedly, this approach may be characterized by some as “old-fashioned,” in my opinion it is rather useful.

This book grew out of a course on the behavior of liquids and solutions, which contained already all the essential ingredients. This course, which was conducted at the Department of Chemical Engineering and Chemistry at Eindhoven University of Technology, originated from a total revision of the curriculum some 10 years ago and the introduction of liquid-state physical chemistry (or as said, equivalently, liquid-state chemical physics) some seven years ago. The overall set-up as given here has evolved during the last few years, and hopefully both the balance in topics and their presentation is improved. I am obliged to our students and instructors who have followed and used this course and have provided many useful remarks. In particular, I wish to thank my colleagues Dr Paul van der Varst, Dr Jozua Laven, and Dr Frank Peters for their careful reading of, and commenting on, several parts of the manuscript, and their discussions on many of the topics covered. Hopefully, this has led to an improvement in the presentation. I realize that a significant part of writing a book is usually done outside office hours, and this inevitably interferes considerably with one's domestic life. This text is no exception: for my wife, this is the second experience along this line, and I hope that this second book has “removed” less attention than the first. I am, therefore, indebted to my wife Ada for her patience and forbearance. Finally, I would like to thank Dr Martin Graf-Utzmann (Wiley-VCH, publisher) and Mrs Bernadette Cabo (Toppan Best-set Premedia Limited, typesetter) for all their efforts during the production of this book.

Obviously, the border between various classical disciplines is fading out nowadays. Consequently, it is hoped that these notes are useful not only for the original target audience, chemists, and chemical engineers, but also for materials scientists, mechanical engineers, physicists, and the like. Finally, we fear that the text will not be free from errors, and these are our responsibility. Hence, any comments, corrections, or indications of omissions will be appreciated.

Gijsbertus de With

January 2013

Note

1) I refer here to the preface of Introduction to Chemical Physics by J.C. Slater (1939), where he states: “It is probably unfortunate that physics and chemistry were ever separated. Chemistry is the science of atoms and the way they combine. Physics deals with the interatomic forces and with the large-scale properties of matter resulting from those forces. … A wide range of study is common to both subjects. The sooner we realize this, the better”.

Acknowledgments

Wiley-VCH and the author have attempted to trace the copyright holders of all material from various websites, journals, or books reproduced in this publication to obtain permission to reproduce this material, and apologize herewith to copyright holders if permission to publish in this form has not been obtained.

Fig. 1.4a: Courtesy of Oak Ridge National Laboratory, U.S. Dept. of Energy: http://www.ornl.gov/info/ornlreview/v34_2_01/shrinking.htm

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Fig. 13.7: Reprinted from E.F. Casassa (1976), J. Polymer Sci. Part C: Polymer Symposia, 54, 53. Copyright 1976 Wiley. This material is reproduced with permission of John Wiley & Sons. Inc.

Fig. 13.8a: Reprinted with permission from P.J. Flory (1970), Disc. Far. Soc., 49, 7 (fig. 1). Copyright 1970 Royal Society of Chemistry.

Fig. 13.8b: Reprinted with permission from I.C. Sanchez, R.H. Lacombe (1978), Macromolecules, 11, 1145 (fig. 6). Copyright 1978 American Chemical Society.

Fig. 13.9: Reprinted from H. Xie, E. Nies, A. Stroeks, R. Simha (1992), Pol. Eng. Sci., 32, 1654 (fig. 3 and fig. 9). Copyright 1992 John Wiley & Sons.

Fig. 13.10a: Reprinted from C.S. Wu, Y.P. Chen Y.P. (1994), Fluid Phase Equilibria, 100, 103 (fig. 4), with permission from Elsevier.

Fig. 13.10b: Reprinted with permission from I.G. Economou (2002), Ind. Eng. Chem. Res., 41, 953 (fig. 5). Copyright 2002 American Chemical Society.

Fig. 13.11a: Reprinted with permission from J. Gross, G. Sadowski (2001), Ind. Eng. Chem. Res., 40, 1244 (fig. 3). Copyright 2001 American Chemical Society.

Fig. 13.11b: Reprinted from N. von Solms et al. (2006), Fluid Phase Equilibria 241, 344 (fig. 1), with permission from Elsevier.

Fig. 14.1: Reprinted from Physical Chemistry, 3rd ed., by R.J. Silbey, R.A. Alberty, J. Wiley & Sons, NY 2001 (fig. 19.2, page 709). This material is reproduced with permission of John Wiley & Sons. Inc.

Fig. 14.4: Reprinted from The Theory of Rate Processes, by S. Glasstone, K.J. Laidler and H. Eyring, McGraw-Hill, NY 1941 (fig. 105 and fig. 106, page 420), with permission of McGraw-Hill Higher Education.

Fig. 14.6: Reprinted from The Theory of Rate Processes, by S. Glasstone, K.J. Laidler and H. Eyring, McGraw-Hill, NY 1941 (fig. 108, page 429 and fig. 109, page 431), with permission of McGraw-Hill Higher Education.

Fig. 15.4: Reprinted with permission from R.F. Crul, K. Pitzer (1958), Ind. Eng. Chem., 50, 265 (fig. 4). Copyright 1958 American Chemical Society.

Fig. 16.3: This image is from the ChemEd DL video on- Critical Point of Benzene. Video from JCE Web Software, Chemistry Comes Alive: Copyright ACS Division of Chemical Education, Inc. Used with permission. http://www.jce.divched.org/

Fig. 16.6: Reprinted with permission from P. Heller (1967), Rep. Prog. Phys., 30, 731 (fig. 10). Copyright 1967 IOP Science.

Fig. 16.7: Reprinted with permission from P. Heller (1967), Rep. Prog. Phys., 30, 731 (fig. 18). Copyright 1967 IOP Science.

Fig. 16.11: Reprinted from H.E. Stanley (1971), Introduction to Phase Transistions and Critical Phenomena, Oxford University Press (fig. 1.5, page 7), with permission from Oxford University Press, USA.

Fig. 16.12: This image is used with permission from M.R. Foster from the percolation article on his website: http://philosophy.wisc.edu/forster/Percolation.pdf

Fig. App. C2: Reprinted from Statististical Mechanics and Dynamics, 2nd ed., by H. Eyring, D. Henderson, B.J. Stover, E. M. Eyring, Wiley-Interscience, Chichester 1982 (fig. 2, page 474 and fig. 1, page 473). This material is reproduced with permission of John Wiley & Sons Inc.

List of Important Symbols and Abbreviations

(X)dimension dependent on property, (−) dimensionless propertyΦpotential energy (J)Ξgrand partition function (−)Ψwave function (−)Ωexternal potential energy (J) grand potential (J)Λthermal wave length (m)αconstant [X] activity coefficient [−] thermal expansion coefficient (K−1) polarizability (C2 m2 J−1)βconstant (X) 1/kT (J−1) activity coefficient (−)γactivity coefficient (−)δsolubility parameter (MPa1/2) Dirac delta function (−)εsmall scalar (−) energy (J)η(bulk) viscosity (Pa·s)κinverse Debye length (m−1) compressibility (m2 N−1)λparameter (X) wave length (m)μdipole moment (C m)νfrequency (s−1)ρnumber or mass density (m−3 or kg m−3) radius of curvature (m)ρ′mass density (kg m−3)σ(hard sphere) diameter (m)τcharacteristic time (s)ϕ(pair) potential energy (J) electrical potential (V m−1) volume fraction (−)χFlory parameter (−)ωcircular frequency (s−1)Eelectric field (V m−1)Fforce (N)Qquadrupole moment (C m2)eunit vector (m)fforce (N)pgeneralized momentum (X)qgeneralized coordinate (X)rcoordinate (m)udisplacement (m)vvelocity (m s−1)xcoordinate (m)Aarea (m2) generalized force (X) constant (X)Bconstant (X)Bivirial coefficients (X)Cconstant (X)Ddiffusivity (m2 s–1)Eenergy (J) electric field (V m−1)FHelmholtz energy (J) force (N) Faraday constant (C mol−1)GGibbs energy (J)Henthalpy (J)Imoment of inertia (kg m2)Kequilibrium constant (X)Llength (m)Nnumber of molecules (particles)NAAvogadro's number (mol−1)Ppressure (MPa) probability (−) polarization (m3)Qconfiguration integral (−)Rgas constant (J K−1 mol−1) radius (m) distance (m)Sentropy (J K−1)Tkinetic energy (J) temperature (K)U(internal) energy (J)Vpotential energy (J) volume (m3)Wwork (J)Zcanonical partition function (−)ageneralized displacement (X) constant (X)bsecond virial coefficient (m3) constant (X)cconstant (X) inverse spring constant (compliance) (m N−1)eunit charge (C)f(volume) fraction (−) specific Helmholtz energy (J kg−1) force (N) spring constant (N m−1) rate constant (X)gspecific Gibbs energy (J kg−1) density of states (J−1)jflux (s−1 m−2)kBoltzmann constant (J K−1) spring constant (N−1) rate constant (X)llength (m)mMie constant (−) mass (kg)nMie constant (−) material constant (X)nXnumber of moles of component Xpiprobability of state i (−)qcharge (C)rdistance (m) rate (X)sspecific entropy (J K−1 kg−1)ttime (s)u(pair) potential energy (J)vvolume (m3)wregular solution parameter (J)ximole fraction of component i (−)zsingle particle partition function (−) coordination number (−)zivalency of particle i (−)BCCbody-centered cubicCNcoordination numberDoFdegrees of freedomDoSdensity of statesEoSequation of stateFCCface-centered cubicHCPhexagonal close packedHNChypernetted chain equationHShard-sphereMCMonte CarloMDmolecular dynamicsLJLennard-JonesNRDNeutron-ray diffractionOZOrnstein–ZernikePoCSPrinciple of corresponding statesPYPercus–Yevick equationRDFradial distribution functionSCsimple cubicSLSSignificant liquid structureSTPstandard temperature and pressureSWsquare wellXRDX-ray diffractionYBGYvon–Born–Green equationlhsleft-hand siderhsright-hand sidevdWvan der Waals≅approximately equal≡identical~proportional to⇔corresponds with(x)order of magnitude x

Superscripts

Eexcess∞infinite dilution°standard*pure substance‡activated complexidideal

Subscripts

fformation reactionfusfusionmixmixingmmolarrreaction in generalsolsolutionsubsublimationtrstransitionvapvaporization

1

Introduction

Whilst liquids and solutions are known to play an essential role in many processes in science and technology, the treatment of these topics in the literature have in the past appeared to be limited to either rather basic or rather advanced levels, with intermediate-level texts being scarce, despite the practical importance of liquids and solutions. A brief outline of the differences and similarities between solids, gases, and liquids would help to clarify the reasons for this, and this book represents an attempt to remedy the situation. In this first chapter, an outline of what will be dealt with, and the reasons for these choices, will be given.

1.1 The Importance of Liquids

A brief moment of reflection will make it clear that liquids play an important role in daily life, and in the life sciences and natural sciences, as well as in technology. Hence, these areas of interest will be considered briefly in turn.

Undoubtedly, the most important liquid is water. Water is essential for life itself, and its interaction with other liquids, ions and polymers is vital to many life processes. The basic component of blood, the solvent, is water, and blood itself is an example of a highly complex dispersion of red and white blood cells within a complex mixture of water, ions, and polymeric molecules. As is well known, blood not only transports oxygen through the body but also distributes required molecules to a variety of locations in the body, as well as removes waste material. The miscibility of water with other liquids (such as alcohol) is well known and exploited in alcoholic drinks.

Two other arbitrary examples of liquids that are highly relevant to daily life are petrol – a complex mixture of several types of aliphatic molecules and other species – for cars, and milk – a dispersion of fat globules stabilized in water by a complex of large and small molecules. Without petrol, modern society would be unthinkable, while milk provides a valuable (some say indispensable) part of the nutrition of humankind.