PRENTICE HALL INTERNATIONAL SERIES
IN THE PHYSICAL AND CHEMICAL ENGINEERING SCIENCES
NEAL R. AMUNDSON, SERIES EDITOR, University of Houston
ADVISORY EDITORS
ANDREAS ACRIVOS, Stanford University
JOHNDAHLER, University of Minnesota
H. SCOTT FOGLER, University of Michigan
THOMAS J. HANRATTY, University of Illinois
JOHNM. PRAUSNITZ, University of California
L. E. SCRIVEN, University of Minnesota
BALZHISER, SAMUELS, & ELLIASSEN Chemical Engineering Thermodynamics
BEQUETTE Process Dynamics
BIEGLER, GROSSMAN, & WESTERBERG Systematic Methods of Chemical Process Design
CROWL & LOUVAR Chemical Process Safety
CUTLIP & SHACHAM Problem Solving in Chemical Engineering with Numerical Methods
DENN Process Fluid Mechanics
ELLIOT & LIRA Introductory Chemical Engineering Thermodynamics
FOGLER Elements of Chemical Reaction Engineering, 3rd Edition
HANNA & SANDALL Computational Methods in Chemical Engineering
HIMMELBLAU Basic Principles and Calculations in Chemical Engineering, 6th edition
HINES & MADDOX Mass Transfer
KYLE Chemical and Process Thermodynamics, 3rd edition
NEWMAN Electrochemical Systems, 2nd edition
PRAUSNITZ, LICHTENTHALER, & DE AZEVEDO Molecular Thermodynamics
of Fluid-Phase Equilibria, 3rd edition
PRENTICE Electrochemical Engineering Principles
SHULER & KARGI Bioprocess Engineering
STEPHANOPOULOS Chemical Process Control
TESTER & MODELL Thermodynamics and Its Applications, 3rd edition
TURTON, BAILIE, WHITING, & SHAEWITZ Analysis, Synthesis and Design of Chemical
Processes
WILKES Fluid Mechanics for Chemical Engineering
Molecular Thermodynamics of Fluid-Phase Equilibria
Third Edition
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Contents
1 The Phase-Equilibrium Problem
1.2 Application of Thermodynamics to Phase-Equilibrium Problems
2 Classical Thermodynamics of Phase Equilibria
2.1 Homogeneous Closed Systems
2.3 Equilibrium in a Heterogeneous Closed System
2.8 A Simple Application: Raoult’s Law
3 Thermodynamic Properties from Volumetric Data
3.1 Thermodynamic Properties with Independent Variables P and T
3.2 Fugacity of a Component in a Mixture at Moderate Pressures
3.3 Fugacity of a Pure Liquid or Solid
3.4 Thermodynamic Properties with Independent Variables V and T
3.5 Fugacity of a Component in a Mixture According to van der Waals’ Equation
3.6 Phase Equilibria from Volumetric Properties
4 Intermolecular Forces, Corresponding States and Osmotic Systems
4.1 Potential-Energy Functions
4.3 Polarizability and Induced Dipoles
4.4 Intermolecular Forces between Nonpolar Molecules
4.5 Mie’s Potential-Energy Function for Nonpolar Molecules
4.7 Specific (Chemical) Forces
4.9 Electron Donor-Electron Acceptor Complexes
4.11 Molecular Interactions in Dense Fluid Media
4.12 Molecular Theory of Corresponding States
4.13 Extension of Corresponding-States Theory to More Complicated Molecules
5.2 The Virial Equation of State
5.4 Fugacities from the Virial Equation
5.5 Calculation of Virial Coefficients from Potential Functions
5.7 Virial Coefficients from Corresponding-States Correlations
5.8 The “Chemical” Interpretation of Deviations from Gas-Phase Ideality
5.9 Strong Dimerization: Carboxylic Acids
5.10 Weak Dimerizations and Second Virial Coefficients
5.11 Fugacities at High Densities
5.12 Solubilities of Solids and Liquids in Compressed Gases
6 Fugacities in Liquid Mixtures: Excess Functions
6.2 Fundamental Relations of Excess Functions
6.3 Activity and Activity Coefficients
6.4 Normalization of Activity Coefficients
6.5 Activity Coefficients from Excess Functions in Binary Mixtures
6.6 Activity Coefficients for One Component from Those of the Other Components
6.7 Partial Pressures from Isothermal Total-Pressure Data
6.8 Partial Pressures from Isobaric Boiling-Point Data
6.9 Testing Equilibrium Data for Thermodynamic Consistency
6.10 Wohl’s Expansion for the Excess Gibbs Energy
6.11 Wilson, NRTL, and UNIQUAC Equations
6.12 Excess Functions and Partial Miscibility
6.13 Upper and Lower Consolute Temperatures
6.14 Excess Functions for Multicomponent Mixtures
6.15 Wilson, NRTL, and UNIQUAC Equations for Multicomponent Mixtures
7 Fugacities in Liquid Mixtures: Models and Theories of Solutions
7.2 The Scatchard-Hildebrand Theory
7.3 Excess Functions from an Equation of State
7.5 Calculation of the Interchange Energy from Molecular Properties
7.6 Nonrandom Mixtures of Simple Molecules
7.8 Activity Coefficients from Group-Contribution Methods
7.10 Activity Coefficients in Associated Solutions
7.11 Associated Solutions with Physical Interactions
7.12 Activity Coefficients in Solvated Solutions
7.13 Solutions Containing Two (or More) Complexes
7.14 Distribution of a Solute between Two Immiscible Solvents
7.15 The Generalized van der Waals Partition Function
7.16 Perturbed-Hard-Chain Theory
Statistical Associated-Fluid Theory
Perturbed Hard-Sphere-Chain Theory
8 Polymers: Solutions, Blends, Membranes, and Gels
8.2 Lattice Models: The Flory-Huggins Theory
8.3 Equations of State for Polymer Solutions
Prigogine-Flory-Patterson Theory
Statistical Associated Fluid Theory
Perturbed Hard-Sphere-Chain Theory
8.4 Nonporous Polymeric Membranes and Polymer Gels
9.1 Activity Coefficient of a Nonvolatile Solute in Solution and Osmotic Coefficient for the Solvent
9.2 Solution of an Electrolyte. Electroneutrality
9.3 Osmotic Coefficient in an Electrolyte Solution
9.4 Relation of Osmotic Coefficient to Mean Ionic Activity Coefficient
9.5 Temperature and Pressure Dependence of the Mean Ionic Activity Coefficient
9.6 Excess Properties of Electrolyte Solutions
9.9 Salting-out and Salting-in of Volatile Solutes
9.10 Models for Concentrated Ionic Solutions
9.13 Models Based on the Local-Composition Concept
9.15 The “Chemical” Hydration Model of Robinson and Stokes
9.16 Conversion from McMillan-Mayer to Lewis-Randall Formalisms
9.17 Phase Equilibria in Aqueous Solutions of Volatile Electrolytes
9.18 Protein Partitioning in Aqueous Two-Phase Systems
10 Solubilities of Gases in Liquids
10.1 The Ideal Solubility of a Gas
10.2 Henry’s Law and Its Thermodynamic Significance
10.3 Effect of Pressure on Gas Solubility
10.4 Effect of Temperature on Gas Solubility
10.5 Estimation of Gas Solubility
10.6 Gas Solubility in Mixed Solvents
10.7 Chemical Effects on Gas Solubility
11 Solubilities of Solids in Liquids
11.2 Calculation of the Pure-Solute Fugacity Ratio
11.5 Solubility of a Solid in a Mixed Solvent
11.7 Solubility of Antibiotics in Mixed Nonaqueous Solvents
12 High-Pressure Phase Equilibria
12.1 Fluid Mixtures at High Pressures
12.2 Phase Behavior at High Pressure
Interpretation of Phase Diagrams
Classification of Phase Diagrams for Binary Mixtures
Critical Phenomena in Binary Fluid Mixtures
12.3 Liquid-Liquid and Gas-Gas Equilibria
12.5 Supercritical-Fluid Extraction
12.6 Calculation of High-Pressure Vapor-Liquid Equilibria
12.7 Phase Equilibria from Equations of State
12.8 Phase Equilibria from a Corresponding-States Correlation
12.9 Vapor-Liquid Equilibria from the Perturbed-Hard-Chain Theory
12.10 Phase Equilibria Using the Chemical Theory
A Uniformity of Intensive Potentials as a Criterion of Phase Equilibrium
B A Brief Introduction to Statistical Thermodynamics
Thermodynamic States and Quantum States of a System
Ensembles and Basic Postulates
The Semiclassical Partition Function
Appendix B.1: Two Basic Combinatorial Relations
Appendix B.2: Maximum-Term Method
Appendix B.3: Stirling’s Formula
C Virial Coefficients for Quantum Gases
Virial Equation as a Power Series in Density or Pressure
Virial Coefficients for Hydrogen, Helium, and Neon
E Liquid-Liquid Equilibria in Binary and Multicomponent Systems
F Estimation of Activity Coefficients
Estimation from Activity Coefficients at Infinite Dilution
Estimation from Group-Contribution Methods
G A General Theorem for Mixtures with Associating or Solvating Molecules
H Brief Introduction to Perturbation Theory of Dense Fluids
I The Ion-Interaction Model of Pitzer for Multielectrolyte Solutions
J Conversion Factors and Constants
SI Units and Conversion Factors
Some Fundamental Constants in Various Units
Critical Constants and Acentric Factors for Selected Fluids
Preface
The first edition of this book appeared in 1969; the second edition in 1986. The purpose of this book remains unchanged: to present to senior or first-year graduate students in chemical engineering (and related sciences) a broad introduction to the thermodynamics of phase equilibria typically encountered in design of chemical products and processes, in particular, in separation operations. Thermodynamic tools are provided for efficient design and improvement of conventional and new separation processes including those that may be useful for environmental protection.
This book is suitable as a text for those students who have completed a first course in chemical engineering thermodynamics. While most of the material is based on classical thermodynamics, molecular properties are introduced to facilitate applications to real systems. Although no effort is made to teach statistical thermodynamics, useful results from statistical thermodynamics are included to connect thermodynamic and molecular properties.
The new edition presents an expanded discussion of theoretical concepts to describe and interpret solution properties, with emphasis on those concepts that bear promise for practical applications. Attention is given to a variety of models including the lattice-fluid theory and the statistical associated-fluid theory (SAFT).
A new chapter is devoted to polymer solutions including gas-polymer equilibria at ordinary and high pressures, polymer blends, polymeric membranes and gels. Other novel sections of the third edition include discussions of osmotic pressure and Donnan equilibria.
A serious omission in previous editions has now been corrected: the third edition contains an entirely new chapter on electrolyte solutions. This new chapter first gives the thermodynamic basis for describing activities of components in electrolyte solutions and then presents some semi-empirical models for solutions containing salts or volatile electrolytes. Also discussed are some applications of these models to phase-equilibrium calculations relevant to chemical, environmental and biochemical engineering.
All chapters have been updated primarily through presentation of some recent examples and some new homework problems.
It is a pleasure for the senior author to indicate here his thanks for the essential contributions of his two co-authors. Without their dedicated devotion and attention to numerous details, this third edition could not have been completed.
For helpful advice and comments, the authors are grateful to numerous colleagues, especially to Allan Harvey, Dan Kuehner, Huen Lee, Gerd Maurer, Van Nguyen, John O’Connell, and Jianzhong Wu.
Since 1986, the literature concerning fluid-phase thermodynamics has grown tremendously. To keep the book to a reasonable size, it has been necessary to omit many fine contributions. The authors apologize to their many colleagues whose important work could not be included lest the book become excessively long.
Chemical engineering thermodynamics is now in a state of transition. Classical thermodynamics is becoming increasingly replaced by new tools from applied statistical thermodynamics and molecular simulations. However, many – indeed most – of these new tools are not as yet sufficiently developed for practical applications. For the present and near future, it remains necessary to rely primarily on classical thermodynamics informed and extended through molecular physics and physical chemistry. Molecular thermodynamics, as presented here, is characterized by a combination of classical methods augmented by molecular science and supported by fundamental experimental data.
As in previous editions, this book is motivated by the authors’ enthusiasm for explaining and extending the insights of thermodynamics towards useful applications in chemical engineering. If that enthusiasm can be communicated to students and to practicing engineers, the purpose of this book will be fulfilled. As in previous editions, the motto of the third remains, as before: Felix qui potuit rerum cognoscere causas.
J. M. Prausnitz
Berkeley, California
Effective teamwork that did not leave anything to be desired was the corner-stone for completing the third edition of this book during the time we spent in Berkeley. We thank John for preparing the ground correspondingly, for his leadership as senior author and for his support.
Because we were responsible for electronic typesetting, layout, artwork and figures (many from the previous edition), it was a challenge to take care of all details, requiring from us skills that we learned by doing. We did our best to prepare this book to meet professional standards.
Coming back to Berkeley and to collaborate once again with John was for us an enriching experience. In doing so we asked from our families even more sacrifices than we usually request as academic scientists.
I (R.N.L.) express most sincere thanks to my wife Brigitte, and to my children, Ulrike, Heike, Felix, Philipp, and Martin who provided the support necessary to commit myself in Berkeley exclusively to the revision of this book. I am also grateful to my colleagues at the Institute of Physical Chemistry of the University of Heidelberg for stepping in to meet my teaching duties while I was in Berkeley. Further, I want to thank Siegfried Kraft, Chancellor of the University of Heidelberg, whose understanding and advice made part of my stay in Berkeley possible.
I (E.G.A.) am thankful to my family, Cristina, Miguel and Marta, for their encouragement, understanding and support during the long and difficult months we were apart. Also I am grateful to Instituto Superior Técnico for a leave of absence, and to the Fulbright Program, Programa de Bolsas de Estudos da OTAN, and Fundação Luso-Americana para o Desenvolvimento for financial support of my residence in Berkeley during the academic year 1992/93 (when the preparation of the present edition started) and during the first semester of 1998.
R. N. Lichtenthaler
Heidelberg, Germany
[email protected]
E. Gomes de Azevedo
Lisbon, Portugal
[email protected]
http://alfa.1st.utl.pt/~ejsga
Preface to the Second Edition
Molecular thermodynamics is an engineering science in the sense that its goal is to provide quantitative estimates of equilibrium properties for mixtures as required for chemical process design. To provide these estimates, molecular thermodynamics uses not only classical thermodynamics but also concepts from statistical thermodynamics and chemical physics; the operational procedure can be summarized by these steps:
1. Use statistical thermodynamics whenever possible, at least as a point of departure.
2. Apply appropriate concepts from molecular science.
3. Construct physically grounded models for expressing (abstract) thermodynamic functions in terms of (real) measurable properties.
4. Obtain model parameters from a few, but representative, experimental measurements.
5. Reduce the model to practice through a computer program that efficiently interfaces with engineering-design calculations.
The second edition, like the first, attempts to provide some guidance toward establishing the principles of molecular thermodynamics. This guidance is intended primarily for seniors or first-year graduate students in chemical engineering, but practicing engineers also may find it useful.
In preparing the second edition, I have taken a position of compromise between on the one hand, a “scientific” book that stresses molecular theory and on the other, an “engineering” book that gives practical advice toward specific design procedures. As in the first edition, emphasis is placed on fundamental concepts and how they can be reduced to practice to yield useful results.
Like the earlier edition, the second edition contains ten chapters and several appendices. All chapters have been partially revised and updated. Major changes are in t Chapters 4, 6, 7, and 8, and much of Chapter 10 is totally new. Some earlier appendices have been removed and others have been added: Appendix II gives a brief introduction to statistical thermodynamics, while Appendices VIII and IX present summa-ties of some special aspects of the theory of solutions as addenda to Chapter 7.
Many new problems have been added. Solving problems is essential for serious students, Numerical answers to numerous problems are given in the final Appendix.
Since work for the first edition ceased in 1968, there have been formidable developments in a variety of areas that bear on molecular thermodynamics. It is not possible, in a reasonable number of pages, to do justice to all or even a major part of these developments. I have bad to omit much that might have been included, lest this book become even larger; I can only ask my colleagues to forgive me if some of their contributions are not here mentioned for reasons of economy.
Perhaps the most promising development in the last fifteen years is in the statistical thermodynamics of fluids and fluid mixtures, especially through perturbation theory and computer simulation. There is little doubt that these developments will continue toward eventual direct application in engineering design. However, it is also likely that such direct application is not in the immediate future and that therefore, the semi-empirical methods discussed in this book will be utilized for many more years. Nevertheless, chemical-engineering students should now receive at least some introduction to the statistical thermodynamics of fluids, not only because of utility in the future, but also because idealized results from contemporary statistical thermodynamics are already now of much use in guiding development of semi-theoretical models toward thermodynamic-property correlations. Therefore, some limited discussion of applied statistical thermodynamics is now included in Chapters 4, 7, and 10.
I am deeply grateful to many colleagues who have contributed to my understanding of molecular thermodynamics and its applications, and thereby to this book; perhaps the most helpful of these has been B. J. Alder. In addition to those mentioned in the Preface to the First Edition, I want to record here my thanks to R. A. Heidemann, E. U. Franck, K. E. Gubbins, R. C. Reid, the late T. K. Sherwood, H. Knapp, F. Kohler, C. Tsonopoulos, L. C. Claitor, H. C. van Ness, F. Selleck, and C. J. King. Further, I owe much to my numerous co-workers (graduate students and post-doctoral visitors) who have provided me with new information, stimulating questions and good fellowship. I am, however, especially grateful to my two co-authors, R. N. Lichtenthaler and E. G. Azevedo, who ably assisted me in making revisions and additions to the original manuscript. Their contributions to the second edition are considerable and they deserve much credit for whatever success the second edition may achieve. All three authors are particularly indebted to P. Rasmussen for his critical review, to S. F. Barreiros for preparing the index and to R. Spontak for assistance in proof-reading.
Almost all of the new and revised sections of the second edition were prepared in the period 1978-80. It is unfortunate that, for a variety of reasons, publication was so long delayed. The final manuscript was sent to the publisher in February 1983.
The second edition maintains the pragmatic (engineering-science) philosophy that characterized the first edition: it is useful and ultimately economic to utilize whatever theoretical concepts may be suitable, but it is also important consistently to bear in mind the ultimate applied objective. To attain that objective, theory is rarely sufficient and inevitably at least some experimental data are required. The goal must always be to attain a healthy balance between theory and experiment, to avoid extreme emphasis in either direction.
This need for balance was recognized many years ago by a pioneer in applied science, Sir Francis Bacon, who used an analogy between scientific enterprise and the world of insects. In “Novum Organum” (1620), Bacon wrote about ants, spiders, and bees:
Those who have handled sciences, have been either men of experiment or men of dogmas. The men of experiment are like the ant; they only collect and use. The reasoners resemble spiders who make cobwebs out of their own substance. But the bee takes a middle course: it gathers its material from the flowers of the garden and of the field, and transforms and digests it by a power of its own. Therefore, from a closer and purer league between these two faculties, the experimental and the rational, much may be hoped.
Finally, as in the Preface to the First Edition, I want to stress once again that studying, practicing and extending molecular thermodynamics is not only a useful activity but also one that provides a sense of joy and satisfaction. I shall be glad if some of that sense is infectious so that the reader may attain from molecular thermodynamics the same generous rewards that it has given to me.
J. M. Prausnitz
Berkeley, California
About 14 years ago I met J. M. Prausnitz for the first time. He immediately stimulated my interest in the exciting science of phase-equilibrium thermodynamics and ever since he has strongly sustained my work in this field. Throughout the years, we usually agreed quickly on how to approach and to solve problems but when we did not, open, honest and sometimes tough discussions always brought us to mutual agreement. To be one of the co-authors of this book is the culminating point so far in our joint effort to establish molecular thermodynamics as a useful engineering science for practical application. Thank you, John!
A scientist demands a lot of sacrifice from those who share his life. Therefore I owe many, many thanks to my wife Brigitte, and to my children, Ulrike, Heike, Felix and Philipp who give me enduringly all the support I need to pursue my scientific work in the way I do it.
R. N. Lichtenthaler
Heidelberg, Federal Republic of Germany
Preface to the First Edition
Since the generality of thermodynamics makes it independent of molecular considerations, the expression “molecular thermodynamics” requires explanation.
Classical thermodynamics presents broad relationships between macroscopic properties, but it is not concerned with quantitative prediction of these properties. Statistical thermodynamics, on the other hand, seeks to establish relationships between macroscopic properties and intermolecular forces through partition functions; it is very much concerned with quantitative prediction of bulk properties. However, useful configurational partition functions have been constructed only for nearly ideal situations and, therefore, statistical thermodynamics is at present insufficient for many practical purposes.
Molecular thermodynamics seeks to overcome some of the limitations of both classical and statistical thermodynamics. Molecular phase-equilibrium thermodynamics is concerned with application of molecular physics and chemistry to the interpretation, correlation, and prediction of the thermodynamic properties used in phase-equilibrium calculations. It is an engineering science, based on classical thermodynamics but relying on molecular physics and statistical thermodynamics to supply insight into the behavior of matter. In application, therefore, molecular thermodynamics is rarely exact; it must necessarily have an empirical flavor.
In the present work I have given primary attention to gaseous and liquid mixtures. I have been concerned with the fundamental problem of how best to calculate fugacities of components in such mixtures; the analysis should therefore be useful to engineers engaged in design of equipment for separation operations. Chapters 1, 2, and 3 deal with basic thermodynamics and, to facilitate molecular interpretation of thermodynamic properties, Chapter 4 presents a brief discussion of intermolecular forces. Chapter 5 is devoted to calculation of fugacities in gaseous mixtures and Chapter 6 is concerned with excess functions of liquid mixtures. Chapter 7 serves as an introduction to the theory of liquid solutions with attention to both “physical” and “chemical” theories. Fugacities of gases dissolved in liquids are discussed in Chapter 8 and those of solids dissolved in liquids in Chapter 9. Finally, Chapter 10 considers fluid-phase equilibria at high pressures.
While it is intended mainly for chemical engineers, others interested in fluid-phase equilibria may also find the book useful. It should be of value to university seniors or first-year graduate students in chemistry or chemical engineering who have completed a standard one-year course in physical chemistry and who have had some previous experience with classical thermodynamics.
The subjects discussed follow quite naturally from my own professional activities. Phase-equilibrium thermodynamics is a vast subject, and no attempt has been made to be exhaustive. I have arbitrarily selected those topics with which I am familiar and have omitted others which I am not qualified to discuss; for example, I do not con-skier solutions of metals or electrolytes. In essence, I have written about those topics which interest me, which I have taught in the classroom, and which have comprised much of my research. As a result, emphasis is given to results from my own research publications, not because they are in any sense superior, but because they encompass material with which I am most closely acquainted.
In the preparation of this book I have been ably assisted by many friends and former students; I am deeply grateful to all. Helpful comments were given by J. C. Berg, R. F. Blanks, P. L. Chueh, C. A. Eckert, M. L. McGlashan, A. L. Myers, J. P. O’Connell, Otto Redlich, Henri Renon, F. B. Sprow, and H. C. Van Ness. Generous assistance towards improvement of the manuscript was given by R. W. Missen and by
C. Tsonopoulos who also prepared the index. Many drafts of the manuscript were cheerfully typed by Mrs. Irene Blowers and Miss Mary Ann Williams and especially by my faithful assistant for over twelve years, Mrs. Edith Taylor, whose friendship and conscientious service deserve special thanks.
Much that is here presented is a reflection of what I have learned from my teachers of thermodynamics and phase equilibria: G. J. Su, R. K. Toner, R. L. Von Berg, and the late R. H. Wilhelm; and from my colleagues at Berkeley: B. J. Alder, Leo Brewer, K. S. Pitzer and especially J. H. Hildebrand, whose strong influence on my thought is evident on many pages.
I hope that I have been able to communicate to the reader some of the fascination I have experienced in working on and writing about phase-equilibrium thermodynamics. To think about and to describe natural phenomena, to work in science and engineering - all these are not only useful but they are enjoyable to do. In writing this book I have become aware that for me phase-equilibrium thermodynamics is a pleasure as well as a profession; I shall consider it a success if a similar awareness can be awakened in those students and colleagues for whom this book is intended. Felix qui potuit rerum cognoscere causas.
Finally, I must recognize what is all too often forgotten - that no man lives or works alone, but that he is molded by those who share his life, who make him what he truly is. Therefore I dedicate this book to Susie, who made it possible, and to Susi and Toni, who prepared the way.
J. M. Prausnitz
Berkeley, California
