Chemical Thermodynamics

Irving M. Klotz, PhD, deceased, was a noted expert in chemical thermodynamics and the physical chemistry of proteins. Dr. Klotz was elected to the American Academy of Arts & Sciences in 1968 and the National Academy of Sciences in 1970. He joined the Northwestern faculty in 1940 and retired in 1986. Dr. Klotz was named a Fellow of the Royal Society of Medicine in 1971 and published more than 200 scientific articles in peer-reviewed journals. He wrote Chemical Thermodynamics: Basic Theory and Methods in 1950. Dr. Rosenberg began working with him as coauthor with the third edition. ROBERT M. ROSENBERG, PhD, is Emeritus Professor of Chemistry at Lawrence University and an Adjunct Professor of Chemistry at Northwestern University.

• Preface xix1 Introduction 11.1 Origins of Chemical Thermodynamics 11.2 Objectives of Chemical Thermodynamics 41.3 Limitations of Classic Thermodynamics 4References 62 Mathematical Preparation for Thermodynamics 92.1 Variables of Thermodynamics 10Extensive and Intensive Quantities 10Units and Conversion Factors 102.2 Analytic Methods 10Partial Differentiation 10Exact Differentials 15Homogeneous Functions 18Exercises 21References 273 The First Law of Thermodynamics 293.1 Definitions 29Temperature 31Work 333.2 The First Law of Thermodynamics 37Energy 37Heat 38General Form of the First Law 38Exercises 40References 414 Enthalpy, Enthalpy of Reaction, and Heat Capacity 434.1 Enthalpy 44Definition 44Relationship between QV and QP  464.2 Enthalpy of Reactions 47Definitions and Conventions 474.3 Enthalpy as a State Function 52Enthalpy of Formation from Enthalpy of Reaction 52Enthalpy of Formation from Enthalpy of Combustion 53Enthalpy of Transition from Enthalpy of Combustion 53Enthalpy of Conformational Transition of a Protein from Indirect Calorimetric Measurements 54Enthalpy of Solid-State Reaction from Measurements of Enthalpy of Solution 564.4 Bond Enthalpies 57Definition of Bond Enthalpies 57Calculation of Bond Enthalpies 58Enthalpy of Reaction from Bond Enthalpies 594.5 Heat Capacity 60Definition 61Some Relationships between CP and CV  62Heat Capacities of Gases 64Heat Capacities of Solids 67Heat Capacities of Liquids 68Other Sources of Heat Capacity Data 684.6 Enthalpy of Reaction as a Function of Temperature 68Analytic Method 69Arithmetic Method 71Graphical or Numerical Methods 72Exercises 72References 785 Applications of the First Law to Gases 815.1 Ideal Gases 81Definition 81Enthalpy as a Function of Temperature Only 83Relationship Between CP and CV 84Calculation of the Thermodynamic Changes in Expansion Processes 845.2 Real Gases 94Equations of State 94Joule–Thomson Effect 98Calculations of Thermodynamic Quantities in Reversible Expansions 102Exercises 104References 1086 The Second Law of Thermodynamics 1116.1 The Need for a Second Law 1116.2 The Nature of the Second Law 112Natural Tendencies Toward Equilibrium 112Statement of the Second Law 112Mathematical Counterpart of the Verbal Statement 1136.3 The Carnot Cycle 113The Forward Cycle 114The Reverse Cycle 116Alternative Statement of the Second Law 117Carnot’s Theorem 1186.4 The Thermodynamic Temperature Scale 1206.5 The Definition of S, the Entropy of a System 1256.6 The Proof that S is a Thermodynamic Property 126Any Substance in a Carnot Cycle 126Any Substance in Any Reversible Cycle 127Entropy S Depends Only on the State of the System 1296.7 Entropy Changes in Reversible Processes 130General Statement 130Isothermal Reversible Changes 130Adiabatic Reversible Changes 131Reversible Phase Transitions 131Isobaric Reversible Temperature Changes 132Isochoric Reversible Temperature Changes 1336.8 Entropy Changes in Irreversible Processes 133Irreversible Isothermal Expansion of an Ideal Gas 133Irreversible Adiabatic Expansion of an Ideal Gas 135Irreversible Flow of Heat from a Higher Temperature to a Lower Temperature 136Irreversible Phase Transitions 137Irreversible Chemical Reactions 138General Statement 1396.9 General Equations for the Entropy of Gases 142Entropy of the Ideal Gas 142Entropy of a Real Gas 1436.10 Temperature–Entropy Diagram 1446.11 Entropy as an Index of Exhaustion 146Exercises 150References 1577 Equilibrium and Spontaneity for Systems at Constant Temperature 1597.1 Reversibility, Spontaneity, and Equilibrium 159Systems at Constant Temperature and Volume 160Systems at Constant Temperature and Pressure 162Heat of Reaction as an Approximate Criterion of Spontaneity 1647.2 Properties of the Gibbs, Helmholtz, and Planck Functions 165The Functions as Thermodynamic Properties 165Relationships among G, Y, and A 165Changes in the Functions for Isothermal Conditions 165Equations for Total Differentials 166Pressure and Temperature Derivatives of the Functions 167Equations Derived from the Reciprocity Relationship 1697.3 The Gibbs Function and Chemical Reactions 170Standard States 1707.4 Pressure and Temperature Dependence of ΔG 1727.5 Useful Work and the Gibbs and Helmholtz Functions 175Isothermal Changes 175Changes at Constant Temperature and Pressure 177Relationship between ΔHP and QP When Useful Work is Performed 178Application to Electrical Work 179Gibbs–Helmholtz Equation 180The Gibbs Function and Useful Work in Biologic Systems 181Exercises 185References 1918 Application of the Gibbs Function and the Planck Function to Some Phase Changes 1938.1 Two Phases at Equilibrium as a Function of Pressure and Temperature 193Clapeyron Equation 194Clausius–Clapeyron Equation 1968.2 The Effect of an Inert Gas on Vapor Pressure 198Variable Total Pressure at Constant Temperature 199Variable Temperature at Constant Total Pressure 2008.3 Temperature Dependence of Enthalpy of Phase Transition 2008.4 Calculation of Change in the Gibbs Function for Spontaneous Phase Change 202Arithmetic Method 202Analytic Method 203Exercises 205References 2109 Thermodynamics of Systems of Variable Composition 2119.1 State Functions for Systems of Variable Composition 2119.2 Criteria of Equilibrium and Spontaneity in Systems of Variable Composition 2139.3 Relationships Among Partial Molar Properties of a Single Component 2159.4 Relationships Between Partial Molar Quantities of Different Components 216Partial Molar Quantities for Pure Phase 2189.5 Escaping Tendency 219Chemical Potential and Escaping Tendency 2199.6 Chemical Equilibrium in Systems of Variable Composition 221Exercises 223Reference 22610 Mixtures of Gases and Equilibrium in Gaseous Mixtures 22710.1 Mixtures of Ideal Gases 227The Entropy and Gibbs Function for Mixing Ideal Gases 228The Chemical Potential of a Component of an Ideal Gas Mixture 230Chemical Equilibrium in Ideal Gas Mixtures 231Dependence of K on Temperature 232Comparison of Temperature Dependence of ΔG°m and ln K 23410.2 The Fugacity Function of a Pure Real Gas 236Change of Fugacity with Pressure 237Change of Fugacity with Temperature 23810.3 Calculation of the Fugacity of a Real Gas 239Graphical or Numerical Methods 240Analytical Methods 24410.4 Joule–Thomson Effect for a Van der Waals Gas 247Approximate Value of a for a Van der Waals Gas 247Fugacity at Low Pressures 248Enthalpy of a Van der Waals Gas 248Joule–Thomson Coefficient 24910.5 Mixtures of Real Gases 249Fugacity of a Component of a Gaseous Solution 250Approximate Rule for Solutions of Real Gases 251Fugacity Coefficients in Gaseous Solutions 251Equilibrium Constant and Change in Gibbs Functions and Planck Functions for Reactions of Real Gases 252Exercises 253References 25611 The Third Law of Thermodynamics 25911.1 Need for the Third Law 25911.2 Formulation of the Third Law 260Nernst Heat Theorem 260Planck’s Formulation 261Statement of Lewis and Randall 26211.3 Thermodynamic Properties at Absolute Zero 263Equivalence of G and H 263ΔCP in an Isothermal Chemical Reaction 263Limiting Values of CP and CV  264Temperature Derivatives of Pressure and Volume 26411.4 Entropies at 298 K 265Typical Calculations 266Apparent Exceptions to the Third Law 270Tabulations of Entropy Values 274Exercises 277References 28012 Application of the Gibbs Function to Chemical Changes 28112.1 Determination of ΔG°m from Equilibrium Measurements 28112.2 Determination of ΔG°m from Measurements of Cell potentials 28412.3 Calculation of ΔG°m from Calorimetric Measurements 28512.4 Calculation of a Gibbs Function of a Reaction from Standard Gibbs Function of Formation 28612.5 Calculation of a Standard Gibbs Function from Standard Entropies and Standard Enthalpies 287Enthalpy Calculations 287Entropy Calculations 290Change in Standard Gibbs Function 290Exercises 293References 30113 The Phase Rule 30313.1 Derivation of the Phase Rule 303Nonreacting Systems 304Reacting Systems 30613.2 One-Component Systems 30713.3 Two-Component Systems 309Two Phases at Different Pressures 312Phase Rule Criterion of Purity 315Exercises 316References 31614 The Ideal Solution 31914.1 Definition 31914.2 Some Consequences of the Definition 321Volume Changes 321Heat Effects 32214.3 Thermodynamics of Transfer of a Component from One Ideal Solution to Another 32314.4 Thermodynamics of Mixing 32514.5 Equilibrium between a Pure Solid and an Ideal Liquid Solution 327Change of Solubility with Pressure at a Fixed Temperature 328Change of Solubility with Temperature 32914.6 Equilibrium between an Ideal Solid Solution and an Ideal Liquid Solution 332Composition of the Two Phases in Equilibrium 332Temperature Dependence of the Equilibrium Compositions 333Exercises 333References 33515 Dilute Solutions of Nonelectrolytes 33715.1 Henry’s Law 33715.2 Nernst’s Distribution Law 34015.3 Raoult’s Law 34115.4 Van’t Hoff’s Law of Osmotic Pressure 344Osmotic Work in Biological Systems 34915.5 Van’t Hoff’s Law of Freezing-Point Depression and Boiling-Point Elevation 350Exercises 353References 35516 Activities, Excess Gibbs Functions, and Standard States for Nonelectrolytes 35716.1 Definitions of Activities and Activity Coefficients 358Activity 358Activity Coefficient 35816.2 Choice of Standard States 359Gases 359Liquids and Solids 36016.3 Gibbs Function and the Equilibrium Constant in Terms of Activity 36516.4 Dependence of Activity on Pressure 36716.5 Dependence of Activity on Temperature 368Standard Partial Molar Enthalpies 368Equation for Temperature Derivative of the Activity 36916.6 Standard Entropy 37016.7 Deviations from Ideality in Terms of Excess Thermodynamic Functions 373Representation of G E m as a Function of Composition 37416.8 Regular Solutions and Henry’s Law 37616.9 Regular Solutions and Limited Miscibility 378Exercises 381References 38417 Determination of Nonelectrolyte Activities and Excess Gibbs Functions From Experimental Data 38517.1 Activity from Measurements of Vapor Pressure 385Solvent 385Solute 38617.2 Excess Gibbs Function from Measurement of Vapor Pressure 38817.3 Activity of a Solute from Distribution between Two Immiscible Solvents 39117.4 Activity from Measurement of Cell Potentials 39317.5 Determination of the Activity of One Component from the Activity of the Other 397Calculation of Activity of Solvent from That of Solute 398Calculation of Activity of Solute from That of Solvent 39917.6 Measurements of Freezing Points  400Exercises  401References 40618 Calculation of Partial Molar Quantities and Excess Molar Quantities from Experimental Data: Volume and Enthalpy 40718.1 Partial Molar Quantities by Differentiation of J as a Function of Composition 407Partial Molar Volume 409Partial Molar Enthalpy 413Enthalpies of Mixing 414Enthalpies of Dilution 41718.2 Partial Molar Quantities of One Component from those of Another Component by Numerical Integration 420Partial Molar Volume 421Partial Molar Enthalpy 42118.3 Analytic Methods for Calculation of Partial Molar Properties 422Partial Molar Volume 422Partial Molar Enthalpy 42318.4 Changes in J for Some Processes in Solutions 423Transfer Process 423Integral Process 42518.5 Excess Properties: Volume and Enthalpy 426Excess Volume 426Excess Enthalpy 426Exercises 427References 43619 Activity, Activity Coefficients, and Osmotic Coefficients of Strong Electrolytes 43919.1 Definitions and Standard states for Dissolved Electrolytes 440Uni-univalent Electrolytes 440Multivalent Electrolytes 443Mixed Electrolytes 44619.2 Determination of Activities of Strong Electrolytes 448Measurement of Cell Potentials 449Solubility Measurements 453Colligative Property Measurement: The Osmotic Coefficient 455Extension of Activity Coefficient Data to Additional Temperatures with Enthalpy of Dilution Data 46019.3 Activity Coefficients of Some Strong Electrolytes 462Experimental Values 462Theoretical Correlation 462Exercises 464References 47020 Changes in Gibbs Function for Processes in Solutions 47120.1 Activity Coefficients of Weak Electrolytes 47120.2 Determination of Equilibrium Constants for Dissociation of Weak Electrolytes 472From Measurements of Cell Potentials 473From Conductance Measurements 47520.3 Some Typical Calculations for ΔfG°m  480Standard Gibbs Function for Formation of Aqueous Solute: HCl 480Standard Gibbs Function of Formation of Individual Ions: HCl 482Standard Gibbs Function for Formation of Solid Solute in Aqueous Solution 482Standard Gibbs Function for Formation of Ion of Weak Electrolyte 484Standard Gibbs Function for Formation of Moderately Strong Electrolyte 485Effect of Salt Concentration on Geological Equilibrium Involving Water 486General Comments 48620.4 Entropies of Ions 487The Entropy of an Aqueous Solution of a Salt 488Entropy of Formation of Individual Ions 488Ion Entropies in Thermodynamic Calculations 491Exercises 491References 49621 Systems Subject to a Gravitational or a Centrifugal Field 49921.1 Dependence of the Gibbs Function on External Field 49921.2 System in a Gravitational Field 50221.3 System in a Centrifugal Field 505Exercises 509References 51022 Estimation of Thermodynamic Quantities 51122.1 Empirical Methods 511Group Contribution Method of Andersen, Beyer, Watson, and Yoneda 512Typical Examples of Estimating Entropies 516Other Methods 522Accuracy of the Approximate Methods 522Equilibrium in Complex Systems 523Exercises 523References 52423 Concluding Remarks 527References 529Appendix a Practical Mathematical Techniques 531A.1 Analytical Methods 531Linear Least Squares 531Nonlinear Least Squares 534A.2 Numerical and Graphical Methods 535Numerical Differentiation 535Numerical Integration 538Use of the Digital Computer 540Graphical Differentiation 541Graphical Integration 542Exercises 542References 543Index 545

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