CHEMICAL THERMODYNAMICS

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1 CHEMICAL THERMODYNAMICS Basic Theory and Methods Sixth Edition IRVING M. KLOTZ Morrison Professor Emeritus Northwestern University ROBERT M. ROSENBERG MacMillen Professor Emeritus Lawrence University Visiting Professor of Chemistry Northwestern University A Wiley-Interscience Publication JOHN WILEY & SONS, INC. New York / Chichester / Weinheim / Brisbane / Singapore / Toronto

2 CONTENTS PREFACE xix CHAPTER 1 INTRODUCTION Origins of Chemical Thermodynamics / Objectives of Chemical Thermodynamics / Limitations of Classical Thermodynamics / 4 References / 6 CHAPTER 2 MATHEMATICAL PREPARATION FOR THERMODYNAMICS Variables of Thermodynamics / 8 Extensive and Intensive Quantities / 8 Units and Conversion Factors / Theoretical Methods / 9 Partial Differentiation / 9 Equation for the Total Differential I 9 Conversion Formulas I 12 Exact Differentials / 14 Example of the Gravitational Field I 14 General Formulation I 14 Reciprocity Characteristic I 15 Homogeneous Functions / 16 Definition I 17 vii

3 VÜi CONTENTS Euler 's Theorem I 18 References / 26 CHAPTER 3 THE FIRST LAW OF THERMODYNAMICS 3-1 Definitions / 28 Temperature / 30 Work / The First Law of Thermodynamics / 37 Energy / 37 Heat / 37 General Form of the First Law / 37 Exercises / 39 References / 40 CHAPTER 4 ENTHALPY, ENTHALPY OF REACTION, AND HEAT CAPACITY 4-1 Enthalpy / 43 Definition / 43 Relationship between Q v and Q P I Enthalpy of Reactions / 46 Definitions and Conventions / 46 Some Standard States I 46 Enthalpy of Formation I Additivity of Enthalpies of Reaction / 50 Enthalpy of Formation from Enthalpy of Reaction / 51 Enthalpy of Formation from Enthalpy of Combustion / 51 Enthalpy of Transition from Enthalpy of Combustion / 52 Enthalpy of Conformational Transition of a Protein from Indirect Calorimetric Measurements / 52 Enthalpy of Solid State Reaction from Measurements of Enthalpy of Solution / Bond Enthalpies / 55 Definition of Bond Enthalpies / 55 Calculation of Bond Enthalpies / 56 Enthalpy of Reaction from Bond Enthalpies / HeatCapacity / 59 Definition / 59 Fundamental Statement I 59 Derived Relationships I 60 Some Relationships between C P and C v I 60 Heat Capacities of Gases / 63 Heat Capacities of Solids / 63

4 Heat Capacities of Liquids / 66 Sources of Heat Capacity Data / Enthalpy of Reaction as a Function of Temperature / 67 Analytic Method / 68 Arithmetic Method / 70 Graphical or Numerical Methods / 71 Exercises / 71 References / 76 CHAPTER 5 APPLICATION OF THE FIRST LAW TO GASES 5-1 Ideal Gases / 78 Definition / 78 Enthalpy a Function of Temperature Only / 80 Relationship between C P and C v I 80 Calculation of the Thermodynamic Changes in Expansion Processes / 81 Isothermal I 81 Adiabatic I Real Gases / 91 Semiempirical Equations / 91 Virial Function I 94 Joule-Thomson Effect / 94 Isenthalpic Nature I 95 Joule-Thomson Coefficient I 97 Joule-Thomson Inversion Temperature I 99 Calculation of Thermodynamic Quantities in Reversible Expansions / 100 Isothermal / 100 Adiabatic I 101 Exercises / 102 References / 105 CHAPTER 6 THE SECOND LAW OF THERMODYNAMICS 6-1 The Need for a Second Law / The Nature of the Second Law / 108 Natural Tendencies Toward Equilibrium / 108 Statement of the Second Law / 108 Mathematical Counterpart of the Verbal Statement / The Carnot Cycle / 109 The Forward Cycle /HO The Reverse Cycle / 112 Alternative Statement of the Second Law / 113 Carnot's Theorem / 113

5 X CONTENTS 6-4 The Thermodynamic Temperature Scale / The Definition of S, The Entropy of a System / The Proof that S Is a Thermodynamic Property / 122 Any Substance in a Camot Cycle / 122 Any Substance in Any Reversible Cycle / 123 Entropy S Depends Only on the State of the System / Entropy Changes in Reversible Processes / 126 General Statement / 126 Isothermal Reversible Changes / 126 Adiabatic Reversible Changes / 127 Reversible Phase Transitions / 127 Isobaric Reversible Temperature Change / 128 Isochoric Reversible Temperature Change / Entropy Changes in Irreversible Processes / 129 Irreversible Isothermal Expansion of an Ideal Gas / 129 Irreversible Adiabatic Expansion of an Ideal Gas / 131 Irreversible Flow of Heat from a Higher to a Lower Temperature / 132 Irreversible Phase Transition / 133 Irreversible Chemical Reaction / 135 General Statement / General Equations for the Entropy of Gases / 138 Entropy of an Ideal Gas / 138 Entropy of a Real Gas / Temperature-Entropy Diagram / Entropy as an Index of Exhaustion / 142 Exercises / 146 References / 152 CHAPTER 7 EQUILIBRIUM AND SPONTANEITY FOR SYSTEMS AT CONSTANT TEMPERATURE: THE GIBBS, HELMHOLTZ, PLANCK, AND MASSIEU FUNCTIONS Reversibility, Spontaneity, and Equilibrium / 154 Systems at Constant Temperature and Volume / 155 Systems at Constant Temperature and Pressure / 157 Heat of Reaction as an Approximate Criterion of Spontaneity / Properties of the Gibbs, Helmholtz, and Planck Functions / 160 The Functions as Thermodynamic Properties / 160 Relationships among G, Y, and A / 160 Changes in the Functions for Isothermal Conditions / 160

6 CONTENTS Equations for Total Differentials / 161 Pressure and Temperature Coefficients of the Functions / 162 Equations Derived from the Reciprocity Relationship / The Planck Function and the Equilibrium Constant / 165 Standard States / 165 Relationship between AY^, and the Equilibrium Constant for Gaseous Reactions / 166 Dependence of K on Temperature / 172 Pressure and Temperature Dependence of AG / 173 Temperature Dependence I IIA Pressure Dependence / 175 General Expression / 175 Comparison of Temperature Dependence of AG^ and In K I Useful Work and the Gibbs and Helmholtz Functions / 178 Isothermal Changes / 178 Changes at Constant Temperature and Pressure / 181 Relationship between AH P and Q P When Useful Work Is Done / 182 Application to Electrical Work / 182 Gibbs-Helmholtz Equation / 184 The Gibbs Function and Useful Work in Biological Systems / 185 Biosynthetic Work / 185 Mechanical Work / 189 Osmotic Work I 189 Exercises / 189 References / 196 CHAPTER 8 APPLICATION OF THE GIBBS FUNCTION AND THE PLANCK FUNCTION TO SOWIE PHASE CHANGES 8-1 Two Phases at Equilibrium as a Function of Pressure and Temperature / 197 Clapeyron Equation / 198 Clausius-Clapeyron Equation / The Effect of an Inert Gas on Vapor Pressure / 202 Variable Total Pressure at Constant Temperature / 203 Variable Temperature at Constant Total Pressure / Temperature Dependence of Enthalpy of Phase Transition / Calculation of Change in the Gibbs Function and Change in the Planck Function for Spontaneous Phase Change / 206 Arithmetic Method / 207 Analytic Method / 207

7 XII CONTENTS Exercises / 209 References / 215 CHAPTER9 THE THIRD LAW OF THERMODYNAMICS Need for the Third Law / Formulation of the Third Law / 217 Nernst Heat Theorem / 218 Planck's Formulation / 218 Statement of Lewis and Randall / Thermodynamic Properties at Absolute Zero / 220 Equivalence of G and H I 220 AC P in an Isothermal Chemical Transformation / 220 Limiting Values of C P and C v I 221 Temperature Coefficients of Pressure and Volume / Entropies at 298 K / 223 Typical Calculations / 223 For Solid or Liquid I 223 For a Gas I 226 Apparent Exceptions to the Third Law / 227 Tabulation of Entropy Values / 231 Exercises / 205 References / 237 CHAPTER 10 APPLICATION OF THE GIBBS FUNCTION AND THE PLANCK FUNCTION TO CHEMICAL CHANGES Determination of Gibbs Function and Planck Function from Equilibrium Measurements / Determination of Gibbs Function and Planck Function from Measurements of Cell Potentials / Calculation of Gibbs Function and Planck Function from Calorimetric Measurements / Calculation of Gibbs Function and Planck Function of Reaction from Standard Gibbs Function and Standard Planck Function of Formation / Calculation of Standard Gibbs Function and Standard Planck Function from Standard Entropies and Standard Enthalpies / 245 Enthalpy Calculations / 245 Entropy Calculations / 247 Change in Standard Gibbs Function and Standard Planck Function / 249 Exercises / 252 References / 260

8 CONTENTS XÜi CHAPTER 11 THERMODYNAMICS OF SYSTEMS OF VARIABLE COMPOSITION State Functions for Systems of Variable Composition / Criteria of Equilibrium and Spontaneity in Systems of Variable Composition / Relationships among Partial Molar Properties of a Single Component / Relationships between Partial Molar Quantities of Different Components / 267 Partial Molar Quantities for Pure Phase / Escaping Tendency / 270 Chemical Potential and Escaping Tendency / Chemical Equilibrium in Systems of Variable Composition / 272 Exercises / 275 Reference / 278 CHAPTER 12 MIXTURES OF GASES Mixtures of Ideal Gases / 279 The Entropy and Gibbs Function for Mixing Ideal Gases / 280 The Chemical Potential of a Component of an Ideal Gas Mixture / 281 Chemical Equilibrium in Ideal Gas Mixtures / The Fugacity Function of a Pure Real Gas / 284 Change of Fugacity with Pressure / 285 Change of Fugacity with Temperature / Calculation of the Fugacity of a Real Gas / 288 Graphical or Numerical Methods / 288 Using the a Function I 288 Using the Compressibility Factor I 290 Analytical Methods / 291 Based on the Virial Equation I 291 Based on the Redlich-Kwong Equation of State I 293 An Approximate Method I Joule-Thomson Effect for a van der Waals Gas / 296 Approximate Value of a for a van der Waals Gas / 296 Fugacity at Low Pressures / 297 Enthalpy of a van der Waals Gas / 298 Joule-Thomson Coefficient / Mixtures of Real Gases / 299 Fugacity of a Component of a Gaseous Solution / 299 Approximate Rule for Solutions of Real Gases / 300 Fugacity Coefficients in Gaseous Solution / 301

9 XIV CONTENTS Equilibrium Constant and Change in Gibbs Function and Planck Function for Reactions Involving Real Gases / 301 Exercises / 302 References / 305 CHAPTER13 THE PHASE RULE Derivation of the Phase Rule / 307 Nonreacting Systems / 307 Mechanical Equilibrium I 308 Thermal Equilibrium I 308 Transfer Equilibrium I 309 The Phase Rule / 310 Reacting Systems / One-Component Systems / Two-Component Systems / 313 Two Phases at Different Pressures / 316 Phase Rule Criterion of Purity / 319 Exercises / 319 References / 320 CHAPTER14 THE IDEAL SOLUTION Definition / Some Consequences of the Definition / 324 Volume Changes / 324 Heat Effects / Thermodynamics of Transfer of a Component from One Ideal Solution to Another / Thermodynamics of Mixing / Equilibrium between a Pure Solid and an Ideal Liquid Solution / 330 Change of Solubility with Pressure at a Fixed Temperature / 332 Change of Solubility with Temperature / Equilibrium between an Ideal Solid Solution and an Ideal Liquid Solution / 336 Composition of the Two Phases in Equilibrium / 336 Temperature Dependence of the Equilibrium Compositions / 337 Exercises / 338 References / 339 CHAPTER15 DILUTE SOLUTIONS OF NONELECTROLYTE Henry's Law / Nernst's Distribution Law / Raoult's Law / 344

10 CONTENTS XV 15-4 van't Hoff's Law of Osmotic Pressure / 347 Osmotic Work in Biological Systems / van't Hoff's Law of Freezing Point Depression and Boiling Point Elevation / 353 Exercises / 356 References / 358 CHAPTER 16 ACTIVITIES, EXCESS GIBBS FUNCTION, AND STANDARD STATES FOR NONELECTROLYTES Definitions of Activities and Activity Coefficients / 360 Activity / 360 Activity Coefficient / Choice of Standard States / 361 Gases / 361 Liquids and Solids / 362 Pure Substances I 362 Solvent in Solution I 362 Solute in Solution I Gibbs Function and the Equilibrium Constant in Terms of Activity / Dependence of Activity on Pressure / Dependence of Activity on Temperature / 370 Standard Partial Molar Enthalpies / 370 Solvent I 370 Solute I 370 Equation for Temperature Coefficient of the Activity / Standard Entropy / Deviations from Ideality in Terms of Excess Thermodynamic Quantities / 375 Representation of Excess Gibbs Function as a Function of Composition / 378 Exercises / 380 References / 383 CHAPTER 17 DETERMINATION OF NONELECTROLYTE ACTIVITIES AND EXCESS GIBBS FUNCTION FROM EXPERIMENTAL DATA Activity from Measurements of Vapor Pressure / 384 Solvent / 384 Solute / Excess Gibbs Function from Measurement of Vapor Pressure / 387

11 XVI CONTENTS 17-3 Activity of a Solute from Distribution of Solute between Two Immiscible Solvents / Activity from Measurements of Cell Potentials / Determination of the Activity of One Component from Known Values of the Activity of the Other / 397 Calculation of Activity of Solvent from That of Solute / 397 Calculation of Activity of Solute from That of Solvent / Measurements of Freezing Points / 400 Exercises / 400 References / 405 CHAPTER 18 CALCULATION OF PARTIAL MOLAR QUANTITIES AND EXCESS MOLAR QUANTITIES FROM EXPERIMENTAL DATA: VOLUME AND ENTHALPY Partial Molar Quantities by Differentiation of / as a Function of Composition / 407 Partial Molar Volumes / 409 Partial Molar Enthalpies / 413 Enthalpies ofmixing / 413 Enthalpies ofdilution I All 18-2 Partial Molar Quantities of One Component from those of Another Component by Numerical Integration / 420 Partial Molar Volumes / 421 Partial Molar Enthalpies / Analytic Methods for Partial Molar Properties / 422 Partial Molar Volumes / 422 Partial Molar Enthalpies / Changes in J for Some Processes Involving Solutions / 424 Differential Process / 424 Integral Process / Excess Properties: Volume and Enthalpy / 427 Excess Volume / 427 Excess Enthalpy / 428 Exercises / 428 References / 436 CHAPTER 19 ACTIVITY, ACTIVITY COEFFICIENTS, AND OSMOTIC COEFFICIENTS OF STRONG ELECTROLYTES Definitions and Standard States for Dissolved Electrolytes / 438 Uni-univalent Electrolytes / 438 Multivalent Electrolytes / 442

12 CONTENTS XVÜ Symmetrical Salts I 442 Unsymmetrical Salts I 442 General Case I 445 Mixed Electrolytes / Determination of Activities of Strong Electrolytes / 448 Measurement of Cell Potentials / 448 Solubility Measurements / 453 Colligative Property Measurement: the Osmotic Coefficient / 454 Extension of Activity Coefficient Data to Additional Temperatures with Enfhalpy of Dilution Data / 459» 19-3 Activity Coefficients of Some Strong Electrolytes / 462 Experimental Values / 462 Theoretical Correlation / 462 Exercises / 465 References / 470 CHAPTER 20 CHANGES IN GIBBS FUNCTION FOR PROCESSES INVOLVING SOLUTIONS Activity Coefficients of Weak Electrolytes / Determination of Equilibrium Constants for Dissociation of Weak Electrolytes / 473 From Measurements of Cell Potentials / 474 From Conductance Measurements / Some Typical Calculations for Gibbs Function of Formation / 482 Standard Gibbs Function for Formation of Aqueous Solute: HCl / 482 Standard Gibbs Function for Formation of Individual Ions: HCl / 483 Standard Gibbs Function for Formation of Solid Solute in Aqueous Solution / 484 Solute Very Soluble: Sodium Chloride I 484 Slightly Soluble Solute: Silver Chloride I 485 Standard Gibbs Function for Formation of Ion of Weak Electrolyte / 486 Standard Gibbs Function for Formation of Moderately Strong Electrolyte / 487 Effect of Salt Concentration on Geological Equilibrium Involving Water / 488 General Comments / Entropies of Ions / 490 The Entropy of an Aqueous Solution of a Salt / 490 Calculation of Entropy of Formation of Individual Ions / 491 Utilization of Ion Entropies in Thermodynamic Calculations / 492

13 XVIII CONTENTS Exercises / 493 References / 499 CHAPTER 21 SYSTEMS SUBJECT TO A GRAVITATIONAL FIELD Dependence of the Gibbs Function on Field / System in a Gravitational Field / System in a Centrifugal Field / 505 Exercises / 510 References / 511 CHAPTER 22 ESTIMATION OF THERMODYNAMIC QUANTITIES Empirical Methods / 512 Group Contribution Method of Andersen, Beyer, Watson, and Yoneda / 513 Typical Problems in Estimating Entropies / 517 Other Methods / 518 Accuracy of the Approximate Methods / 523 Equilibrium in Complex Systems / 523 Exercises / 523 References / 524 CHAPTER 23 PRACTICAL MATHEMATICAL TECHNIQUES Analytical Methods / 526 Linear Least Squares / 526 Nonlinear Least Squares / Numerical and Graphical Methods / 531 Numerical Differentiation / 531 Numerical Integration / 533 Use of the Digital Computer / 535 Graphical Differentiation / 536 Graphical Integration / 538 Exercises / 538 References / 538 CHAPTER 24 CONCLUDING REMARKS 540 References / 542 INDEX 544

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