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

CONTENTS

PREFACE xix

CHAPTER 1 INTRODUCTION 1

1-1 Origins of Chemical Thermodynamics / 1 1-2 Objectives of Chemical Thermodynamics / 4 1-3 Limitations of Classical Thermodynamics / 4

References / 6

CHAPTER 2 MATHEMATICAL PREPARATION FOR THERMODYNAMICS 8

2-1 Variables of Thermodynamics / 8 Extensive and Intensive Quantities / 8 Units and Conversion Factors / 9

2-2 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

VÜi CONTENTS

Euler 's Theorem I 18 References / 26

CHAPTER 3 THE FIRST LAW OF THERMODYNAMICS

3-1 Definitions / 28 Temperature / 30 Work / 32

3-2 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 Qv and QP I 44

4-2 Enthalpy of Reactions / 46 Definitions and Conventions / 46

Some Standard States I 46 Enthalpy of Formation I 47

4-3 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 / 54

4-4 Bond Enthalpies / 55 Definition of Bond Enthalpies / 55 Calculation of Bond Enthalpies / 56 Enthalpy of Reaction from Bond Enthalpies / 57

4-5 HeatCapacity / 59 Definition / 59

Fundamental Statement I 59 Derived Relationships I 60

Some Relationships between CP and Cv I 60 Heat Capacities of Gases / 63 Heat Capacities of Solids / 63

Heat Capacities of Liquids / 66 Sources of Heat Capacity Data / 66

4-6 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 CP and Cv I 80 Calculation of the Thermodynamic Changes in Expansion Processes / 81

Isothermal I 81 Adiabatic I 87

5-2 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 / 107 6-2 The Nature of the Second Law / 108

Natural Tendencies Toward Equilibrium / 108 Statement of the Second Law / 108 Mathematical Counterpart of the Verbal Statement / 109

6-3 The Carnot Cycle / 109 The Forward Cycle / H O The Reverse Cycle / 112 Alternative Statement of the Second Law / 113 Carnot's Theorem / 113

X CONTENTS

6-4 The Thermodynamic Temperature Scale / 116 6-5 The Definition of S, The Entropy of a System / 121 6-6 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 / 125

6-7 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 / 128

6-8 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 / 135

6-9 General Equations for the Entropy of Gases / 138 Entropy of an Ideal Gas / 138 Entropy of a Real Gas / 139

6-10 Temperature-Entropy Diagram / 141 6-11 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 154

7-1 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 / 159

7-2 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

CONTENTS

Equations for Total Differentials / 161 Pressure and Temperature Coefficients of the Functions / 162 Equations Derived from the Reciprocity Relationship / 164

7-3 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 176 7-4 Useful Work and the Gibbs and Helmholtz Functions / 178

Isothermal Changes / 178 Changes at Constant Temperature and Pressure / 181 Relationship between AHP and QP 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 / 200

8-2 The Effect of an Inert Gas on Vapor Pressure / 202 Variable Total Pressure at Constant Temperature / 203 Variable Temperature at Constant Total Pressure / 204

8-3 Temperature Dependence of Enthalpy of Phase Transition / 204 8-4 Calculation of Change in the Gibbs Function and Change in the Planck

Function for Spontaneous Phase Change / 206 Arithmetic Method / 207 Analytic Method / 207

XII CONTENTS

Exercises / 209 References / 215

CHAPTER9 THE THIRD LAW OF THERMODYNAMICS 216

9-1 Need for the Third Law / 216 9-2 Formulation of the Third Law / 217

Nernst Heat Theorem / 218 Planck's Formulation / 218 Statement of Lewis and Randall / 219

9-3 Thermodynamic Properties at Absolute Zero / 220 Equivalence of G and H I 220 ACP in an Isothermal Chemical Transformation / 220 Limiting Values of CP and Cv I 221 Temperature Coefficients of Pressure and Volume / 222

9-4 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 239

10-1 Determination of Gibbs Function and Planck Function from Equilibrium Measurements / 239

10-2 Determination of Gibbs Function and Planck Function from Measurements of Cell Potentials / 242

10-3 Calculation of Gibbs Function and Planck Function from Calorimetric Measurements / 243

10-4 Calculation of Gibbs Function and Planck Function of Reaction from Standard Gibbs Function and Standard Planck Function of Formation / 245

10-5 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

CONTENTS XÜi

CHAPTER 11 THERMODYNAMICS OF SYSTEMS OF VARIABLE COMPOSITION 262

11-1 State Functions for Systems of Variable Composition / 262 11-2 Criteria of Equilibrium and Spontaneity in Systems of Variable

Composition / 264 11-3 Relationships among Partial Molar Properties of a Single

Component / 266 11-4 Relationships between Partial Molar Quantities of Different

Components / 267 Partial Molar Quantities for Pure Phase / 269

11-5 Escaping Tendency / 270 Chemical Potential and Escaping Tendency / 270

11-6 Chemical Equilibrium in Systems of Variable Composition / 272 Exercises / 275 Reference / 278

CHAPTER 12 MIXTURES OF GASES 279

12-1 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 / 283

12-2 The Fugacity Function of a Pure Real Gas / 284 Change of Fugacity with Pressure / 285 Change of Fugacity with Temperature / 286

12-3 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 295

12-4 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 / 298

12-5 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

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 307

13-1 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 / 310 13-2 One-Component Systems / 311 13-3 Two-Component Systems / 313

Two Phases at Different Pressures / 316 Phase Rule Criterion of Purity / 319 Exercises / 319 References / 320

CHAPTER14 THE IDEAL SOLUTION 322

14-1 Definition / 322 14-2 Some Consequences of the Definition / 324

Volume Changes / 324 Heat Effects / 325

14-3 Thermodynamics of Transfer of a Component from One Ideal Solution to Another / 326

14-4 Thermodynamics of Mixing / 328 14-5 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 / 332

14-6 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 340

15-1 Henry's Law / 340 15-2 Nernst's Distribution Law / 343 15-3 Raoult's Law / 344

CONTENTS XV

15-4 van't Hoff's Law of Osmotic Pressure / 347 Osmotic Work in Biological Systems / 352

15-5 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 359

16-1 Definitions of Activities and Activity Coefficients / 360 Activity / 360 Activity Coefficient / 360

16-2 Choice of Standard States / 361 Gases / 361 Liquids and Solids / 362

Pure Substances I 362 Solvent in Solution I 362 Solute in Solution I 364

16-3 Gibbs Function and the Equilibrium Constant in Terms of Activity / 367

16-4 Dependence of Activity on Pressure / 369 16-5 Dependence of Activity on Temperature / 370

Standard Partial Molar Enthalpies / 370 Solvent I 370 Solute I 370

Equation for Temperature Coefficient of the Activity / 371 16-6 Standard Entropy / 373

16-7 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 384

17-1 Activity from Measurements of Vapor Pressure / 384 Solvent / 384 Solute / 385

17-2 Excess Gibbs Function from Measurement of Vapor Pressure / 387

XVI CONTENTS

17-3 Activity of a Solute from Distribution of Solute between Two Immiscible Solvents / 388

17-4 Activity from Measurements of Cell Potentials / 393 17-5 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 / 398

17-6 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 407

18-1 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 / 422

18-3 Analytic Methods for Partial Molar Properties / 422 Partial Molar Volumes / 422 Partial Molar Enthalpies / 423

18-4 Changes in J for Some Processes Involving Solutions / 424 Differential Process / 424 Integral Process / 426

18-5 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 438

19-1 Definitions and Standard States for Dissolved Electrolytes / 438 Uni-univalent Electrolytes / 438 Multivalent Electrolytes / 442

CONTENTS XVÜ

Symmetrical Salts I 442 Unsymmetrical Salts I 442 General Case I 445

Mixed Electrolytes / 446 19-2 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 472

20-1 Activity Coefficients of Weak Electrolytes / 472 20-2 Determination of Equilibrium Constants for Dissociation of Weak

Electrolytes / 473 From Measurements of Cell Potentials / 474 From Conductance Measurements / 476

20-3 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 / 489

20-4 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

XVIII CONTENTS

Exercises / 493 References / 499

CHAPTER 21 SYSTEMS SUBJECT TO A GRAVITATIONAL FIELD 500

21-1 Dependence of the Gibbs Function on Field / 502 21-2 System in a Gravitational Field / 502 21-3 System in a Centrifugal Field / 505

Exercises / 510 References / 511

CHAPTER 22 ESTIMATION OF THERMODYNAMIC QUANTITIES 512

22-1 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 526

23-1 Analytical Methods / 526 Linear Least Squares / 526 Nonlinear Least Squares / 530

23-2 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