CHEMICAL THERMODYNAMICS - GBV
Transcript of CHEMICAL THERMODYNAMICS - GBV
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
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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
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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