Chemical and Engineering Thermodynamics [3 ed.] 0471182109

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Abbreviated list of SI units Physical Quantity Basic units Length Mass Time Electric current Temperature Amount of substance Luminous intensity

SI Unit

Symbol

meter kilogram second ampere kelvin mole candela

m kg s A K mol cd

Derived units with assigned names Energy joule Force newton Power watt Electric charge coloumb Electric potential difference volt Pressure pascal Frequency hertz

J N W C V Pa Hz

Derived units without assigned names Area square meter Volume cubic meter Density cubic meter kilogram per Molar heat capacity joule per mole Kelvin Specific heat capacity joule per kilogram Kelvin Concentration mole per cubic meter

m2 m3 kg m−1 J mol−1 K−1 J kg−1 K−1 mol m−3

Units and conversion factors Length: Mass: Energy:

Pressure:

Molar Heat Capacity: Specific Heat Capacity:

Power:

Relation to Other SI Units

J = kg m2 s−2 N = kg m s−2 = J m−1 W = kg m2 s−3 = J s−1 C = As V = kg m2 s−3 A−1 = J A−1 s−1 Pa = kg m−1 s−2 = N m−2 s−1

The Gas Constant 1 m = 3.281 feet 1 kg = 2.2046 pounds 1 J = 1 watt-second = 107 ergs = 107 dyne-cm = 0.2390 cal = 0.948 × 10−3 BTU = 0.7376 ft-lb = 0.9868 × 10−2 liter-atm 1 Pa = 1 newton m−2 = 1 joule m−3 = 0.9869 × 10−5 atmospheres = 0.750 × 10−2 millimeters of energy = 1 × 10−5 bars = 1.450 × 10−4 psi

1 J mol−1 K−1 = 0.2390 cal(mol K)−1 = 0.2390 BTU(lb-mol ◦ F)−1 1 J g−1 K−1 = 0.2390 cal(g K)−1 = 0.2390 BTU(lb ◦ F)−1 = 1 kJ (kg K)−1 1 J sec−1 = 1 watt = 0.1341 × 10−2 horsepower (hp) = 0.7356 ft-lbf /sec = 0.948 × 10−3 BTU/sec

R = 8.314 = 8.314 = 8.314 × 10−3 = 8.314 × 10−5 = 8.314 × 10−2 = 8.314 × 10−6

J/mol K N m/mol K kPa m3 /mol K bar m3 /mol K bar m3 /kmol K MPa m3 /mol K

Contents NOTATION

xv

CHAPTERl

INTRODUCTION 1.1 The Central Problems of Thermodynamics 1 1.2 A System of Units 3 1.3 The Equilibrium State 5 1.4 Pressure, Temperature, and Equilibrium 7 1.5 Heat, Work, and the Conservation of Energy 12 1.6 Specification of the Equilibrium State; Intensive and Extensive Variables; Equations of State 15 1.7 A Summary of Important Experimental Observations 18 1.8 A Comment on the Development of Thermodynamics 20 Problems 20

1

CHAPTER 2

CONSERVATION OF MASS AND ENERGY 2.1 A General Balance Equation and Conserved Quantities 23 2.2 Conservation of Mass 27 2.3 Conservation of Energy 30 2.4 The Thermodynamic Properties of Matter 43 2.5 Applications of the Mass and Energy Balances 51 2.6 Conservation of Momentum 75 2.7 The Microscopic Equations of Change for Thermodynamics and Fluid Mechanics (Optional) 76 Problems 82

22

CHAPTER 3

ENTROPY: AN ADDITIONAL BALANCE EQUATION 3.1 Entropy: A New Concept 90 3.2 The Entropy Balance and Reversibility 97 3.3 Heat, Work, Engines, and Entropy 103 3.4 Entropy Changes of Matter 112 3.5 Applications of the Entropy Balance 115 3.6 Liquefaction 128

89

xi

xii

Contents 3.7 Power Generation and Refrigeration Cycles 132 3.8 The Thermodynamics of Mechanical Explosions 154 3.9 The Microscopic Entropy Balance (Optional) 163 Problems 165

CHAPTER 4

THE THERMODYNAMIC PROPERTIES OF REAL SUBSTANCES

17S

4.1 4.2 4.3 4.4

Some Mathematical Preliminaries 175 The Evaluation of Thermodynamic Partial Derivatives 179 The Ideal Gas and Absolute-Temperature Scales 194 The Evaluation of Changes in the Thermodynamic Properties of Real Substances Accompanying a Change of State 195 4.5 An Example Involving the Change of State of a Real Gas 219 4.6 The Principle of Corresponding States 225 4.7 Generalized Equations of State 238 4.8 The Third Law of Thermodynamics 242 4.9 More About Thermodynamic Partial Derivatives (Optional) 243 Appendix A4.1 A Program for Thermodynamic Properties Calculations Using the Peng-Robinson Cubic Equation of State, PR1 249 Problems 251

CHAPTERS

EQUILIBRIUM AND STABILITY IN ONE-COMPONENT SYSTEMS

260

5.1 The Criteria for Equilibrium 260 5.2 Stability of Thermodynamic Systems 265 5.3 Phase Equilibria: Application of the Equilibrium and Stability Criteria to the Equation of State 272 5.4 The Molar Gibbs Free Energy and Fugacity of a Pure Component 279 5.5 The Calculation of Pure Fluid-Phase Equilibrium: The Computation of Vapor Pressure from an Equation of State 295 5.6 The Specification of the Equilibrium Thermodynamic State of a System of Several Phases: The Gibbs Phase Rule for a One-Component System 303 5.7 Thermodynamic Properties of Phase Transitions 307 Problems 313

CHAPTER 6

THE THERMODYNAMICS OF MULTICOMPONENT MIXTURES 6.1 The Thermodynamic Description of Mixtures 324 6.2 The Partial Molar Gibbs Free Energy and the Generalized Gibbs-Duhem Equation 333 6.3 A Notation for Chemical Reactions 337 6.4 The Equations of Change for a Multicomponent System 340

324

Contents xiii 6.5 The Heat of Reaction and a Convention for the Thermodynamic Properties of Reacting Mixtures 349 6.6 The Experimental Determination of the Partial Molar Volume and Enthalpy 354 6.7 Criteria for Phase Equilibrium in Multicomponent Systems 364 6.8 The Criteria for Chemical Equilibrium, and Combined Chemical and Phase Equilibrium 368 6.9 The Specification of the Equilibrium Thermodynamic State of a Multicomponent, Multiphase System; the Gibbs Phase Rule 373 6.10 Some Concluding Remarks 377 Problems 377

CHAPTER 7

THE ESTIMATION OF THE GIBBS FREE ENERGY AND FUGACITY OF A COMPONENT IN A MIXTURE

388

7.1 7.2 7.3 7.4 7.5

The Ideal Gas Mixture 388 The Partial Molar Gibbs Free Energy and Fugacity 392 The Ideal Mixture and Excess Mixture Properties 396 The Fugacity of Species in Gaseous, Liquid, and Solid Mixtures 406 Several Correlative Liquid Mixture (Activity Coefficient) Models 414 7.6 Two Predictive Activity Coefficient Models 428 7.7 A Corresponding States Principle for Mixtures; The Pseudocritical Constant Method 437 7.8 The Fugacity of Species in Nonsimple Mixtures 444 7.9 Some Comments on Reference and Standard States 451 7.10 A Combined Equation-of-State-Excess Gibbs Free Energy Models 452 7.11 Electrolyte Solutions 455 7.12 Concluding Remarks 461 Appendix A7.1 A Statistical Mechanical Interpretation of the Entropy of Mixing in an Ideal Mixture 464 Appendix A7.2 A Program for Multicomponent Vapor-Liquid Equilibrium Calculations Using the Peng-Robinson Cubic Equation of State, VLMU 467 Appendix A7.3 Multicomponent Excess Gibbs Free Energy (Activity Coefficient) Models 468 Appendix A7.4 A Program for the Prediction of Activity Coefficients and Low Pressure Vapor-Liquid Equilibrium Using the UNIFAC Model, UNIFAC. 470 Problems 471

CHAPTERS

PHASE EQUILIBRIUM IN MIXTURES 8.1 Vapor-Liquid Equilibria Using Activity Coefficient Models Problems for Section 8.1 511 8.2 Vapor-Liquid Equilibria Using Equations of State 518 Problems for Section 8.2 534 8.3 The Solubility of a Gas in a Liquid 536

478 478

xiv Contents Problems for Section 8.3 547 8.4 The Solubility of a Liquid in a Liquid and Vapor-Liquid-Liquid Equilibrium 550 Problems for Section 8.4 571 8.5 The Solubility of a Solid in a Liquid, Gas, or Supercritical Fluid 575 Problems for Section 8.5 585 8.6 The Partitioning of a Solute Among Two Coexisting Liquid Phases; The Distribution Coefficient 586 Problems for Section 8.6 597 8.7 Freezing-Point Depression of a Solvent Due to the Presence of a Solute; the Freezing Point of Liquid Mixtures 598 Problems for Section 8.7 602 8.8 Osmotic Equilibrium and Osmotic Pressure 603 Problems for Section 8.8 606 8.9 The Phase Behavior Modeling of Chemicals in the Environment 608 Problems for Section 8.9 613 8.10 The Phase Behavior of Solid Mixtures 614 Problems for Section 8.10 622 8.11 Concluding Remarks 623 Additional Phase Equilibrium Problems 624

CHAPTER 9

CHEMICAL EQUILIBRIUM AND THE BALANCE EQUATIONS FOR CHEMICALLY REACTING SYSTEMS

630

9.1 Chemical Equilibrium in a Single-Phase System 630 9.2 Heterogeneous Chemical Reactions 663 9.3 Chemical Equilibrium When Several Reactions Occur in a Single Phase 676 9.4 Combined Chemical and Phase Equilibrium 683 9.5 The Balance Equations for a Tank-Type Chemical Reactor 691 9.6 The Balance Equations for a Thbular Reactor 699 9.7 Overall Reactor Balance Equations and the Adiabatic Reaction Temperature 702 9.8 The Thermodynamics of Chemical Explosions 711 9.9 Introduction to Electrochemical Processes 717 9.10 Coupled Chemical Reactions 727 Appendix A9.1 A Program for the Calculation of Chemical Equilibrium Constants As a Function of Temperature, CHEMEQ 730 Problems 731

APPENDIXES

744 Appendix I Conversion Factors for SI Units 744 Appendix II The Molar Heat Capacities of Gases in the Ideal Gas (Zero Pressure) State 745 Appendix III The Thermodynamic Properties of Water and Steam 748 Appendix IV Enthalpies and Free Energies of Formation 758 Appendix V Heats of Combustion 761

INDEX

763