Devoe - Thermodynamics and Chemistry

SECOND EDITION HO W ARD DEV OE Thermodynamics and Chemistry Second Edition V ersion 4, March 2012 Ho ward DeV oe Associate Professor of Chemistry Emeritus Uni versity of Maryland, College P ark, Maryland The ﬁrst edition of this book was pre viously published by Pearson Education, Inc. It was copyright ©2001 by Prentice-Hall, Inc. The second edition, version 4 is cop yright ©2012 by Howard DeV oe. This work is licensed under a Creati ve Commons Attrib ution-NonCommercial-NoDerivs License, whose full text is at http://creativecommons.org/licenses/by- nc- nd/3.0 Y ou are free to read, store, copy and print the PDF ﬁle for personal use. Y ou are not allowed to alter , transform, or build upon this w ork, or to sell it or use it for any commercial purpose whatsoe ver , without the written consent of the copyright holder . The book was typeset using the L A T E X typesetting system and the memoir class. Most of the ﬁgures were produced with PST ricks, a related software program. The fonts are Adobe T imes, MathT ime, Helvetica, and Computer Modern T ype writer . I thank the Department of Chemistry and Biochemistry , Uni versity of Maryland, College Park, Maryland ( http://www.chem.umd.edu ) for hosting the W eb site for this book. The most recent version can al ways be found online at http://www.chem.umd.edu/thermobook If you are a faculty member of a chemistry or related department of a college or uni- versity , you may send a request to hdev oe@umd.edu for a complete Solutions Manual in PDF format for your personal use. In order to protect the integrity of the solutions, requests will be subject to veriﬁcation of your f aculty status and your agreement not to reproduce or transmit the manual in any form. S H O R T C ONTENTS Biographical Sketches 15 Preface to the Second Edition 16 From the Pr eface to the First Edition 17 1 Introduction 19 2 Systems and Their Properties 27 3 The First Law 56 4 The Second Law 102 5 Thermodynamic Potentials 135 6 The Third Law and Cry ogenics 150 7 Pure Substances in Single Phases 164 8 Phase T ransitions and Equilibria of Pure Substances 193 9 Mixtures 223 10 Electrolyte Solutions 286 11 Reactions and Other Chemical Processes 303 12 Equilibrium Conditions in Multicomponent Systems 367 13 The Phase Rule and Phase Diagrams 419 14 Galvanic Cells 450 A ppendix A Deﬁnitions of the SI Base Units 471 4 S H O RT C O N T E N T S 5 A ppendix B Physical Constants 472 A ppendix C Symbols for Ph ysical Quantities 473 A ppendix D Miscellaneous Abbr eviations and Symbols 477 A ppendix E Calculus Review 480 A ppendix F Mathematical Properties of State Functions 482 A ppendix G F orces, Energy , and W ork 487 A ppendix H Standard Molar Thermodynamic Properties 505 A ppendix I Answers to Selected Problems 508 Bibliography 512 Index 521 Thermodynamics and Chemistr y , second edition, version 4 © 2012 b y Howard DeV oe. Latest v ersion: www.chem.umd.edu/thermobook C ONTENTS Biographical Sketches 15 Preface to the Second Edition 16 From the Pr eface to the First Edition 17 1 Introduction 19 1 . 1 U n i t s ..................................... 19 1.1.1 Amount of substance and amount . . . . . . . . . . . . . . . . . . 21 1 . 2 Q u a n t i t y C a l c u l u s .............................. 22 1 . 3 D i m e n s i o n a l A n a l y s i s ............................ 24 P r o b l e m ....................................... 26 2 Systems and Their Properties 27 2.1 The System, Surroundings, and Boundary . . . . . . . . . . . . . . . . . . 27 2.1.1 Extensi ve and intensive properties . . . . . . . . . . . . . . . . . . 28 2.2 Phases and Physical States of Matter . . . . . . . . . . . . . . . . . . . . . 30 2.2.1 Physical states of matter . . . . . . . . . . . . . . . . . . . . . . . 30 2.2.2 Phase coexistence and phase transitions . . . . . . . . . . . . . . . 31 2 . 2 . 3 F l u i d s................................. 32 2.2.4 The equation of state of a ﬂuid . . . . . . . . . . . . . . . . . . . . 33 2.2.5 V irial equations of state for pure gases . . . . . . . . . . . . . . . . 34 2 . 2 . 6 S o l i d s................................. 36 2.3 Some Basic Properties and Their Measurement . . . . . . . . . . . . . . . 36 2 . 3 . 1 M a s s ................................. 36 2 . 3 . 2 V o l u m e ................................ 37 2 . 3 . 3 D e n s i t y ................................ 38 2 . 3 . 4 P r e s s u r e ................................ 38 2 . 3 . 5 T e m p e r a t u r e ............................. 40 2 . 4 T h e S t a t e o f t h e S y s t e m ........................... 45 2.4.1 State functions and independent v ariables . . . . . . . . . . . . . . 45 2.4.2 An example: state functions of a mixture . . . . . . . . . . . . . . 46 2.4.3 More about independent v ariables . . . . . . . . . . . . . . . . . . 47 6 C ONTENTS 7 2.4.4 Equilibrium states . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2 . 4 . 5 S t e a d y s t a t e s ............................. 50 2 . 5 P r o c e s s e s a n d P a t h s .............................. 50 2.6 The Energy of the System . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.6.1 Energy and reference frames . . . . . . . . . . . . . . . . . . . . . 53 2 . 6 . 2 I n t e r n a l e n e r g y ............................ 53 P r o b l e m s ...................................... 55 3 The First Law 56 3.1 Heat, W ork, and the First Law . . . . . . . . . . . . . . . . . . . . . . . . 56 3.1.1 The concept of thermodynamic work . . . . . . . . . . . . . . . . 57 3.1.2 W ork coefﬁcients and work coordinates . . . . . . . . . . . . . . . 59 3.1.3 Heat and work as path functions . . . . . . . . . . . . . . . . . . . 60 3 . 1 . 4 H e a t a n d h e a t i n g ........................... 61 3 . 1 . 5 H e a t c a p a c i t y ............................. 62 3 . 1 . 6 T h e r m a l e n e r g y ............................ 62 3.2 Spontaneous, Re versible, and Irreversible Processes . . . . . . . . . . . . . 64 3.2.1 Re versible processes . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2.2 Irre versible processes . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.2.3 Purely mechanical processes . . . . . . . . . . . . . . . . . . . . . 66 3 . 3 H e a t T r a n s f e r ................................. 67 3.3.1 Heating and cooling . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.3.2 Spontaneous phase transitions . . . . . . . . . . . . . . . . . . . . 69 3 . 4 D e f o r m a t i o n W o r k .............................. 69 3.4.1 Gas in a cylinder -and-piston device . . . . . . . . . . . . . . . . . 70 3.4.2 Expansion work of a gas . . . . . . . . . . . . . . . . . . . . . . . 72 3.4.3 Expansion work of an isotropic phase . . . . . . . . . . . . . . . . 73 3 . 4 . 4 G e n e r a l i t i e s .............................. 74 3.5 Applications of Expansion W ork . . . . . . . . . . . . . . . . . . . . . . . 75 3.5.1 The internal energy of an ideal gas . . . . . . . . . . . . . . . . . . 75 3.5.2 Re versible isothermal expansion of an ideal gas . . . . . . . . . . . 75 3.5.3 Re versible adiabatic expansion of an ideal gas . . . . . . . . . . . . 75 3.5.4 Indicator diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.5.5 Spontaneous adiabatic expansion or compression . . . . . . . . . . 78 3.5.6 Free expansion of a gas into a vacuum . . . . . . . . . . . . . . . . 79 3.6 W ork in a Gravitational Field . . . . . . . . . . . . . . . . . . . . . . . . . 80 3 . 7 S h a f t W o r k .................................. 82 3 . 7 . 1 S t i r r i n g w o r k ............................. 83 3.7.2 The Joule paddle wheel . . . . . . . . . . . . . . . . . . . . . . . . 84 3 . 8 E l e c t r i c a l W o r k ................................ 86 3.8.1 Electrical work in a circuit . . . . . . . . . . . . . . . . . . . . . . 86 3 . 8 . 2 E l e c t r i c a l h e a t i n g........................... 88 3.8.3 Electrical work with a galvanic cell . . . . . . . . . . . . . . . . . 89 3.9 Irre versible W ork and Internal Friction . . . . . . . . . . . . . . . . . . . . 91 3.10 Rev ersible and Irrev ersible Processes: Generalities . . . . . . . . . . . . . 95 P r o b l e m s ...................................... 97 Thermodynamics and Chemistr y , second edition, version 4 © 2012 b y Howard DeV oe. Latest v ersion: www.chem.umd.edu/thermobook C ONTENTS 8 4 The Second Law 102 4 . 1 T y p e s o f P r o c e s s e s .............................. 102 4.2 Statements of the Second Law . . . . . . . . . . . . . . . . . . . . . . . . 103 4.3 Concepts De veloped with Carnot Engines . . . . . . . . . . . . . . . . . . 106 4.3.1 Carnot engines and Carnot cycles . . . . . . . . . . . . . . . . . . 106 4.3.2 The equi valence of the Clausius and K elvin–Planck statements . . . 109 4.3.3 The ef ﬁciency of a Carnot engine . . . . . . . . . . . . . . . . . . 111 4.3.4 Thermodynamic temperature . . . . . . . . . . . . . . . . . . . . . 114 4.4 Deri vation of the Mathematical Statement of the Second La w . . . . . . . 116 4.4.1 The existence of the entropy function . . . . . . . . . . . . . . . . 116 4.4.2 Using re versible processes to deﬁne the entropy . . . . . . . . . . . 120 4.4.3 Some properties of the entropy . . . . . . . . . . . . . . . . . . . . 123 4 . 5 I r r e v e r s i b l e P r o c e s s e s ............................. 124 4.5.1 Irre versible adiabatic processes . . . . . . . . . . . . . . . . . . . 124 4.5.2 Irre versible processes in general . . . . . . . . . . . . . . . . . . . 125 4 . 6 A p p l i c a t i o n s ................................. 126 4.6.1 Re versible heating . . . . . . . . . . . . . . . . . . . . . . . . . . 127 4.6.2 Re versible expansion of an ideal gas . . . . . . . . . . . . . . . . . 127 4.6.3 Spontaneous changes in an isolated system . . . . . . . . . . . . . 128 4.6.4 Internal heat ﬂo w in an isolated system . . . . . . . . . . . . . . . 128 4.6.5 Free expansion of a gas . . . . . . . . . . . . . . . . . . . . . . . . 129 4.6.6 Adiabatic process with work . . . . . . . . . . . . . . . . . . . . . 129 4 . 7 S u m m a r y ................................... 130 4.8 The Statistical Interpretation of Entropy . . . . . . . . . . . . . . . . . . . 130 P r o b l e m s ...................................... 133 5 Thermodynamic Potentials 135 5.1 T otal Differential of a Dependent V ariable . . . . . . . . . . . . . . . . . . 135 5.2 T otal Differential of the Internal Energy . . . . . . . . . . . . . . . . . . . 136 5.3 Enthalpy , Helmholtz Energy , and Gibbs Energy . . . . . . . . . . . . . . . 138 5 . 4 C l o s e d S y s t e m s ................................ 140 5 . 5 O p e n S y s t e m s ................................ 141 5.6 Expressions for Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . 143 5 . 7 S u r f a c e W o r k................................. 144 5.8 Criteria for Spontaneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 P r o b l e m s ...................................... 148 6 The Third Law and Cry ogenics 150 6 . 1 T h e Z e r o o f E n t r o p y ............................. 150 6 . 2 M o l a r E n t r o p i e s ............................... 152 6.2.1 Third-law molar entropies . . . . . . . . . . . . . . . . . . . . . . 152 6.2.2 Molar entropies from spectroscopic measurements . . . . . . . . . 155 6 . 2 . 3 R e s i d u a l e n t r o p y ........................... 156 6 . 3 C r y o g e n i c s .................................. 157 6.3.1 Joule–Thomson expansion . . . . . . . . . . . . . . . . . . . . . . 157 6 . 3 . 2 M a g n e t i z a t i o n ............................ 159 Thermodynamics and Chemistr y , second edition, version 4 © 2012 b y Howard DeV oe. Latest v ersion: www.chem.umd.edu/thermobook C ONTENTS 9 P r o b l e m ....................................... 163 7 Pure Substances in Single Phases 164 7 . 1 V o l u m e P r o p e r t i e s .............................. 164 7 . 2 I n t e r n a l P r e s s u r e ............................... 166 7 . 3 T h e r m a l P r o p e r t i e s .............................. 168 7.3.1 The relation between C V ; m and C p; m ................. 168 7.3.2 The measurement of heat capacities . . . . . . . . . . . . . . . . . 169 7 . 3 . 3 T y p i c a l v a l u e s ............................ 174 7.4 Heating at Constant V olume or Pressure . . . . . . . . . . . . . . . . . . . 175 7.5 Partial Deri v ativ es with Respect to T , p , and V ............... 177 7.5.1 T ables of partial deriv ativ es . . . . . . . . . . . . . . . . . . . . . 177 7.5.2 The Joule–Thomson coef ﬁcient . . . . . . . . . . . . . . . . . . . 180 7.6 Isothermal Pressure Changes . . . . . . . . . . . . . . . . . . . . . . . . . 181 7 . 6 . 1 I d e a l g a s e s .............................. 181 7 . 6 . 2 C o n d e n s e d p h a s e s .......................... 181 7.7 Standard States of Pure Substances . . . . . . . . . . . . . . . . . . . . . 182 7.8 Chemical Potential and Fugacity . . . . . . . . . . . . . . . . . . . . . . . 182 7 . 8 . 1 G a s e s ................................. 183 7 . 8 . 2 L i q u i d s a n d s o l i d s .......................... 186 7.9 Standard Molar Quantities of a Gas . . . . . . . . . . . . . . . . . . . . . 186 P r o b l e m s ...................................... 189 8 Phase T ransitions and Equilibria of Pure Substances 193 8 . 1 P h a s e E q u i l i b r i a ............................... 193 8.1.1 Equilibrium conditions . . . . . . . . . . . . . . . . . . . . . . . . 193 8.1.2 Equilibrium in a multiphase system . . . . . . . . . . . . . . . . . 194 8.1.3 Simple deri vation of equilibrium conditions . . . . . . . . . . . . . 195 8.1.4 T all column of gas in a gravitational ﬁeld . . . . . . . . . . . . . . 196 8.1.5 The pressure in a liquid droplet . . . . . . . . . . . . . . . . . . . 198 8.1.6 The number of independent v ariables . . . . . . . . . . . . . . . . 199 8.1.7 The Gibbs phase rule for a pure substance . . . . . . . . . . . . . . 200 8.2 Phase Diagrams of Pure Substances . . . . . . . . . . . . . . . . . . . . . 200 8.2.1 Features of phase diagrams . . . . . . . . . . . . . . . . . . . . . . 201 8.2.2 T wo-phase equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 204 8 . 2 . 3 T h e c r i t i c a l p o i n t ........................... 206 8 . 2 . 4 T h e l e v e r r u l e ............................. 207 8 . 2 . 5 V o l u m e p r o p e r t i e s .......................... 210 8 . 3 P h a s e T r a n s i t i o n s ............................... 212 8.3.1 Molar transition quantities . . . . . . . . . . . . . . . . . . . . . . 212 8.3.2 Calorimetric measurement of transition enthalpies . . . . . . . . . 214 8.3.3 Standard molar transition quantities . . . . . . . . . . . . . . . . . 214 8 . 4 C o e x i s t e n c e C u r v e s .............................. 214 8.4.1 Chemical potential surfaces . . . . . . . . . . . . . . . . . . . . . 215 8.4.2 The Clapeyron equation . . . . . . . . . . . . . . . . . . . . . . . 216 8.4.3 The Clausius–Clapeyron equation . . . . . . . . . . . . . . . . . . 219 Thermodynamics and Chemistr y , second edition, version 4 © 2012 b y Howard DeV oe. Latest v ersion: www.chem.umd.edu/thermobook C ONTENTS 10 P r o b l e m s ...................................... 221 9 Mixtures 223 9 . 1 C o m p o s i t i o n V a r i a b l e s ............................ 223 9.1.1 Species and substances . . . . . . . . . . . . . . . . . . . . . . . . 223 9.1.2 Mixtures in general . . . . . . . . . . . . . . . . . . . . . . . . . . 223 9 . 1 . 3 S o l u t i o n s ............................... 224 9 . 1 . 4 B i n a r y s o l u t i o n s ........................... 225 9.1.5 The composition of a mixture . . . . . . . . . . . . . . . . . . . . 226 9.2 Partial Molar Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 9.2.1 Partial molar volume . . . . . . . . . . . . . . . . . . . . . . . . . 227 9.2.2 The total dif ferential of the volume in an open system . . . . . . . . 229 9.2.3 Ev aluation of partial molar volumes in binary mixtures . . . . . . . 231 9 . 2 . 4 G e n e r a l r e l a t i o n s ........................... 233 9.2.5 Partial speciﬁc quantities . . . . . . . . . . . . . . . . . . . . . . . 235 9.2.6 The chemical potential of a species in a mixture . . . . . . . . . . . 236 9.2.7 Equilibrium conditions in a multiphase, multicomponent system . . 236 9.2.8 Relations in volving partial molar quantities . . . . . . . . . . . . . 238 9 . 3 G a s M i x t u r e s ................................. 239 9 . 3 . 1 P a r t i a l p r e s s u r e ............................ 240 9.3.2 The ideal gas mixture . . . . . . . . . . . . . . . . . . . . . . . . . 240 9.3.3 Partial molar quantities in an ideal gas mixture . . . . . . . . . . . 240 9 . 3 . 4 R e a l g a s m i x t u r e s ........................... 243 9.4 Liquid and Solid Mixtures of Nonelectrolytes . . . . . . . . . . . . . . . . 246 9 . 4 . 1 R a o u l t ’ s l a w ............................. 246 9 . 4 . 2 I d e a l m i x t u r e s ............................. 248 9.4.3 Partial molar quantities in ideal mixtures . . . . . . . . . . . . . . 249 9 . 4 . 4 H e n r y ’ s l a w .............................. 250 9.4.5 The ideal-dilute solution . . . . . . . . . . . . . . . . . . . . . . . 253 9.4.6 Solvent behavior in the ideal-dilute solution . . . . . . . . . . . . . 255 9.4.7 Partial molar quantities in an ideal-dilute solution . . . . . . . . . . 256 9.5 Acti vity Coefﬁcients in Mixtures of Nonelectrolytes . . . . . . . . . . . . 258 9.5.1 Reference states and standard states . . . . . . . . . . . . . . . . . 258 9 . 5 . 2 I d e a l m i x t u r e s ............................. 259 9 . 5 . 3 R e a l m i x t u r e s ............................. 259 9.5.4 Nonideal dilute solutions . . . . . . . . . . . . . . . . . . . . . . . 261 9.6 Ev aluation of Activity Coefﬁcients . . . . . . . . . . . . . . . . . . . . . . 262 9.6.1 Acti vity coefﬁcients from gas fugacities . . . . . . . . . . . . . . . 262 9.6.2 Acti vity coefﬁcients from the Gibbs–Duhem equation . . . . . . . 265 9.6.3 Acti vity coefﬁcients from osmotic coefﬁcients . . . . . . . . . . . 266 9.6.4 Fugacity measurements . . . . . . . . . . . . . . . . . . . . . . . . 268 9.7 Acti vity of an Uncharged Species . . . . . . . . . . . . . . . . . . . . . . 270 9 . 7 . 1 S t a n d a r d s t a t e s ............................ 270 9.7.2 Acti vities and composition . . . . . . . . . . . . . . . . . . . . . . 272 9.7.3 Pressure factors and pressure . . . . . . . . . . . . . . . . . . . . . 273 9.8 Mixtures in Gravitational and Centrifugal Fields . . . . . . . . . . . . . . 275 Thermodynamics and Chemistr y , second edition, version 4 © 2012 b y Howard DeV oe. 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Devoe - Thermodynamics and Chemistry

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