PHYSICAL AND CHEMICAL EQUILIBRIUM FOR CHEMICAL ENGINEERS PHYSICAL AND CHEMICAL EQUILIBRIUM FOR CHEMICAL ENGINEERS Second Edition NOEL DE NEVERS Universityof Utah Department ofChemicalEngineering SaltLake City, Utah Copyright(cid:2)2012byJohnWiley&Sons,Inc.Allrightsreserved PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey PublishedsimultaneouslyinCanada Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorbyanymeans,electronic,mechanical, photocopying,recording,scanning,orotherwise,exceptaspermittedunderSection107or108ofthe1976UnitedStatesCopyrightAct,withouteitherthe priorwrittenpermissionofthePublisher,orauthorizationthroughpaymentoftheappropriateper-copyfeetotheCopyrightClearanceCenter,Inc., 222RosewoodDrive,Danvers,MA01923,(978)750-8400,fax(978)750-4470,oronthewebatwww.copyright.com.RequeststothePublisherfor permissionshouldbeaddressedtothePermissionsDepartment,JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ07030,(201)748-6011, fax(201)748-6008,oronlineathttp://www.wiley.com/go/permission. 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TP155.2.T45D42012 6600.2969–dc23 2011046731 PrintedintheUnitedStatesofAmerica 10 9 8 7 6 5 4 3 2 1 Conversion Factors* Length: 1ft ¼0.3048 m¼12 in¼mile/5280¼nautical mile/6076¼km/3281 1m¼3.281ft¼39.37 in¼100cm¼1000mm¼106 micron¼1010A(cid:2) ¼km/1000 Mass: 1lbm¼0.45359kg¼short ton/2000¼long ton/2240¼16 oz (av.) ¼14.58oz (troy)¼metric ton(tonne)/2204.63¼7000 grains¼slug/32.2 1kg ¼2.2046 lbm¼1000g¼(metric tonortonne orMg)/1000 Force: 1lbf¼4.4482N¼32.2lbm(cid:3)ft/s2¼32.2 poundal¼0.4536 kgf 1N ¼kg(cid:3)m/s2¼105 dyne¼kgf/9.81¼0.2248 lbf Volume: 1ft3 ¼0.02831 m3¼28.31 liter¼7.48US gallons¼6.23 Imperial gallons¼acre-ft/43,560 1USgallon¼231 in3¼barrel (petroleum)/42¼barrel (beer, USA)/31 ¼4 USquarts¼8US pints¼3.785 liter¼0.003785 m3 1m3 ¼1000 liter¼35.29ft3 Energy: 1Btu¼1055J¼1.055 kW(cid:3)s¼2.93(cid:3)10(cid:4)4 kWh¼252 cal¼778.17ft lbf¼3.93(cid:3)10(cid:4)4 hp(cid:3)h 1J ¼1 N(cid:3)m¼1W(cid:3)s¼1 volt(cid:3)coulomb¼9.48(cid:3)10(cid:4)4 Btu¼0.239 cal¼107erg ¼6.24(cid:3)1018 electronvolt kWh ¼kilowatt(cid:3)hour¼3.6 MJ¼3413 Btu Power: 1hp¼550ft(cid:3)lbf/s¼33,000ft(cid:3)lbf/min¼2545Btu/hr¼0.746 kW 1W¼J/s¼N(cid:3)m/s¼Volt(cid:3)ampere¼0.239cal/s¼9.48(cid:3)10(cid:4)4Btu/s¼1.34(cid:3)10(cid:4)3 hp Pressure: 1atm¼101.3 kPa¼1.013 bar¼14.696lbf/in2¼33.89ft ofwater¼29.92 inchesofmercury ¼1.033kgf/cm2¼10.33m ofwater¼760mm of mercury¼760 torr 1psi ¼atm/14.696¼6.89 kPa¼27.7in H O¼51.7 torr 2 1Pa ¼N/m2¼kg/m s2¼10(cid:4)5 bar¼1.450(cid:3)10(cid:4)4lbf/in2¼0.0075 torr¼0.0040 inH O 2 Viscosity: 1cp¼0.01 poise¼0.01g/cm(cid:3)s¼0.001kg/m(cid:3)s¼0.001 Pa(cid:3)s ¼6.72(cid:3)10(cid:4)4lbm/ft(cid:3)s¼2.42lbm/ft(cid:3)hr¼2.09(cid:3)10(cid:4)5lbf(cid:3)s/ft2¼0.01dyne(cid:3)s/cm2 Kinematic viscosity: 1cs¼0.01 stoke¼0.01cm2/s¼10(cid:4)6m2/s¼1cp/(g/cm3) ¼ 1.08(cid:3)10(cid:4)5ft2/s¼cp/(62.4lbm/ft3) Temperature: K ¼(cid:2)C+273.15¼(cid:2)R/1.8(cid:5)(cid:2)C+273: (cid:2)C¼((cid:2)F (cid:4)32)/1.8 (cid:2)R¼(cid:2)F+459.67(cid:5)(cid:2)F+460¼1.8K: (cid:2)F¼1.8(cid:2)C+32 Ppm: Inthechemicalandenvironmentalengineeringliteratureandinthisbook,ppmappliedtoagasalwaysmeanspartspermillionby volumeorbymol.Theseareidenticalforanidealgas,andpracticallyidenticalformostcommongasesat1atmpressure.Ppm applied toa liquid or solidalmost always means parts per million by mass. Psia,psig: Psia means pounds per square inch, absolute.Psig means pounds per square inch, gauge, that is, above orbelow the local atmospheric pressure. *Thesevaluesaremostlyrounded.Thereareseveraldefinitionsforsomeofthesequantities,suchastheBtuandthecalorie;thesedifferfromeachotherbyupto 0.2%.ForthemostaccuratevaluesseeAmericanNationalStandardforUseoftheInternationalSystemofUnits(SI):TheModernMetricSystem,IEEE/ASTM 10(cid:2)-2002,ASTM,WestConshohocken,PA. CONTENTS Preface xiii About the Author xv Nomenclature xvii 1 Introduction toEquilibrium 1 1.1 Why Study Equilibrium?, 1 1.2 Stability and Equilibrium, 4 1.3 Time Scales andthe Approach to Equilibrium, 5 1.4 Looking Ahead,Gibbs Energy, 5 1.5 Units, Conversion Factors, and Notation, 6 1.6 Reality and Equations, 8 1.7 Phases and Phase Diagrams, 8 1.8 ThePlan ofthis Book, 10 1.9 Summary, 10 References, 11 2 Basic Thermodynamics 13 2.1 Conservation and Accounting, 13 2.2 Conservation of Mass, 14 2.3 Conservation of Energy;the First Lawof Thermodynamics, 15 2.4 TheSecond LawofThermodynamics, 17 2.4.1 Reversibility, 17 2.4.2 Entropy, 18 2.5 ConvenienceProperties, 19 2.6 Using the FirstandSecondLaws, 19 2.7 Datums andReference States, 21 2.8 Measurable andImmeasurableProperties, 22 2.9 Workand Heat, 22 2.10 ThePropertyEquation, 23 2.11 Equations of State (EOS), 24 2.11.1 EOSs Based on Theory, 25 2.11.2 EOSs Based on Pure Data Fitting, 25 v vi CONTENTS 2.12 Corresponding States, 26 2.13 Departure Functions, 28 2.14 TheProperties ofMixtures, 28 2.15 TheCombined First and Second LawStatement;ReversibleWork, 29 2.16 Summary, 31 References, 33 3 The SimplestPhaseEquilibrium Examples and Some Simple EstimatingRules 35 3.1 Some GeneralStatements About Equilibrium, 35 3.2 TheSimplest Example of Phase Equilibrium, 37 3.2.1 ADigression, the Distinction between Vapor andGas, 37 3.2.2 Back tothe Simplest Equilibrium, 37 3.3 TheNextLevelofComplexityinPhase Equilibrium, 37 3.4 Some Simple Estimating Rules: Raoult’s and Henry’s“Laws”, 39 3.5 TheGeneral Two-Phase Equilibrium Calculation, 43 3.6 Some Simple Applications ofRaoult’s andHenry’s Laws, 43 3.7 TheUsesand Limits ofRaoult’s and Henry’s Laws, 46 3.8 Summary, 46 References, 48 4 Minimization of Gibbs Energy 49 4.1 TheFundamental Thermodynamic Criterion ofPhase andChemical Equilibrium, 49 4.2 TheCriterion of Equilibrium Applied toTwo Nonreacting Equilibrium Phases, 51 4.3 TheCriterion of Equilibrium Applied toChemicalReactions, 53 4.4 Simple Gibbs EnergyDiagrams, 54 4.4.1 ComparisonwithEnthalpy andEntropy, 55 4.4.2 Gibbs Energy Diagrams for Pressure-DrivenPhase Changes, 55 4.4.3 Gibbs Energy Diagrams for ChemicalReactions, 57 4.5 LeChatelier’s Principle, 58 4.6 Summary, 58 References, 60 5 Vapor Pressure, the Clapeyron Equation, and SinglePure Chemical Species Phase Equilibrium 61 5.1 Measurement of Vapor Pressure, 61 5.2 ReportingVapor-Pressure Data, 61 5.2.1 Normal Boiling Point(NBP), 61 5.3 TheClapeyron Equation, 62 5.4 TheClausius–ClapeyronEquation, 63 5.5 TheAccentric Factor, 64 5.6 TheAntoine Equation andOther Data-FittingEquations, 66 5.6.1 Choosinga Vapor-Pressure Equation, 67 5.7 Applying the Clapeyron Equation toOther Kinds ofEquilibrium, 67 5.8 Extrapolating Vapor-Pressure Curves, 68 5.9 Vapor Pressure ofSolids, 69 5.10 Vapor Pressures ofMixtures, 69 5.11 Summary, 69 References, 72 CONTENTS vii 6 Partial Molar Properties 73 6.1 Partial Molar Properties, 73 6.2 ThePartialMolar Equation, 74 6.3 Tangent Slopes, 74 6.4 Tangent Intercepts, 77 6.5 TheTwo Equations for PartialMolar Properties, 78 6.6 Using the Idea ofTangent Intercepts, 79 6.7 Partial Mass Properties, 80 6.8 Heats ofMixingand Partial Molar Enthalpies, 80 6.8.1 Differential Heat of Mixing, 80 6.8.2 IntegralHeat of Mixing, 81 6.9 TheGibbs–Duhem Equationand the Counterintuitive Behaviorofthe Chemical Potential, 82 6.10 Summary, 84 References, 87 7 Fugacity, Ideal Solutions, Activity, Activity Coefficient 89 7.1 Why Fugacity?, 89 7.2 Fugacity Defined, 89 7.3 TheUse of the Fugacity, 90 7.4 Pure Substance Fugacities, 90 7.4.1 TheFugacity of Pure Gases, 91 7.4.2 TheFugacity of Pure Liquids and Solids, 94 7.5 Fugacities of Species inMixtures, 95 7.6 Mixtures ofIdeal Gases, 95 7.7 Why IdealSolutions?, 95 7.8 IdealSolutions Defined, 96 7.8.1 TheConsequences ofthe IdealSolution Definition, 96 7.9 Why Activity andActivity Coefficients?, 98 7.10 Activity and ActivityCoefficients Defined, 98 7.11 Fugacity Coefficient for Pure Gases andGas Mixtures, 100 7.12 Estimating Fugacities ofIndividual Species inGas Mixtures, 100 7.12.1 Fugacities fromGas PvT Data, 100 7.12.2 Fugacities froman EOS for Gas Mixtures, 102 7.12.3 TheLewisand Randall(L-R) Fugacity Rule, 102 7.12.4 Other Mixing Rules, 103 7.13 Liquid Fugacities fromVapor-Liquid Equilibrium, 104 7.14 Summary, 104 References, 105 8 Vapor–Liquid Equilibrium(VLE) atLow Pressures 107 8.1 Measurement of VLE, 107 8.2 Presenting Experimental VLE Data, 110 8.3 TheMathematicalTreatment of Low-Pressure VLE Data, 110 8.3.1 Raoult’s LawAgain, 111 8.4 TheFourMost CommonTypes of Low-Pressure VLE, 112 8.4.1 Ideal SolutionBehavior(Type I), 114 8.4.2 PositiveDeviationsfrom Ideal Solution Behavior(Type II), 114 8.4.3 NegativeDeviations from Ideal Solution Behavior(Type III), 115 viii CONTENTS 8.4.4 Azeotropes, 117 8.4.5 Two-LiquidPhase orHeteroazeotropes (TypeIV), 118 8.4.6 Zero Solubility and Steam Distillation, 120 8.4.7 Distillationof the Four Types ofBehavior, 121 8.5 Gas–LiquidEquilibrium, Henry’s LawAgain, 122 8.6 TheEffect of ModestPressureson VLE, 122 8.6.1 Liquids, 123 8.6.2 Gases, the L-R Rule, 123 8.7 Standard States Again, 124 8.8 Low-Pressure VLE Calculations, 125 8.8.1 Bubble-Point Calculations, 127 8.8.1.1 Temperature-SpecifiedBubble Point, 127 8.8.1.2 Pressure-Specified Bubble Point, 128 8.8.2 Dew-Point Calculations, 129 8.8.2.1 Temperature-SpecifiedDewPoint, 129 8.8.2.2 Pressure-Specified DewPoint, 129 8.8.3 IsothermalFlashes (T-and P-SpecifiedFlashes), 130 8.8.4 AdiabaticFlashes, 131 8.9 Traditional K-FactorMethods, 132 8.10 More Uses for Raoult’s Law, 132 8.10.1 NonvolatileSolutes, Boiling-PointElevation, 132 8.10.2 Freezing-Point Depression, 135 8.10.3 ColligativeProperties ofSolutions, 136 8.11 Summary, 136 References, 143 9 Correlating and PredictingNonideal VLE 145 9.1 TheMost Common Observations ofLiquid-Phase ActivityCoefficients, 145 9.1.1 WhyNonideal Behavior?, 145 9.1.2 The Shapes of ln,g(cid:2)x Curves, 146 9.2 Limits onActivity CoefficientCorrelations, the Gibbs–Duhem Equation, 147 9.3 Excess Gibbs EnergyandActivity CoefficientEquations, 148 9.4 ActivityCoefficients at InfiniteDilution, 150 9.5 Effects of Pressure andTemperatureon Liquid-Phase Activity Coefficients, 151 9.5.1 Effect ofPressure Changes onLiquid-Phase ActivityCoefficients, 151 9.5.2 Effect ofTemperature Changes on Liquid-Phase ActivityCoefficients, 152 9.6 Ternary andMultispeciesVLE, 153 9.6.1 Liquid-Phase Activity Coefficients for TernaryMixtures, 154 9.7 Vapor-Phase Nonideality, 155 9.8 VLE from EOS, 158 9.9 SolubilityParameter, 158 9.10 TheSolubility of Gases in Liquids, Henry’s Law Again, 160 9.11 Summary, 163 References, 167 CONTENTS ix 10 Vapor–Liquid Equilibrium(VLE) atHigh Pressures 169 10.1 Critical Phenomena of Pure Species, 169 10.2 Critical Phenomena of Mixtures, 170 10.3 Estimating High-Pressure VLE, 174 10.3.1 Empirical K-Value Correlations, 175 10.3.2 Estimation Methods for Each Phase Separately, NotBased on Raoult’s Law, 175 10.3.3 Estimation Methods Based onCubic EOSs, 176 10.4 Computer Solutions, 178 10.5 Summary, 178 References, 179 11 Liquid–Liquid,Liquid–Solid, and Gas–Solid Equilibrium 181 11.1 Liquid–LiquidEquilibrium (LLE), 181 11.2 TheExperimental DeterminationofLLE, 181 11.2.1 Reportingand PresentingLLE Data, 182 11.2.2 Practically Insoluble Liquid Pairsat 25(cid:3)C, 183 11.2.3 Partially SolubleLiquid Pairsat 25(cid:3)C, 183 11.2.4 Miscible LiquidPairsat 25(cid:3)C, 183 11.2.5 Ternary LLE at 25(cid:3)C, 184 11.2.6 LLE at Temperatures Other Than 25(cid:3)C, 186 11.3 TheElementary Theory ofLLE, 187 11.4 TheEffect of Pressure on LLE, 190 11.5 Effect of Temperature onLLE, 191 11.6 Distribution Coefficients, 194 11.7 Liquid–Solid Equilibrium (LSE), 195 11.7.1 One-Species LSE, 195 11.7.2 TheExperimental Determinationof LSE, 195 11.7.3 Presenting LSE Data, 195 11.7.4 Eutectics, 197 11.7.5 Gas Hydrates (Clathrates), 199 11.8 TheElementary ThermodynamicsofLSE, 200 11.9 Gas–Solid Equilibrium (GSE)at LowPressures, 202 11.10 GSE at High Pressures, 203 11.11 Gas–Solid Adsorption, Vapor–SolidAdsorption, 204 11.11.1 Langmuir’s Adsorption Theory, 205 11.11.2 Vapor-solidAdsorption, BET Theory, 207 11.11.3 Adsorption fromMixtures, 208 11.11.4 Heat ofAdsorption, 209 11.11.5 Hysteresis, 210 11.12 Summary, 211 References, 215 12 ChemicalEquilibrium 217 12.1 Introduction toChemical Reactionsand Chemical Equilibrium, 217 12.2 FormalDescriptionof ChemicalReactions, 217 12.3 Minimizing Gibbs Energy, 218 12.4 Reaction Rates,Energy Barriers, Catalysis, andEquilibrium, 219 12.5 TheBasicThermodynamics of ChemicalReactions and Its ConvenientFormulations, 220 12.5.1 TheLawofMass Action andEquilibriumConstants, 222 x CONTENTS 12.6 Calculating EquilibriumConstants fromGibbsEnergy Tables and then Using EquilibriumConstants toCalculate Equilibrium Concentrations, 223 12.6.1 Change ofReactant Concentration, Reaction Coordinate, 224 12.6.2 Reversible andIrreversible Reactions, 227 12.7 More on Standard States, 227 12.8 TheEffect of Temperature on ChemicalReaction Equilibrium, 229 12.9 TheEffect of Pressure onChemical Reaction Equilibrium, 234 12.9.1 Ideal Solution of Ideal Gases, 235 12.9.2 NonidealSolution, Nonideal Gases, 236 12.9.3 Liquids andSolids, 237 12.10 TheEffect of NonidealSolution Behavior, 238 12.10.1 Liquid-Phase Nonideality, 238 12.11 Other Formsof K, 238 12.12 Summary, 239 References, 242 13 Equilibriumin ComplexChemicalReactions 243 13.1 ReactionsInvolving Ions, 243 13.2 Multiple Reactions, 244 13.2.1 Sequential Reactions, 244 13.2.2 Simultaneous Reactions, 245 13.2.3 The ChargeBalance CalculationMethod andBuffers, 246 13.3 Reactionswith More Than One Phase, 249 13.3.1 SolubilityProduct, 249 13.3.2 Gas-LiquidReactions, 249 13.4 Electrochemical Reactions, 252 13.5 Chemicaland Physical Equilibrium inTwo Phases, 255 13.5.1 Dimerization(Association), 255 13.6 Summary, 257 References, 262 14 Equilibriumwith Gravityor Centrifugal Force, OsmoticEquilibrium, Equilibriumwith SurfaceTension 265 14.1 Equilibrium with Other Forms ofEnergy, 265 14.2 Equilibrium inthe Presence of Gravity, 266 14.2.1 Centrifuges, 268 14.3 Semipermeable Membranes, 269 14.3.1 Osmotic Pressure, 270 14.4 Small is Interesting! Equilibrium with Surface Tension, 271 14.4.1 Bubbles,Dropsand Nucleation, 271 14.4.2 Capillary Condensation, 275 14.5 Summary, 275 References, 278 15 The Phase Rule 279 15.1 HowManyPhases Can Coexistina GivenEquilibrium Situation?, 279 15.2 What Does the Phase Rule Tell Us? What Does It Not TellUs?, 280