LEO LUE CHEMICAL THERMODYNAMICS DOWNLOAD FREE TEXTBOOKS AT BOOKBOON.COM NO REGISTRATION NEEDED Leo Lue Chemical Thermodynamics Download free books at BookBooN.com 2 Chemical Thermodynamics © 2009 Leo Lue & Ventus Publishing ApS ISBN 978-87-7681-497-7 Download free books at BookBooN.com 3 Chemical Thermodynamics Contents Contents 1 Introduction 8 1.1 Basic concepts 8 1.1.1 State function versus path function 8 1.1.2 Intensive property versus extensive property 8 1.2 Brief review of thermodynamics 8 1.2.1 The fi rst law of thermodynamics 8 1.2.2 The second law of thermodynamics 9 1.3 The fundamental equation of thermodynamics 9 1.4 The calculus of thermodynamics 11 1.5 Open systems 13 1.6 Legendre transforms and free energies 14 2 Single component systems 17 2.1 General phase behavior 17 2.2 Conditions for phase equilibrium 18 2.3 The Clapeyron equation 20 rt e v d a e h k t c cli e We have ambitions. Also for you. s a e Pl SimCorp is a global leader in financial software. At SimCorp, you will be part of a large network of competent and skilled colleagues who all aspire to reach common goals with dedication and team spirit. We invest in our employees to ensure that you can meet your ambitions on a personal as well as on a professional level. SimCorp employs the best qualified people within economics, finance and IT, and the majority of our colleagues have a university or business degree within these fields. Ambitious? Look for opportunities at www.simcorp.com/careers www.simcorp.com Download free books at BookBooN.com 4 Chemical Thermodynamics Contents 3 Multicomponent systems 22 3.1 Thermodynamics of multicomponent systems 22 3.1.1 The fundamental equation of thermodynamics 22 3.1.2 Phase equilibria 22 3.1.3 Gibbs phase rule 23 3.2 Binary mixtures 25 3.2.1 Vapor-liquid equilibrium 25 3.2.2 Liquid-liquid equilibria 30 3.2.3 Vapor-liquid-liquid equilibria 31 3.3 Ternary mixtures 34 4 The ideal solution model 36 4.1 Defi nition of the ideal solution model 36 4.2 Derivation of Raoult’s law 37 5 Partial molar properties 40 5.1 Defi nition 40 5.2 Relationship between total properties and partial molar properties 41 5.3 Properties changes on mixing 43 5.4 Graphical representation for binary systems 43 rt e v d a e h k t c cli e s a e Pl Download free books at BookBooN.com 5 Chemical Thermodynamics Contents 6 Nonideal solutions 47 6.1 Deviations from Raoult’s law and the activity coeffi cient 47 6.2 Modifi ed Raoult’s law 48 6.3 Empirical activity coeffi cient models 51 6.4 The Gibbs-Duhem equation 52 6.5 Azeotropic systems 53 7 Stability 56 7.1 Introduction 56 7.2 Liquid-liquid equilibrium 60 8 Solid-liquid equilibrium 62 8.1 Introduction 62 8.2 Phase behavior 62 8.3 Conditions for equilibrium 62 9 Gas solubility and Henry’s law 66 9.1 Henry’s law 66 9.2 Activity coeffi cients 67 rt e v d a e h k t c cli e s a e Pl Download free books at BookBooN.com 6 Chemical Thermodynamics Contents 10 Equations of state 70 10.1 The principle of corresponding states 70 10.2 The van der Waals equation and cubic equations of state 72 10.3 Equations of state for mixtures 76 11 Thermodynamics from equations of state 77 11.1 The residual Helmholtz free energy 77 11.2 Fugacity 81 11.3 Vapor-liquid equilibrium with a non-ideal vapor phase 82 12 Chemical reaction equilibria 84 12.1 Conditions for equilibrium 84 12.2 The phase rule for chemically reacting systems 86 12.3 Gas phase reactions 86 12.4 The standard Gibbs free energy of formation 87 12.5 The infl uence of temperature 88 12.6 Liquid phase reactions 90 what‘s missing in this equation? rt e v d a e h k t c cli e s You could be one of our future talents a e Pl maeRsK inteRnationaL teChnoLogY & sCienCe PRogRamme Are you about to graduate as an engineer or geoscientist? Or have you already graduated? If so, there may be an exciting future for you with A.P. Moller - Maersk. www.maersk.com/mitas Download free books at BookBooN.com 7 Chemical Thermodynamics Introduction 1 Introduction In this Chapter, we quickly review some basic definitions and concepts from thermodynamics. We thenprovideabriefdescriptionofthefirstandsecondlawsofthermodynamics. Next,wediscussthe mathematicalconsequences oftheselawsandcoversomerelevanttheoremsinmultivariatecalculus. Finally,freeenergies andtheirimportanceareintroduced. 1.1 Basicconcepts 1.1.1 Statefunctionversuspathfunction Astatefunctionisafunctionthatdependsonlyonthecurrentpropertiesofthesystemandnotonthe historyofthesystem. Examplesofstatefunctions include density, temperature, andpressure. A path function is a function that depends on the history of the system. Examples of path functions includeworkandheat. 1.1.2 Intensivepropertyversusextensiveproperty An extensive property is a characteristic of a system that is proportional to the size of the system. That is, if we double the size of the system, then the value of an extensive property would also double. Examples ofextensive properties include total volume, total mass, total internal energy, etc. Extensive properties will be underlined. For example, the total entropy of the system, which is an extensiveproperty, willbedenoted asS. ¯ An intensive property is a characteristic of a system that does not depend on the size of the system. Thatis,doublingthesizeofthesystemleavethevalueofanintensivepropertyunchanged. Examples ofintensive properties arepressure, temperature, density, molarvolume, etc. Bydefinition, aninten- sivepropertycanonlybeafunctionofotherintensiveproperties. Itcannotbeafunctionofproperties thatareextensivebecauseitwouldthendependonthesizeofthesystem. 1.2 Brief review ofthermodynamics 1.2.1 Thefirstlawofthermodynamics Thefirstlawofthermodynamicsissimplyastatementoftheconservationofenergy. Energycantake onavarietyofforms,forexamplekineticenergy,chemicalenergy,orthermalenergy. Thesedifferent formsofenergy cantransform fromonetoanother; however, thesum totalofallthetypesofenergy mustremainconstant. Download free books at BookBooN.com 8 Chemical Thermodynamics Introduction Let’s apply the firstlaw of thermodynamics to aclosed system (i.e. asystem that can exchange heat andworkwithitssurroundings, butnotmatter). Thefirstlawforaclosedsystemcanbewrittenas dU = δQ−δW +··· (1.1) ¯ whereU istheinternalenergyofthesystem,δQistheheat(thermalenergy)transferredtothesystem, ¯ and δW is the work performed by the system. Other forms of energy may contribute to the energy balance, suchaskineticenergy orpotential energy(e.g.,fromagravitational orelectrostatic field). 1.2.2 Thesecondlawofthermodynamics Thesecond lawofthermodynamics formalizestheobservation thatheatisspontaneously transferred only from higher temperatures to lower temperatures. From this observation, one can deduce the existence of a state function of a system: the entropy S. The second law of thermodynamics states ¯ thattheentropychange dS ofaclosed, constant-volume systemobeysthefollowinginequality ¯ δQ dS ≥ (1.2) ¯ T where T is the absolute temperature of the system, and δQ is the amount of heat transfered to the system. A process will occur spontaneously in a closed, constant-volume system only if Eq. (1.2) is satisfied. Forareversible process, the equality is satisfied; for an irreversible process, the entropy changeisgreaterthantheright-hand sideoftherelation. Note that the second law of thermodynamics is unique among the various laws of nature in that it is not symmetric in time. It sets a direction in time, and consequently there is a distinction between running forward intimeandrunning backwards intime. Wecannotice thatafilmisbeing played in reversebecauseweobserveeventsthatseemtoviolatethesecondlaw. 1.3 The fundamental equationofthermodynamics Now consider a closed system that can alter its volume V. In this case, the work performed by the ¯ system is δW = pdV. Combining the first and the second laws of thermodynamics for a closed ¯ system(i.e.inserting theinequality inEq.(1.2)intoEq.(1.1)),weobtain dU ≤ TdS −pdV forconstant N (1.3) ¯ ¯ ¯ Foranyspontaneouschange(process)inthesystem,theinequalitygiveninEq.(1.3)willbesatisfied. Theequality willbesatisfiedonlyinareversible process. An isolated system is a system that does not exchange work δW = 0, heat δQ = 0, or matter dN = 0 with its surroundings. Consequently, the total internal energy and volume remain constant; Download free books at BookBooN.com 9 Chemical Thermodynamics Introduction that implies that dU = 0 and dV = 0. Substituting these relations into Eq. (1.3), we find that ¯ ¯ processes occur spontaneously in an isolated system only if the entropy does not decrease. In this case, dS ≥ 0 (1.4) ¯ Notethatinanisolatedsystem,everyspontaneouseventthatoccursalwaysincreasesthetotalentropy. Therefore, at equilibrium, where the properties of a system no longer change, the entropy of the systemwillbemaximized. Forasystem whereentropy andvolumeareheldfixed(i.e.dS = 0andV = 0),aprocess willoccur ¯ ¯ spontaneously if dU ≤ 0 atconstant S,V,andN (1.5) ¯ ¯ ¯ Forareversibleprocess,wherethesystemisalwaysinfinitesmallyclosetoequilibrium,theequalityin Eq.(1.3)issatisfied. Theresultingequationisknownasthefundamentalequationofthermodynamics dU = TdS −pdV atconstant N (1.6) ¯ ¯ ¯ Engineer your Future at DTU MSc in Engineering programs All of DTU 26 English-taught MSc programs consist of research-based courses taught rt by faculty members performing research at e v the highest international levels. d a e In 2008, the Leiden Ranking rated DTU h k t number 5 among Europe’s 100 technical clic universities, and THES ranked DTU number e 20 globally and number 3 in Europe measured s by scientific impact in engineering. a e Pl A study by iGraduate shows that more than 90 pct. International Students will recommend DTU. Click here www.dtu.dk Download free books at BookBooN.com 10