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Chapter11Solutionthermodynamics:TheoryPurpose:Inthechemicalpetroleumandpharmaceuticalindustriesmulti-componentgasesorliquidscommonlyundergocompositionchangesastheresultofmixingandseparationprocessesthetransferofspeciesfromonephasetoanotherorchemicalreaction.Todevelopthetheoreticalfoundationforapplicationsofthermodynamicstogasmixturesandliquidsolutions目的
1、了解溶液热力学的基本概念
2、学习溶液热力学的基本原理
3、为相平衡的学习打下基础content
11.1FundamentalPropertyRelation
11.2ThechemicalPotentialandPhaseEquilibrium
11.3PartialProperties
11.4Ideal-GasMixture
11.5FugacityandFugacityCoefficient:PureSpecies
11.6FugacityandFugacityCoefficient:SpeciesinSolution
11.7GeneralizedCorrelationsfortheFugacityCoefficient
11.8TheIdealSolution
11.9ExcessProperties
11.1FundamentalPropertyRelationREVIEWFundamentalPropertyRelationsofThermodynamicsforHomogeneousPhaseSystemForonemolFornmol使用这些方程时一定要注意一下几点
1.恒组分,恒质量体系,也就是封闭体系;
2.均相体系(单相);
3.平衡态间的变化;只存在体积功;
4.常用于1摩尔的时的性质Forthemoregeneralcaseofasingle-phaseopensystemChemicalpotentialInthesamewayFundamentalPropertyRelationForthecaseofnmoleofsolutionForthecaseofonemoleofsolutionn=1ni=xi→
11.2ThechemicalPotentialandPhaseEquilibriumForaclosedsystemconsistingoftwophasesinequilibriumEachindividualphaseisanopensystemThetotalsystempropertyisexpressedbySincethetwo-phasesystemisclosedForaclosedsystemconsistingofπphasesinequilibriumMultiplephasesatthesameTandPareinequilibriumwhenthechemicalpotentialofeachspeciesisthesameinallphasesAttentionKeypointsinthissection
11.3PartialProperties
11.
3.1Definitionofthepartialmolarpropertythepartialmolarpropertyofspeciesiinsolution在恒温、恒压下,物系的容量性质随某种组分摩尔数的变化率叫做该组分的偏摩尔性质Attention SolutionpropertiesPure-speciespropertiesPartialproperties偏摩尔自由焓是一种化学位ATTENTION偏摩尔性质的三个重要要素
①恒温、恒压;
②容量性质;
③随某组分摩尔数的变化率.物理意义在恒温、恒压下,物系中某组分摩尔数的变化所引起物系的一系列热力学性质的变化偏摩尔性质的物理意义可通过实验来理解如在一个无限大的、颈部有刻度的容量瓶中,盛入大量的乙醇水溶液,在乙醇水溶液的温度、压力、浓度都保持不变的情况下,加入1mol乙醇,充分混合后,量取瓶上的溶液体积的变化,这个变化值即为乙醇在这个温度、压力和浓度下的偏摩尔体积ATTENTION偏摩尔性质的三个重要要素
①恒温、恒压;
②容量性质;
③随某组分摩尔数的变化率.溶液性质纯组分性质偏摩尔性质偏摩尔自由焓定义为化学位是偏摩尔性质的一个特例,而化学位的连等式,只是在数值上相等,物理意义完全不同
11.3PartialProperties
11.
3.1DefinitionofthepartialmolarpropertyThinking11-1onlyAttention Chemicalpotential
11.
3.2EquationsRelationMolarandPartialMolarPropertiesForasystemTPx1x2…anythermodynamicpropertyMHUGSetc.is1SummabilityRelationCanbeusedtocalculatemixturepropertiesfrompartialproperties?2Gibbs/Duhemequation作用1检验实验测得的混合物热力学性质数据的正确性;2从一个组元的偏摩尔量推算另一组元的偏摩尔量3Genericrelation
11.
3.3PartialPropertiesinBinarySolutionsGenericrelation→SummabilityRelation→Gibbs/Duhemequation→Example
11.3Solution
11.3ThemolarvolumeofthebinaryantifreezesolutionThetotalnumberofmolesrequiredisThevolumeofeachpurespeciesisExample
11.4Solution
11.4(a)x2=1-x1→→→Anothermethodbc例题4-1在100 ℃和
0.1013MPa下,丙烯腈
(1)-乙醛
(2)二元混合气体的摩尔体积为,是常数,其单位与V的单位一致试推导偏摩尔体积与组成的关系,并讨论纯组分
(1)的偏摩尔性质和组分
(1)在无限稀时的偏摩尔性质解从公式推导偏摩尔性质Genericrelation对于纯组分
(1)对于无限稀组分
(1)定义组分i的无限稀偏摩尔性质注意例题4-2在25℃和
0.1MPa时,测得甲醇
(1)中水
(2)的摩尔体积近似为cm3mol-1,及纯甲醇的摩尔体积为cm3mol-1试求该条件下的甲醇的偏摩尔体积和混合物的摩尔体积解在保持T、P不变化的情况下,由Gibbs-Duhem方程cm3mol-
111.
3.4RelationsamongPartialPropertiesEveryequationthatprovidesalinearrelationamongthermodynamicpropertiesofaconstant-compositionsolutionhasasitscounterpartanequationconnectingthecorrespondingpartialpropertiesofeachspeciesinthesolution对于恒定组成多组分流体中,所有线性的热力学性质关系式,多组分流体中各组分的偏摩尔性质都有对应的类比关系式
11.
3.4RelationsamongPartialPropertiesDemonstratethisbyexamplepnj=const.→ForpuresubstanceTnj=const.→
11.
3.4RelationsamongPartialPropertiesDemonstratethisbyexampleDefinitionFornmoles→溶液中某组分的偏摩尔性质间的关系式与关联纯物质各摩尔热力学性质间的方程式相似Thinking11-
21.二元混合物的焓的表达式为则(由偏摩尔性质的定义求得)Thinking11-
22.有人提出了一定温度下二元液体混合物的偏摩尔体积的模型是,其中V1,V2为纯组分的摩尔体积,a,b为常数,问所提出的模型是否有问题?若模型改为情况又如何?由G-D方程得ab不可能是常数,故提出的模型有问题;由G-D方程得提出的模型有一定的合理性Thinking11-
23.某二元混合物的中组分的偏摩尔焓可表示为则b1与b2的关系是.()Thinking11-
24.在一定的温度和常压下,二元溶液中的组分1的偏摩尔焓如服从下式试求出和H表达式
11.4Ideal-GasMixtureReviewMixturepropertiesPure-speciespropertiesPartialpropertiesPurposeofthissectionCalculatethemixturepropertiessuchasHSUV…foridealgas
11.4Ideal-GasMixture
11.
4.1Gibbs’stheoremApartialmolarpropertyotherthanvolumeofaconstituentspeciesinanidealgasmixtureisequaltocorrespondingmolarpropertyofthespeciesasapureidealgasatthemixturetemperaturebutatapressureequaltoitspartialpressureinthemixture理想气体混合物中,某组分的偏摩尔性质(除偏摩尔体积外),等于在与气体混合物相同的温度而压力等于该组分在混合物中分压的条件下,该组分作为纯理想气体的对应摩尔性质ForMHUGS…ThemixtureThepurespeciesTppiTpiForV→ForHForSIntegrationfrompitopMoresimplyForSInthesamewayForUForGForVAccordingtosummabilityrelationForHForSForUForGForV
11.
4.2FortheChemicalPotentialIntegrationfromareferencestateTP=1atmidealgas
11.5FugacityandFugacityCoefficient:PureSpecies
11.
5.1Whystudyfugacity
11.
5.2TheoriginofthefugacityconceptFortheidealgasForarealfluid→fi Thefugacityofpurespecies→fi ThefugacitycoefficientofpurespeciesCompletedefinition
11.
5.3Calculationoffugacityandfugacitycoefficient1Byp-V-TdataorstateequationsByp-V-TdataorZ~pdata:Graphicalintegration如果有足够多的从低压开始的等温PVT数据,作出(V-RT/P)~P图上的等温线,即可对上式进行图解积分Bystateequations:ThevirialequationThecubicequationForexampleRKequationSRKequation2ByHandSdataForastateatpressurepForalow-pressurereferencestateIfthepressureofreferenceislowenough3BygeneralizedcorrelationsInsection
11.
711.
5.4Vapor/LiquidEquilibriumforPureSpeciesForasaturatedvaporVaporphaseForasaturatedliquidLiquidphaseTherefore
11.
5.5FugacityofaPureLiquidForarealfluidIntegratinAssumeViconstantVliPoyntingfactor
11.5ExampleSolution
11.5Analyzingbysteamtable:at300℃thelowestpressureis1kPaThesaturationpressureis
8592.7kPaThreestagesSuperheatedsteamp=1-
8592.7kPaSaturationsteamandliquidp=
8592.7kPaliquidp=
8592.7-10000kPa300℃1kPa→300℃
8592.7kPa→300℃10000kPa1Superheatedsteamp=1-
8592.7kPaCalculatefiandbyHandSdataThelow-pressurereferencestate:Sowecancalculatethefugacityandfugacitycoefficientat300℃andanypressurefrom1kPatothesaturationpressure
8592.7kPaForexampleForthestateat4000kPaand300℃Similarcalculationsatotherpressureleadtothevaluesplottedthelinefi~pΦi~p.2Saturationsteamandliquidp=
8592.7kPaInthesameway3liquidp=
8592.7-10000kPaForthestateat10000kPaand300℃Similarcalculationsatotherpressureleadtothevaluesplottedthelinefi~pΦi~p.plottedthelinefi~pΦi~pFugacityandfugacitycoefficientofsteamat300℃Forideal-gasfi=pForactualsteamForsaturationstateForliquid
11.6FugacityandFugacityCoefficient:SpeciesinSolution
11.
6.1definitionoffugacityandfugacitycoefficientForspeciesinsolutiondefinitionoffugacityforspeciesinsolutiondefinitionoffugacitycoefficientforspeciesinsolutionreviewForpureidealgasForpurespeciesrealfluidsFortheidealgasmixture
11.
6.2FugacityandequilibriuminsolutionForπ-phasesystemwithNconstituentspeciesinequilibriumMultiplephasesatthesameTandPareinequilibriumwhenthefugacityofeachconstituentspeciesisthesameinallphases在相同的温度压力下,当每个组分在所有的相中的逸度都相等时,多相系统处于平衡
11.
6.3FugacityCoefficientandthePartialResidualPropertyReviewFortheresidualpropertyForthepartialproperty
11.
6.4TheFundamentalResidual-PropertyRelationReview partialpropertyisapartialpropertywithrespecttoGR/RT
11.
6.5Calculationoffromp-V-TdataExample
11.6Solution
11.6Review
11.
6.6FugacityCoefficientsfromtheVirialEquationItallowsthecalculationofvaluesfromvirialequationForexampleForabinarysystemofgasesThegeneralequation
11.
7.1Forapure-gassystemForsimplicitydroppingsubscriptiCanbefoundintablesE13throughE15givenbyLee/KeslerasfunctionofTrandprReview
11.
7.2ForgasmixturePrausnitzmixingruleExample
11.9Solution
11.9Prausnitzmixingrule
11.8FugacityandFugacityCoefficientofMixture
11.
8.1DefinitionFortheideal-gasmixtureForthemixturefugacityofmixturefugacitycoefficientofmixtureAttention!PurespeciesSpeciesinsolutionSolution
11.
8.2RelationbetweenFugacitiesofSolutionandSpecies推推导过程见陈忠秀或陈新志教材isapartialpropertywithrespecttoisapartialpropertywithrespecttoAttention!possessallcharacteristicsofpartialpropertiesThinking11-5SolutionpropertyPartialpropertySummabilityRelationG-Dequation
11.
8.3InfectofTandPonFugacity
(1)InfectofponfiforpurespeciesForspeciesinmixture
(2)InfectofTonfiforpurespeciesForspeciesinmixture推导过程见陈新志或陈忠秀教材Thinking11-3混合物逸度有无相似关系?
11.9TheIdealSolutionWhyistheidealsolutionintroduced利用混合物的状态方程,计算溶液中组分的逸度和逸度系数,对于气体混合物是有效的但对液体混合物来说,状态方程难以描述,混合法则的发展不成熟,计算结果精度差故引入理想溶液和活度系数
11.
9.1DefinitionoftheIdealSolutionInanidealgasmixtureforspeciesiDefineanidealsolution—理想溶液中组分i的偏摩尔自由焓;—同温、同压、同组成下纯物质i的自由焓理想溶液的行为通常近似于物理性质相同而分子大小相差不大的分子所组成的溶液因而同分异构物的混合物,象邻、间、对二甲苯所组成的三元混合物,就可以称为理想溶液Attention理想溶液表现出特殊的物理性质,其主要特征⑴分子结构相似,大小一样;⑵分子间的作用力相同;⑶混合时没有热效应;⑷混合时没有体积效应凡是符合上述四个条件者,都是理想溶液,这四个条件缺少任何一个,就不能称作理想溶液
11.
9.2PropertiesoftheIdealSolutionAtthesameTandPThepartialpropertiesThetotalproperties
11.
9.3TheLewis/RandallruleForpurespeciesrealfluidsForspeciesinanidealsolutionForspeciesinsolutionForspeciesinanidealsolutionLewis-RandallRuleForspeciesinanidealsolutionLewis-RandallRuleThefugacityofpurespeciesiinthesamephysicalstateasthesolutionandatthesameTandP真实稀溶液的溶剂组分符合Lewis-RandallRule,一般称为理想溶液Thinking11-
51.在一定温度和压力下的理想溶液的组分逸度与其摩尔分数成正比(对)
2.对于理想溶液的某一容量性质M,则(错)
3.对于理想溶液,所有的混合过程性质变化均为零(错V,H,U,CP,CV的混合过程性质变化等于零,对S,G,A则不等于零)
4.理想气体混合物就是一种理想溶液(对)
5.温度和压力相同的两种理想气体混合后,则温度和压力不变,总体积为原来两气体体积之和,总热力学能为原两气体热力学能之和,总熵为原来两气体熵之和(错总熵不等于原来两气体的熵之和)
6.温度和压力相同的两种纯物质混合成理想溶液,则混合过程的温度、压力、焓、热力学能、吉氏函数的值不变(错吉氏函数的值要发生变化)
7.理想溶液一定符合Lewis-Randall规则和Henry规则(对)
8.符合Lewis-Randall规则或Henry规则的溶液一定是理想溶液(错,如非理想稀溶液)
11.10ExcessProperties
11.
10.1TheDefinitionforExcessProperties超额性质过量性质ME≡M-MidM——TheactualextensivepropertyofasolutionMid——TheextensivepropertyofanidealsolutionatthesametemperaturepressureandcompositionNote ExcesspropertieshavenomeaningforpurespecieswhereasresidualpropertiesexistforpurespeciesaswellasformixturesCorrelationsofexcesspropertyresidualpropertyandpartialpropertyfortheideal-gasmixtureThefundamentalexcess-propertyrelationanalogoustothefundamentalresidual-propertyrelationReviewTable
11.1SummaryofEquationsfortheGibbsEnergyandRelatedPropertiesMinRelationtoGMRinRelationtoGRMEinRelationtoGE
11.
10.2TheGibbsEnergyandtheActivityCoefficientForspeciesinsolutionForspeciesinanidealsolutionBydifferenceDefinitionofactivitycoefficientWhence活度系数是真实溶液与同温、同压、同组成的理想溶液的组分逸度之比表明可以从理想溶液性质、溶液组成和活度系数得到真实溶液的性质ForspeciesinsolutionForspeciesinanidealsolutionBydifferenceDefinitionofactivitycoefficientWhenceReviewForspeciesinidealsolutionForspeciesinsolutionpositivedeviationsolutionnegativedeviationsolutionisapartialpropertywithrespecttoThinking11-
61.对于理想溶液所有的超额性质均为零
2.理想溶液中所有组分的活度系数为零
3.理想气体有f=P,而理想溶液有
4.纯流体的汽液平衡准则为fv=fl
5.混合物体系达到汽液平衡时,总是有
6.对于二元混合物体系,当在某浓度范围内组分2符合Henry规则,则在相同的浓度范围内组分1符合Lewis-Randall规则例4-639C°、2MPa下二元溶液中的组分1的逸度为确定在该温度、压力状态下1纯组分1的逸度与逸度系数;2组分1的亨利系数k1;3γ1与x1的关系式(若组分1的标准状态是以Lewis-Randall定则为基础)解:1x1=1f1=6-9+4=1MPa23若组分1的标准状态是以Lewis-Randall定则为基础αphaseβphase。