化工热力学授课教案ch.doc

Chapter 11 Solution thermodynamics: TheoryPurpose: In the chemical, petroleum, and pharmaceutical industries multi-component gases or liquids commonly undergo composition changes as the result of mixing and separation processes, the transfer of species from one phase to another, or chemical reaction. To develop the theoretical foundation for applications of thermodynamics to gas mixtures and liquid solutions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content11.1 Fundamental Property Relation11.2 The chemical Potential and Phase Equilibrium11.3 Partial Properties11.4 Ideal-Gas Mixture11.5 Fugacity and Fugacity Coefficient: Pure Species 11.6 Fugacity and Fugacity Coefficient: Species in Solution11.7 Generalized Correlations for the Fugacity Coefficient11.8 The Ideal Solution11.9 Excess Properties11.1 Fundamental Property RelationREVIEW Fundamental Property Relations of Thermodynamics for Homogeneous Phase SystemFor one mol For n mol 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。For the more general case of a single-phase, open system Chemical potential In the same wayFundamental Property RelationFor the case of n mole of solutionFor the case of one mole of solutionn=1 ni=xi11.2 The chemical Potential and Phase EquilibriumFor a closed system consisting of two phases in equilibriumEach individual phase is an open systemphase phaseThe total system property is expressed bySince the two-phase system is closed For a closed system consisting ofphases in equilibrium Multiple phases at the same T and P are in equilibrium when the chemical potential of each species is the same in all phases Attention Key points in this section11.3 Partial Properties11.3.1 Definition of the partial molar propertythe partial molar property of species i in solution 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 ：Solution properties Pure-species propertiesPartial properties 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：恒温、恒压；容量性质；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：恒温、恒压；容量性质；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11.3 Partial Properties11.3.1 Definition of the partial molar propertyThinking(11-1) ?onlyAttention ： Chemical potential11.3.2 Equations Relation Molar and Partial Molar PropertiesFor a system (T, P, x1, x2 ) any thermodynamic property M (H, U, G, S, etc.) is 1) Summability RelationCan be used to calculate mixture properties from partial properties？2) Gibbs/Duhem equation 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。3) Generic relation11.3.3 Partial Properties in Binary SolutionsGeneric relation Summability RelationGibbs/Duhem equationExample 11.3 Solution 11.3 The molar volume of the binary antifreeze solutionThe total number of moles required is The volume of each pure species is Example 11.4 Solution 11.4（a） x2 = 1-x1Another method , (b) (c)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Generic relation 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 cm3 mol-1，及纯甲醇的摩尔体积为cm3 mol-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 (cm3 mol-1)11.3.4 Relations among Partial Properties Every equation that provides a linear relation among thermodynamic properties of a constant-composition solution has as its counterpart an equation connecting the corresponding partial properties of each species in the solution 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。11.3.4 Relations among Partial PropertiesDemonstrate this by examplep, nj =const. For pure substanceT, nj =const.11.3.4 Relations among Partial PropertiesDemonstrate this by exampleDefinition For n moles 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。Thinking(11-2) 1. 二元混合物的焓的表达式为 则（由偏摩尔性质的定义求得） Thinking(11-2) 2. 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 a,b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。 Thinking(11-2) 3. 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 . （）Thinking(11-2) 4. 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 。 11.4 Ideal-Gas MixtureReviewMixture properties Pure-species properties Partial properties Purpose of this section Calculate the mixture properties such as H, S, U, V, for ideal gas11.4 Ideal-Gas Mixture11.4.1 Gibbss theoremA partial molar property (other than volume) of a constituent species in an ideal gas mixture is equal to corresponding molar property of the species as a pure ideal gas at the mixture temperature but at a pressure equal to its partial pressure in the mixture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 For M (H,U,G,S,) The mixture The pure species T, p, pi T, piFor V For H For S Integration from pi to p More simplyFor S In the same wayFor U For G For V According to summability relationFor H For S For U For G For V 11.4.2 For the Chemical Potential Integration from a reference state (T, P=1atm, ideal gas ) 11.5 Fugacity and Fugacity Coefficient: Pure Species 11.5.1 Why study fugacity ? 11.5.2 The origin of the fugacity concept ? For the ideal gas For a real fluid fi：The fugacity of pure species fi：The fugacity coefficient ofpure speciesComplete definition 11.5.3 Calculation of fugacity and fugacity coefficient 1) By p-V-T data or state equations By p-V-T data or Zp data: Graphical integration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By state equations:The virial equation The cubic equation For example RK equation SRK equation 2) By H and S dataFor a state at pressure p For a low-pressure reference state If the pressure of reference is low enough 3) By generalized correlations In section 11.711.5.4 Vapor/Liquid Equilibrium for Pure Species For a saturated vapor Vapor phase For a saturated liquid Liquid phase Therefore 11.5.5 Fugacity of a Pure Liquid For a real fluid Integratin Assume Vi constant, Vli Poynting factor 11.5 Exam pleSolution 11.5Analyzing by steam table: at 300the lowest pressure is 1 kPa The saturation pressure is 8592.7 kPaThree stagesSuperheated steam ( p = 18592.7 kPa)Saturation steam and liquid ( p = 8592.7 kPa)liquid ( p = 8592.7 10000 kPa)300 1 kPa 300 8592.7 kPa 300 10000 kPa1) Superheated steam ( p = 18592.7 kPa)Calculate fi and by H and S dataThe low-pressure reference state: So we can calculate the fugacity and fugacity coefficient at 300and any pressure from 1 kPa to the saturation pressure 8592.7 kPa For exampleFor the state at 4000 kPa and 300 Similar calculations at other pressure lead to the values plotted the line fi p, i p . 2) Saturation steam and liquid ( p = 8592.7 kPa) In the same way 3) liquid ( p = 8592.7 10000 kPa ) For the state at 10000 kPa and 300 Similar calculations at other pressure lead to the values plotted the line fi p, i p . plotted the line fi p, i p Fugacity and fugacity coefficient of steam at 300For ideal-gas f i = pFor actual steam For saturation state For liquid 11.6 Fugacity and Fugacity Coefficient: Species in Solution 11.6.1 definition of fugacity and fugacity coefficient For species in solution definition of fugacity for species in solution definition of fugacity coefficient for species in solution reviewFor pure ideal gas For pure species (real fluids) For the ideal gas mixture 11.6.2 Fugacity and equilibrium in solutionFor -phase system with N constituent species in equilibrium Multiple phases at the same T and P are in equilibrium when the fugacity of each constituent species is the same in all phases 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 11.6.3 Fugacity Coefficient and the Partial Residual PropertyReviewFor the residual property For the partial property 11.6.4 The Fundamental Residual-Property Relation Review：partial property is a partial property with respect to GR/RT 11.6.5 Calculation of from p-V-T data Example 11.6Solution 11.6 Review 11.6.6 Fugacity Coefficients from the Virial Equation It allows the calculation of values from virial equationFor example For a binary system of gases The general equation 11.7.1 For a pure-gas system For simplicity, dropping subscript i Can be found in tables E13 through E15 given by Lee/Kesler as function of Tr and prReview 11.7.2 For gas mixture Prausnitz mixing rule Example 11.9Solution 11.9Prausnitz mixing rule 11.8 Fugacity and Fugacity Coefficient of Mixture 11.8.1 DefinitionFor the ideal-gas mixture For the mixture fugacity of mixture fugacity coefficient of mixtureAttention ! Pure species Species in solution Solution 11.8.2 Relation between Fugacities of Solution and Species推 推导过程见陈忠秀或陈新志教材 is a partial property with respect to is a partial property with respect to Attention ! possess all characteristics of partial properties Thinking(11-5) SolutionpropertyPartial propertySummability RelationG-D equation11.8.3 Infect of T and P on Fugacity （1） Infect of p on fi for pure species For species in mixture （2） Infect of T on fi for pure species For species in mixture 推导过程见陈新志或陈忠秀教材Thinking(11-3) 混合物逸度有无相似关系？11.9 The Ideal SolutionWhy is the ideal solution introduced ?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。11.9.1 Definition of the Ideal Solution In an ideal gas mixture, for species i Define an ideal solution 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： 分子结构相似，大小一样； 分子间的作用力相同； 混合时没有热效应； 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。11.9.2 Properties of the Ideal Solution At the same T and P The partial properties The total properties 11.9.3 The Lewis/Randall ruleFor pure species (real fluids) For species in an ideal solution For species in solutionFor species in an ideal solutionLewis-Randall RuleFor species in an ideal solution Lewis-Randall RuleThe fugacity of pure species i in the same physical state as the solution and at the same T and P真实稀溶液的溶剂组分符合 Lewis-Randall Rule，一般称为理想溶液Thinking(11-5) 1. 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）11.10 Excess Properties11.10.1 The Definition for Excess Properties 超额性质 过量性质M E M M idM The actual extensive property of a solutionM id The extensive property of an ideal solutionat the same temperature, pressure and composition Note ：Excess properties have no meaning for pure species, whereas residual properties exist for pure species as well as for mixturesC