2022年化工热力学授课教案ch .pdf
学习好资料欢迎下载Chapter 12 Solution Thermodynamics: Application 12.1 Liquid-phase Properties from VLE data 12.1.1 Fugacity For species in the vapor mixture ?vviiifyPAccording to the criterion of equilibrium ?1,2,lviiffiN?lviiifyPWhen P105?1vi?lviiiffy PFor example Methyl ethyl ketone (1) /toluene (2) system at 50 See Table 12.1 f x diagram Vapor T P yi Liquid T P xi 11satfP20 30 10 ?/ifkPa1?ify P22?fy P111?idfx f222?idfx f22satfP精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 1 页，共 7 页学习好资料欢迎下载if?ifiHConstant T, PHenry s law 12.1.2 Activity Coefficient Easy calculation of activity coefficient is allowed from experimental low-pressure Review Definition of activity coefficient Lewis/Randall rule ?idiiifx fxi1Henry s lawxi0 ?limidiiixfx H0?l i miiixifHxHenry s law applies to a species as it approaches infinite dilution in a binary solution, and the G-D equation insures validity of the Lewis/Randall rule for the other species as it approaches purity G-D 方程可以证明：在一定T、P 下，若二元溶液的一个组分逸度符合Lewis-Randall 规则， 那么另一个组分逸度必定符合Henry 规则将遵守 Lewis/Randall 规则的溶液称为理想溶液、 或 Lewis/Randall 规则意义上的理想溶液。?iiiidiiiffx ffiiisatiiiiy Py Px fx P?iiidiffLewis/Randall rule ifxi精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 2 页，共 7 页学习好资料欢迎下载将遵守 Henry 定律的溶液称为理想稀溶液或Henry 定律意义上的理想溶液。真实稀溶液的溶剂和溶质分别符合Lewis/Randall 规则和 Henry 定律。12.1.3 活度系数的对称归一化对于理想溶液或 Lewis/Randall 规则意义上的理想溶液?iiiifx fFor species in real solution 1l i m1iix活度系数的对称归一化或对称归一化活度系数12.1.4 活度系数的不对称归一化对于理想稀溶液或Henry 规则意义上的理想溶液*?iiiifx HFor species in ideal solution *1iFor species in solution *1ipositive deviation solution 1inegative deviation solution For species in real dilution solution *0lim1iix活度系数的不对称归一化或不对称归一化活度系数12.1.5 两种活度系数的关系对于液体混合物中的i 组分，其逸度不会因采用不同的活度系数而变化即?lliiiiiiiff xH x或*iiliiHf对于二元溶液，仅与 T,P 有关，与浓度无关，可以通过取xi0 时的极限获得因为0lim1iix0limiiix0*00limlimlimiiiixiiilxiiixHf精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 3 页，共 7 页学习好资料欢迎下载*lnlnlniii即为两种活度系数之间的关系类似地推出*(1)iiiix例 4-6 39C 、2MPa 下二元溶液中的组分 1 的逸度为231111?694fxxxMPa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；(3)1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 : (1) x1 = 1 f1=6-9+4=1MPa1110. 52fP(2) 11101?limxfHx123111101694lim6xxxxHMPax(3) 若组分 1 的标准状态是以 Lewis-Randall定则为基础1111?fx f2321111111111?6946941fxxxxxx fx12.2 Models For the Excess Gibbs The definition of Excess property M E M M idat the same T, P and x The actual extensive property of a solution The extensive property of an ideal solution 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 4 页，共 7 页学习好资料欢迎下载In general ( , )EGg T P xRTFor liquid at low to moderate P and constant T 12(,)ENGg xxxRT12.2.1 The Margules equation For binary system 122112121212EA AGx x RTA xA x2212111221222122211214ln12ln1A xbbacAA xaA xAA x111222210ln0lnxAxA12.2.2 Local-Composition Model The concept of Local-composition ：Example：for binary solution x1 =0.5 and x2=0.5 （1）The Wilson equation For binary system 1112222211ln()ln()EGxxxxxxRTAround 1 molecules x1=0.4 and x2=0.6 Around 2 molecules x1 =0.6 and x2=0.4 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 5 页，共 7 页学习好资料欢迎下载12211112221122221121122221 1122111122lnln()()lnln()()xxxxxxxxxxxxxx（2）NRTL equation For binary system 212112121212212112EGGGx x RTxx Gxx G222112 121221212212112221221212112221121221lnlnGGxxx Gxx GGGxxx Gxx G（3）UNIQUAC and UNIFAC equation For multi-component system Only the parameters of binary system required 12.3 Property Changes of Mixing The Excess properties of real solutions lnEiiiiiiSSx SRxxlnEiiiiiiGGx GRTxxEEiiiiiiVVx VHHx HProperty changes of mixing iiiMMxMa t the same T, P and x Another idEMMMA molar (or unit-mass) solution property A molar (or unit-mass) pure- species property 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 6 页，共 7 页学习好资料欢迎下载iiMxMProperty changes of mixing For binary system 1112111d MMMxdxd MMMxdxGibbs-Duhem equation 1,0NiiiPxTxMMdTdPx d MTPProperty changes of mixing lnEiiiSSRxxlnEiiiGGRTxxEEVVHHExample 12.2 The excess enthalpy (heat of mixing) for a liquid mixture of species 1 and 2 at fixed T and P is represented by the equation : 1212(4020)EHx xxxwhere HE is in J mol-1. Determine expressions for 12EEHHas functions of x1Solution 12.2 112111(1)EEEEEEdHdHHHxHHxdxdx1212(4020)EHx xxx3112020EHxxWhence 2112 06 0EdHxdx233111212 06 04 04 0EEHxxHx精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 7 页，共 7 页
