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Chemical and Engineering Thermodynamics. Chapter 8 Phase equilibrium in mixtures Parts B : Illustration Sandler. Illustration 8.1-1 Using azeotropic data to predict VLE of a binary mixture - PowerPoint PPT Presentation
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Chemical and Engineering
Thermodynamics
Chapter 8Phase equilibrium in mixtures
Parts B : IllustrationSandler
2 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
Illustration 8.1-1 Using azeotropic data to predict VLE of a bin
ary mixture Benzene and cyclohexane form an azeotrope at
0.525 mole fraction benzene at temperature of 77.6C and a total pressure of 1.013 bar. At this temperature the vapor pressure of pure benzene is 0.993 bar, and that of pure cyclohexane is 0.980 bar.
3 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
Illustration 8.1-1 Q1. Using the van Laar model, estimate the activity coeffi
cients of benzene and cyclohexane over the whole composition range. Use this activity coefficient information to compute the equilibrium pressure versus liquid composition and equilibrium vapor composition versus liquid composition curves at 77.6C.
Q2. Make predictions for activity coefficients of benzene and cyclohexane using regular solution theory, and compare these with the results obtained in part a.
4 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
利用共沸數據提供熱力學模式參數
製備活性係數之組成關係圖
製備壓力與組成關係圖
系統簡化計算之假設
5 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
氣液平衡的準據
組成的計算式之推演
Van Laar model
6 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
模式係數計算式之推導
7 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
共沸組成提供模式係數計算
取得本題目之混合物系統之兩個成分活性係數模式
數學分析的應用 自由度分析
8 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
系統自由度分析
獨立方程式共計 10 個
系統自由度為 0 可解
9 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
計算程序思考
Regular solution 模式
體積分率:將粒子大小的貢獻在記算式中表達
10 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
取得成分之活性係數模式
依前節之計算程序作計算
11 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
Illustration 8.1-2 Estimation of dew point and bubble point te
mperature Estimate the bubble-point and dew-point temperatures
of a 25mole percent n-pentane, 45 mole percent n-hexane, and 30 mole percent n-pentane mixture at 1.013 bar.
for P in bar, T in K, and R=8.314 J/mol K. The subscripts 5, 6, and 7 designate pentane, hexane, and heptane, respectively.
RT
BAPln i
ivap
i
12 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
計算霧點溫度與泡點溫度
三成份系統
提供飽和蒸汽壓模式
提供溶解度參數
13 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
溶解度參數表示可運用Regular solution model
多成分之平均溶解度參數定義
體積分率之定義
問題 已知液相組成與系統壓力
計算泡點溫度 已知氣相組成與系統壓力
計算霧點溫度
14 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
由溶解度參數判定溶液混合行為的複雜度
相律的自由度分析
系統自由度的分析
變數的個數
15 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
獨立方程式
系統自由度為 0 可解
16 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
計算程序分析 由各獨立方程式之自由度
分析無法順利建構一個計算程序
須採用疊代計算
疊代計算程序的思考架構
疊代計算收斂的指標
17 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
Illustration 8.1-3 Vapor-liquid equilibrium calculation A liquid mixture of 25mole percent n-
pentane, 45 mole percent n-hexane, and 30 mole percent n-pentane, initially at 69C and a high pressure , is partially vaporized by isothermally lowering the pressure to 1.013 bar. Find the relative amounts of vapor and liquid in the equilibrium and their compositions.
18 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
Flash distillation
在定溫與定壓下之閃沸蒸餾計算
定義 K-value
19 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
系統自由度分析 相律自由度分析
20 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
系統自由度為 0 可解
各個獨立方程式之自由度分析可之需要進行疊代計算
將運算式簡化整理
21 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
疊代計算程序
疊代計算收斂指標
計算結果
22 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
Illustration 8.1-4 Correlation of vapor-liquid equilibrium data Weissman and Wood have made very accurate
measurements of vapor-liquid equilibria in benzene-2,2,4-trimethyl pentane mixtures over a range of temperatures.
23 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
Their data for the vapor and liquid compositions and equilibrium total pressure at 55C are given in the following table:
xB yB P(bar) 0.0819 0.1869 0.26892 0.2192 0.4065 0.31573 0.3584 0.5509 0.35463 0.3831 0.5748 0.36088 0.5256 0.6787 0.39105 0.8478 0.8741 0.43277 0.9872 0.9863 0.43641
The vapor pressure of pure benzene at 55C is 0.43596 bar, and that of 2,2,4-trimethyl pentane is 0.23738 bar.
Calculate the activity coefficients of benzene and 2,2,4-trimethyl pentane and at each of the experimental points.
24 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
氣液相平橫數據的關連 求取熱力學模式的系統參
數
25 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
問題 計算活性係數與過剩 Gib
bs 自由能 求取活性係數模式參數
相平橫準據
活性係數計算關係式
剩餘 Gibbs 自由能與活性係數的關係式
26 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
選定ㄧ個溶液理論模式 最適化計算取得參數
活性係數模式的推演
27 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
活性係數之組成關係
28 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
Illustration 8.1-5 Predicting vapor-phase compositions from
P-T-x data Using only the liquid-phase mole fraction and
pressure data fir the n-pentane-propionaldehyde system at 40C given in Table 8.1-1, estimate the vapor compositions.
29 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
Table 8.1-1 x1 y1 P(bar) x1 y1 P(bar)
0 0 0.7609 0.4463 0.5877 1.3354 0.0503 0.2121 0.9398 0.5031 0.6146 1.3494 0.1014 0.3452 1.0643 0.5610 0.6311 1.3568 0.1647 0.4288 1.1622 0.6812 0.6827 1.3636 0.2212 0.4685 1.2173 0.7597 0.7293 1.3567 0.3019 0.5281 1.2756 0.8333 0.7669 1.3353 0.3476 0.5539 1.2949 0.9180 0.8452 1.2814 0.4082 0.5686 1.3197 1.0 1.0 1.1541
30 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
相平衡計算 P-T-x-y 數據 P-T-x 數據
( 預測氣相組成 )
採用 van Laar model
最適化計算的目標函數
31 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
取得最適化計算結果之模式參數
計算程序有關的討論與分析
溫度已知 液相組成已知 氣相成份行為與混合行為
皆視為理想的行為
32 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
Illustration 8.1-6 Predicting VLE from infinite dilution activit
y coefficients determined from Ebulliometry
A recent ebulliometric study of the n-pentane-propionaldehyde at 40C has shown that =3.848 and =3.979. Use this information to compute the P-x-y diagram for this system at 40C.
33 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
由 Ebulliometry 量測無限稀釋溶液之性質
問題 製作壓力與組成的關係圖
滑性係數模式由無限稀釋溶液性質求取
34 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
計算程序思考
35 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
Illustration 8.1-7 Computing the solvent partial
pressure above a polymer + solvent mixture
The Flory-Huggins model
volume fraction
2)1(11
1lnln BBB
BB mx
jjj
BBB nVx
Vn
36 Chapter 8Phase equilibrium in mixture
sParts B : Illustration In the processing of polymers, and als
o for polymer devolatilization (the removal of the solvent from the polymer), it is important to be able to calculate the equilibrium partial pressure of a solvent above solvent-polymer mixtures of different compositions. Calculate the partial pressure of benzene in benzene + polyisobutylene (PIB) mixtures at 298.15 and 312.75 K.
37 Chapter 8Phase equilibrium in mixture
sParts B : Illustration In this calculation you can assume that
polyisobutylene has a negligible vapor pressure, and that the Flory-Huggins model describes the solution behavior of this polymer + solvent mixture. Do the calculations for values of the Flory-Huggins parameter equal 0.5 to 1.0.
38 Chapter 8Phase equilibrium in mixture
sParts B : Illustration Data
The molar volume of benzene is 88.26 cm3/mol, its molecular weight is 78, and its vapor pressures are =0.1266 bar at 298.15 K and 0.2392 bar at 312.75 K, respectively.The molecular weight of the PIB is 40,000, the monomeric unit in PIB has a molecular weight of 104, and the monomeric volume is 131.9 cm3/mol monomer.
39 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
聚合物溶液系統的計算 計算溶劑分壓
物理性質數據
40 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
計算苯的分壓 工程應用上的價值?
解題 聚合物單體數
莫耳分率 體積分率 聚合物的片斷數
以溶劑分子大小為基準
41 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
聚合物的活性係數模式
相平衡時的推導計算式
計算程序 選定溫度 設定溶劑重 選定溶解度參數
42 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
計算莫耳分率與體積分率 計算溶劑的活性係數 計算溶劑苯在氣相的分壓
另一個組成的計算
43 Chapter 8Phase equilibrium in mixture
sParts B : Illustration
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