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 Benzene and cyclohexane form an azeotrope at 0.525 mole fraction benzene at temperature of 77.6C 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.

Illustration 8.1-1 Q1. Using the van Laar model, estimate the activity coefficients 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 77.6C. Q2. Make predictions for activity coefficients of benzene and cyclohexane using regular solution theory, and compare these with the results obtained in part a.

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

氣液平衡的準據 組成的計算式之推演 Van Laar model

模式係數計算式之推導

取得本題目之混合物系統之兩個成分活性係數模式 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

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

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

取得成分之活性係數模式 依前節之計算程序作計算

Illustration 8.1-2 Estimation of dew point and bubble point temperature 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.

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

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

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

獨立方程式 系統自由度為 0 可解

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

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 69C 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.

Flash distillation 在定溫與定壓下之閃沸蒸餾計算 定義 K-value

系統自由度分析 相律自由度分析

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

疊代計算程序 疊代計算收斂指標 計算結果

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.

Their data for the vapor and liquid compositions and equilibrium total pressure at 55C 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 55C 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.

氣液相平橫數據的關連 求取熱力學模式的系統參數

問題 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 計算活性係數與過剩 Gibbs 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

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

活性係數之組成關係

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 40C given in Table 8.1-1, estimate the vapor compositions.

Table 8.1-1 x1 y1 P(bar) x1 y1 P(bar) 0 0 0.7609 0.4463 0.5877 1.3354 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

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

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

Illustration 8.1-6 Predicting VLE from infinite dilution activity coefficients determined from Ebulliometry A recent ebulliometric study of the n-pentane-propionaldehyde at 40C has shown that =3.848 and =3.979. Use this information to compute the P-x-y diagram for this system at 40C.

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

計算程序思考

Illustration 8.1-7 Computing the solvent partial pressure above a polymer + solvent mixture The Flory-Huggins model volume fraction

In the processing of polymers, and also 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.

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.

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.

聚合物溶液系統的計算 計算溶劑分壓 物理性質數據

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

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

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

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