ChE_130_HW01

1. Chemical Engineering 120 – Separation Processes Homework #1. Due: Friday, 12 April 2002. Question 1 – Thermodynamics of separation process (Problem 2.2 in text) In petroleum refineries, a mixture of paraffins and cycloparaffins is commonly reformed in a fixed-bed catalytic reactor to produce blending stocks for gasoline and aromatic precursors for making petrochemicals. A typical multi-component product from catalytic reforming is a mixture of ethyl benzene with the three xylene isomers. If this mixture is separated, these four chemicals can then be subsequently processed to make styrene, phthalic anhydride, isophthalic acid and terephthalic acid. Compute, using the following data, the minimum work of separation in Btu/h for T0=560°R if the mixture below is separated at 20 psia into three products. Split Fraction (SF) Product 1 0.96 0.005 0.004 0.00 Component Feed, lbmol/h 150 190 430 230 Product 2 0.04 0.99 0.99 0.015 Product 3 0.00 0.00 0.00 0.985 Ethylbenzene p-Xylene m-Xylene o-Xylene Feed Liquid 305 29,290 15.32 Product 1 Liquid 299 29,750 12.47 Product 2 Liquid 304 29,550 13.60 Product 3 Liquid 314 28,320 14.68 Phase condition Temperature, °F Enthalpy, Btu/lbmol Entropy, Btu/lbmol-°R Question 2 – Azeotropic mixture and non-ideal solution model (Prob. 2.23 in text) Benzene can be used to break the ethanol/water azeotrope so as to produce nearly pure ethanol. The Wilson constants for the ethanol(1)/benzene(2) system at 45°C are Λ12=0.124 and Λ21=0.523. Use these constants with the Wilson equation, one of the emperical non-ideal solution model that relates activity coefficient with local composition concept, to predict the liquid-phase activity coefficients for this system over the entire range of composition and compare them with the following experimental result[Austral J. Chem.,7,264(1954)]: ln γ1 2.0937 1.6153 0.7090 0.3136 0.1079 0.0002 -0.0077 ln γ2 0.0220 0.0519 0.2599 0.5392 0.8645 1.3177 1.3999 x1 0.0374 0.0972 0.3141 0.5199 0.7087 0.9193 0.9591

2. Hint: Wilson Equation(two constants)   Λ Λ     = − + Λ + − 12 21 ln ln( x x ) x 1 1 12 2 2 + Λ + Λ x x x x 1 12 2 2 21 1   Λ Λ     = − + Λ − − 12 21 ln ln( x x ) x 2 2 21 1 1 + Λ + Λ x x x x 1 12 2 2 21 1 Question 3 – Vapor liquid equilibrium of binary mixtures(Problem 4.8 in text) The relative volatility,α, of benzene to toluene at 1 atm is 2.5. Construct an x-y diagram for this system at 1 atm. Repeat the construction using vapor pressure data for benzene and for toluene from the following table in conjunction with Raoult’s and Dalton’s laws. Also construct a T-x-y diagram. (a)A liquid containing 70 mol% benzene and 30 mol% toluene is heated in a container at 1 atm until 25 mol% of the original liquid is evaporated. Determine the temperature. The phases are then separated mechanically, and the vapors condensed. Determine the composition of the condensed vapor and the liquid residue. (b)Calculate and plot the K-values as a function of temperature at 1atm. Vapor Pressure of Benzene Vapor pressure, Torr Temperature, °C 20 -2.6 40 7.6 60 15.4 100 26.1 200 42.2 400 60.6 760 80.1 Vapor Pressure of Toluene Vapor pressure, Torr Temperature, °C 20 18.4 40 31.8 60 40.3 100 51.9 200 69.5 400 89.5 760 110.6 1520 136 Hint: 1. The relative volatility of A with respect to B is defined by αA,B=KA/KB=(yA/xA)/(yB/xB) 2. Vapor pressures Ps(in torr) of pure benzene and pure toluene as functions of temperature T (in K) are given by the following equation. k k Ps + 3 Constants for benzene: k1= 15.5645, k2 = -2602.34, k3=211.271 Constants for toluene: k1= 17.2741, k2 = -3896.3, k3= 255.67 = + 2 ln 1 k T