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Separation Process Principles- 2n - Seader &amp; Henley - Solutions Manual

# 1 xi zi also then ki xi ki zi yi and therefore c i

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Unformatted text preview: ocess simulator with ideal K-values. The results are as follows: Case Vapor, kmol Liquid, kmol Vapor mol frac: Benzene Toluene o-Xylene Liquid mol frac: Benzene Toluene o-Xylene (a) 100oC, 1 atm 67.64 32.36 (b) 100oC, 2 atm. 0 100 0.395 0.305 0.300 (d) 150oC, 1 atm 100 0 0.60 0.25 0.15 0.698 0.224 0.078 (c)105oC, 0.1 atm. 100 0 0.60 0.25 0.15 0.60 0.25 0.15 Only in the Case (a), are two phases formed. At 1 atm, the bubble point is 91.3oC and the dew point is 107.5oC. Exercise 4.30 Subject: Prove that, at equilibrium, vapor is at its dew point and liquid is at its bubble point. Analysis: After equilibrium is achieved, separate the vapor from the liquid and analyze the separate phases. zi xi = (1) For the liquid: Apply Eq. (5), Table 4.4, 1 + Ψ Ki − 1 At the bubble point, Ψ = V/F = 0 and, therefore, from Eq. (1), xi = zi . Also, then, Ki xi = Ki zi = yi and, therefore, C i =1 Ki xi = C i =1 Ki zi = C i =1 For the vapor: Apply Eq. (6), Table 4.4, yi = 1, which is the bubble-point equation, Eq. (4-12). yi = Ki zi 1 + Ψ Ki − 1 (2) At the dew point, Ψ = V/F = 1 and, therefore, from Eq. (2), yi = zi . Also, then, xi = yi /Ki = zi /Ki C C yi C zi and, therefore, = = xi = 1 , which is the bubble-point equation, Eq. (4-12). i =1 Ki i =1 Ki i =1 Exercise 4.31 Subject: Bubble-point temperature of feed to a distillation column. Given: 2.8. Find: Feed at 1.72 MPa (250 psia) with a composition in kmol/h below. K-values in Fig. Bubble-point temperature. Analysis: Iterate on temperature until the bubble-point equation, Eq. (4-12), is satisfied, C i =1 Ki zi = 1 (1) For the first guess, take the temperature that gives the K-value for nC4 = 1.0, that is 225oF. This result and one for 200oF is as follows: T = 225oF T = 200oF Component fi , kmol/h zi Ki K i zi Ki K i zi C2 1.5 0.03 4.8 0.144 4.3 0.129 C3 10.0 0.20 2.1 0.420 1.9 0.380 nC4 18.5 0.36 1.0 0.360 0.81 0.292 nC5 17.5 0.34 0.44 0.150 0.34 0.116 nC6 3.5 0.07 0.21 0.015 0.15 0.011 Sum: 51.0 1.00 1.089 0.928 o By linear interpolation, T = 211 F for Eq. (1) to be satisfied. Exercise 4.32 Subject: Bubble and dew point pressures of binary mixture at constant temperature. Given: Mixture of 50 mol% benzene (A) and 50 mol% toluene (B) at 90oC (194oF). Vapor pressures from Fig. 2.4 (19.5 psia for A and 7.9 psia for B). Assumptions: Raoult's law for K-values. Find: Bubble and dew point pressures. Analysis: Substitution of Raoult's law, Eq. (3) in Table 2.3, into Eqs. (4-12) and (4-13) for the bubble and dew points, respectively, gives, Bubble point: C i =1 Dew point: C i =1 Ki zi = C i =1 Pi s zi = 10 or . P C zi zi P = = 10 or . Ki i =1 Pi s C Pi s zi = P (1) i =1 C i =1 Eq. (1) gives 13.70 psia for the bubble point. zi 1 = s Pi P (2) Eq. (2) gives 15.8 psia for the dew point. Exercise 4.33 Subject: Bubble point, dew point, and flash of a water (W) - acetic acid (A) mixture. Given: Equimolar mixture of W and A at 1 atm. Correlations of liquid-phase activity coefficients for W and A as a function of liquid-phase mole fractions and temperature: Assu...
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