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

# 0 0911 0850 655 0889 0800 660 0870 0750 665 0855 0700

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Unformatted text preview: om Antoine equations and liquid-phase activity coefficients over the entire composition range from fitting the infinitedilution coefficients to the van Laar equation, Eq. (3) in Table 2.9, using Eqs. (2-75). Thus, KA = yA γ A PAs = xA P γ A = exp (1) and AAW xA 1+ A WA xW AAW 2 KW = s yW γ W PW = xW P (3) and γ W = exp (2) AWA xA 1 + W AW xA AWA 2 (4) ∞ AAW = ln γ A = ln(8.12) = 2.094 AWA = ln γ ∞ = ln(4.13) = 1418 . W Substituting these van Laar coefficients into Eqs. (3) and (4), 2.094 1418 . γ A = exp (5) and γ W = exp 2 1 − xA xA 1 + 0.6772 1+1.477 xA 1 − xA 2 (6) From the 7th edition of Perry's Chemical Engineers' Handbook, page 13-21, 1210.595 1730.630 s log PAs = 7.11714 − (7) and log PW = 8.07131 − (8) T + 229.664 T + 233.426 where Pi s = vapor pressure of component i in torr and T = o C Minimum stages by the Fenske equation: First determine the relative volatilities at the top and bottom and take the geometric average for use in the Fenske equation. Exercise 9.6 (continued) Analysis: Fenske equation (continued) Bubble point for the distillate composition. γ Ps From Eqs. (4-12), (1), and (2): x Di Ki = x Di i i =1 (9) P i i In the distillate, xA = 0.95 and xW = 0.05. From Eqs. (3) and (4), 2.094 1418 . γ A = exp = 1.003 and γ W = exp 2 0.95 2.094 0.05 1418 . 1+ 1+ 0.05 1418 . 0.95 2.094 2 = 3.75 1003 PAs . 3.75 PAs + 0.05 = 1 where vapor pressure is in torr. 975 975 Using Eqs. (7) and (8) with a spreadsheet, a trial and error calculation gives a distillate temperature of 64oC. Then from Eqs. (1) and (2), αA,W = KA/KW = 1.48 Bubble point for the bottoms composition. In the bottoms, xA = 0.02 and xW = 0.98. From Eqs. (3) and (4), 2.094 1418 . γ A = exp = 7.19 and γ W = exp = 1.001 2 2 0.02 2.094 0.98 1418 . 1+ 1+ 0.98 1.418 0.02 2.094 Eq. (9) becomes: 0.95 7.19 PAs 1001PAs . + 0.98 = 1 where vapor pressure is in torr. 975 975 Using Eqs. (7) and (8) with a spreadsheet, a trial and error calculation gives a distillate temperature of 95oC. Then from Eqs. (1) and (2), αA,W = KA/KW = 27.7 The geometric mean relative volatility = [(1.48)(27.7)]1/2 = 6.40 Eq. (9) becomes: 0.02 log From the Fenske equation (9-11), N min = xDA xBW xBA xDW log α A,W log = 0.95 0.98 0.02 0.05 log 6.40 = 3.7 Minimum stages by the McCabe-Thiele method: To obtain a y-x equilibrium curve at 975 torr in terms of acetone mole fractions, we can run bubble-point temperature calculations, as above, for a set of points in the range of liquid compositions between the distillate and bottoms compositions. For each point, the K-value and vapor mole fraction for acetone are computed from Eq. (1). The results from a spreadsheet are as follows: Exercise 9.6 (continued) Analysis: McCabe-Thiele method (continued) T, oC yA xA ------------------------------------63.6 1.000 1.000 64.0 0.965 0.950 64.5 0.936 0.900 65.0 0.911 0.850 65.5 0.889 0.800 66.0 0.870 0.750 66.5 0.855 0.700 67.0 0.842 0.650 67.5 0.833 0.600 67.9 0.824 0.550 68.3 0.817 0.500 68.6 0.811 0.450 68.9 0.806 0.40...
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## This document was uploaded on 02/24/2014 for the course CBE 2124 at NYU Poly.

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