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

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Unformatted text preview: using Eqs. (3), Table 2.9 for the van Laar equations and Eqs. (4), Table 2.9 for the Wilson equations. Results from a spreadsheet are as follows: x1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 γ1 21.17 10.13 5.56 3.44 2.35 1.75 1.40 1.198 1.079 1.018 1.000 van Laar γ2 1.000 1.039 1.154 1.354 1.661 2.11 2.77 3.71 5.06 7.02 9.84 γ1 21.17 6.63 3.76 2.61 2.00 1.631 1.387 1.219 1.103 1.029 1.000 Wilson______ γ2 1.000 1.054 1.162 1.310 1.510 1.784 2.174 2.77 3.74 5.58 9.84 Exercise 2.24 (continued) Analysis: (c) (continued) Note that the Wilson activity coefficients vary more steeply at the infinitedilution ends. (d) At the azeotropic point, x1 = 0.5941 and x2 = 0.4059. Using the van Laar constants from part (a) with Eqs. (3), Table 2.9, van Laar gives γ1 = 1.419, compared to 1.44 experimental van Laar gives γ2 = 2.72, compared to 2.18 experimental Using the Wilson constants from part (b) with Eqs. (4), Table 2.9, Wilson gives γ1 = 1.400, compared to 1.44 experimental Wilson gives γ2 = 2.147, compared to 2.18 experimental The Wilson equation is acceptable for both components. The van Laar equation gives poor agreement for isooctane. (e) At 50oC, the vapor pressures are 221 torr for ethanol and 146 torr for isooctane. Thus, system pressure will be low over the entire range of composition. Therefore, the modified Raoult's law K-value expression, given by Eq. (4), Table 2.3 applies. When combined with Eq. (2-19), we obtain the following expression for predicting the y - x curve: x1γ 1 P1s y1 = (3) P Exercise 2.24 (continued) Analysis: (e) (continued) By Raoult's law, partial pressure is given by pi = xiPis Therefore, the modified Raoult's law gives pi = xi γi Pis By Dalton's law, the sum of the partial pressures equals total pressure. Thus, P= pi = i xi γ i Pi s (4) i Using a spreadsheet with Eqs. (3) and (4) and the van Laar activity coefficients from the table above in part (c), values of y1 are computed for values of x1: x1 P, torr y1 0.0 146 0.000 0.1 361 0.620 0.2 381 0.645 0.3 367 0.622 0.4 356 0.587 0.5 348 0.556 0.6 349 0.553 0.7 348 0.532 0.8 339 0.563 0.9 305 0.663 1.0 221 1.000 The y-x plot exhibits the same characteristics as the system in Fig. 2.20. Therefore, the van Laar equation erroneously predicts phase splitting. Exercise 3.1 Subject: Evaporation of a mixture of ethanol (AL) and ethyl acetate (AC) from a beaker into still air within the beaker. Given: Initial equimolar mixture of AL and AC, evaporating into still air at 0oC and 1 atm. Vapor pressures and diffusivities in air of AL and AC at 0oC. Assumptions: Well-mixed liquid and Raoult's law. Negligible bulk flow effect. Air sweeps across the top of the beaker at a rate such the mole fractions of AL and AC in the air at the top of the beaker are zero. Find: Composition of the remaining liquid when 50% of the initial AL has evaporated. Analysis: All of the mass-transfer resistance is in the still air layer in the beaker, which increases in height, z, as evaporation takes place. Apply Fick's law to both AL and AC with negligible bulk flow...
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