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

02 a 1 a yso 7 4 12 12 combining eqs 1 5 6

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Unformatted text preview: following procedure was used. First, fit Eq. (1) with the nonlinear regression program of Polymath. Then fit Eq. (2). The following results are obtained, with both equations giving good fits: Coefficient (q0)1 (q0)2 k1 k2 n1 n2 Eq. (1) 3.456 14.92 14.95 1.295 2.469 Eq. (2) Refit of Eq. (2) 37.4 13.65 2.14 3.906 1.290 2.492 14.92 20.48 1.295 1.136 Refit of Eq. (1) 1.855 14.92 20.48 1.295 1.136 Next, Eq. (2) is refitted, holding k1 and n1 at the values above that were obtained from fitting Eq. (1). The refit gives the above values. Eq. (1) is refitted to determine only (q0)1. The results are also given above. The final fits of Eqs. (1) and (2) are as follows with sum of squares of deviations of 0.0144 and 0.0163, respectively. A simultaneous fit would give better values. q1 = 1 1.855(14.92)c1 /1.295 1/1.295 1 + 14.92c1 + 20.48c1/1.136 2 q2 = 2.492(20.48)c1/1.136 2 1/1.295 1 + 14.92c1 + 20.48c1/1.136 2 The fits of the data are shown in the bar charts on the following page. Exercise 15.10 (continued) Analysis: (continued) Exercise 15.11 Subject: Analysis of liquid adsorption data for a mixture of cyclohexane (1) and ethyl alcohol (2) on activated carbon at 30oC. Given: Data table for loading of (1) as a function of its mole fraction. Assumption: No adsorption of (2). Find: (a) Plot of loading as a function of mole fraction. Explain shape of curve. (b) Fit of Freundlich equation over the low mole fraction region. Analysis: (a) Using Polymath, the data for cyclohexane liquid adsorption are shown below for the entire composition region, with fitting to a cubic equation. The curve is of the type of Fig. 15.12c. The explanation for the shape of the curve is obtained from Fig. 15.13d. At low concentrations of (1), it begins to adsorb, with increasing adsorption for increasing mole fraction of (1), much like a Freundlich isotherm. The solvent, (2), contrary to the assumption of no adsorption is highly adsorbed at low concentrations of (1), but its adsorption gradually diminishes as the concentration of (2) decreases. (b) For the cyclohexane mole fraction region from 0 to 0.250, the data are fitted with the Regress program of Polymath to a modification of the Freundlich Eq. (15-35), using mole fraction instead of concentration, with a plot on the following page. 1 q = 0.94511 x 3.813 Exercise 15.11 (continued) Analysis: (b) (continued) Exercise 15.12 Subject: Fitting adsorption equilibria data for small concentrations of toluene in water with activated carbon, and small concentrations of water in toluene with activated alumina, to Langmuir and Feundlich isotherms. Given: Table of adsorption equilibrium data for toluene in water with activated carbon at 25oC. Table of adsorption equilibrium data for water in toluene with activated alumina at 25oC. Assumptions: Negligible adsorption of water on activated carbon. Negligible adsorption of toluene on activated alumna. Find: Best fitting isotherms from Langmuir, Freundlich, and linear. Analysis: Use the nonlinear regression program of Polymath. However, for toluene in water, the data point at c = 2 for q = 70....
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