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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. (1535), 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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This document was uploaded on 02/24/2014 for the course CBE 2124 at NYU Poly.
 Spring '11
 Levicky
 The Land

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