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Unformatted text preview: 11.5
q, wt%
7.0
p, torr
0.012 0.027 0.043 0.070 0.094 0.147
Find: Best fit of the data to linear, Freundlich, and Langmuir isotherms, with q in mol/g and p
in atm. Which isotherm fits best?
Analysis: First convert the given adsorption data to the desired units:
q in mols TMB/gram NaX = (wt% q/MW of TMB)/(100  wt% q)
(1)
MW of TMB = 134.1
Substitution of the data into Eq. (1) plus converting pressure from torr to atm gives:
0.000747
0.000856
0.000903
0.000931
0.000969
q, mol/g
0.000562
p, atm
0.0000158 0.0000355 0.0000566 0.0000921 0.0001237 0.0001934
The regression program of POLYMATH can be used to do nonlinear curve fits or a spreadsheet
program can be used to do least squares curve fits on the linearized isotherms. For the former,
the following results are obtained for fitting Eqs. (1516), (1519), and (1524). Somewhat
different results would be obtained with the linearized equations (1520) and (1525).
Linear:
Freundlich:
Langmuir: q = kp = 7.12557 p
q = kp1/n = 0.00532 p1/5.15605
q = Kqmp/(1 + Kp) = (75410)(0.001036) p/(1 + 75410 p) The fits are shown on the next page, where it is clear that:
Linear model is a very poor fit.
Freundlich model is a fairly good fit.
Langmuir model is a very good fit and is the best fit. Exercise 15.8 (continued)
Analysis: (continued)
0.0016
0.0014 TMB Loading, mol/g 0.0012
0.001
0.0008
0.0006
0.0004
0.0002
0
0 0.00005 0.0001
TMB Pressure, atm 0.00015 0.0002 Exercise 15.9
Subject:
Fitting pure component and mixture adsorption data for gaseous propane (C3) and
propylene (C3=) on silica gel (SG) at 25oC to Freundlich and Langmuir isotherms.
Given: Pure component adsorption equilibrium data for C3 and C3= on SG in the exercise
statement. Adsorption equilibrium data for mixtures of C3 and C3= on SG in the exercise
statement. Surface area of SG = 832 m2/g, pore volume = 0.43 cm3/g, particle density = 1.13
g/cm3, and average pore diameter = 22 angstroms.
Find: (a) Fit of the data to Freundlich and Langmuir isotherms. Which isotherm is best?
Which component is most strongly adsorbed?
(b) Prediction of mixture adsorption from the extended Langmuir isotherm based on the
pure component fits.
(c) Fit of the mixture data to the extended Langmuir isotherm. Comparison to Part (b).
(d) Fit of the mixture data to the extended LangmuirFreundlich isotherm. Comparison
to Part (c).
(e) Relative selectivity from the mixture data. Does it vary widely?
Analysis: (a) The regression program of POLYMATH can be used to do nonlinear curve fits or
a spreadsheet program, such as Excel, can be used to do least squares curve fits on the linearized
isotherms. For the latter, the following results are obtained for fitting Eqs. (1520) and (1525).
Somewhat different results would be obtained with the nonlinear Eqs. (1519) and (1524).
Component Freundlich:
Langmuir:
k
n
K
qm
Propane
0.01062
1.311
0.001853
2.5213
Propylene
0.06242
1.8306
0.003916
2.8201
For C3, the Freundlich equation, with R2 = 0.995, is a slightly better fit than the Langmuir
equat...
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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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