Transcript Isotherm parameters for lead onto peat: Comparison of

Isotherm Parameters for Lead onto Peat: Comparison of Linear and Nonlinear Methods
Pei-Yu Lin1#, Ming-Huang Wang1, Wen-Ta Chiu2,3 and Yuh-Shan Ho4*
1School of Public Health, Taipei Medical University
2Graduate Institute of Injury Prevention and Control, Taipei Medical University
3Department of Neurosurgery, Taipei Medical University - Wan-Fang Hospital
4Bibliometric Centre, Taipei Medical University - Wan-Fang Hospital
Introduction
Equilibrium relationships between sorbents and sorbates are described by sorption isotherms which give the capacity of a sorbent for a sorbate. Isotherms can be
obtained by examining batch reactions at fixed temperatures. Linear regression is frequently used to determine the best-fitting isotherm. The linear least-squares
method with linearly transformed isotherm equations has also been widely applied to confirm experimental data and isotherms using coefficients of determination.
In this study, the linear least-squares method and a non-linear method of three widely used isotherms, the Langmuir, Freundlich, and Redlich-Peterson, were
compared in an experiment examining lead ion sorption onto peat. A trial-and-error procedure was used for the non-linear method using the solver add-in with
Microsoft’s spreadsheet, Microsoft Excel.
Methods
Equilibrium isotherms were determined by shaking a fixed mass of peat (0.4 g) with 100 ml of lead(II) solutions in conical flasks. A range of lead(II) concentrations
(20 to 120 mg/dm3) was tested at an initial value of pH 6.0. Initial pH adjustments were carried out by adding either a sulphuric acid or sodium hydroxide solution.
After shaking the flasks for 4 h, the reaction mixtures were filtered through filter paper, and then the filtrates was analysed for the remaining lead(II) concentration
with atomic absorption spectrometry (AAS).
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Results
Table 1. Isotherms and their linear forms
Isotherm
Langmuir-1
qe  K F Ce1/ n
qe 
qm K a Ce
1  K a Ce
Langmuir-2
Plot
logqe   logK F   1 n logCe 
logqe  vs. logCe 
Ce
1
1

Ce 
qe qm
K a qm
Ce vs. C
e
qe
1  1  1
1
 

qe  K a qm  Ce qm
1 vs. 1
Ce
qe
10
5
 1  qe

qe  qm  
 K a  Ce
qe vs. qe
Ce
Langmuir-4
qe
 K a qm  K a qe
Ce
qe
Ce
 C

ln A e  1  g lnCe   lnB 
 qe

 C
 vs.
ln  A e  1
 qe

qe 
ACe
g
1  BCe
15
T = 303 K
Redlich-Peterson linear
Langmuir-3
Redlich-Peterson
20
qe (mg/g)
Freundlich
25
Linear form
Redlich-Peterson non-linear
0
vs. qe
0
5
10
15
20
C e (mg/dm 3)
Figure 1: Redich-Peterson Isotherms obtained using linear
and non-linear methods for the sorption of lead(II) onto peat
lnCe 
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Table 2. Isotherm parameters obtained using the linear method
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T (K)
283
293
303
313
Langmuir-1
qm (mg/g)
27.8
28.3
29.5
30.8
Ka (dm3/mg)
0.437 0.416 0.415 0.382
r2
0.995 0.992 0.996 0.984
qm (mg/g)
23.2
Ka (dm3/mg)
0.733 0.984 0.718 1.01
r2
0.991 0.969 0.983 0.959
Langmuir-2
Langmuir-3
qm (mg/g)
25.0
Freundlich
Redlich-Peterson
23.5
23.7
26.2
T = 303 K
Langmuir-1 non-linear
10
21.4
Freundlich non-linear
5
Redlich-Peterson non-linear
0
24.3
Ka (dm /mg)
0.623 0.780 0.583 0.784
r2
0.939 0.837 0.900 0.775
qm (mg/g)
25.6
Ka (dm3/mg)
0.585 0.652 0.525 0.608
r2
0.939 0.837 0.900 0.775
1/n
0.410 0.409 0.448 0.447
KF (mg/g)(dm3/mg)1/n
8.51
r2
0.970 0.987 0.973 0.993
g
25.0
8.58
27.3
8.57
26.7
8.75
0.811 0.703 0.749 0.608
3
15
0
3
Langmuir-4
21.1
20
qe (mg/g)
Isotherm
g
B (dm /mg)
1.41
3.54
1.67
7.77
A (dm3/g)
22.0
41.1
24.2
78.7
r2
1.000 0.999 0.997 0.997
5
10
C e (mg/dm 3)
15
20
Figure 2: Isotherms obtained using the linear method
Conclusions

It is not appropriate to use the coefficient of determination of the linear
regression method for comparing the best-fitting isotherms.

The non-linear method is a better way to obtain the isotherm parameters.

Langmuir-1 is the most-popular linear form which had the highest
coefficient of determination compared with other Langmuir linear
equations.

Both the two-parameter Langmuir and the three-parameter RedlichPeterson isotherms had higher values for the coefficient of determination
for the sorption of lead ion onto peat.

The Freundlich isotherm can be applied in a range of lower equilibrium
concentrations.