Derivation of Langmuir and Freundlich Isotherms by Using HPLC
Abstract:
Different amounts of granulated activated carbon were combined with a phenol
solution in eight bottles. After the phenol was allowed to adsorb onto the surface of the
activated carbon the remaining phenol in solution was measured by HPLC. Langmuir
and Freundlich isotherms were then derived from our data. The Langmuir isotherm is a
better representation for lower concentrations and the Freundlich isotherm is a better
representation at higher concentrations.
Introduction:
The fate of many chemical pollutants in the environment depends on whether or
not it is capable of adsorbing to particles. Sorption isotherms are used to describe
equilibrium between sorbed and desorbed phases. There are many different sorption
isotherms each with a different shape (1). The two isotherms used in this lab were the
Langmuir and Freundlich isotherms. The Freundlich isotherm is described by the
following equation:
Cis  K iF  Ciwni
The Langmuir isotherm is described by this equation:
  K C
Cis  max iL iw
1  K iL  Ciw
In this lab granular activated carbon was put into a phenol solution to allow the
adsorption of phenol on its surface. The remaining phenol in the solution was then
measured by high performance liquid chromatography (HPLC). HPLC uses a liquid
phase that is forced through a column at high pressure (2). The purpose of this
experiment was to determine whether the Langmuir isotherm or Freundlich isotherm is a
better fit for the adsorption of phenol to granular activated carbon.
Procedure:
Standard Preparation: Standards were prepared from a 100mg/L buffered phenol solution
(190 mg/L KH2PO4 and 100 mg/L K2HPO4). The concentrations of the standards were
as follows:
Std
(mg/L)
5.08
10.16
25.4
50.8
101.6
Sample Preparation: The samples were prepared by adding differing amounts of granular
activated carbon (GAC) and the phenol solution in eight different bottles. The bottles
preparation is summarized in the following table:
Bottle
#
Bottle
(g)
1
2
3
4
5
6
7
8
62.706
62.797
63.175
62.248
62.903
62.970
63.013
62.731
GAC
(g)
Phenol
Vol
(ml)
0.0910
0.0770
0.0570
0.0430
0.0290
0.0140
0.0060
0.0000
48.16
48.21
48.88
47.50
50.49
49.92
48.02
47.34
Bottle+GAC Bottle+GAC+Phenol
(g)
(g)
62.797
62.874
63.232
62.291
62.932
62.984
63.019
62.731
110.959
111.082
112.115
109.794
113.421
112.903
111.034
110.071
Analysis: After the samples were left in a shaker for seven days the phenol solution was
separated from the GAC and analyzed using HPLC. The Freundlich and Langmuir
Isotherms were then calculated by using the following formulas:
Langmuir:
  K C
 1
1 
1
1
Cis  max iL iw



1  K iL  Ciw


Cis  Cis,max  K iL  Ciw Cis,max
ni
Freundlich: Cis  K iF  Ciw
log Cis  n log Ciw  log K iF
Results:
Figure 1: Standard Curve
Phenol Standard Curve
y = 32.65018x - 1.13831
R2 = 0.99999
3500
3000
Area
2500
2000
1500
1000
500
0
0
20
40
60
80
100
120
Concentration (m g/L)
This standard curve was used to calculate phenol concentration in the samples.
Table 1: Calculated Values for Cw and Cs
Bottle
#
Cw
(mg/L)
Cs
(mg/g)
log Cw
log Cs
1/Cw
1/Cs
1
2
3
4
5
6
7
1.5
2.0
5.1
6.6
22.9
51.6
80.2
53.0
62.4
82.8
105.0
137.0
178.2
170.9
0.173093
0.297276
0.706324
0.818834
1.359692
1.712778
1.904424
1.724142
1.794963
1.917876
2.021025
2.136815
2.250975
2.232701
0.671286
0.504341
0.196642
0.151763
0.043683
0.019374
0.012462
0.018874
0.016034
0.012082
0.009527
0.007298
0.005611
0.005852
Figure 2: Sorption Curve
Cs vs. Cw
Cs (mg/g)
200
150
100
50
0
0
20
40
60
80
100
Cw (mg/L)
Figure 3: Langmuir Isotherm
Langmuir Isotherm
y = 0.019516x + 0.006294
R2 = 0.963782
0.025
0.02
1/Cs
0.015
0.01
0.005
0
0
0.2
0.4
1/Cw
 1
1 
1
1




Cis  Cis,max  K iL  Ciw Cis,max
0.6
0.8
Figure 4: Freundlich Isotherm
log Cs
Freundlich Isotherm
2.4
2.3
2.2
2.1
2
1.9
1.8
1.7
1.6
1.5
y = 0.3021x + 1.7103
R2 = 0.9649
0
0.5
1
1.5
2
log Cw
log Cis  n log Ciw  log K iF
Table 2: Isotherm Values
Freundlich
n
log KF
KF
0.3021
1.7103
51.32158
Langmuir
Cs max
KL
158.8815
0.32201
These values were obtained from the linearization of each isotherm.
Table 3: Comparison of Langmuir and Freundlich Isotherm
Langmuir vs. Freundlich Isotherms
250.0
Cs (mg/g)
200.0
Cs (mg/g)
150.0
Freundlich
Langmuir
100.0
50.0
0.0
0.0
20.0
40.0
60.0
Cw (mg/L)
80.0
100.0
Conclusions:
The Langmuir isotherm was a better adsorption model at lower Cw concentrations
and the Freundlich was the better model at higher Cw concentrations. This gives reason
to believe that the adsorption of phenol to GAC is most likely a mixed isotherm that
combines both the Freundlich and Langmuir isotherms. A better representation of which
isotherm is the better fit may be achievable by testing a larger amount of samples with
differing amounts of phenol and GAC. This would give us more points to plot on a graph
which would hopefully allow us to more accurately plot the isotherms.
There was little error in this study. All of the values we calculated make sense.
Also the sample we used that did not have any GAC did not show any significant
detection of phenol adsorption so blank subtraction was not necessary.
We achieved our purpose in this experiment by showing that both the Langmuir
and Freundlich isotherms are good representations of adsorption at different
concentration. The only part of this study that could be improved would be an increased
number of samples.
Acknowledgements:
I’d like to thank Dr. Lisa Rodenburg and Jia Guo for their assistance with this lab.
References:
1. Rodenburg, L. Sorption to organic matter. Power Point Presentation. 2008.
2. Rodenburg, L. Introduction to Chromatography. Lecture. 2008.