Research Article, Issue 4
Analytical Methods in Environmental Chemistry Journal
Journal home page: www.amecj.com/ir
AMECJ
------------------------
Beniah Obinna Isiuku
a,*
and Francis Chizoruo Ibe
a
a
Department of Chemistry, Imo State University, PMB 2000, Owerri, Imo State, Nigeria Obinna Isiuku
due to their organic and toxic nature. The presence
of dyes in water bodies hinders photosynthesis
[3]. Dye wastewaters discharged from textile and
dyestuff industries into water bodies generate
growing public concern due to their toxicity and
carcinogenicity [4]. Hen egg membrane comprises
majorly of two parts: the egg membrane made up
of protein fibers that are interwoven and spherical
masses, and the calcified eggshell composed of
interstitial calcite or calcium carbonate crystals [5].
Hen egg membrane is situated on the inner surface
of the eggshell. The membrane is a dual membrane
with structure that can be said to be an intricate
Removal of metanil yellow by batch biosorption from
aqueous phase on egg membrane: Equilibrium and isotherm
studies
1. Introduction
The production of different kinds of chemical
compounds due to rapid large-scale industrialization
has created serious environmental pollution [1].
Dyes are organic compounds used for imparting
color in textile, printing and paint industries. Due to
their chemical structures, synthetic dyes dissolved
in wastewaters are not degraded on exposure to
light, chemical and biological treatments [2].
The discharge of dyes into water bodies cause
immediate visible pollution and contamination
*
Corresponding Author: Beniah Obinna Isiuku
Email: obinnabisiuku@yahoo.com
DOI: https://doi.org/10.24200/amecj
A R T I C L E I N F O:
Received 25 Aug 2019
Revised form 21 Oct 2019
Accepted 17 Nov 2019
Available online 25 Dec 2019
Keywords:
Batch biosorption,
Hen egg membrane,
Isotherm modeling,
Metanil yellow,
Physisorption
A B S T R A C T
The biosorption of metanil yellow on hen egg membrane from
aqueous solution in a batch process was investigated at 29
o
C with
a view to determine the potential of the membrane in removing
metanil yellow from aqueous solution. The effects of contact time,
initial biosorbate concentration, biosorbent dosage and initial
biosorbate pH were determined. Various isotherm models were used
to analyze experimental data. The highest experimental equilibrium
biosorption capacity obtained was 129.88 mg g
-1
. The optimum pH
was 3. Adsorption capacity increased with increase in initial solution
concentration but decreased with increase in time. The isotherm
models applied were good fits based on correlation coefficients.
Flory-Huggins isotherm was the best fit (R
2
=0.986). The biosorption
was endothermic, good, physisorptive and spontaneous. This work
shows that hen egg membrane is a potential biosorbent for the
removal of metanil yellow from aqueous solution.
Removal of metanil yellow by batch biosorption Beniah Obinna Isiuku et al
Analytical Methods in Environmental Chemistry Journal Vol 2 (2019) 15-26
16
Analytical Methods in Environmental Chemistry Journal; Vol. 2 (2019)
lattice meshwork of large and small fibers which
interlock with each other to form a tenacious sheath.
Apart from collagen, egg membrane contains
polysaccharides [6]. Due to the polysaccharide
and collagen contents which provide hydroxyl,
amine and sulphonic functional groups on which
adsorbate particles can stick, hen egg membrane
exhibits good biosorption properties [7]. Eggs
from hens are used in large quantities by food
manufacturers, hatcheries, hotels and restaurants
and the shells are disposed of as waste [8]. Metanil
yellow is a water-soluble azo dye used in the
beverages, leather, paper, and textile industries. It
is also used as a stain and as an indicator in acid-
base titrations [9]. Metanil yellow has detrimental
health effects on humans [10]. It is toxic if absorbed
through the skin, respiratory and intestinal tract and
may act as a skin, eye or respiratory tract irritant.
It is harmful when swallowed or inhaled and may
be carcinogenic under long time exposure [11, 12].
Different methods have been developed to remove
synthetic dyes from wastewater in order to reduce
their impact on the environment. The methods
include floatation, electro-coagulation, ozonation,
photo-catalytic degradation, chemical oxidation,
precipitation, filtration and adsorption [3, 13].
Adsorption is superior to the other mentioned
methods due its low cost, flexibility, simplicity
of design, ease of operation and insensitivity to
toxic pollutants [13]. Biosorption is the type of
adsorption whereby contaminants in air or water
are removed using natural biological materials.
Adsorption is mostly applied in cases where the
contaminants do not readily undergo biological
degradation and their concentrations are very low
[14–17]. Batch adsorption experiments are usually
done to measure the effectiveness of adsorption
for removing specific adsorbates as well as to
determine the maximum adsorption capacity [18].
Hen egg membrane had been used to remove
metal ions and Levafix Brilliant Red E-4BA from
aqueous solutions by biosorption [6]. Pramanpol
and Nitayapat [8] used eggshell and egg shell
containing the membrane to remove Reactive
Yellow 205. Their results showed a 10 – 27 fold
increase in biosorption capacity due the presence of
the membrane. Hassan and Salih [7] used eggshell
containing the membrane to effectively remove
methylene blue, a cationic dye from aqueous
solution. The aim of this work was to determine
the performance of hen egg membrane in the
removal of metanil yellow from aqueous solution.
The impacts of initial dye solution concentration,
contact time, biosorbent dosage and initial solution
pH were investigated.
2. Experimental
2.1. Preparation of dye solution
The metanil yellow (Merck, Switzerland) of 70 %
purity, used in this study was purchased at Onitsha,
Nigeria and used directly without further treatment.
The structure of metanil yellow, an anionic dye is
shown in Figure 1. The stock solution was prepared
by dissolving 1g dye per litre solution using distilled
water. Different solution concentrations (25-100
mgL
-1
) used in this work, were obtained by diluting
the stock solution. 1M nitric acid and 1M sodium
hydroxide solutions were used for pH adjustments.
2.2. Preparation of hen egg membrane
The hen eggshells were obtained from restaurants
and hatcheries in Owerri, Imo State, Nigeria. The
eggshells were washed with hot water and rinsed
thrice with hot distilled water to remove odor
and dirt. The eggshells were boiled for 30 min
and cooled. While soaked, the membranes were
Fig. 1. The structure of metanil yellow (MY)
S
O
O
-
O
N N
NH
Na
+
17
Removal of metanil yellow by batch biosorption Beniah Obinna Isiuku et al
peeled off, packed in a lattice and allowed for
water to drain off. The membrane biomass was
dried at 110
o
C in a hot air oven for 1h, and cooled.
The dried membrane biomass was ground with a
blender and sieved to obtain 0.42 – 0.84 mm size
particles and packed in an airtight plastic container.
2.3. Analysis of egg membrane
Infra-red spectrophotometric analysis was run
with a sample of the hen egg membrane with
(FTIR-8400S, Shimadzu, Japan) UV/Visible
spectrophotometer. Proximate analysis of the
biosorbent was carried out using the method of
the Association of Official Analytical Chemists
(AOAC) [19]. The surface structure of the egg
membrane was examined with a scanning electron
microscope (SEM model Phenom Prox, Phenom
World, Netherlands).
2.4. Batch biosorption studies
Batch biosorption of metanil yellow from aqueous
solution was carried out by agitating 0.01g
membrane portions with 25mL portions of different
initial concentration of the dye solution in 50 mL
volumetric flasks. The stoppered sample flasks
were put in a water-bath shaker (SHA-C DFS KW-
1000BH) and agitated for 6 h at 29
o
C and a speed
of 175rpm. A sample was collected each hour,
filtered and the filtrate analyzed using UV-Visible
spectrophotometer (Model 752 Shimadzu, Japan)
at λ
max
440nm. Amounts of dye were absorbed
on the biosorbent and determined by applying in
Equations 1 -3.
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
Batch biosorption of metanil yellow from aqueous solution was carried out by agitating 0.01g
membrane portions with 25mL portions of different initial concentration of the dye solution in
50 mL volumetric flasks. The stoppered sample flasks were put in a water-bath shaker (SHA-C
DFS KW-1000BH) and agitated for 6 h at 29
o
C and a speed of 175rpm. A sample was
collected each hour, filtered and the filtrate analyzed using UV-Visible spectrophotometer
(Model 752 Shimadzu, Japan) at λ
max
440nm. Amounts of dye were absorbed on the biosorbent
and determined by applying in Equation 1 -3.
3. Results and Discussion
3.1. Analysis of the hen egg membrane
Fourier Transform Infra-red spectrophotomeric analysis and proximate analysis were carried
out on the egg membrane. Table 1 shows the protein, carbohydrate, fiber, and lipid contents of
the biomass. Figure 2 shows the infra-red spectrum of the biosorbent. The infra-red peaks at
2341.66, 2843.17, 3036.06, 3255.95, and 3618.58 cm
-1
show presence of –NH- and –OH
functional groups, while 1238.34, 1408.08, 1519.96, and1658.84 cm
-1
show presence of –CO-
functional group. The –NH- and –CO- functional groups are present as amide group in protein
fibers; the –OH in carbohydrate; and –CO-, –C-O- , in carboxylate group. [20 – 22]. These
functional groups are responsible for the biosorption. Figure 3 shows the morphology of the
biosorbent; it shows a well arranged lattice structure of intertwined fibres. This creates a good
network of pores contributing to biosorption [6].
Table 1. Proximate analytical data for hen egg membrane
Parameter Value (%)
Ash 8.39
Moisture 11.70
Crude protein 2.11
Carbohydrate 36.57
Fiber 27.59
Lipid 13.65
3. Results and Discussion
3.1. Analysis of the hen egg membrane
Fourier Transform Infra-red spectrophotomeric
analysis and proximate analysis were carried out
on the egg membrane. Table 1 shows the protein,
carbohydrate, fiber, and lipid contents of the
biomass. Figure 2 shows the infra-red spectrum
of the biosorbent. The infra-red peaks at 2341.66,
2843.17, 3036.06, 3255.95, and 3618.58 cm
-1
show
presence of (–NH) and (–OH) functional groups,
while 1238.34, 1408.08, 1519.96, and1658.84 cm
-1
show presence of –CO- functional group. The –NH-
and –CO- functional groups are present as amide
group in protein fibers; the (–OH) in carbohydrate;
and (–CO; –CO–) , in carboxylate group. [20-
22]. These functional groups are responsible for
Fig. 2. FTIR spectrum of hen egg membrane
Table 1. Proximate analytical data for hen egg membrane
Parameter Value (%)
Ash 8.39
Moisture 11.70
Crude protein 2.11
Carbohydrate 36.57
Fiber 27.59
Lipid 13.65
18
Analytical Methods in Environmental Chemistry Journal; Vol. 2 (2019)
the biosorption. Figure 3 shows the morphology
of the biosorbent; it shows a well arranged lattice
structure of intertwined fibres. This creates a good
network of pores contributing to biosorption [6].
3.2. Biosorption studies
3.2.1. Effect of initial dye concentration and con-
tact time
The effects of initial biosorbate concentration
and contact time at 29
o
C, agitation speed 175
rpm and pH 3 are shown in Figure 4. Maximum
biosorption was within the first sixty minutes for
all the concentrations. Generally the equilibrium
biosorption capacities were high for all the initial
concentrations. However, there was appreciable
decline in biosorption with time for the initial
concentration 100 mg/L. Results show increase
in equilibrium biosorption capacity with increase
in initial concentration. This agrees with the work
of Njoku and Hameed [23]. The optimum time
of biosorption for initial concentrations 25 and 50
mg/L was 120 min. For initial concentration 100
mg/L, equilibrium was not reached at 360 min. The
appreciable decrease in equilibrium biosorption
capcity with time for initial concentration 100
mg/L might be as a result of competition of the
biosorbate anions for available binding sites
[24, 25]. The increase in equilibrium biosorption
Fig. 3. Scanning electron micrograph of hen egg membrane 500x before biosorption
Fig. 4. Effect of initial concentration on the biosorption of metanil yellow on hen egg membrane
19
Removal of metanil yellow by batch biosorption Beniah Obinna Isiuku et al
capacity with increase in initial concentration
is as a result of the increase in the driving force
from the concentration gradient. At highest initial
concentration the active sites of the egg membrane
were surrounded by much more biosorbate ions
leading to more enhanced biosorption [26].
3.2.2. Effect of biosorbent dosage
Various dosages (0.04-1.28 % w/v) of the egg
membrane were interacted with 25 mL portions
of the dye of initial concentration 25 mg/L at
pH 3, temperature 29
o
C and agitation speed of
175 rpm for 6 h in order to study the effect of
biosorbent dosage. The results of Figure 5 showed
that equilibrium biosorption capacity decreased
with increase in biosorbent dosage. This is in
agreement with the work of Koumanova et al, [27].
At higher biosorbent dosage, there was a very fast
superficial biosorption onto the biosorbent surface
that produced a lower solute concentration in the
solution than when biosorbent dosage was lower.
Thus with increasing biosorbent dosage, the
amount of metanil yellow biosorbed per unit
mass of egg membrane reduced, hence leading
to a decrease in equilibrium biosorption
capacity. This is in conformity with the report
of Han et al., [26]. Increasing the biosorbent
dosage from 0.04 – 1.28 % led to a decrease
in q
e
from 54.38 to 1.80 mg g
-1
. The optimum
biosorbent dosage was found to be 0.04 %
(w/v).
3.2.3. Effect of initial biosorbate pH
Solution pH affects the properties of both biosorbate
and biosorbent and is therefore a very important
parameter that affects biosorption in aqueous
solutions [23]. The effect of initial solution pH
on the biosorption of metanil yellow by hen egg
membrane was investigated within the pH range
2-7 and the result is shown in Figure 6. The
figure shows the highest equilibrium biosorption
capacity of 29.40 mg g
-1
for pH 3, initial dye
concentration 25 mgL
-1
, biosorbent dosage 0.08 %
w/v, and temperature 29
o
C. There was decrease in
equilibrium biosorption capacity with increase in
pH. At pH 7, there was virtually no biosorption.
The pH values 3 was optimum for the biosorption
process. The equilibrium biosorption capacity
decreased from 29.40 mg g
-1
at pH 3 to 26.45 mgL
-1
at pH 2. The reason for the decrease was attributed
to the increase in H
+
concentration leading to the
formation of aqua complexes thereby retarding the
biosorption process. This agrees with the report of
Mas Haris and Sathasivam, [28]. At low pH, the
carboxylate anion of the protein fiber present in
Fig. 5. Effect of adsorbent dosage on the biosorption of metanil yellow on hen egg membrane
20
Analytical Methods in Environmental Chemistry Journal; Vol. 2 (2019)
the membrane as part of the amino acid functional
group was protonated and the amino acid existed
primarily in the ammonium ion form; the oxo
functional group present in the polysaccharide
was also protonated. These conditions created
positively charged surface on the biosorbent
hence, high biosorption; as the pH was raised, the
ammonium ion site in the protein was deprotonated,
and the molecule existed as the carboxylate anion;
the oxo functional group was hydrated generating
hydroxyl ions which repelled the metanil yellow
anions [21, 29]. These conditions were responsible
for poor biosorption at higher pH values.
3.3. Adsorption Isotherm modeling
An adsorption isotherm indicates how adsorbed
particles distribute between the liquid phase
and the solid phase when the adsorption process
reaches an equilibrium state [26]. To enhance
the description of an adsorption process in terms
of batch equilibrium process a finite amount of
adsorbent is brought into contact with various
concentrations of the adsorbate. Batch equilibrium
studies yield information as to the total capacity
of an adsorbent for a particular material in single
component systems. However, isotherms are
obtained under equilibrium conditions, whereas in
most adsorption treatment applications the retention
time is too short for equilibrium to be attained [6].
The analysis of the isotherm data by fitting them
to different isotherm models is an important step
to find the suitable model that can be used for
design purposes [5, 26]. An adsorption isotherm
is critical in optimizing the use of adsorbents. In
this study many isotherm models were used to
model experimental data. The applicability of the
isotherm models to the biosorption was compared
by judging the correlation coefficient values.
3.3.1. Langmuir isotherm model
The Langmuir isotherm assumes a homogenous
surface with identical sites in terms of energy for
the biosorbent [30, 31]. It is represented by Eq. 4:
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
3.3.1. Langmuir isotherm model
The Langmuir isotherm assumes a homogenous surface with identical sites in terms of energy
for the biosorbent [30, 31]. It is represented by Eq. 4:
The type 2 linearized Langmuir equation is given as Eq. 5:
A plot of 1/q
e
against 1/C
e
, gave a straight line with slope 1/K
L
and intercept 1/q
m
as shown in
Figure 7. Table 2 shows the model parameters (K
L
, q
m
and R
L
). R
2
value (0.977) shows that the
experimental results fitted well into the Langmuir isotherm model. The essential characteristics
of the Langmuir isotherm can be expressed in terms of a dimensionless constant, the Hall
separation factor R
L
[32] expressed as Eq. 6:
The value of R
L
indicates the type of isotherm to be either favorable (0<R
L
<1), unfavorable
(R
L
>1), linear (R
L
=1) or irreversible (R
L
= 0). R
L
value was found to be 0.314. The result
shows the isotherm to be favorable. The Langmuir constant K
L
was used to determine the
spontaneity of the adsorption by calculating the Gibbs free energy (33) applying Eq. 7:
The free energy value (-5.009 kJ/mol) shows that the process was spontaneous.
3.3.2. Freundlich isotherm model
The Freundlich isotherm model is empirical. Assumptions made in applying this model are that,
multilayer adsorption occurs on a heterogeneous adsorbent surface, and that the concentration
of the adsorbate on adsorbent increases infinitely with increase in the concentration of the
adsorbate [34]. The adsorbent surface has unequal available sites with different energies of
adsorption [35]. It does not predict any saturation of the adsorbent by the adsorbate [30]. The
Freundlich model is mathematically expressed as Eq. 8:
Its linear logarithmic form [31] is Eq. 9:
…………………………………. (9)
A plot of In q
e
against In C
e
,
gave a straight line, with slope 1/n, and intercept In K
F
.
K
F
is the adsorption or distribution coefficient and represents the quantity of dye adsorbed onto
the membrane for a unit equilibrium concentration. The mechanism and the rate of adsorption
are functions of 1/n and K
F
. For a good adsorbent, 0.2 ˂ 1/n ˂ 0.8, while a smaller value of 1/n
indicates better adsorption and formation of stronger bond between the adsorbate and adsorbent
[36]. The plot of In q
e
against In C
e
(Fig.8) gave values of 1/n, n, K
F
and R
2
as shown in Table
2. The 1/n value (0.34 < 1) shows that the biosorption was physisorptive; n (2.941) > 1 shows
that the biosorption was good [34]. The R
2
value (0.872) shows that Freundlich isotherm model
simulated experimental data well.
3.3.3 Temkin isotherm model
The Temkin model presumes that the heat of adsorption of adsorbate particles in the layer
decreases linearly with coverage with consideration of the effects of indirect adsorbent-
adsorbate interaction, and adsorption process is characterized by a uniform distribution of
binding energies, up to some maximum binding energy [13, 37]. The linear form of Temkin
equation [13, 38] is expressed as Eq. 10:
The type 2 linearized Langmuir equation is given
as Eq. 5:
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
3.3.1. Langmuir isotherm model
The Langmuir isotherm assumes a homogenous surface with identical sites in terms of energy
for the biosorbent [30, 31]. It is represented by Eq. 4:
The type 2 linearized Langmuir equation is given as Eq. 5:
A plot of 1/q
e
against 1/C
e
, gave a straight line with slope 1/K
L
and intercept 1/q
m
as shown in
Figure 7. Table 2 shows the model parameters (K
L
, q
m
and R
L
). R
2
value (0.977) shows that the
experimental results fitted well into the Langmuir isotherm model. The essential characteristics
of the Langmuir isotherm can be expressed in terms of a dimensionless constant, the Hall
separation factor R
L
[32] expressed as Eq. 6:
The value of R
L
indicates the type of isotherm to be either favorable (0<R
L
<1), unfavorable
(R
L
>1), linear (R
L
=1) or irreversible (R
L
= 0). R
L
value was found to be 0.314. The result
shows the isotherm to be favorable. The Langmuir constant K
L
was used to determine the
spontaneity of the adsorption by calculating the Gibbs free energy (33) applying Eq. 7:
The free energy value (-5.009 kJ/mol) shows that the process was spontaneous.
3.3.2. Freundlich isotherm model
The Freundlich isotherm model is empirical. Assumptions made in applying this model are that,
multilayer adsorption occurs on a heterogeneous adsorbent surface, and that the concentration
of the adsorbate on adsorbent increases infinitely with increase in the concentration of the
adsorbate [34]. The adsorbent surface has unequal available sites with different energies of
adsorption [35]. It does not predict any saturation of the adsorbent by the adsorbate [30]. The
Freundlich model is mathematically expressed as Eq. 8:
Its linear logarithmic form [31] is Eq. 9:
…………………………………. (9)
A plot of In q
e
against In C
e
,
gave a straight line, with slope 1/n, and intercept In K
F
.
K
F
is the adsorption or distribution coefficient and represents the quantity of dye adsorbed onto
the membrane for a unit equilibrium concentration. The mechanism and the rate of adsorption
are functions of 1/n and K
F
. For a good adsorbent, 0.2 ˂ 1/n ˂ 0.8, while a smaller value of 1/n
indicates better adsorption and formation of stronger bond between the adsorbate and adsorbent
[36]. The plot of In q
e
against In C
e
(Fig.8) gave values of 1/n, n, K
F
and R
2
as shown in Table
2. The 1/n value (0.34 < 1) shows that the biosorption was physisorptive; n (2.941) > 1 shows
that the biosorption was good [34]. The R
2
value (0.872) shows that Freundlich isotherm model
simulated experimental data well.
3.3.3 Temkin isotherm model
The Temkin model presumes that the heat of adsorption of adsorbate particles in the layer
decreases linearly with coverage with consideration of the effects of indirect adsorbent-
adsorbate interaction, and adsorption process is characterized by a uniform distribution of
binding energies, up to some maximum binding energy [13, 37]. The linear form of Temkin
equation [13, 38] is expressed as Eq. 10:
A plot of 1/q
e
against 1/C
e
, gave a straight line
with slope 1/K
L
and intercept 1/q
m
as shown in
Figure 7. Table 2 shows the model parameters
(K
L
, q
m
and R
L
). R
2
value (0.977) shows that the
experimental results fitted well into the Langmuir
isotherm model. The essential characteristics of
the Langmuir isotherm can be expressed in terms
of a dimensionless constant, the Hall separation
factor R
L
[32] expressed as Eq. 6:
Fig. 6. Effect of initial pH on biosorption of metanil yellow on hen egg membrane
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
3.3.1. Langmuir isotherm model
The Langmuir isotherm assumes a homogenous surface with identical sites in terms of energy
for the biosorbent [30, 31]. It is represented by Eq. 4:
The type 2 linearized Langmuir equation is given as Eq. 5:
A plot of 1/q
e
against 1/C
e
, gave a straight line with slope 1/K
L
and intercept 1/q
m
as shown in
Figure 7. Table 2 shows the model parameters (K
L
, q
m
and R
L
). R
2
value (0.977) shows that the
experimental results fitted well into the Langmuir isotherm model. The essential characteristics
of the Langmuir isotherm can be expressed in terms of a dimensionless constant, the Hall
separation factor R
L
[32] expressed as Eq. 6:
The value of R
L
indicates the type of isotherm to be either favorable (0<R
L
<1), unfavorable
(R
L
>1), linear (R
L
=1) or irreversible (R
L
= 0). R
L
value was found to be 0.314. The result
shows the isotherm to be favorable. The Langmuir constant K
L
was used to determine the
spontaneity of the adsorption by calculating the Gibbs free energy (33) applying Eq. 7:
The free energy value (-5.009 kJ/mol) shows that the process was spontaneous.
3.3.2. Freundlich isotherm model
The Freundlich isotherm model is empirical. Assumptions made in applying this model are that,
multilayer adsorption occurs on a heterogeneous adsorbent surface, and that the concentration
of the adsorbate on adsorbent increases infinitely with increase in the concentration of the
adsorbate [34]. The adsorbent surface has unequal available sites with different energies of
adsorption [35]. It does not predict any saturation of the adsorbent by the adsorbate [30]. The
Freundlich model is mathematically expressed as Eq. 8:
Its linear logarithmic form [31] is Eq. 9:
…………………………………. (9)
A plot of In q
e
against In C
e
,
gave a straight line, with slope 1/n, and intercept In K
F
.
K
F
is the adsorption or distribution coefficient and represents the quantity of dye adsorbed onto
the membrane for a unit equilibrium concentration. The mechanism and the rate of adsorption
are functions of 1/n and K
F
. For a good adsorbent, 0.2 ˂ 1/n ˂ 0.8, while a smaller value of 1/n
indicates better adsorption and formation of stronger bond between the adsorbate and adsorbent
[36]. The plot of In q
e
against In C
e
(Fig.8) gave values of 1/n, n, K
F
and R
2
as shown in Table
2. The 1/n value (0.34 < 1) shows that the biosorption was physisorptive; n (2.941) > 1 shows
that the biosorption was good [34]. The R
2
value (0.872) shows that Freundlich isotherm model
simulated experimental data well.
3.3.3 Temkin isotherm model
The Temkin model presumes that the heat of adsorption of adsorbate particles in the layer
decreases linearly with coverage with consideration of the effects of indirect adsorbent-
adsorbate interaction, and adsorption process is characterized by a uniform distribution of
binding energies, up to some maximum binding energy [13, 37]. The linear form of Temkin
equation [13, 38] is expressed as Eq. 10:
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
3.3.1. Langmuir isotherm model
The Langmuir isotherm assumes a homogenous surface with identical sites in terms of energy
for the biosorbent [30, 31]. It is represented by Eq. 4:
The type 2 linearized Langmuir equation is given as Eq. 5:
A plot of 1/q
e
against 1/C
e
, gave a straight line with slope 1/K
L
and intercept 1/q
m
as shown in
Figure 7. Table 2 shows the model parameters (K
L
, q
m
and R
L
). R
2
value (0.977) shows that the
experimental results fitted well into the Langmuir isotherm model. The essential characteristics
of the Langmuir isotherm can be expressed in terms of a dimensionless constant, the Hall
separation factor R
L
[32] expressed as Eq. 6:
The value of R
L
indicates the type of isotherm to be either favorable (0<R
L
<1), unfavorable
(R
L
>1), linear (R
L
=1) or irreversible (R
L
= 0). R
L
value was found to be 0.314. The result
shows the isotherm to be favorable. The Langmuir constant K
L
was used to determine the
spontaneity of the adsorption by calculating the Gibbs free energy (33) applying Eq. 7:
The free energy value (-5.009 kJ/mol) shows that the process was spontaneous.
3.3.2. Freundlich isotherm model
The Freundlich isotherm model is empirical. Assumptions made in applying this model are that,
multilayer adsorption occurs on a heterogeneous adsorbent surface, and that the concentration
of the adsorbate on adsorbent increases infinitely with increase in the concentration of the
adsorbate [34]. The adsorbent surface has unequal available sites with different energies of
adsorption [35]. It does not predict any saturation of the adsorbent by the adsorbate [30]. The
Freundlich model is mathematically expressed as Eq. 8:
Its linear logarithmic form [31] is Eq. 9:
…………………………………. (9)
A plot of In q
e
against In C
e
,
gave a straight line, with slope 1/n, and intercept In K
F
.
K
F
is the adsorption or distribution coefficient and represents the quantity of dye adsorbed onto
the membrane for a unit equilibrium concentration. The mechanism and the rate of adsorption
are functions of 1/n and K
F
. For a good adsorbent, 0.2 ˂ 1/n ˂ 0.8, while a smaller value of 1/n
indicates better adsorption and formation of stronger bond between the adsorbate and adsorbent
[36]. The plot of In q
e
against In C
e
(Fig.8) gave values of 1/n, n, K
F
and R
2
as shown in Table
2. The 1/n value (0.34 < 1) shows that the biosorption was physisorptive; n (2.941) > 1 shows
that the biosorption was good [34]. The R
2
value (0.872) shows that Freundlich isotherm model
simulated experimental data well.
3.3.3 Temkin isotherm model
The Temkin model presumes that the heat of adsorption of adsorbate particles in the layer
decreases linearly with coverage with consideration of the effects of indirect adsorbent-
adsorbate interaction, and adsorption process is characterized by a uniform distribution of
binding energies, up to some maximum binding energy [13, 37]. The linear form of Temkin
equation [13, 38] is expressed as Eq. 10:
21
Removal of metanil yellow by batch biosorption Beniah Obinna Isiuku et al
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
3.3.1. Langmuir isotherm model
The Langmuir isotherm assumes a homogenous surface with identical sites in terms of energy
for the biosorbent [30, 31]. It is represented by Eq. 4:
The type 2 linearized Langmuir equation is given as Eq. 5:
A plot of 1/q
e
against 1/C
e
, gave a straight line with slope 1/K
L
and intercept 1/q
m
as shown in
Figure 7. Table 2 shows the model parameters (K
L
, q
m
and R
L
). R
2
value (0.977) shows that the
experimental results fitted well into the Langmuir isotherm model. The essential characteristics
of the Langmuir isotherm can be expressed in terms of a dimensionless constant, the Hall
separation factor R
L
[32] expressed as Eq. 6:
The value of R
L
indicates the type of isotherm to be either favorable (0<R
L
<1), unfavorable
(R
L
>1), linear (R
L
=1) or irreversible (R
L
= 0). R
L
value was found to be 0.314. The result
shows the isotherm to be favorable. The Langmuir constant K
L
was used to determine the
spontaneity of the adsorption by calculating the Gibbs free energy (33) applying Eq. 7:
The free energy value (-5.009 kJ/mol) shows that the process was spontaneous.
3.3.2. Freundlich isotherm model
The Freundlich isotherm model is empirical. Assumptions made in applying this model are that,
multilayer adsorption occurs on a heterogeneous adsorbent surface, and that the concentration
of the adsorbate on adsorbent increases infinitely with increase in the concentration of the
adsorbate [34]. The adsorbent surface has unequal available sites with different energies of
adsorption [35]. It does not predict any saturation of the adsorbent by the adsorbate [30]. The
Freundlich model is mathematically expressed as Eq. 8:
Its linear logarithmic form [31] is Eq. 9:
…………………………………. (9)
A plot of In q
e
against In C
e
,
gave a straight line, with slope 1/n, and intercept In K
F
.
K
F
is the adsorption or distribution coefficient and represents the quantity of dye adsorbed onto
the membrane for a unit equilibrium concentration. The mechanism and the rate of adsorption
are functions of 1/n and K
F
. For a good adsorbent, 0.2 ˂ 1/n ˂ 0.8, while a smaller value of 1/n
indicates better adsorption and formation of stronger bond between the adsorbate and adsorbent
[36]. The plot of In q
e
against In C
e
(Fig.8) gave values of 1/n, n, K
F
and R
2
as shown in Table
2. The 1/n value (0.34 < 1) shows that the biosorption was physisorptive; n (2.941) > 1 shows
that the biosorption was good [34]. The R
2
value (0.872) shows that Freundlich isotherm model
simulated experimental data well.
3.3.3 Temkin isotherm model
The Temkin model presumes that the heat of adsorption of adsorbate particles in the layer
decreases linearly with coverage with consideration of the effects of indirect adsorbent-
adsorbate interaction, and adsorption process is characterized by a uniform distribution of
binding energies, up to some maximum binding energy [13, 37]. The linear form of Temkin
equation [13, 38] is expressed as Eq. 10:
The value of R
L
indicates the type of isotherm to
be either favorable (0<R
L
<1), unfavorable (R
L
>1),
linear (R
L
=1) or irreversible (R
L
= 0). R
L
value was
found to be 0.314. The result shows the isotherm to
be favorable. The Langmuir constant K
L
was used
to determine the spontaneity of the adsorption by
calculating the Gibbs free energy (33) applying Eq.
7:
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
3.3.1. Langmuir isotherm model
The Langmuir isotherm assumes a homogenous surface with identical sites in terms of energy
for the biosorbent [30, 31]. It is represented by Eq. 4:
The type 2 linearized Langmuir equation is given as Eq. 5:
A plot of 1/q
e
against 1/C
e
, gave a straight line with slope 1/K
L
and intercept 1/q
m
as shown in
Figure 7. Table 2 shows the model parameters (K
L
, q
m
and R
L
). R
2
value (0.977) shows that the
experimental results fitted well into the Langmuir isotherm model. The essential characteristics
of the Langmuir isotherm can be expressed in terms of a dimensionless constant, the Hall
separation factor R
L
[32] expressed as Eq. 6:
The value of R
L
indicates the type of isotherm to be either favorable (0<R
L
<1), unfavorable
(R
L
>1), linear (R
L
=1) or irreversible (R
L
= 0). R
L
value was found to be 0.314. The result
shows the isotherm to be favorable. The Langmuir constant K
L
was used to determine the
spontaneity of the adsorption by calculating the Gibbs free energy (33) applying Eq. 7:
The free energy value (-5.009 kJ/mol) shows that the process was spontaneous.
3.3.2. Freundlich isotherm model
The Freundlich isotherm model is empirical. Assumptions made in applying this model are that,
multilayer adsorption occurs on a heterogeneous adsorbent surface, and that the concentration
of the adsorbate on adsorbent increases infinitely with increase in the concentration of the
adsorbate [34]. The adsorbent surface has unequal available sites with different energies of
adsorption [35]. It does not predict any saturation of the adsorbent by the adsorbate [30]. The
Freundlich model is mathematically expressed as Eq. 8:
Its linear logarithmic form [31] is Eq. 9:
…………………………………. (9)
A plot of In q
e
against In C
e
,
gave a straight line, with slope 1/n, and intercept In K
F
.
K
F
is the adsorption or distribution coefficient and represents the quantity of dye adsorbed onto
the membrane for a unit equilibrium concentration. The mechanism and the rate of adsorption
are functions of 1/n and K
F
. For a good adsorbent, 0.2 ˂ 1/n ˂ 0.8, while a smaller value of 1/n
indicates better adsorption and formation of stronger bond between the adsorbate and adsorbent
[36]. The plot of In q
e
against In C
e
(Fig.8) gave values of 1/n, n, K
F
and R
2
as shown in Table
2. The 1/n value (0.34 < 1) shows that the biosorption was physisorptive; n (2.941) > 1 shows
that the biosorption was good [34]. The R
2
value (0.872) shows that Freundlich isotherm model
simulated experimental data well.
3.3.3 Temkin isotherm model
The Temkin model presumes that the heat of adsorption of adsorbate particles in the layer
decreases linearly with coverage with consideration of the effects of indirect adsorbent-
adsorbate interaction, and adsorption process is characterized by a uniform distribution of
binding energies, up to some maximum binding energy [13, 37]. The linear form of Temkin
equation [13, 38] is expressed as Eq. 10:
The free energy value (-5.009 kJ mol
-1
) shows that
the process was spontaneous.
3.3.2. Freundlich isotherm model
The Freundlich isotherm model is empirical.
Assumptions made in applying this model are that,
multilayer adsorption occurs on a heterogeneous
adsorbent surface, and that the concentration of
the adsorbate on adsorbent increases infinitely
with increase in the concentration of the adsorbate
[34]. The adsorbent surface has unequal available
sites with different energies of adsorption [35]. It
does not predict any saturation of the adsorbent
by the adsorbate [30]. The Freundlich model is
mathematically expressed as Eq. 8:
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
3.3.1. Langmuir isotherm model
The Langmuir isotherm assumes a homogenous surface with identical sites in terms of energy
for the biosorbent [30, 31]. It is represented by Eq. 4:
The type 2 linearized Langmuir equation is given as Eq. 5:
A plot of 1/q
e
against 1/C
e
, gave a straight line with slope 1/K
L
and intercept 1/q
m
as shown in
Figure 7. Table 2 shows the model parameters (K
L
, q
m
and R
L
). R
2
value (0.977) shows that the
experimental results fitted well into the Langmuir isotherm model. The essential characteristics
of the Langmuir isotherm can be expressed in terms of a dimensionless constant, the Hall
separation factor R
L
[32] expressed as Eq. 6:
The value of R
L
indicates the type of isotherm to be either favorable (0<R
L
<1), unfavorable
(R
L
>1), linear (R
L
=1) or irreversible (R
L
= 0). R
L
value was found to be 0.314. The result
shows the isotherm to be favorable. The Langmuir constant K
L
was used to determine the
spontaneity of the adsorption by calculating the Gibbs free energy (33) applying Eq. 7:
The free energy value (-5.009 kJ/mol) shows that the process was spontaneous.
3.3.2. Freundlich isotherm model
The Freundlich isotherm model is empirical. Assumptions made in applying this model are that,
multilayer adsorption occurs on a heterogeneous adsorbent surface, and that the concentration
of the adsorbate on adsorbent increases infinitely with increase in the concentration of the
adsorbate [34]. The adsorbent surface has unequal available sites with different energies of
adsorption [35]. It does not predict any saturation of the adsorbent by the adsorbate [30]. The
Freundlich model is mathematically expressed as Eq. 8:
Its linear logarithmic form [31] is Eq. 9:
…………………………………. (9)
A plot of In q
e
against In C
e
,
gave a straight line, with slope 1/n, and intercept In K
F
.
K
F
is the adsorption or distribution coefficient and represents the quantity of dye adsorbed onto
the membrane for a unit equilibrium concentration. The mechanism and the rate of adsorption
are functions of 1/n and K
F
. For a good adsorbent, 0.2 ˂ 1/n ˂ 0.8, while a smaller value of 1/n
indicates better adsorption and formation of stronger bond between the adsorbate and adsorbent
[36]. The plot of In q
e
against In C
e
(Fig.8) gave values of 1/n, n, K
F
and R
2
as shown in Table
2. The 1/n value (0.34 < 1) shows that the biosorption was physisorptive; n (2.941) > 1 shows
that the biosorption was good [34]. The R
2
value (0.872) shows that Freundlich isotherm model
simulated experimental data well.
3.3.3 Temkin isotherm model
The Temkin model presumes that the heat of adsorption of adsorbate particles in the layer
decreases linearly with coverage with consideration of the effects of indirect adsorbent-
adsorbate interaction, and adsorption process is characterized by a uniform distribution of
binding energies, up to some maximum binding energy [13, 37]. The linear form of Temkin
equation [13, 38] is expressed as Eq. 10:
Its linear logarithmic form [31] is Eq. 9:
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
3.3.1. Langmuir isotherm model
The Langmuir isotherm assumes a homogenous surface with identical sites in terms of energy
for the biosorbent [30, 31]. It is represented by Eq. 4:
The type 2 linearized Langmuir equation is given as Eq. 5:
A plot of 1/q
e
against 1/C
e
, gave a straight line with slope 1/K
L
and intercept 1/q
m
as shown in
Figure 7. Table 2 shows the model parameters (K
L
, q
m
and R
L
). R
2
value (0.977) shows that the
experimental results fitted well into the Langmuir isotherm model. The essential characteristics
of the Langmuir isotherm can be expressed in terms of a dimensionless constant, the Hall
separation factor R
L
[32] expressed as Eq. 6:
The value of R
L
indicates the type of isotherm to be either favorable (0<R
L
<1), unfavorable
(R
L
>1), linear (R
L
=1) or irreversible (R
L
= 0). R
L
value was found to be 0.314. The result
shows the isotherm to be favorable. The Langmuir constant K
L
was used to determine the
spontaneity of the adsorption by calculating the Gibbs free energy (33) applying Eq. 7:
The free energy value (-5.009 kJ/mol) shows that the process was spontaneous.
3.3.2. Freundlich isotherm model
The Freundlich isotherm model is empirical. Assumptions made in applying this model are that,
multilayer adsorption occurs on a heterogeneous adsorbent surface, and that the concentration
of the adsorbate on adsorbent increases infinitely with increase in the concentration of the
adsorbate [34]. The adsorbent surface has unequal available sites with different energies of
adsorption [35]. It does not predict any saturation of the adsorbent by the adsorbate [30]. The
Freundlich model is mathematically expressed as Eq. 8:
Its linear logarithmic form [31] is Eq. 9:
…………………………………. (9)
A plot of In q
e
against In C
e
,
gave a straight line, with slope 1/n, and intercept In K
F
.
K
F
is the adsorption or distribution coefficient and represents the quantity of dye adsorbed onto
the membrane for a unit equilibrium concentration. The mechanism and the rate of adsorption
are functions of 1/n and K
F
. For a good adsorbent, 0.2 ˂ 1/n ˂ 0.8, while a smaller value of 1/n
indicates better adsorption and formation of stronger bond between the adsorbate and adsorbent
[36]. The plot of In q
e
against In C
e
(Fig.8) gave values of 1/n, n, K
F
and R
2
as shown in Table
2. The 1/n value (0.34 < 1) shows that the biosorption was physisorptive; n (2.941) > 1 shows
that the biosorption was good [34]. The R
2
value (0.872) shows that Freundlich isotherm model
simulated experimental data well.
3.3.3 Temkin isotherm model
The Temkin model presumes that the heat of adsorption of adsorbate particles in the layer
decreases linearly with coverage with consideration of the effects of indirect adsorbent-
adsorbate interaction, and adsorption process is characterized by a uniform distribution of
binding energies, up to some maximum binding energy [13, 37]. The linear form of Temkin
equation [13, 38] is expressed as Eq. 10:
A plot of In q
e
against In C
e
,
gave a straight line,
with slope 1/n, and intercept In K
F
.
K
F
is the adsorption or distribution coefficient and
represents the quantity of dye adsorbed onto the
membrane for a unit equilibrium concentration.
The mechanism and the rate of adsorption are
functions of 1/n and K
F
. For a good adsorbent, 0.2
˂ 1/n ˂ 0.8, while a smaller value of 1/n indicates
better adsorption and formation of stronger bond
between the adsorbate and adsorbent [36]. The plot
of In q
e
against In C
e
(Fig.8) gave values of 1/n, n,
K
F
and R
2
as shown in Table 2. The 1/n value (0.34
< 1) shows that the biosorption was physisorptive;
n (2.941) > 1 shows that the biosorption was good
[34]. The R
2
value (0.872) shows that Freundlich
isotherm model simulated experimental data well.
3.3.3 Temkin isotherm model
The Temkin model presumes that the heat of
Table 2. Isotherm parameters for batch biosorption of
of metanil yellow on egg membrane at 29°C
Model Parameter Value
Langmuir q
m
(mgg
-1
) 129.880
q
e expt
(mgg
-1
) 158.730
K
L
(mgL
-1
) 0.132
R
L
0.070
R
2
0.977
∆G
o
ads
(kJ mol
-1
) -5.009
Freundlich 1/n 0.34
n 2.941
K
F
[mgg
-1
(L/mg)
-1/n
] 37.487
R
2
0.872
Temkin B (J mol
-1
) 29.525
b
T
(J/mol/K) 85.041
A
T
(L g
-1
) 3.025
R
2
0.935
Dubinin-
Radushkevich
q
m
(mg g
-1
) 123.273
R
2
3
E (J mol
-1
) 408.248
R
2
0.98
Elovich q
m
(mg g
-1
) 50.505
K
E
0.912
R
2
0.809
Harkin-Jura A
HJ
(g
2
L
-1
) 3333.33
B
HJ
(mg
2
L
-1
) 1.667
R
2
0.743
Halsey n
H
0.034
K
H
(mg L
-1
) 3.025
R
2
0.935
Flory-Huggins n
FH
2.551
K
FH
(L mol
-1
) 616.464
∆G
o
ads
(kJ mol
-1
) -16.13
R
2
0.986
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
3.3.1. Langmuir isotherm model
The Langmuir isotherm assumes a homogenous surface with identical sites in terms of energy
for the biosorbent [30, 31]. It is represented by Eq. 4:
The type 2 linearized Langmuir equation is given as Eq. 5:
A plot of 1/q
e
against 1/C
e
, gave a straight line with slope 1/K
L
and intercept 1/q
m
as shown in
Figure 7. Table 2 shows the model parameters (K
L
, q
m
and R
L
). R
2
value (0.977) shows that the
experimental results fitted well into the Langmuir isotherm model. The essential characteristics
of the Langmuir isotherm can be expressed in terms of a dimensionless constant, the Hall
separation factor R
L
[32] expressed as Eq. 6:
The value of R
L
indicates the type of isotherm to be either favorable (0<R
L
<1), unfavorable
(R
L
>1), linear (R
L
=1) or irreversible (R
L
= 0). R
L
value was found to be 0.314. The result
shows the isotherm to be favorable. The Langmuir constant K
L
was used to determine the
spontaneity of the adsorption by calculating the Gibbs free energy (33) applying Eq. 7:
The free energy value (-5.009 kJ/mol) shows that the process was spontaneous.
3.3.2. Freundlich isotherm model
The Freundlich isotherm model is empirical. Assumptions made in applying this model are that,
multilayer adsorption occurs on a heterogeneous adsorbent surface, and that the concentration
of the adsorbate on adsorbent increases infinitely with increase in the concentration of the
adsorbate [34]. The adsorbent surface has unequal available sites with different energies of
adsorption [35]. It does not predict any saturation of the adsorbent by the adsorbate [30]. The
Freundlich model is mathematically expressed as Eq. 8:
Its linear logarithmic form [31] is Eq. 9:
…………………………………. (9)
A plot of In q
e
against In C
e
,
gave a straight line, with slope 1/n, and intercept In K
F
.
K
F
is the adsorption or distribution coefficient and represents the quantity of dye adsorbed onto
the membrane for a unit equilibrium concentration. The mechanism and the rate of adsorption
are functions of 1/n and K
F
. For a good adsorbent, 0.2 ˂ 1/n ˂ 0.8, while a smaller value of 1/n
indicates better adsorption and formation of stronger bond between the adsorbate and adsorbent
[36]. The plot of In q
e
against In C
e
(Fig.8) gave values of 1/n, n, K
F
and R
2
as shown in Table
2. The 1/n value (0.34 < 1) shows that the biosorption was physisorptive; n (2.941) > 1 shows
that the biosorption was good [34]. The R
2
value (0.872) shows that Freundlich isotherm model
simulated experimental data well.
3.3.3 Temkin isotherm model
The Temkin model presumes that the heat of adsorption of adsorbate particles in the layer
decreases linearly with coverage with consideration of the effects of indirect adsorbent-
adsorbate interaction, and adsorption process is characterized by a uniform distribution of
binding energies, up to some maximum binding energy [13, 37]. The linear form of Temkin
equation [13, 38] is expressed as Eq. 10:
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
3.3.1. Langmuir isotherm model
The Langmuir isotherm assumes a homogenous surface with identical sites in terms of energy
for the biosorbent [30, 31]. It is represented by Eq. 4:
The type 2 linearized Langmuir equation is given as Eq. 5:
A plot of 1/q
e
against 1/C
e
, gave a straight line with slope 1/K
L
and intercept 1/q
m
as shown in
Figure 7. Table 2 shows the model parameters (K
L
, q
m
and R
L
). R
2
value (0.977) shows that the
experimental results fitted well into the Langmuir isotherm model. The essential characteristics
of the Langmuir isotherm can be expressed in terms of a dimensionless constant, the Hall
separation factor R
L
[32] expressed as Eq. 6:
The value of R
L
indicates the type of isotherm to be either favorable (0<R
L
<1), unfavorable
(R
L
>1), linear (R
L
=1) or irreversible (R
L
= 0). R
L
value was found to be 0.314. The result
shows the isotherm to be favorable. The Langmuir constant K
L
was used to determine the
spontaneity of the adsorption by calculating the Gibbs free energy (33) applying Eq. 7:
The free energy value (-5.009 kJ/mol) shows that the process was spontaneous.
3.3.2. Freundlich isotherm model
The Freundlich isotherm model is empirical. Assumptions made in applying this model are that,
multilayer adsorption occurs on a heterogeneous adsorbent surface, and that the concentration
of the adsorbate on adsorbent increases infinitely with increase in the concentration of the
adsorbate [34]. The adsorbent surface has unequal available sites with different energies of
adsorption [35]. It does not predict any saturation of the adsorbent by the adsorbate [30]. The
Freundlich model is mathematically expressed as Eq. 8:
Its linear logarithmic form [31] is Eq. 9:
…………………………………. (9)
A plot of In q
e
against In C
e
,
gave a straight line, with slope 1/n, and intercept In K
F
.
K
F
is the adsorption or distribution coefficient and represents the quantity of dye adsorbed onto
the membrane for a unit equilibrium concentration. The mechanism and the rate of adsorption
are functions of 1/n and K
F
. For a good adsorbent, 0.2 ˂ 1/n ˂ 0.8, while a smaller value of 1/n
indicates better adsorption and formation of stronger bond between the adsorbate and adsorbent
[36]. The plot of In q
e
against In C
e
(Fig.8) gave values of 1/n, n, K
F
and R
2
as shown in Table
2. The 1/n value (0.34 < 1) shows that the biosorption was physisorptive; n (2.941) > 1 shows
that the biosorption was good [34]. The R
2
value (0.872) shows that Freundlich isotherm model
simulated experimental data well.
3.3.3 Temkin isotherm model
The Temkin model presumes that the heat of adsorption of adsorbate particles in the layer
decreases linearly with coverage with consideration of the effects of indirect adsorbent-
adsorbate interaction, and adsorption process is characterized by a uniform distribution of
binding energies, up to some maximum binding energy [13, 37]. The linear form of Temkin
equation [13, 38] is expressed as Eq. 10:
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
3.3.1. Langmuir isotherm model
The Langmuir isotherm assumes a homogenous surface with identical sites in terms of energy
for the biosorbent [30, 31]. It is represented by Eq. 4:
The type 2 linearized Langmuir equation is given as Eq. 5:
A plot of 1/q
e
against 1/C
e
, gave a straight line with slope 1/K
L
and intercept 1/q
m
as shown in
Figure 7. Table 2 shows the model parameters (K
L
, q
m
and R
L
). R
2
value (0.977) shows that the
experimental results fitted well into the Langmuir isotherm model. The essential characteristics
of the Langmuir isotherm can be expressed in terms of a dimensionless constant, the Hall
separation factor R
L
[32] expressed as Eq. 6:
The value of R
L
indicates the type of isotherm to be either favorable (0<R
L
<1), unfavorable
(R
L
>1), linear (R
L
=1) or irreversible (R
L
= 0). R
L
value was found to be 0.314. The result
shows the isotherm to be favorable. The Langmuir constant K
L
was used to determine the
spontaneity of the adsorption by calculating the Gibbs free energy (33) applying Eq. 7:
The free energy value (-5.009 kJ/mol) shows that the process was spontaneous.
3.3.2. Freundlich isotherm model
The Freundlich isotherm model is empirical. Assumptions made in applying this model are that,
multilayer adsorption occurs on a heterogeneous adsorbent surface, and that the concentration
of the adsorbate on adsorbent increases infinitely with increase in the concentration of the
adsorbate [34]. The adsorbent surface has unequal available sites with different energies of
adsorption [35]. It does not predict any saturation of the adsorbent by the adsorbate [30]. The
Freundlich model is mathematically expressed as Eq. 8:
Its linear logarithmic form [31] is Eq. 9:
…………………………………. (9)
A plot of In q
e
against In C
e
,
gave a straight line, with slope 1/n, and intercept In K
F
.
K
F
is the adsorption or distribution coefficient and represents the quantity of dye adsorbed onto
the membrane for a unit equilibrium concentration. The mechanism and the rate of adsorption
are functions of 1/n and K
F
. For a good adsorbent, 0.2 ˂ 1/n ˂ 0.8, while a smaller value of 1/n
indicates better adsorption and formation of stronger bond between the adsorbate and adsorbent
[36]. The plot of In q
e
against In C
e
(Fig.8) gave values of 1/n, n, K
F
and R
2
as shown in Table
2. The 1/n value (0.34 < 1) shows that the biosorption was physisorptive; n (2.941) > 1 shows
that the biosorption was good [34]. The R
2
value (0.872) shows that Freundlich isotherm model
simulated experimental data well.
3.3.3 Temkin isotherm model
The Temkin model presumes that the heat of adsorption of adsorbate particles in the layer
decreases linearly with coverage with consideration of the effects of indirect adsorbent-
adsorbate interaction, and adsorption process is characterized by a uniform distribution of
binding energies, up to some maximum binding energy [13, 37]. The linear form of Temkin
equation [13, 38] is expressed as Eq. 10:
Removal of metanil yellow by batch biosorption
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3.3.1. Langmuir isotherm model
The Langmuir isotherm assumes a homogenous surface with identical sites in terms of energy
for the biosorbent [30, 31]. It is represented by Eq. 4:
The type 2 linearized Langmuir equation is given as Eq. 5:
A plot of 1/q
e
against 1/C
e
, gave a straight line with slope 1/K
L
and intercept 1/q
m
as shown in
Figure 7. Table 2 shows the model parameters (K
L
, q
m
and R
L
). R
2
value (0.977) shows that the
experimental results fitted well into the Langmuir isotherm model. The essential characteristics
of the Langmuir isotherm can be expressed in terms of a dimensionless constant, the Hall
separation factor R
L
[32] expressed as Eq. 6:
The value of R
L
indicates the type of isotherm to be either favorable (0<R
L
<1), unfavorable
(R
L
>1), linear (R
L
=1) or irreversible (R
L
= 0). R
L
value was found to be 0.314. The result
shows the isotherm to be favorable. The Langmuir constant K
L
was used to determine the
spontaneity of the adsorption by calculating the Gibbs free energy (33) applying Eq. 7:
The free energy value (-5.009 kJ/mol) shows that the process was spontaneous.
3.3.2. Freundlich isotherm model
The Freundlich isotherm model is empirical. Assumptions made in applying this model are that,
multilayer adsorption occurs on a heterogeneous adsorbent surface, and that the concentration
of the adsorbate on adsorbent increases infinitely with increase in the concentration of the
adsorbate [34]. The adsorbent surface has unequal available sites with different energies of
adsorption [35]. It does not predict any saturation of the adsorbent by the adsorbate [30]. The
Freundlich model is mathematically expressed as Eq. 8:
Its linear logarithmic form [31] is Eq. 9:
…………………………………. (9)
A plot of In q
e
against In C
e
,
gave a straight line, with slope 1/n, and intercept In K
F
.
K
F
is the adsorption or distribution coefficient and represents the quantity of dye adsorbed onto
the membrane for a unit equilibrium concentration. The mechanism and the rate of adsorption
are functions of 1/n and K
F
. For a good adsorbent, 0.2 ˂ 1/n ˂ 0.8, while a smaller value of 1/n
indicates better adsorption and formation of stronger bond between the adsorbate and adsorbent
[36]. The plot of In q
e
against In C
e
(Fig.8) gave values of 1/n, n, K
F
and R
2
as shown in Table
2. The 1/n value (0.34 < 1) shows that the biosorption was physisorptive; n (2.941) > 1 shows
that the biosorption was good [34]. The R
2
value (0.872) shows that Freundlich isotherm model
simulated experimental data well.
3.3.3 Temkin isotherm model
The Temkin model presumes that the heat of adsorption of adsorbate particles in the layer
decreases linearly with coverage with consideration of the effects of indirect adsorbent-
adsorbate interaction, and adsorption process is characterized by a uniform distribution of
binding energies, up to some maximum binding energy [13, 37]. The linear form of Temkin
equation [13, 38] is expressed as Eq. 10:
22
Analytical Methods in Environmental Chemistry Journal; Vol. 2 (2019)
adsorption of adsorbate particles in the layer
decreases linearly with coverage with consideration
of the effects of indirect adsorbent-adsorbate
interaction, and adsorption process is characterized
by a uniform distribution of binding energies, up to
some maximum binding energy [13, 37]. The linear
form of Temkin equation [13, 38] is expressed as
Eq. 10:
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
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3.3.1. Langmuir isotherm model
The Langmuir isotherm assumes a homogenous surface with identical sites in terms of energy
for the biosorbent [30, 31]. It is represented by Eq. 4:
The type 2 linearized Langmuir equation is given as Eq. 5:
A plot of 1/q
e
against 1/C
e
, gave a straight line with slope 1/K
L
and intercept 1/q
m
as shown in
Figure 7. Table 2 shows the model parameters (K
L
, q
m
and R
L
). R
2
value (0.977) shows that the
experimental results fitted well into the Langmuir isotherm model. The essential characteristics
of the Langmuir isotherm can be expressed in terms of a dimensionless constant, the Hall
separation factor R
L
[32] expressed as Eq. 6:
The value of R
L
indicates the type of isotherm to be either favorable (0<R
L
<1), unfavorable
(R
L
>1), linear (R
L
=1) or irreversible (R
L
= 0). R
L
value was found to be 0.314. The result
shows the isotherm to be favorable. The Langmuir constant K
L
was used to determine the
spontaneity of the adsorption by calculating the Gibbs free energy (33) applying Eq. 7:
The free energy value (-5.009 kJ/mol) shows that the process was spontaneous.
3.3.2. Freundlich isotherm model
The Freundlich isotherm model is empirical. Assumptions made in applying this model are that,
multilayer adsorption occurs on a heterogeneous adsorbent surface, and that the concentration
of the adsorbate on adsorbent increases infinitely with increase in the concentration of the
adsorbate [34]. The adsorbent surface has unequal available sites with different energies of
adsorption [35]. It does not predict any saturation of the adsorbent by the adsorbate [30]. The
Freundlich model is mathematically expressed as Eq. 8:
Its linear logarithmic form [31] is Eq. 9:
…………………………………. (9)
A plot of In q
e
against In C
e
,
gave a straight line, with slope 1/n, and intercept In K
F
.
K
F
is the adsorption or distribution coefficient and represents the quantity of dye adsorbed onto
the membrane for a unit equilibrium concentration. The mechanism and the rate of adsorption
are functions of 1/n and K
F
. For a good adsorbent, 0.2 ˂ 1/n ˂ 0.8, while a smaller value of 1/n
indicates better adsorption and formation of stronger bond between the adsorbate and adsorbent
[36]. The plot of In q
e
against In C
e
(Fig.8) gave values of 1/n, n, K
F
and R
2
as shown in Table
2. The 1/n value (0.34 < 1) shows that the biosorption was physisorptive; n (2.941) > 1 shows
that the biosorption was good [34]. The R
2
value (0.872) shows that Freundlich isotherm model
simulated experimental data well.
3.3.3 Temkin isotherm model
The Temkin model presumes that the heat of adsorption of adsorbate particles in the layer
decreases linearly with coverage with consideration of the effects of indirect adsorbent-
adsorbate interaction, and adsorption process is characterized by a uniform distribution of
binding energies, up to some maximum binding energy [13, 37]. The linear form of Temkin
equation [13, 38] is expressed as Eq. 10:
A plot of q
e
against In C
e
(Fig. 9) gave a straight line
with slope B and intercepts B In A. The B, A, b
T
and
R
2
values are shown in Table 2. The correlation
coefficient R
2
(0.935) shows that the Temkin model
is a good fit for simulating experimental data.
3.3.4. Dubinin-Radushkevich isotherm model
This model is applied in estimating the characteristic
porosity of an adsorbent and the apparent adsorption
energy. The model neither assumes homogenous
adsorbent surface nor a constant adsorption
potential as the Langmuir model [32]. The model
equation is expressed a Eq.12:
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A plot of q
e
against In C
e
(Fig. 9) gave a straight line with slope B and intercepts B In A. The B,
A, b
T
and R
2
values are shown in Table 2. The correlation coefficient R
2
(0.935) shows that the
Temkin model is a good fit for simulating experimental data.
3.3.4. Dubinin-Radushkevich isotherm model
This model is applied in estimating the characteristic porosity of an adsorbent and the apparent
adsorption energy. The model neither assumes homogenous adsorbent surface nor a constant
adsorption potential as the Langmuir model [32]. The model equation is expressed a Eq.12:
The linearized logarithmic expression [39] of Eq.12 is Eq.13:
A plot of ln q
e
against ε
2
(Fig. 10) gave a straight line with slope B
D
and intercept ln q
m
. The
values of q
D
and B
D
are in Table 2.
The free energy of adsorption E (J/mol) is related to the porosity factor B
D
by Eq. 15:
E values less than 8kJ/mol indicate physisorption [32]. The value of E in this work was 0.408
kJ/mol showing physisorption. Positive E values show that the adsorption was endothermic and
that higher temperatures would favor the adsorption [40]. B
D
(3x10
-6
mol
2
/J
2
) is
less than unity,
indicating microporous adsorbent surface [41] and that the adsorbent may require less number
of cycles to reduce the concentration of the adsorbate below regulatory levels [42].
Fig. 7-10. The isotherm plot for biosorption of metanil yellow on hen egg membrane:
Langmuir (Fig. 7), Freundlich (Fig.8), Temkin isotherm (Fig.9) and Dubinin-Radushkevich
(Fig. 10)
3.3.5. Elovich isotherm
The Elovich isotherm model [43] was originally designed to describe chemisorptions of gas on
solids [44]. The model assumes that there is exponential increase in adsorption sites with the
adsorption process showing multilayer adsorption [45]. The Elovich isotherm model is
expressed as Eq. 16:
The linear logarithmic form of Eq. 16 is Eq. 17:
A plot of In (q
e
/C
e
) versus q
e
(Fig. 11) gave a straight line with slope 1/q
m
and intercept In
(K
E
q
m
) from which K
E
and q
m
were calculated. Table 2 shows the parameters K
E
, q
m
and R
2
.
The R
2
value (0.809) proves the Elovich model a good fit for experimental data.
3.3.6. Harkin-Jura isotherm
In the application of Harkin-Jura isotherm model, it is assumed that the adsorbent surface is
heterogeneous in pore distribution and that adsorption is multilayer [43]. The model is
expressed as Eq. 18:
The linearized logarithmic expression [39] of
Eq.12 is Eq.13:
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A plot of q
e
against In C
e
(Fig. 9) gave a straight line with slope B and intercepts B In A. The B,
A, b
T
and R
2
values are shown in Table 2. The correlation coefficient R
2
(0.935) shows that the
Temkin model is a good fit for simulating experimental data.
3.3.4. Dubinin-Radushkevich isotherm model
This model is applied in estimating the characteristic porosity of an adsorbent and the apparent
adsorption energy. The model neither assumes homogenous adsorbent surface nor a constant
adsorption potential as the Langmuir model [32]. The model equation is expressed a Eq.12:
The linearized logarithmic expression [39] of Eq.12 is Eq.13:
A plot of ln q
e
against ε
2
(Fig. 10) gave a straight line with slope B
D
and intercept ln q
m
. The
values of q
D
and B
D
are in Table 2.
The free energy of adsorption E (J/mol) is related to the porosity factor B
D
by Eq. 15:
E values less than 8kJ/mol indicate physisorption [32]. The value of E in this work was 0.408
kJ/mol showing physisorption. Positive E values show that the adsorption was endothermic and
that higher temperatures would favor the adsorption [40]. B
D
(3x10
-6
mol
2
/J
2
) is
less than unity,
indicating microporous adsorbent surface [41] and that the adsorbent may require less number
of cycles to reduce the concentration of the adsorbate below regulatory levels [42].
Fig. 7-10. The isotherm plot for biosorption of metanil yellow on hen egg membrane:
Langmuir (Fig. 7), Freundlich (Fig.8), Temkin isotherm (Fig.9) and Dubinin-Radushkevich
(Fig. 10)
3.3.5. Elovich isotherm
The Elovich isotherm model [43] was originally designed to describe chemisorptions of gas on
solids [44]. The model assumes that there is exponential increase in adsorption sites with the
adsorption process showing multilayer adsorption [45]. The Elovich isotherm model is
expressed as Eq. 16:
The linear logarithmic form of Eq. 16 is Eq. 17:
A plot of In (q
e
/C
e
) versus q
e
(Fig. 11) gave a straight line with slope 1/q
m
and intercept In
(K
E
q
m
) from which K
E
and q
m
were calculated. Table 2 shows the parameters K
E
, q
m
and R
2
.
The R
2
value (0.809) proves the Elovich model a good fit for experimental data.
3.3.6. Harkin-Jura isotherm
In the application of Harkin-Jura isotherm model, it is assumed that the adsorbent surface is
heterogeneous in pore distribution and that adsorption is multilayer [43]. The model is
expressed as Eq. 18:
A plot of ln q
e
against ε
2
(Fig. 10) gave a straight
line with slope B
D
and intercept ln q
m
. The values of
q
D
and B
D
are in Table 2.
The free energy of adsorption E (J/mol) is related to
the porosity factor B
D
by Eq. 15:
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A plot of q
e
against In C
e
(Fig. 9) gave a straight line with slope B and intercepts B In A. The B,
A, b
T
and R
2
values are shown in Table 2. The correlation coefficient R
2
(0.935) shows that the
Temkin model is a good fit for simulating experimental data.
3.3.4. Dubinin-Radushkevich isotherm model
This model is applied in estimating the characteristic porosity of an adsorbent and the apparent
adsorption energy. The model neither assumes homogenous adsorbent surface nor a constant
adsorption potential as the Langmuir model [32]. The model equation is expressed a Eq.12:
The linearized logarithmic expression [39] of Eq.12 is Eq.13:
A plot of ln q
e
against ε
2
(Fig. 10) gave a straight line with slope B
D
and intercept ln q
m
. The
values of q
D
and B
D
are in Table 2.
The free energy of adsorption E (J/mol) is related to the porosity factor B
D
by Eq. 15:
E values less than 8kJ/mol indicate physisorption [32]. The value of E in this work was 0.408
kJ/mol showing physisorption. Positive E values show that the adsorption was endothermic and
that higher temperatures would favor the adsorption [40]. B
D
(3x10
-6
mol
2
/J
2
) is
less than unity,
indicating microporous adsorbent surface [41] and that the adsorbent may require less number
of cycles to reduce the concentration of the adsorbate below regulatory levels [42].
Fig. 7-10. The isotherm plot for biosorption of metanil yellow on hen egg membrane:
Langmuir (Fig. 7), Freundlich (Fig.8), Temkin isotherm (Fig.9) and Dubinin-Radushkevich
(Fig. 10)
3.3.5. Elovich isotherm
The Elovich isotherm model [43] was originally designed to describe chemisorptions of gas on
solids [44]. The model assumes that there is exponential increase in adsorption sites with the
adsorption process showing multilayer adsorption [45]. The Elovich isotherm model is
expressed as Eq. 16:
The linear logarithmic form of Eq. 16 is Eq. 17:
A plot of In (q
e
/C
e
) versus q
e
(Fig. 11) gave a straight line with slope 1/q
m
and intercept In
(K
E
q
m
) from which K
E
and q
m
were calculated. Table 2 shows the parameters K
E
, q
m
and R
2
.
The R
2
value (0.809) proves the Elovich model a good fit for experimental data.
3.3.6. Harkin-Jura isotherm
In the application of Harkin-Jura isotherm model, it is assumed that the adsorbent surface is
heterogeneous in pore distribution and that adsorption is multilayer [43]. The model is
expressed as Eq. 18:
E values less than 8kJ/mol indicate physisorption
[32]. The value of E in this work was 0.408 kJ/mol
showing physisorption. Positive E values show that
the adsorption was endothermic and that higher
Fig. 7-10. The isotherm plot for biosorption of metanil yellow on hen egg membrane: Langmuir (Fig. 7), Freundlich
(Fig.8), Temkin isotherm (Fig.9) and Dubinin-Radushkevich (Fig. 10)
Removal of metanil yellow by batch biosorption
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Fig. 7-10. The isotherm plot for biosorption of metanil yellow on hen egg membrane:
Langmuir (Fig. 7), Freundlich (Fig.8), Temkin isotherm (Fig.9) and Dubinin-Radushkevich
(Fig. 10)
3.3.5. Elovich isotherm
The Elovich isotherm model [43] was originally designed to describe chemisorptions of gas on
solids [44]. The model assumes that there is exponential increase in adsorption sites with the
adsorption process showing multilayer adsorption [45]. The Elovich isotherm model is
expressed as Eq. 16:
The linear logarithmic form of Eq. 16 is Eq. 17:
A plot of In (q
e
/C
e
) versus q
e
(Fig. 11) gave a straight line with slope 1/q
m
and intercept In
(K
E
q
m
) from which K
E
and q
m
were calculated. Table 2 shows the parameters K
E
, q
m
and R
2
.
The R
2
value (0.809) proves the Elovich model a good fit for experimental data.
3.3.6. Harkin-Jura isotherm
In the application of Harkin-Jura isotherm model, it is assumed that the adsorbent surface is
heterogeneous in pore distribution and that adsorption is multilayer [43]. The model is
expressed as Eq. 18:
A plot of 1/q
e
2
against log C
e
(Fig. 12) gave a straight line with slope 1/A
HJ
and intercept
B
HJ
/A
HJ
. The values of A
HJ
and B
HJ
are shown in Table 2. The R
2
value (0.743) shows that this
model is a good fit for experimental data.
0.019
0.01
0.008
y = 0.0479x + 0.0063
R² = 0.9769
0.004
0.008
0.012
0.016
0.02
0 0.1 0.2 0.3
1/ce(mg L-1)
1/qe (g mg-1)
Fig. 7
3.967
4.601
4.867
y = 0.3397x + 3.6242
R² = 0.8719
3.5
4
4.5
5
5.5
0 1 2 3 4
In qe
In Ce
Fig.8
52.87
99.6
129.88
y = 29.525x + 19.882
R² = 0.9354
20
40
60
80
100
120
140
1 2 3 4
qe (mg g
-1
)
In Ce
Fig. 9
3.967
4.601
4.867
y = -3E-06x + 4.8144
R² = 0.9796
3.5
3.9
4.3
4.7
5.1
5.5
0 100000 200000 300000
in q
e
(mg/g)
Ɛ
2
Fig. 10
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3.3.1. Langmuir isotherm model
The Langmuir isotherm assumes a homogenous surface with identical sites in terms of energy
for the biosorbent [30, 31]. It is represented by Eq. 4:
The type 2 linearized Langmuir equation is given as Eq. 5:
A plot of 1/q
e
against 1/C
e
, gave a straight line with slope 1/K
L
and intercept 1/q
m
as shown in
Figure 7. Table 2 shows the model parameters (K
L
, q
m
and R
L
). R
2
value (0.977) shows that the
experimental results fitted well into the Langmuir isotherm model. The essential characteristics
of the Langmuir isotherm can be expressed in terms of a dimensionless constant, the Hall
separation factor R
L
[32] expressed as Eq. 6:
The value of R
L
indicates the type of isotherm to be either favorable (0<R
L
<1), unfavorable
(R
L
>1), linear (R
L
=1) or irreversible (R
L
= 0). R
L
value was found to be 0.314. The result
shows the isotherm to be favorable. The Langmuir constant K
L
was used to determine the
spontaneity of the adsorption by calculating the Gibbs free energy (33) applying Eq. 7:
The free energy value (-5.009 kJ/mol) shows that the process was spontaneous.
3.3.2. Freundlich isotherm model
The Freundlich isotherm model is empirical. Assumptions made in applying this model are that,
multilayer adsorption occurs on a heterogeneous adsorbent surface, and that the concentration
of the adsorbate on adsorbent increases infinitely with increase in the concentration of the
adsorbate [34]. The adsorbent surface has unequal available sites with different energies of
adsorption [35]. It does not predict any saturation of the adsorbent by the adsorbate [30]. The
Freundlich model is mathematically expressed as Eq. 8:
Its linear logarithmic form [31] is Eq. 9:
…………………………………. (9)
A plot of In q
e
against In C
e
,
gave a straight line, with slope 1/n, and intercept In K
F
.
K
F
is the adsorption or distribution coefficient and represents the quantity of dye adsorbed onto
the membrane for a unit equilibrium concentration. The mechanism and the rate of adsorption
are functions of 1/n and K
F
. For a good adsorbent, 0.2 ˂ 1/n ˂ 0.8, while a smaller value of 1/n
indicates better adsorption and formation of stronger bond between the adsorbate and adsorbent
[36]. The plot of In q
e
against In C
e
(Fig.8) gave values of 1/n, n, K
F
and R
2
as shown in Table
2. The 1/n value (0.34 < 1) shows that the biosorption was physisorptive; n (2.941) > 1 shows
that the biosorption was good [34]. The R
2
value (0.872) shows that Freundlich isotherm model
simulated experimental data well.
3.3.3 Temkin isotherm model
The Temkin model presumes that the heat of adsorption of adsorbate particles in the layer
decreases linearly with coverage with consideration of the effects of indirect adsorbent-
adsorbate interaction, and adsorption process is characterized by a uniform distribution of
binding energies, up to some maximum binding energy [13, 37]. The linear form of Temkin
equation [13, 38] is expressed as Eq. 10:
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
3.3.1. Langmuir isotherm model
The Langmuir isotherm assumes a homogenous surface with identical sites in terms of energy
for the biosorbent [30, 31]. It is represented by Eq. 4:
The type 2 linearized Langmuir equation is given as Eq. 5:
A plot of 1/q
e
against 1/C
e
, gave a straight line with slope 1/K
L
and intercept 1/q
m
as shown in
Figure 7. Table 2 shows the model parameters (K
L
, q
m
and R
L
). R
2
value (0.977) shows that the
experimental results fitted well into the Langmuir isotherm model. The essential characteristics
of the Langmuir isotherm can be expressed in terms of a dimensionless constant, the Hall
separation factor R
L
[32] expressed as Eq. 6:
The value of R
L
indicates the type of isotherm to be either favorable (0<R
L
<1), unfavorable
(R
L
>1), linear (R
L
=1) or irreversible (R
L
= 0). R
L
value was found to be 0.314. The result
shows the isotherm to be favorable. The Langmuir constant K
L
was used to determine the
spontaneity of the adsorption by calculating the Gibbs free energy (33) applying Eq. 7:
The free energy value (-5.009 kJ/mol) shows that the process was spontaneous.
3.3.2. Freundlich isotherm model
The Freundlich isotherm model is empirical. Assumptions made in applying this model are that,
multilayer adsorption occurs on a heterogeneous adsorbent surface, and that the concentration
of the adsorbate on adsorbent increases infinitely with increase in the concentration of the
adsorbate [34]. The adsorbent surface has unequal available sites with different energies of
adsorption [35]. It does not predict any saturation of the adsorbent by the adsorbate [30]. The
Freundlich model is mathematically expressed as Eq. 8:
Its linear logarithmic form [31] is Eq. 9:
…………………………………. (9)
A plot of In q
e
against In C
e
,
gave a straight line, with slope 1/n, and intercept In K
F
.
K
F
is the adsorption or distribution coefficient and represents the quantity of dye adsorbed onto
the membrane for a unit equilibrium concentration. The mechanism and the rate of adsorption
are functions of 1/n and K
F
. For a good adsorbent, 0.2 ˂ 1/n ˂ 0.8, while a smaller value of 1/n
indicates better adsorption and formation of stronger bond between the adsorbate and adsorbent
[36]. The plot of In q
e
against In C
e
(Fig.8) gave values of 1/n, n, K
F
and R
2
as shown in Table
2. The 1/n value (0.34 < 1) shows that the biosorption was physisorptive; n (2.941) > 1 shows
that the biosorption was good [34]. The R
2
value (0.872) shows that Freundlich isotherm model
simulated experimental data well.
3.3.3 Temkin isotherm model
The Temkin model presumes that the heat of adsorption of adsorbate particles in the layer
decreases linearly with coverage with consideration of the effects of indirect adsorbent-
adsorbate interaction, and adsorption process is characterized by a uniform distribution of
binding energies, up to some maximum binding energy [13, 37]. The linear form of Temkin
equation [13, 38] is expressed as Eq. 10:
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A plot of q
e
against In C
e
(Fig. 9) gave a straight line with slope B and intercepts B In A. The B,
A, b
T
and R
2
values are shown in Table 2. The correlation coefficient R
2
(0.935) shows that the
Temkin model is a good fit for simulating experimental data.
3.3.4. Dubinin-Radushkevich isotherm model
This model is applied in estimating the characteristic porosity of an adsorbent and the apparent
adsorption energy. The model neither assumes homogenous adsorbent surface nor a constant
adsorption potential as the Langmuir model [32]. The model equation is expressed a Eq.12:
The linearized logarithmic expression [39] of Eq.12 is Eq.13:
A plot of ln q
e
against ε
2
(Fig. 10) gave a straight line with slope B
D
and intercept ln q
m
. The
values of q
D
and B
D
are in Table 2.
The free energy of adsorption E (J/mol) is related to the porosity factor B
D
by Eq. 15:
E values less than 8kJ/mol indicate physisorption [32]. The value of E in this work was 0.408
kJ/mol showing physisorption. Positive E values show that the adsorption was endothermic and
that higher temperatures would favor the adsorption [40]. B
D
(3x10
-6
mol
2
/J
2
) is
less than unity,
indicating microporous adsorbent surface [41] and that the adsorbent may require less number
of cycles to reduce the concentration of the adsorbate below regulatory levels [42].
Fig. 7-10. The isotherm plot for biosorption of metanil yellow on hen egg membrane:
Langmuir (Fig. 7), Freundlich (Fig.8), Temkin isotherm (Fig.9) and Dubinin-Radushkevich
(Fig. 10)
3.3.5. Elovich isotherm
The Elovich isotherm model [43] was originally designed to describe chemisorptions of gas on
solids [44]. The model assumes that there is exponential increase in adsorption sites with the
adsorption process showing multilayer adsorption [45]. The Elovich isotherm model is
expressed as Eq. 16:
The linear logarithmic form of Eq. 16 is Eq. 17:
A plot of In (q
e
/C
e
) versus q
e
(Fig. 11) gave a straight line with slope 1/q
m
and intercept In
(K
E
q
m
) from which K
E
and q
m
were calculated. Table 2 shows the parameters K
E
, q
m
and R
2
.
The R
2
value (0.809) proves the Elovich model a good fit for experimental data.
3.3.6. Harkin-Jura isotherm
In the application of Harkin-Jura isotherm model, it is assumed that the adsorbent surface is
heterogeneous in pore distribution and that adsorption is multilayer [43]. The model is
expressed as Eq. 18:
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A plot of q
e
against In C
e
(Fig. 9) gave a straight line with slope B and intercepts B In A. The B,
A, b
T
and R
2
values are shown in Table 2. The correlation coefficient R
2
(0.935) shows that the
Temkin model is a good fit for simulating experimental data.
3.3.4. Dubinin-Radushkevich isotherm model
This model is applied in estimating the characteristic porosity of an adsorbent and the apparent
adsorption energy. The model neither assumes homogenous adsorbent surface nor a constant
adsorption potential as the Langmuir model [32]. The model equation is expressed a Eq.12:
The linearized logarithmic expression [39] of Eq.12 is Eq.13:
A plot of ln q
e
against ε
2
(Fig. 10) gave a straight line with slope B
D
and intercept ln q
m
. The
values of q
D
and B
D
are in Table 2.
The free energy of adsorption E (J/mol) is related to the porosity factor B
D
by Eq. 15:
E values less than 8kJ/mol indicate physisorption [32]. The value of E in this work was 0.408
kJ/mol showing physisorption. Positive E values show that the adsorption was endothermic and
that higher temperatures would favor the adsorption [40]. B
D
(3x10
-6
mol
2
/J
2
) is
less than unity,
indicating microporous adsorbent surface [41] and that the adsorbent may require less number
of cycles to reduce the concentration of the adsorbate below regulatory levels [42].
Fig. 7-10. The isotherm plot for biosorption of metanil yellow on hen egg membrane:
Langmuir (Fig. 7), Freundlich (Fig.8), Temkin isotherm (Fig.9) and Dubinin-Radushkevich
(Fig. 10)
3.3.5. Elovich isotherm
The Elovich isotherm model [43] was originally designed to describe chemisorptions of gas on
solids [44]. The model assumes that there is exponential increase in adsorption sites with the
adsorption process showing multilayer adsorption [45]. The Elovich isotherm model is
expressed as Eq. 16:
The linear logarithmic form of Eq. 16 is Eq. 17:
A plot of In (q
e
/C
e
) versus q
e
(Fig. 11) gave a straight line with slope 1/q
m
and intercept In
(K
E
q
m
) from which K
E
and q
m
were calculated. Table 2 shows the parameters K
E
, q
m
and R
2
.
The R
2
value (0.809) proves the Elovich model a good fit for experimental data.
3.3.6. Harkin-Jura isotherm
In the application of Harkin-Jura isotherm model, it is assumed that the adsorbent surface is
heterogeneous in pore distribution and that adsorption is multilayer [43]. The model is
expressed as Eq. 18:
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A plot of q
e
against In C
e
(Fig. 9) gave a straight line with slope B and intercepts B In A. The B,
A, b
T
and R
2
values are shown in Table 2. The correlation coefficient R
2
(0.935) shows that the
Temkin model is a good fit for simulating experimental data.
3.3.4. Dubinin-Radushkevich isotherm model
This model is applied in estimating the characteristic porosity of an adsorbent and the apparent
adsorption energy. The model neither assumes homogenous adsorbent surface nor a constant
adsorption potential as the Langmuir model [32]. The model equation is expressed a Eq.12:
The linearized logarithmic expression [39] of Eq.12 is Eq.13:
A plot of ln q
e
against ε
2
(Fig. 10) gave a straight line with slope B
D
and intercept ln q
m
. The
values of q
D
and B
D
are in Table 2.
The free energy of adsorption E (J/mol) is related to the porosity factor B
D
by Eq. 15:
E values less than 8kJ/mol indicate physisorption [32]. The value of E in this work was 0.408
kJ/mol showing physisorption. Positive E values show that the adsorption was endothermic and
that higher temperatures would favor the adsorption [40]. B
D
(3x10
-6
mol
2
/J
2
) is
less than unity,
indicating microporous adsorbent surface [41] and that the adsorbent may require less number
of cycles to reduce the concentration of the adsorbate below regulatory levels [42].
Fig. 7-10. The isotherm plot for biosorption of metanil yellow on hen egg membrane:
Langmuir (Fig. 7), Freundlich (Fig.8), Temkin isotherm (Fig.9) and Dubinin-Radushkevich
(Fig. 10)
3.3.5. Elovich isotherm
The Elovich isotherm model [43] was originally designed to describe chemisorptions of gas on
solids [44]. The model assumes that there is exponential increase in adsorption sites with the
adsorption process showing multilayer adsorption [45]. The Elovich isotherm model is
expressed as Eq. 16:
The linear logarithmic form of Eq. 16 is Eq. 17:
A plot of In (q
e
/C
e
) versus q
e
(Fig. 11) gave a straight line with slope 1/q
m
and intercept In
(K
E
q
m
) from which K
E
and q
m
were calculated. Table 2 shows the parameters K
E
, q
m
and R
2
.
The R
2
value (0.809) proves the Elovich model a good fit for experimental data.
3.3.6. Harkin-Jura isotherm
In the application of Harkin-Jura isotherm model, it is assumed that the adsorbent surface is
heterogeneous in pore distribution and that adsorption is multilayer [43]. The model is
expressed as Eq. 18:
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A plot of q
e
against In C
e
(Fig. 9) gave a straight line with slope B and intercepts B In A. The B,
A, b
T
and R
2
values are shown in Table 2. The correlation coefficient R
2
(0.935) shows that the
Temkin model is a good fit for simulating experimental data.
3.3.4. Dubinin-Radushkevich isotherm model
This model is applied in estimating the characteristic porosity of an adsorbent and the apparent
adsorption energy. The model neither assumes homogenous adsorbent surface nor a constant
adsorption potential as the Langmuir model [32]. The model equation is expressed a Eq.12:
The linearized logarithmic expression [39] of Eq.12 is Eq.13:
A plot of ln q
e
against ε
2
(Fig. 10) gave a straight line with slope B
D
and intercept ln q
m
. The
values of q
D
and B
D
are in Table 2.
The free energy of adsorption E (J/mol) is related to the porosity factor B
D
by Eq. 15:
E values less than 8kJ/mol indicate physisorption [32]. The value of E in this work was 0.408
kJ/mol showing physisorption. Positive E values show that the adsorption was endothermic and
that higher temperatures would favor the adsorption [40]. B
D
(3x10
-6
mol
2
/J
2
) is
less than unity,
indicating microporous adsorbent surface [41] and that the adsorbent may require less number
of cycles to reduce the concentration of the adsorbate below regulatory levels [42].
Fig. 7-10. The isotherm plot for biosorption of metanil yellow on hen egg membrane:
Langmuir (Fig. 7), Freundlich (Fig.8), Temkin isotherm (Fig.9) and Dubinin-Radushkevich
(Fig. 10)
3.3.5. Elovich isotherm
The Elovich isotherm model [43] was originally designed to describe chemisorptions of gas on
solids [44]. The model assumes that there is exponential increase in adsorption sites with the
adsorption process showing multilayer adsorption [45]. The Elovich isotherm model is
expressed as Eq. 16:
The linear logarithmic form of Eq. 16 is Eq. 17:
A plot of In (q
e
/C
e
) versus q
e
(Fig. 11) gave a straight line with slope 1/q
m
and intercept In
(K
E
q
m
) from which K
E
and q
m
were calculated. Table 2 shows the parameters K
E
, q
m
and R
2
.
The R
2
value (0.809) proves the Elovich model a good fit for experimental data.
3.3.6. Harkin-Jura isotherm
In the application of Harkin-Jura isotherm model, it is assumed that the adsorbent surface is
heterogeneous in pore distribution and that adsorption is multilayer [43]. The model is
expressed as Eq. 18:
23
Removal of metanil yellow by batch biosorption Beniah Obinna Isiuku et al
temperatures would favor the adsorption [40].
B
D
(3x10
-6
mol
2
/J
2
) is
less than unity, indicating
microporous adsorbent surface [41] and that the
adsorbent may require less number of cycles to
reduce the concentration of the adsorbate below
regulatory levels [42].
3.3.5. Elovich isotherm
The Elovich isotherm model [43] was originally
designed to describe chemisorptions of gas on
solids [44]. The model assumes that there is
exponential increase in adsorption sites with the
adsorption process showing multilayer adsorption
[45]. The Elovich isotherm model is expressed as
Eq. 16:
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A plot of q
e
against In C
e
(Fig. 9) gave a straight line with slope B and intercepts B In A. The B,
A, b
T
and R
2
values are shown in Table 2. The correlation coefficient R
2
(0.935) shows that the
Temkin model is a good fit for simulating experimental data.
3.3.4. Dubinin-Radushkevich isotherm model
This model is applied in estimating the characteristic porosity of an adsorbent and the apparent
adsorption energy. The model neither assumes homogenous adsorbent surface nor a constant
adsorption potential as the Langmuir model [32]. The model equation is expressed a Eq.12:
The linearized logarithmic expression [39] of Eq.12 is Eq.13:
A plot of ln q
e
against ε
2
(Fig. 10) gave a straight line with slope B
D
and intercept ln q
m
. The
values of q
D
and B
D
are in Table 2.
The free energy of adsorption E (J/mol) is related to the porosity factor B
D
by Eq. 15:
E values less than 8kJ/mol indicate physisorption [32]. The value of E in this work was 0.408
kJ/mol showing physisorption. Positive E values show that the adsorption was endothermic and
that higher temperatures would favor the adsorption [40]. B
D
(3x10
-6
mol
2
/J
2
) is
less than unity,
indicating microporous adsorbent surface [41] and that the adsorbent may require less number
of cycles to reduce the concentration of the adsorbate below regulatory levels [42].
Fig. 7-10. The isotherm plot for biosorption of metanil yellow on hen egg membrane:
Langmuir (Fig. 7), Freundlich (Fig.8), Temkin isotherm (Fig.9) and Dubinin-Radushkevich
(Fig. 10)
3.3.5. Elovich isotherm
The Elovich isotherm model [43] was originally designed to describe chemisorptions of gas on
solids [44]. The model assumes that there is exponential increase in adsorption sites with the
adsorption process showing multilayer adsorption [45]. The Elovich isotherm model is
expressed as Eq. 16:
The linear logarithmic form of Eq. 16 is Eq. 17:
A plot of In (q
e
/C
e
) versus q
e
(Fig. 11) gave a straight line with slope 1/q
m
and intercept In
(K
E
q
m
) from which K
E
and q
m
were calculated. Table 2 shows the parameters K
E
, q
m
and R
2
.
The R
2
value (0.809) proves the Elovich model a good fit for experimental data.
3.3.6. Harkin-Jura isotherm
In the application of Harkin-Jura isotherm model, it is assumed that the adsorbent surface is
heterogeneous in pore distribution and that adsorption is multilayer [43]. The model is
expressed as Eq. 18:
The linear logarithmic form of Eq. 16 is Eq. 17:
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A plot of q
e
against In C
e
(Fig. 9) gave a straight line with slope B and intercepts B In A. The B,
A, b
T
and R
2
values are shown in Table 2. The correlation coefficient R
2
(0.935) shows that the
Temkin model is a good fit for simulating experimental data.
3.3.4. Dubinin-Radushkevich isotherm model
This model is applied in estimating the characteristic porosity of an adsorbent and the apparent
adsorption energy. The model neither assumes homogenous adsorbent surface nor a constant
adsorption potential as the Langmuir model [32]. The model equation is expressed a Eq.12:
The linearized logarithmic expression [39] of Eq.12 is Eq.13:
A plot of ln q
e
against ε
2
(Fig. 10) gave a straight line with slope B
D
and intercept ln q
m
. The
values of q
D
and B
D
are in Table 2.
The free energy of adsorption E (J/mol) is related to the porosity factor B
D
by Eq. 15:
E values less than 8kJ/mol indicate physisorption [32]. The value of E in this work was 0.408
kJ/mol showing physisorption. Positive E values show that the adsorption was endothermic and
that higher temperatures would favor the adsorption [40]. B
D
(3x10
-6
mol
2
/J
2
) is
less than unity,
indicating microporous adsorbent surface [41] and that the adsorbent may require less number
of cycles to reduce the concentration of the adsorbate below regulatory levels [42].
Fig. 7-10. The isotherm plot for biosorption of metanil yellow on hen egg membrane:
Langmuir (Fig. 7), Freundlich (Fig.8), Temkin isotherm (Fig.9) and Dubinin-Radushkevich
(Fig. 10)
3.3.5. Elovich isotherm
The Elovich isotherm model [43] was originally designed to describe chemisorptions of gas on
solids [44]. The model assumes that there is exponential increase in adsorption sites with the
adsorption process showing multilayer adsorption [45]. The Elovich isotherm model is
expressed as Eq. 16:
The linear logarithmic form of Eq. 16 is Eq. 17:
A plot of In (q
e
/C
e
) versus q
e
(Fig. 11) gave a straight line with slope 1/q
m
and intercept In
(K
E
q
m
) from which K
E
and q
m
were calculated. Table 2 shows the parameters K
E
, q
m
and R
2
.
The R
2
value (0.809) proves the Elovich model a good fit for experimental data.
3.3.6. Harkin-Jura isotherm
In the application of Harkin-Jura isotherm model, it is assumed that the adsorbent surface is
heterogeneous in pore distribution and that adsorption is multilayer [43]. The model is
expressed as Eq. 18:
A plot of In (q
e
/C
e
) versus q
e
(Fig. 11) gave a
straight line with slope 1/q
m
and intercept In (K
E
q
m
)
from which K
E
and q
m
were calculated. Table 2
shows the parameters K
E
, q
m
and R
2
. The R
2
value
(0.809) proves the Elovich model a good fit for
experimental data.
3.3.6. Harkin-Jura isotherm
In the application of Harkin-Jura isotherm
model, it is assumed that the adsorbent surface
is heterogeneous in pore distribution and that
adsorption is multilayer [43]. The model is
expressed as Eq. 18:
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A plot of q
e
against In C
e
(Fig. 9) gave a straight line with slope B and intercepts B In A. The B,
A, b
T
and R
2
values are shown in Table 2. The correlation coefficient R
2
(0.935) shows that the
Temkin model is a good fit for simulating experimental data.
3.3.4. Dubinin-Radushkevich isotherm model
This model is applied in estimating the characteristic porosity of an adsorbent and the apparent
adsorption energy. The model neither assumes homogenous adsorbent surface nor a constant
adsorption potential as the Langmuir model [32]. The model equation is expressed a Eq.12:
The linearized logarithmic expression [39] of Eq.12 is Eq.13:
A plot of ln q
e
against ε
2
(Fig. 10) gave a straight line with slope B
D
and intercept ln q
m
. The
values of q
D
and B
D
are in Table 2.
The free energy of adsorption E (J/mol) is related to the porosity factor B
D
by Eq. 15:
E values less than 8kJ/mol indicate physisorption [32]. The value of E in this work was 0.408
kJ/mol showing physisorption. Positive E values show that the adsorption was endothermic and
that higher temperatures would favor the adsorption [40]. B
D
(3x10
-6
mol
2
/J
2
) is
less than unity,
indicating microporous adsorbent surface [41] and that the adsorbent may require less number
of cycles to reduce the concentration of the adsorbate below regulatory levels [42].
Fig. 7-10. The isotherm plot for biosorption of metanil yellow on hen egg membrane:
Langmuir (Fig. 7), Freundlich (Fig.8), Temkin isotherm (Fig.9) and Dubinin-Radushkevich
(Fig. 10)
3.3.5. Elovich isotherm
The Elovich isotherm model [43] was originally designed to describe chemisorptions of gas on
solids [44]. The model assumes that there is exponential increase in adsorption sites with the
adsorption process showing multilayer adsorption [45]. The Elovich isotherm model is
expressed as Eq. 16:
The linear logarithmic form of Eq. 16 is Eq. 17:
A plot of In (q
e
/C
e
) versus q
e
(Fig. 11) gave a straight line with slope 1/q
m
and intercept In
(K
E
q
m
) from which K
E
and q
m
were calculated. Table 2 shows the parameters K
E
, q
m
and R
2
.
The R
2
value (0.809) proves the Elovich model a good fit for experimental data.
3.3.6. Harkin-Jura isotherm
In the application of Harkin-Jura isotherm model, it is assumed that the adsorbent surface is
heterogeneous in pore distribution and that adsorption is multilayer [43]. The model is
expressed as Eq. 18:
A plot of 1/q
e
2
against log C
e
(Fig. 12) gave a
straight line with slope 1/A
HJ
and intercept B
HJ
/A
HJ
.
The values of A
HJ
and B
HJ
are shown in Table 2. The
R
2
value (0.743) shows that this model is a good fit
for experimental data.
3.3.7. Halsey isotherm
The Halsey isotherm model is applied in measuring
multilayer adsorption at a relatively large distance
from the adsorbent surface [43]. This model is
expressed as Eq. 19:
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A plot of 1/q
e
2
against log C
e
(Fig. 12) gave a straight line with slope 1/A
HJ
and intercept
B
HJ
/A
HJ
. The values of A
HJ
and B
HJ
are shown in Table 2. The R
2
value (0.743) shows that this
model is a good fit for experimental data.
3.3.7. Halsey isotherm
The Halsey isotherm model is applied in measuring multilayer adsorption at a relatively large
distance from the adsorbent surface [43]. This model is expressed as Eq. 19:
A plot of q
e
versus In C
e
(Fig. 13) gave a straight line with slope 1/n
H
and intercept 1/n
H
InK
H
.
The values of n
H
and K
H
are in Table 2. The R
2
value (0.935) shows that the model is a good fit
for experimental data.
3.3.8. Flory-Huggins isotherm
The relationship between behavior of the surface of the adsorbent and adsorption in terms of
surface coverage is expressed applying the Flory-Huggins isotherm model [46]. The isotherm
model is expressed as Eq. 20:
A plot of In (θ/C
e
) versus In (1-θ) (Fig. 14) gave a straight line with slope nFH and intercept In
K
FH
. The values of K
FH
and n
FH
are in Table 2. The R
2
value (0.986) shows that Flory-Huggins
isotherm model is a good fit for the biosorption experimental data. The Gibbs free energy was
calculated applying K
FH
according to Eq. 22:
The magnitude of the free energy value (16.13 kJ/mol), which is lower than 20 kJ/mol shows
that the biosorption was physisorptive. The negative value of ∆G
o
ads
shows that the process was
spontaneous.
2.614
2.283
0.994
y = -0.0198x + 3.8303
R² = 0.8093
0
0.5
1
1.5
2
2.5
3
50 100 150
ln qe/Ce
qe(mg g-1) Fig. 11
0.00036
0.0001
5.9E-05
y = -0.0003x + 0.0005
R² = 0.7427
0
0.0001
0.0002
0.0003
0.0004
0.5 1 1.5
1/qe (g mg-1)
log Ce Fig. 12
A plot of q
e
versus In C
e
(Fig. 13) gave a straight line
with slope 1/n
H
and intercept 1/n
H
InK
H
. The values
of n
H
and K
H
are in Table 2. The R
2
value (0.935)
shows that the model is a good fit for experimental
data.
3.3.8. Flory-Huggins isotherm
The relationship between behavior of the surface
of the adsorbent and adsorption in terms of surface
coverage is expressed applying the Flory-Huggins
isotherm model [46]. The isotherm model is
expressed as Eq. 20:
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A plot of 1/q
e
2
against log C
e
(Fig. 12) gave a straight line with slope 1/A
HJ
and intercept
B
HJ
/A
HJ
. The values of A
HJ
and B
HJ
are shown in Table 2. The R
2
value (0.743) shows that this
model is a good fit for experimental data.
3.3.7. Halsey isotherm
The Halsey isotherm model is applied in measuring multilayer adsorption at a relatively large
distance from the adsorbent surface [43]. This model is expressed as Eq. 19:
A plot of q
e
versus In C
e
(Fig. 13) gave a straight line with slope 1/n
H
and intercept 1/n
H
InK
H
.
The values of n
H
and K
H
are in Table 2. The R
2
value (0.935) shows that the model is a good fit
for experimental data.
3.3.8. Flory-Huggins isotherm
The relationship between behavior of the surface of the adsorbent and adsorption in terms of
surface coverage is expressed applying the Flory-Huggins isotherm model [46]. The isotherm
model is expressed as Eq. 20:
A plot of In (θ/C
e
) versus In (1-θ) (Fig. 14) gave a straight line with slope nFH and intercept In
K
FH
. The values of K
FH
and n
FH
are in Table 2. The R
2
value (0.986) shows that Flory-Huggins
isotherm model is a good fit for the biosorption experimental data. The Gibbs free energy was
calculated applying K
FH
according to Eq. 22:
The magnitude of the free energy value (16.13 kJ/mol), which is lower than 20 kJ/mol shows
that the biosorption was physisorptive. The negative value of ∆G
o
ads
shows that the process was
spontaneous.
2.614
2.283
0.994
y = -0.0198x + 3.8303
R² = 0.8093
0
0.5
1
1.5
2
2.5
3
50 100 150
ln qe/Ce
qe(mg g-1) Fig. 11
0.00036
0.0001
5.9E-05
y = -0.0003x + 0.0005
R² = 0.7427
0
0.0001
0.0002
0.0003
0.0004
0.5 1 1.5
1/qe (g mg-1)
log Ce Fig. 12
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
A plot of 1/q
e
2
against log C
e
(Fig. 12) gave a straight line with slope 1/A
HJ
and intercept
B
HJ
/A
HJ
. The values of A
HJ
and B
HJ
are shown in Table 2. The R
2
value (0.743) shows that this
model is a good fit for experimental data.
3.3.7. Halsey isotherm
The Halsey isotherm model is applied in measuring multilayer adsorption at a relatively large
distance from the adsorbent surface [43]. This model is expressed as Eq. 19:
A plot of q
e
versus In C
e
(Fig. 13) gave a straight line with slope 1/n
H
and intercept 1/n
H
InK
H
.
The values of n
H
and K
H
are in Table 2. The R
2
value (0.935) shows that the model is a good fit
for experimental data.
3.3.8. Flory-Huggins isotherm
The relationship between behavior of the surface of the adsorbent and adsorption in terms of
surface coverage is expressed applying the Flory-Huggins isotherm model [46]. The isotherm
model is expressed as Eq. 20:
A plot of In (θ/C
e
) versus In (1-θ) (Fig. 14) gave a straight line with slope nFH and intercept In
K
FH
. The values of K
FH
and n
FH
are in Table 2. The R
2
value (0.986) shows that Flory-Huggins
isotherm model is a good fit for the biosorption experimental data. The Gibbs free energy was
calculated applying K
FH
according to Eq. 22:
The magnitude of the free energy value (16.13 kJ/mol), which is lower than 20 kJ/mol shows
that the biosorption was physisorptive. The negative value of ∆G
o
ads
shows that the process was
spontaneous.
2.614
2.283
0.994
y = -0.0198x + 3.8303
R² = 0.8093
0
0.5
1
1.5
2
2.5
3
50 100 150
ln qe/Ce
qe(mg g-1) Fig. 11
0.00036
0.0001
5.9E-05
y = -0.0003x + 0.0005
R² = 0.7427
0
0.0001
0.0002
0.0003
0.0004
0.5 1 1.5
1/qe (g mg-1)
log Ce Fig. 12
A plot of In (θ/C
e
) versus In (1-θ) (Fig. 14) gave a
straight line with slope nFH and intercept In K
FH
.
The values of K
FH
and n
FH
are in Table 2. The R
2
value (0.986) shows that Flory-Huggins isotherm
model is a good fit for the biosorption experimental
data. The Gibbs free energy was calculated applying
K
FH
according to Eq. 22:
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
A plot of 1/q
e
2
against log C
e
(Fig. 12) gave a straight line with slope 1/A
HJ
and intercept
B
HJ
/A
HJ
. The values of A
HJ
and B
HJ
are shown in Table 2. The R
2
value (0.743) shows that this
model is a good fit for experimental data.
3.3.7. Halsey isotherm
The Halsey isotherm model is applied in measuring multilayer adsorption at a relatively large
distance from the adsorbent surface [43]. This model is expressed as Eq. 19:
A plot of q
e
versus In C
e
(Fig. 13) gave a straight line with slope 1/n
H
and intercept 1/n
H
InK
H
.
The values of n
H
and K
H
are in Table 2. The R
2
value (0.935) shows that the model is a good fit
for experimental data.
3.3.8. Flory-Huggins isotherm
The relationship between behavior of the surface of the adsorbent and adsorption in terms of
surface coverage is expressed applying the Flory-Huggins isotherm model [46]. The isotherm
model is expressed as Eq. 20:
A plot of In (θ/C
e
) versus In (1-θ) (Fig. 14) gave a straight line with slope nFH and intercept In
K
FH
. The values of K
FH
and n
FH
are in Table 2. The R
2
value (0.986) shows that Flory-Huggins
isotherm model is a good fit for the biosorption experimental data. The Gibbs free energy was
calculated applying K
FH
according to Eq. 22:
The magnitude of the free energy value (16.13 kJ/mol), which is lower than 20 kJ/mol shows
that the biosorption was physisorptive. The negative value of ∆G
o
ads
shows that the process was
spontaneous.
2.614
2.283
0.994
y = -0.0198x + 3.8303
R² = 0.8093
0
0.5
1
1.5
2
2.5
3
50 100 150
ln qe/Ce
qe(mg g-1) Fig. 11
0.00036
0.0001
5.9E-05
y = -0.0003x + 0.0005
R² = 0.7427
0
0.0001
0.0002
0.0003
0.0004
0.5 1 1.5
1/qe (g mg-1)
log Ce Fig. 12
The magnitude of the free energy value (16.13 kJ/
mol), which is lower than 20 kJ/mol shows that the
biosorption was physisorptive. The negative value
of ∆G
o
ads
shows that the process was spontaneous.
4. Conclusions
Hen egg membrane was successfully applied in the
removal of metanil yellow from aqueous solution
by batch biosorption. Experimental equilibrium
data were simulated with Langmuir, Freundlich,
Temkin, Dubinin-Radushkevich. Elovich, Harkin
Jura, Halsey and Flory Huggins isotherms.
Correlation coefficient values show that the Flory-
Huggins isotherm model analyzed experimental
data most while the Harkin-Jura model was the
least good fit. Results show that the biosorption was
endothermic, good, physisorptive and spontaneous.
Egg membrane is a good adsorbent for removing
metanil yellow from aqueous phase.
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
A plot of q
e
against In C
e
(Fig. 9) gave a straight line with slope B and intercepts B In A. The B,
A, b
T
and R
2
values are shown in Table 2. The correlation coefficient R
2
(0.935) shows that the
Temkin model is a good fit for simulating experimental data.
3.3.4. Dubinin-Radushkevich isotherm model
This model is applied in estimating the characteristic porosity of an adsorbent and the apparent
adsorption energy. The model neither assumes homogenous adsorbent surface nor a constant
adsorption potential as the Langmuir model [32]. The model equation is expressed a Eq.12:
The linearized logarithmic expression [39] of Eq.12 is Eq.13:
A plot of ln q
e
against ε
2
(Fig. 10) gave a straight line with slope B
D
and intercept ln q
m
. The
values of q
D
and B
D
are in Table 2.
The free energy of adsorption E (J/mol) is related to the porosity factor B
D
by Eq. 15:
E values less than 8kJ/mol indicate physisorption [32]. The value of E in this work was 0.408
kJ/mol showing physisorption. Positive E values show that the adsorption was endothermic and
that higher temperatures would favor the adsorption [40]. B
D
(3x10
-6
mol
2
/J
2
) is
less than unity,
indicating microporous adsorbent surface [41] and that the adsorbent may require less number
of cycles to reduce the concentration of the adsorbate below regulatory levels [42].
Fig. 7-10. The isotherm plot for biosorption of metanil yellow on hen egg membrane:
Langmuir (Fig. 7), Freundlich (Fig.8), Temkin isotherm (Fig.9) and Dubinin-Radushkevich
(Fig. 10)
3.3.5. Elovich isotherm
The Elovich isotherm model [43] was originally designed to describe chemisorptions of gas on
solids [44]. The model assumes that there is exponential increase in adsorption sites with the
adsorption process showing multilayer adsorption [45]. The Elovich isotherm model is
expressed as Eq. 16:
The linear logarithmic form of Eq. 16 is Eq. 17:
A plot of In (q
e
/C
e
) versus q
e
(Fig. 11) gave a straight line with slope 1/q
m
and intercept In
(K
E
q
m
) from which K
E
and q
m
were calculated. Table 2 shows the parameters K
E
, q
m
and R
2
.
The R
2
value (0.809) proves the Elovich model a good fit for experimental data.
3.3.6. Harkin-Jura isotherm
In the application of Harkin-Jura isotherm model, it is assumed that the adsorbent surface is
heterogeneous in pore distribution and that adsorption is multilayer [43]. The model is
expressed as Eq. 18:
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
A plot of q
e
against In C
e
(Fig. 9) gave a straight line with slope B and intercepts B In A. The B,
A, b
T
and R
2
values are shown in Table 2. The correlation coefficient R
2
(0.935) shows that the
Temkin model is a good fit for simulating experimental data.
3.3.4. Dubinin-Radushkevich isotherm model
This model is applied in estimating the characteristic porosity of an adsorbent and the apparent
adsorption energy. The model neither assumes homogenous adsorbent surface nor a constant
adsorption potential as the Langmuir model [32]. The model equation is expressed a Eq.12:
The linearized logarithmic expression [39] of Eq.12 is Eq.13:
A plot of ln q
e
against ε
2
(Fig. 10) gave a straight line with slope B
D
and intercept ln q
m
. The
values of q
D
and B
D
are in Table 2.
The free energy of adsorption E (J/mol) is related to the porosity factor B
D
by Eq. 15:
E values less than 8kJ/mol indicate physisorption [32]. The value of E in this work was 0.408
kJ/mol showing physisorption. Positive E values show that the adsorption was endothermic and
that higher temperatures would favor the adsorption [40]. B
D
(3x10
-6
mol
2
/J
2
) is
less than unity,
indicating microporous adsorbent surface [41] and that the adsorbent may require less number
of cycles to reduce the concentration of the adsorbate below regulatory levels [42].
Fig. 7-10. The isotherm plot for biosorption of metanil yellow on hen egg membrane:
Langmuir (Fig. 7), Freundlich (Fig.8), Temkin isotherm (Fig.9) and Dubinin-Radushkevich
(Fig. 10)
3.3.5. Elovich isotherm
The Elovich isotherm model [43] was originally designed to describe chemisorptions of gas on
solids [44]. The model assumes that there is exponential increase in adsorption sites with the
adsorption process showing multilayer adsorption [45]. The Elovich isotherm model is
expressed as Eq. 16:
The linear logarithmic form of Eq. 16 is Eq. 17:
A plot of In (q
e
/C
e
) versus q
e
(Fig. 11) gave a straight line with slope 1/q
m
and intercept In
(K
E
q
m
) from which K
E
and q
m
were calculated. Table 2 shows the parameters K
E
, q
m
and R
2
.
The R
2
value (0.809) proves the Elovich model a good fit for experimental data.
3.3.6. Harkin-Jura isotherm
In the application of Harkin-Jura isotherm model, it is assumed that the adsorbent surface is
heterogeneous in pore distribution and that adsorption is multilayer [43]. The model is
expressed as Eq. 18:
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
A plot of q
e
against In C
e
(Fig. 9) gave a straight line with slope B and intercepts B In A. The B,
A, b
T
and R
2
values are shown in Table 2. The correlation coefficient R
2
(0.935) shows that the
Temkin model is a good fit for simulating experimental data.
3.3.4. Dubinin-Radushkevich isotherm model
This model is applied in estimating the characteristic porosity of an adsorbent and the apparent
adsorption energy. The model neither assumes homogenous adsorbent surface nor a constant
adsorption potential as the Langmuir model [32]. The model equation is expressed a Eq.12:
The linearized logarithmic expression [39] of Eq.12 is Eq.13:
A plot of ln q
e
against ε
2
(Fig. 10) gave a straight line with slope B
D
and intercept ln q
m
. The
values of q
D
and B
D
are in Table 2.
The free energy of adsorption E (J/mol) is related to the porosity factor B
D
by Eq. 15:
E values less than 8kJ/mol indicate physisorption [32]. The value of E in this work was 0.408
kJ/mol showing physisorption. Positive E values show that the adsorption was endothermic and
that higher temperatures would favor the adsorption [40]. B
D
(3x10
-6
mol
2
/J
2
) is
less than unity,
indicating microporous adsorbent surface [41] and that the adsorbent may require less number
of cycles to reduce the concentration of the adsorbate below regulatory levels [42].
Fig. 7-10. The isotherm plot for biosorption of metanil yellow on hen egg membrane:
Langmuir (Fig. 7), Freundlich (Fig.8), Temkin isotherm (Fig.9) and Dubinin-Radushkevich
(Fig. 10)
3.3.5. Elovich isotherm
The Elovich isotherm model [43] was originally designed to describe chemisorptions of gas on
solids [44]. The model assumes that there is exponential increase in adsorption sites with the
adsorption process showing multilayer adsorption [45]. The Elovich isotherm model is
expressed as Eq. 16:
The linear logarithmic form of Eq. 16 is Eq. 17:
A plot of In (q
e
/C
e
) versus q
e
(Fig. 11) gave a straight line with slope 1/q
m
and intercept In
(K
E
q
m
) from which K
E
and q
m
were calculated. Table 2 shows the parameters K
E
, q
m
and R
2
.
The R
2
value (0.809) proves the Elovich model a good fit for experimental data.
3.3.6. Harkin-Jura isotherm
In the application of Harkin-Jura isotherm model, it is assumed that the adsorbent surface is
heterogeneous in pore distribution and that adsorption is multilayer [43]. The model is
expressed as Eq. 18:
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
A plot of 1/q
e
2
against log C
e
(Fig. 12) gave a straight line with slope 1/A
HJ
and intercept
B
HJ
/A
HJ
. The values of A
HJ
and B
HJ
are shown in Table 2. The R
2
value (0.743) shows that this
model is a good fit for experimental data.
3.3.7. Halsey isotherm
The Halsey isotherm model is applied in measuring multilayer adsorption at a relatively large
distance from the adsorbent surface [43]. This model is expressed as Eq. 19:
A plot of q
e
versus In C
e
(Fig. 13) gave a straight line with slope 1/n
H
and intercept 1/n
H
InK
H
.
The values of n
H
and K
H
are in Table 2. The R
2
value (0.935) shows that the model is a good fit
for experimental data.
3.3.8. Flory-Huggins isotherm
The relationship between behavior of the surface of the adsorbent and adsorption in terms of
surface coverage is expressed applying the Flory-Huggins isotherm model [46]. The isotherm
model is expressed as Eq. 20:
A plot of In (θ/C
e
) versus In (1-θ) (Fig. 14) gave a straight line with slope nFH and intercept In
K
FH
. The values of K
FH
and n
FH
are in Table 2. The R
2
value (0.986) shows that Flory-Huggins
isotherm model is a good fit for the biosorption experimental data. The Gibbs free energy was
calculated applying K
FH
according to Eq. 22:
The magnitude of the free energy value (16.13 kJ/mol), which is lower than 20 kJ/mol shows
that the biosorption was physisorptive. The negative value of ∆G
o
ads
shows that the process was
spontaneous.
2.614
2.283
0.994
y = -0.0198x + 3.8303
R² = 0.8093
0
0.5
1
1.5
2
2.5
3
50 100 150
ln qe/Ce
qe(mg g-1) Fig. 11
0.00036
0.0001
5.9E-05
y = -0.0003x + 0.0005
R² = 0.7427
0
0.0001
0.0002
0.0003
0.0004
0.5 1 1.5
1/qe (g mg-1)
log Ce Fig. 12
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
A plot of 1/q
e
2
against log C
e
(Fig. 12) gave a straight line with slope 1/A
HJ
and intercept
B
HJ
/A
HJ
. The values of A
HJ
and B
HJ
are shown in Table 2. The R
2
value (0.743) shows that this
model is a good fit for experimental data.
3.3.7. Halsey isotherm
The Halsey isotherm model is applied in measuring multilayer adsorption at a relatively large
distance from the adsorbent surface [43]. This model is expressed as Eq. 19:
A plot of q
e
versus In C
e
(Fig. 13) gave a straight line with slope 1/n
H
and intercept 1/n
H
InK
H
.
The values of n
H
and K
H
are in Table 2. The R
2
value (0.935) shows that the model is a good fit
for experimental data.
3.3.8. Flory-Huggins isotherm
The relationship between behavior of the surface of the adsorbent and adsorption in terms of
surface coverage is expressed applying the Flory-Huggins isotherm model [46]. The isotherm
model is expressed as Eq. 20:
A plot of In (θ/C
e
) versus In (1-θ) (Fig. 14) gave a straight line with slope nFH and intercept In
K
FH
. The values of K
FH
and n
FH
are in Table 2. The R
2
value (0.986) shows that Flory-Huggins
isotherm model is a good fit for the biosorption experimental data. The Gibbs free energy was
calculated applying K
FH
according to Eq. 22:
The magnitude of the free energy value (16.13 kJ/mol), which is lower than 20 kJ/mol shows
that the biosorption was physisorptive. The negative value of ∆G
o
ads
shows that the process was
spontaneous.
2.614
2.283
0.994
y = -0.0198x + 3.8303
R² = 0.8093
0
0.5
1
1.5
2
2.5
3
50 100 150
ln qe/Ce
qe(mg g-1) Fig. 11
0.00036
0.0001
5.9E-05
y = -0.0003x + 0.0005
R² = 0.7427
0
0.0001
0.0002
0.0003
0.0004
0.5 1 1.5
1/qe (g mg-1)
log Ce Fig. 12
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
A plot of 1/q
e
2
against log C
e
(Fig. 12) gave a straight line with slope 1/A
HJ
and intercept
B
HJ
/A
HJ
. The values of A
HJ
and B
HJ
are shown in Table 2. The R
2
value (0.743) shows that this
model is a good fit for experimental data.
3.3.7. Halsey isotherm
The Halsey isotherm model is applied in measuring multilayer adsorption at a relatively large
distance from the adsorbent surface [43]. This model is expressed as Eq. 19:
A plot of q
e
versus In C
e
(Fig. 13) gave a straight line with slope 1/n
H
and intercept 1/n
H
InK
H
.
The values of n
H
and K
H
are in Table 2. The R
2
value (0.935) shows that the model is a good fit
for experimental data.
3.3.8. Flory-Huggins isotherm
The relationship between behavior of the surface of the adsorbent and adsorption in terms of
surface coverage is expressed applying the Flory-Huggins isotherm model [46]. The isotherm
model is expressed as Eq. 20:
A plot of In (θ/C
e
) versus In (1-θ) (Fig. 14) gave a straight line with slope nFH and intercept In
K
FH
. The values of K
FH
and n
FH
are in Table 2. The R
2
value (0.986) shows that Flory-Huggins
isotherm model is a good fit for the biosorption experimental data. The Gibbs free energy was
calculated applying K
FH
according to Eq. 22:
The magnitude of the free energy value (16.13 kJ/mol), which is lower than 20 kJ/mol shows
that the biosorption was physisorptive. The negative value of ∆G
o
ads
shows that the process was
spontaneous.
2.614
2.283
0.994
y = -0.0198x + 3.8303
R² = 0.8093
0
0.5
1
1.5
2
2.5
3
50 100 150
ln qe/Ce
qe(mg g-1) Fig. 11
0.00036
0.0001
5.9E-05
y = -0.0003x + 0.0005
R² = 0.7427
0
0.0001
0.0002
0.0003
0.0004
0.5 1 1.5
1/qe (g mg-1)
log Ce Fig. 12
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
A plot of 1/q
e
2
against log C
e
(Fig. 12) gave a straight line with slope 1/A
HJ
and intercept
B
HJ
/A
HJ
. The values of A
HJ
and B
HJ
are shown in Table 2. The R
2
value (0.743) shows that this
model is a good fit for experimental data.
3.3.7. Halsey isotherm
The Halsey isotherm model is applied in measuring multilayer adsorption at a relatively large
distance from the adsorbent surface [43]. This model is expressed as Eq. 19:
A plot of q
e
versus In C
e
(Fig. 13) gave a straight line with slope 1/n
H
and intercept 1/n
H
InK
H
.
The values of n
H
and K
H
are in Table 2. The R
2
value (0.935) shows that the model is a good fit
for experimental data.
3.3.8. Flory-Huggins isotherm
The relationship between behavior of the surface of the adsorbent and adsorption in terms of
surface coverage is expressed applying the Flory-Huggins isotherm model [46]. The isotherm
model is expressed as Eq. 20:
A plot of In (θ/C
e
) versus In (1-θ) (Fig. 14) gave a straight line with slope nFH and intercept In
K
FH
. The values of K
FH
and n
FH
are in Table 2. The R
2
value (0.986) shows that Flory-Huggins
isotherm model is a good fit for the biosorption experimental data. The Gibbs free energy was
calculated applying K
FH
according to Eq. 22:
The magnitude of the free energy value (16.13 kJ/mol), which is lower than 20 kJ/mol shows
that the biosorption was physisorptive. The negative value of ∆G
o
ads
shows that the process was
spontaneous.
2.614
2.283
0.994
y = -0.0198x + 3.8303
R² = 0.8093
0
0.5
1
1.5
2
2.5
3
50 100 150
ln qe/Ce
qe(mg g-1) Fig. 11
0.00036
0.0001
5.9E-05
y = -0.0003x + 0.0005
R² = 0.7427
0
0.0001
0.0002
0.0003
0.0004
0.5 1 1.5
1/qe (g mg-1)
log Ce Fig. 12
24
Analytical Methods in Environmental Chemistry Journal; Vol. 2 (2019)
5. Glossary
A
HJ
(g
2
L
-1
) Harkin-Jura isotherm parameter
A
T
(L g
-1
) Temkin constant corresponding to the
maximum binding energy
B (J mol
-1
) Temkin constant related to the heat of
adsorption
B
D
(mol
2
J
-2
) Dubinin-Radushkevich constant related
to average free energy per mole of adsorbate
B
HJ
(mg
2
L
-1
) Harkin-Jura isotherm model constant
b
T
(J/mol/K) Temkin isotherm constant related to
heat of adsorption, showing whether the process is
endothermic or exothermic
C
e
(mg L
-1
) Equilibrium un-adsorbed adsorbate
concentration
C
o
(mg L
-1
) Initial adsorbate concentration
C
om
(mg L
-1
) Maximum initial concentration
C
t
(mg L
-1
) Un-adsorbed adsorbate concentration at
time t
E (kJ mol
-1
) Dubinin-Radushkevich isotherm model
average energy of adsorption
K
E
Elovich isotherm constant
K
F
(mg g
-1
(L/mg)
-1/n
] Freundlich isotherm model
adsorption or distribution coefficient
K
FH
(L mol
-1
) Flory-Huggins equilibrium constant
k
H
(mg L
-1
) Halsey isotherm model constant
K
L
(L mg
-1
) Langmuir constant related to the affinity
of the binding sites and energy of adsorption
m (g) mass of adsorbent
1/n
F
Freundlich constant indicating adsorption intensity
and degree of heterogeneity of adsorbent surface
n
F
Freundlich isotherm model constant
n
FH
Flory-Huggins constant indicating number of
adsorbate particles occupying adsorption sites
n
H
Halsey isotherm exponent
q
D
(mg g
-1
) Dubinin-Radushkevich maximum adsorption
capacity
q
e
(mg g
-1
) Equilibrium adsorption capacity
q
m
(mg g
-1
) Equilibrium adsorption capacity for a
complete monolayer
q
t
(mg g
-1
) Adsorption capacity at time t
Fig. 11-14. The isotherm plot for biosorption of metanil yellow on hen egg membrane: Elovich (Fig. 11), Harkin-Jura
(Fig. 12), Halsey (Fig. 13) and Flory-Huggins (Fig. 14)
Removal of metanil yellow by batch biosorption
Corresponding author: Tel.: +2348035731300
E-mail: obinnabisiuku@yahoo.com
3.3.7. Halsey isotherm
The Halsey isotherm model is applied in measuring multilayer adsorption at a relatively large
distance from the adsorbent surface [43]. This model is expressed as Eq. 19:
A plot of q
e
versus In C
e
(Fig. 13) gave a straight line with slope 1/n
H
and intercept 1/n
H
InK
H
.
The values of n
H
and K
H
are in Table 2. The R
2
value (0.935) shows that the model is a good fit
for experimental data.
3.3.8. Flory-Huggins isotherm
The relationship between behavior of the surface of the adsorbent and adsorption in terms of
surface coverage is expressed applying the Flory-Huggins isotherm model [46]. The isotherm
model is expressed as Eq. 20:
A plot of In (θ/C
e
) versus In (1-θ) (Fig. 14) gave a straight line with slope nFH and intercept In
K
FH
. The values of K
FH
and n
FH
are in Table 2. The R
2
value (0.986) shows that Flory-Huggins
isotherm model is a good fit for the biosorption experimental data. The Gibbs free energy was
calculated applying K
FH
according to Eq. 22:
The magnitude of the free energy value (16.13 kJ/mol), which is lower than 20 kJ/mol shows
that the biosorption was physisorptive. The negative value of ∆G
o
ads
shows that the process was
spontaneous.
2.614
2.283
0.994
y = -0.0198x + 3.8303
R² = 0.8093
0
0.5
1
1.5
2
2.5
3
50 100 150
ln qe/Ce
qe(mg g-1) Fig. 11
0.00036
0.0001
5.9E-05
y = -0.0003x + 0.0005
R² = 0.7427
0
0.0001
0.0002
0.0003
0.0004
0.5 1 1.5
1/qe (g mg-1)
log Ce Fig. 12
52.83
99.6
129.88
y = 29.539x + 19.832
R² = 0.9353
40
60
80
100
120
140
1 3 5
qe (mg/g)
In Ce Fig. 13
-1.519
-2.551
-4.51
y = -2.5513x - 6.4242
R² = 0.9863
-5
-4
-3
-2
-1
-2 -1.5 -1 -0.5
In (θ/C
e
)
In (1-θ)
Fig. 14
25
Removal of metanil yellow by batch biosorption Beniah Obinna Isiuku et al
R (J/mol/K) Universal gas constant
R
L
Hall separation factor or dimensionless constant
R
2
Correlation coefficient
T (K) Kelvin temperature
v (mL) Adsorbate volume
ε (kJ mol
-1
) Polanyi potential
θ Adsorbent surface coverage
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