Application of response surface methodology for optimization of Cr(III) and Cr(VI) adsorption on commercial activated carbons

Abstract

Response surface methodology (RSM) involving D–optimal design was used to optimize the adsorption process of trivalent chromium (Cr(III)) and hexavalent chromium (Cr(VI)) from aqueous solutions by commercial activated carbons. Influence of various process parameters such as initial metal concentration, pH, adsorbent dose, contact time, and type of adsorbent on adsorption process was investigated. From the analysis of variance (ANOVA) results, the significance of various factors and their influence on the response were identified. The regression coefficients (R 2) of the models developed and the results of validation experiments conducted at optimum conditions for the removal of both Cr(III) and Cr(VI) indicate that the predicted values are in good agreement with the experimental results. Contour and response surface plots were used to determine the interaction effects of main factors and optimum conditions of process, respectively for the simultaneous removal of Cr(III) and Cr(VI).

Full text

Research Journal of Chemical Sciences ______________________________________________ ISSN 2231-606X
Vol. 2(2), 40-48, Feb. (2012) Res.J.Chem.Sci.
International Science Congress Association 40
Application of response surface methodology for optimization of Cr(III) and
Cr(VI) adsorption on commercial activated carbons
Gottipati Ramakrishna
*
and Mishra Susmita
Department of Chemical Engineering, National Institute of Technology, Rourkela, Orissa-769008, INDIA
Available online at: www.isca.in
(Received 3
rd
December 2011, revised 18
th
December 2011, accepted 11
th
January 2012)
Abstract
Response surface methodology (RSM) involving D–optimal design was used to optimize the adsorption process of trivalent
chromium (Cr(III)) and hexavalent chromium (Cr(VI)) from aqueous solutions by commercial activated carbons. Influence of
various process parameters such as initial metal concentration, pH, adsorbent dose, contact time, and type of adsorbent on
adsorption process was investigated. From the analysis of variance (ANOVA) results, the significance of various factors and
their influence on the response were identified. The regression coefficients (R
2
) of the models developed and the results of
validation experiments conducted at optimum conditions for the removal of both Cr(III) and Cr(VI) indicate that the predicted
values are in good agreement with the experimental results. Contour and response surface plots were used to determine the
interaction effects of main factors and optimum conditions of process, respectively for the simultaneous removal of Cr(III) and
Cr(VI).
Keywords: Activated carbon, response surface methodology, Cr(III), Cr(VI), optimization.
Introduction
Out of several heavy metal pollutants, chromium compounds
are very toxic. The toxicity of the chromium in aqueous
phase changes with the oxidation state. It is well known that
chromium mainly exists in trivalent (Cr(III)) and hexavalent
(Cr(VI)) states in the solution phase
1,2
. Trivalent chromium is
less toxic compared to the hexavalent chromium, but in
higher amounts it is toxic and mutagenic
3
. Chromium poses a
great threat to human health and environment and also it
confirmed as a carcinogen in hexavalent state
4-6
. Moreover,
Cr(III) can be oxidized to Cr(VI) in the presence of certain
oxidants such as manganese oxides which commonly found
in water environments
7
. Hence, the simultaneous removal of
trivalent and hexavalent chromium ions is focused in this
study.
Adsorption is commonly used technique for the removal of
metal ions from various industrial effluents
8,9
. Among many
types of adsorbents, activated carbons are most widely used
for chromium removal from aqueous solutions because of
their novel porous characteristics, high adsorptive capacity
and low cost
10-13
. Many investigators have studied the
feasibility of activated carbons prepared from various
materials for the removal of chromium from aqueous
solutions through conventional adsorption methods
14-17
.
Conventional methods of studying a process by maintaining
other factors involved at unspecified constant levels does not
depict the combined effect of all the factors. This method is
time consuming and incapable. This calls for a research
effort for developing, improving and optimizing the
adsorption process and to evaluate the significance of all the
factors involved even in the presence of complex
interactions. Recently many statistical experimental design
methods have been employed in chemical process
optimization
18,19
.
Design of experiments is a very useful tool as it provides
statistical models, which help in understanding the
interactions among the parameters that have been
optimized
20
. Response surface methodology (RSM) is one of
the experimental designing methods which can surmount the
limitations of conventional methods collectively
19
. RSM is a
combination of mathematical and statistical techniques used
to determine the optimum operational conditions of the
process or to determine a region that satisfies the operating
specifications
20
. The main advantage of RSM is the reduced
number of experimental trials needed to evaluate multiple
parameters and their interactions
23,24
.
In this study, the simultaneous adsorption of Cr(III) and
Cr(VI) by commercial activated carbons (CACs) was
optimized by studying the effect of various factors like metal
concentration, pH, adsorbent dose, contact time, and type of
adsorbent. D–optimal design in RSM by Design Expert
Version 7.1.6 (Stat Ease, USA) was used to optimize
adsorption process.
Material and Methods
Materials: Commercial activated carbons (CACs) with
different iodine numbers (950 (ACI) and 1050 (ACII)) were
obtained from Kalpaka Chemicals, Tuticorin, India. Cr(III)
and Cr(VI) stock solutions of 10 mg/l were prepared by

Research Journal of Chemical Sciences __________________________________________________________ ISSN 2231-606X
Vol. 2(2), 40-48, Feb. (2012) Res.J.Chem.Sci
International Science Congress Association 41
using chromium chloride (CrCl
3
) and potassium dichromate
(K
2
Cr
2
O
7
) procured from Merck.
Experimental methods: The adsorbents used in this study
were characterized by N
2
adsorption isotherms to determine
porous characteristics like surface area (S), pore volume
(V
o
), and type of pores (micro, meso and macropores) that
take major part in porosity of adsorbent. Imaging of
adsorbents was done by Scanning Electron Microscope
(SEM - JEOL, JSM 6480 LV). Adsorption experiments were
carried out in shake flask system. The stock solutions were
diluted as required to obtain standard solutions of
concentration ranging between 2 and 10 mg/l. Batch
adsorption studies were performed in Erlenmeyer flasks of
250 ml by contacting the selected activated carbon of
different doses (0.5 – 2 g/l) with 50 ml of solution containing
different metal concentrations (2 – 10 mg/l) at solution pH (2
– 11) and for different contact times (1 – 4 h). All the flasks
were maintained at room temperature and provided
continuous shaking of 110 rpm by Environmental Orbital
Shaker Incubator (DENEB Instruments). Concentration of
Cr(III) and Cr(VI) species in the aqueous solutions were
determined by standard procedure
25
using UV/VIS
spectrophotometer (Jasco, V-530). The percentage removal
of Cr(III) and Cr(VI) were calculated according to
Adsorption
ሺ
%
ሻ
=
൫஼
೚
ି஼
೑
൯
஼
೚
X 100 (1)
where, C
o
is the initial concentration and C
f
is the final
concentration of the metal ions. All the experiments were
carried out in duplicate and the mean values are reported.
Selection of factors for experimental design: Modeling of
adsorption process of Cr(III) and Cr(VI) on activated carbons
was carried out by optimizing four numerical factors such as
initial metal concentration (A), pH (B), adsorbent dose (C),
and contact time (D) and one categorical factor i.e. type of
adsorbent (E). A standard RSM design called D–optimal
design was used to determine the main and interaction effects
of all the process parameters.
The low and high levels and ranges of all the factors studied
were given in table 1. The actual values of the process
variables and their ranges were selected based on the
preliminary experiments. Twenty four experiments for
removal of each metal ion (Cr(III) and Cr(VI)) were
conducted. The optimum values of all the variables were
obtained by solving the regression equations and by
analyzing the contour and 3D surface plots.
Results and Discussion
Characterization of adsorbents: The porous characteristics
of CACs analyzed by N
2
adsorption isotherms were shown in
table 2. Figure 1 shows that the isotherms obtained by N
2
gas
adsorption experiments are of type-I that means the
adsorbents mostly contain micropores
26
. Calculation
procedure for porous characteristics of adsorbents was cited
elsewhere
27
. The pore structure network of the adsorbents
was characterized by scanning electron microscope (SEM).
A fully developed pore structure similar to honeycomb voids
can be observed for both the adsorbents shown in figures 2a
and 2b. By N
2
adsorption isotherms, the pores observed by
SEM analysis are assumed to be the channels to the network
of micropores.
Table-1
Experimental range and levels of independent variables
Factors Coded symbol
Range and level
- 1 0 + 1
Initial metal concentration A 2.0 6.0 10.0
pH B 2.0 6.5 11.0
Adsorbent dose C 0.5 1.25 2.0
Contact time D 1.0 2.5 4.0
Adsorbent type (categorical factor) E ACI – ACII
Table-2
Porous characteristics of adsorbents (CACs)
Adsorbent Iodine no
Surface Area (m
2
/g) Pore Volume (cc/g)
S
lang
S
mi
S
me
S
ex
V
tot
V
mi
V
me
ACI 950 1402 1370 32 29.34 0.50 0.46 0.04
ACII 1050 2058 2010 48 31.13 0.73 0.68 0.05

Research Journal of Chemical Sciences __________________________________________________________ ISSN 2231-606X
Vol. 2(2), 40-48, Feb. (2012) Res.J.Chem.Sci
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Figure-1
N
2
adsorption isotherms of adsorbents
(a) (b)
Figure-2
SEM images of adsorbents (a) ACI and (b) ACII
Response surface methodological approach:
Experimental design and development of regression
model equations: The scheme of experiments carried out in
this study was presented in table 3. Regression analysis was
performed to fit the response functions, i.e. percentage
adsorption of Cr(III) and Cr(VI). The regression models
developed represent responses as functions of initial metal
concentration (A), pH (B), adsorbent dose (C), contact time
(D), and adsorbent type (E). An empirical relationship
between the response and input variables expressed by the
following response surface reduced cubic model equations
(in coded terms):
% ܴ
஼௥ሺூூூሻ
= 72.98 + 5.118 X 10
ିଷ
ܣ + 35.8ܤ − 3.38ܥ −
1.47ܦ + 17.97ܧ − 5.17ܣܤ + 1.61ܣܥ + 21.31ܣܦ +
20.41ܤܥ + 0.83ܤܦ − 5.66ܤܧ − 0.86ܥܦ − 24.98ܥܧ −
48.58ܦܧ + 2.52ܣ
ଶ
− 23.49ܤ
ଶ
− 29.85ܥ
ଶ
+ 3.34ܦ
ଶ
−
47.9ܣܤܥ − 28.43ܣܤܦ (2)
% ܴ
஼௥
ሺ
௏ூ
ሻ
= 8.31 + 2.76ܣ − 31.84ܤ + 6.24ܥ + 4.02ܦ +
2.69ܧ − 2.8ܣܤ + 4.08ܣܥ − 0.1ܣܦ − 7.48ܣܧ − 2.47ܤܥ −
1.11ܤܦ − 2.09ܤܧ − 4.74ܥܦ − 4.54ܥܧ − 5.44ܦܧ −
8.16ܣ
ଶ
+ 28.44ܤ
ଶ
+ 12.21ܦ
ଶ
− 9.88ܣܤܥ − 8.9ܣܤܦ (3)
where, R
Cr(III)
and R
Cr(VI)
are the removal percentages of
Cr(III) and Cr(VI), respectively. Insignificant terms which
are not included in the models are aliased as suggested by the
software.
250
300
350
400
450
0 0.2 0.4 0.6 0.8 1
Volumeof N
2
gas adsorbed (cc/g)
P/Po
ACI ACII

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Statistical analysis: The significance of model terms
included in the regression equations (eqs. 2 and 3) were
evaluated by the F–test for analysis of variance (ANOVA).
The ANOVA analysis for both the responses, % R
Cr(III)
and
% R
Cr(VI)
, was shown in table 4. Prob > F value for the
models is less than 0.05 indicates that the model terms are
statistically significant. The non significant values of lack of
fit for both the models showed that developed models are
valid
28
. The actual and predicted values of responses for
Cr(III) and Cr(VI) were shown in figures 3a and 3b,
respectively. Actual values are the measured values for a
particular experiment, whereas predicted values are
generated by using the approximating functions. The values
of R
2
and adjusted R
2
have advocated a high correlation
between actual and predicted values.
Table-3
Experimental design matrix with responses
Run
Factors Response
(A) Metal
conc.(mg/l)
(B) pH
(C) Adsorbent
dose (g/l)
(D) Contact
time (h)
(E) Adsorbent
type
% R
Cr(III)
% R
Cr(VI)
1 +1 +1 -1 -1 -1 6.55 8.79
2 +1 -1 +1 +1 +1 17.13 97.66
3 +1 -1 -1 +1 -1 17.55 78.01
4 +1 +1 +1 -1 +1 71.27 11.86
5 0 0 -1 0 +1 89.62 8.98
6 -1 +1 -1 -1 +1 81.74 1.12
7 +1 -1 +1 0 -1 18.66 95.80
8 -1 -1 -1 -1 -1 11.69 48.92
9 0 +1 0 0 -1 72.27 7.37
10 +1 +1 +1 +1 -1 79.67 12.63
11 +1 +1 -1 +1 +1 67.06 1.92
12 0 -1 +1 +1 -1 10.12 94.49
13 +1 -1 -1 -1 +1 17.90 43.95
14 -1 +1 +1 -1 -1 88.17 1.81
15 -1 +1 -1 +1 -1 21.70 8.33
16 -1 0 +1 +1 -1 75.81 11.60
17 0 +1 0 0 -1 73.58 2.50
18 0 0 +1 0 +1 32.61 11.84
19 +1 -1 +1 -1 +1 21.35 90.15
20 0 0 0 -1 -1 11.34 8.86
21 -1 -1 -1 +1 +1 6.68 86.28
22 -1 -1 +1 -1 +1 11.48 83.51
23 -1 +1 +1 +1 +1 74.35 23.92
24 -1 -1 -1 +1 +1 6.76 83.31
Table-4
ANOVA results
Source Sum of squares DF Mean square F value Prob > F
For % R
Cr(III)
Model 23785.11 20 1189.26 3034.40 <0.0001
Residual 1.18 3 0.39 – –
Lack of fit 0.31 1 0.31 0.72 0.4847
Pure error 0.86 2 0.43 – –
R
2
= 0.9996 – – – – –
Adeq Precision = 141.79 – – – – –
For % R
Cr(VI)
Model 33495.57 20 1674.78 248.08 0.0004
Residual 20.25 3 6.75 – –
Lack of fit 3.97 1 3.97 0.49 0.5575
Pure error 16.29 2 8.14 – –
R
2
= 0.9954 – – – – –
Adeq Precision = 39.72 – – – – –

Research Journal of Chemical Sciences
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Vol. 2(2), 40-48, Feb. (2012)
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(a)
The actual and predicted values of responses (a) % R
(a)
(c)
Perturbation plots: (a) Cr(III) removal by ACI, (b) Cr(III) removal by ACII, (c) Cr(VI) removal by ACI, and (d) Cr(VI)
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International Science Congress Association
(b)
Figure-3
The actual and predicted values of responses (a) % R
Cr(III)
and (b) % R
Cr(VI)
(b)
(d)
Figure-4
Perturbation plots: (a) Cr(III) removal by ACI, (b) Cr(III) removal by ACII, (c) Cr(VI) removal by ACI, and (d) Cr(VI)
removal by ACII
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(b)
Cr(VI)
(b)
(d)
Perturbation plots: (a) Cr(III) removal by ACI, (b) Cr(III) removal by ACII, (c) Cr(VI) removal by ACI, and (d) Cr(VI)

Research Journal of Chemical Sciences
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Vol. 2(2), 40-48, Feb. (2012)
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Effect of factors and response surface esti
Response surface methodology was used to estimate the
effect of five process variables on the removal of Cr(III) and
Cr(VI). Perturbation, contour and 3D surface plots were
drawn by using RSM to investigate the effect of all the
factors on the resp
onses. The inferences so obtained are
discussed below.
Effect of main factors:
The individual effect of numerical
factors such as metal concentration (A), pH (B), adsorbent
dose (C), and contact time (D) was found by perturbation
plots for the removal of Cr(III) and Cr(VI) at each level of
categorical factor, i.e. adsorbent type (E).
Perturbation plots
for the removal of Cr(III) and Cr(VI) were shown in figure 4.
Perturbation plot does not shows the effect of interactions
and it is like one factor at a time experimentation.
Perturbation plot helps to compare the effect of all the fact
at a particular point in the design space. The response is
plotted by changing only one factor over its range while
holding of the other factors constant. A steep slope or
(a)
(c)
Contour plots for interaction of pH (B) and adsorbent dose (C) for Cr(III) removal by (a) ACI and (b) ACII, and
interaction of pH (B) and contact time (D) for Cr(VI) removal by (c) ACI and (d)
______
_________________________________
______________
International Science Congress Association
Effect of factors and response surface esti
mation:
Response surface methodology was used to estimate the
effect of five process variables on the removal of Cr(III) and
Cr(VI). Perturbation, contour and 3D surface plots were
drawn by using RSM to investigate the effect of all the
onses. The inferences so obtained are
The individual effect of numerical
factors such as metal concentration (A), pH (B), adsorbent
dose (C), and contact time (D) was found by perturbation
plots for the removal of Cr(III) and Cr(VI) at each level of
Perturbation plots
for the removal of Cr(III) and Cr(VI) were shown in figure 4.
Perturbation plot does not shows the effect of interactions
and it is like one factor at a time experimentation.
Perturbation plot helps to compare the effect of all the fact
ors
at a particular point in the design space. The response is
plotted by changing only one factor over its range while
holding of the other factors constant. A steep slope or
curvature in a factor shows that the response is sensitive to
that factor. A rel
atively flat line shows insensitivity to
change in that particular factor
29
great influence on the removal of Cr(III) and Cr(VI) by using
both types of activated carbons. Other main factors like
adsorbent dose and contact time
significantly whereas, initial metal concentration has less
effect on the responses compared to other factors.
Effect of interactions:
From the perturbation plots it was
clear that for Cr(III) removal, pH (B) and adsorbent dose (C)
p
layed important role whereas, for Cr(VI) removal the main
influential factors were pH (B) and contact time (D). The
interactions of these factors also have a significant effect on
the responses (from eqs.2 and 3). The contour plots of the
main interactions
which effect the responses, i.e. %
and % R
Cr(VI)
, significantly were presented in figure 5. A
contour plot is a two dimensional representation of the
response for selected factors.
(b)
(d)
Figure-5
Contour plots for interaction of pH (B) and adsorbent dose (C) for Cr(III) removal by (a) ACI and (b) ACII, and
interaction of pH (B) and contact time (D) for Cr(VI) removal by (c) ACI and (d)
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45
curvature in a factor shows that the response is sensitive to
atively flat line shows insensitivity to
29
. From the figure 4, pH has a
great influence on the removal of Cr(III) and Cr(VI) by using
both types of activated carbons. Other main factors like
adsorbent dose and contact time
influence the process
significantly whereas, initial metal concentration has less
effect on the responses compared to other factors.
From the perturbation plots it was
clear that for Cr(III) removal, pH (B) and adsorbent dose (C)
layed important role whereas, for Cr(VI) removal the main
influential factors were pH (B) and contact time (D). The
interactions of these factors also have a significant effect on
the responses (from eqs.2 and 3). The contour plots of the
which effect the responses, i.e. %
R
Cr(III)
, significantly were presented in figure 5. A
contour plot is a two dimensional representation of the
Contour plots for interaction of pH (B) and adsorbent dose (C) for Cr(III) removal by (a) ACI and (b) ACII, and
interaction of pH (B) and contact time (D) for Cr(VI) removal by (c) ACI and (d)
ACII

Research Journal of Chemical Sciences
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Vol. 2(2), 40-48, Feb. (2012)
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Optimization by response surface modeling:
conditions of all the factors were found for the simultaneous
removal of Cr(III) and Cr(VI) by CACs. The efficiency of
both the activated carbons was determined individually. In
ca
se of ACI, at the optimum conditions (metal concentration
– 9.8 mg/l, pH – 2.51, adsorbent dose –
0.58 g/l, and contact
time –
3.83 h) the percentage removal of Cr(III) and Cr(VI)
were 26.26 and 66.01 %, respectively. For ACII, the removal
percentages of C
r(III) and Cr(VI) at optimum conditions
(a)
(c)
3D surface plots: Effect of pH (B) and adsorbent dose (C) on Cr(III) removal by (a) ACI and (b) ACII, and effect of pH (B)
and contact time (D) on Cr(VI)
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International Science Congress Association
Optimization by response surface modeling:
The optimum
conditions of all the factors were found for the simultaneous
removal of Cr(III) and Cr(VI) by CACs. The efficiency of
both the activated carbons was determined individually. In
se of ACI, at the optimum conditions (metal concentration
0.58 g/l, and contact
3.83 h) the percentage removal of Cr(III) and Cr(VI)
were 26.26 and 66.01 %, respectively. For ACII, the removal
r(III) and Cr(VI) at optimum conditions
(metal concentration –
6.85 mg/l, pH
0.5 g/l, and contact time –
1 h) are 89.62 and 71.33 %,
respectively. The response surface plots at optimum
conditions were shown in figure 6 considering k
(observed from perturbation plots, figure 4). A multiple
response method called desirability (
find the optimum conditions for the simultaneous removal of
Cr(III) and Cr(VI) by targeting the process parameters within
the range defined in table 1.
(b)
(d)
Figure-6
3D surface plots: Effect of pH (B) and adsorbent dose (C) on Cr(III) removal by (a) ACI and (b) ACII, and effect of pH (B)
and contact time (D) on Cr(VI)
remova
l by using (c) ACI and (d) ACII
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Res.J.Chem.Sci
46
6.85 mg/l, pH
– 2.0, adsorbent dose –
1 h) are 89.62 and 71.33 %,
respectively. The response surface plots at optimum
conditions were shown in figure 6 considering k
ey factors
(observed from perturbation plots, figure 4). A multiple
response method called desirability (
D) function was used to
find the optimum conditions for the simultaneous removal of
Cr(III) and Cr(VI) by targeting the process parameters within
3D surface plots: Effect of pH (B) and adsorbent dose (C) on Cr(III) removal by (a) ACI and (b) ACII, and effect of pH (B)
l by using (c) ACI and (d) ACII

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Table-5
Validation of models
Adsorbent
type
Chromium
concentration
pH
Adsorbent
Dose
Contact
time
Responses
% R
Cr(III)
% R
Cr(VI)
Experimental
Predicted
Experimental Predicted
ACI 9.8 2.51 0.58 3.83 24.53 26.26 63.76 66.01
ACII 6.85 2.0 0.5 1.0 88.85 89.62 72.53 71.33
Experiments for validation of models: The results obtained
after optimization were verified by conducting the
experiments under the optimized conditions of all the factors.
The experimental values closely agreed to the predicted
values of developed models with acceptable percentage
errors and the details are given in table 5.
Conclusion
The main aim of this study is to find the optimum conditions
to remove Cr(III) and Cr(VI) simultaneously from aqueous
solutions by studying the effect of various process
parameters. Two types of CACs of different adsorption
capacities and porous characteristics were successfully tested
for chromium (trivalent and hexavalent) metal ions removal.
Response surface methodology (RSM) based on five
variables D–optimal design was used to estimate the effect of
initial metal concentration (2 – 10 mg/l), pH (2 – 11),
adsorbent dose (0.5 – 2 g/l), contact time (1 – 4 h), and
adsorbent type (ACI and ACII) on the removal of Cr(III) and
Cr(VI). Models were developed to correlate variables to the
responses by using Design Expert software. Optimization
was carried out by RSM and the major findings are:
Undoubtedly RSM is a good technique to provide optimum
conditions of a process by studying the effect of main factors
and their interactions on response with minimum number of
experiments. Among the adsorbents used in this study, ACII
was found to be more suitable for the simultaneous removal
of Cr(III) (89.62 %) and Cr(VI) (71.33 %) and the optimum
conditions found were: metal concentration – 6.85 mg/l, pH
– 2.0, adsorbent dose – 0.5 g/l, and contact time – 1 h. By
conducting the validation experiments at optimum
conditions, it was concluded that the developed models could
precisely fit to the models developed with acceptable values
of percentage errors.
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