# Application of Central Composite Design in the Adsorption of Ca(II) on Metakaolin Zeolite

Authors: Upenyu Guyo; Lycenter Yard Phiri; Fidelis Chigondo
Journal: Journal of Chemistry
 (2017)

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## Abstract

Metakaolin zeolite-A was synthesized from thermally activated kaolin clay and characterized by Fourier Transform Infrared Spectroscopy and X-Ray Diffraction Spectroscopy. The effects of pH (2–10), contact time (10–180 min), initial concentration (5–120 mgL−1), and dosage (0.1–2 g) and their interactions were investigated using response surface methodology following a central composite design. Optimum removal (87.70%) was obtained at pH 6, contact time 180 min, initial concentration 40.0 mgL−1, and adsorbent dosage 1.0 g by Excel Solver using the GRG solving method. The adsorption data fitted best to the Langmuir model with correlation coefficient R2=0.993 and Chi-square value χ2=4.76. The Freundlich isotherm gave a correlation coefficient R2=0.933 and χ2=37.91. The adsorption process followed the pseudo-second-order model. The calculated thermodynamic parameters showed that the adsorption process was endothermic and not thermodynamically spontaneous. The studied zeolite-A can therefore be used as a promising adsorbent for the removal of Ca(II) ions from aqueous solutions.


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## Body

## 1. Introduction

Zeolites are crystalline, microporous, hydrated aluminosilicates formed by the sharing of oxygen atoms in the framework of aluminum and silicon tetrahedrals [1]. Synthetic zeolites are used commercially more often than natural zeolites due to the purity of their crystalline products, the uniformity of particles, the greater thermal stability, and the fact that they can be engineered with a wide variety of properties and pore sizes [2]. Zeolite synthesis involves the hydrothermal crystallization of aluminosilicate gels in the presence of alkali hydroxides [3]. The type of zeolite is affected by composition of the reaction mixture, the nature of the reactants and their pretreatments, temperature of the process, reaction time, and pH of the reaction mixture. The main problems in zeolite application are availability and cost of raw materials, specifically the silica source [4]. The use of commercial silica in zeolite synthesis is affected by variations in reactivity and selectivity apart from being expensive [5]. Cheaper raw materials such as clay minerals could be an alternative starting material for zeolite synthesis. Kaolin is a cheap clay mineral whose deposits are found vastly around mining areas in Zimbabwe. Many researchers have reported the synthesis of zeolites from kaolin under different conditions [6–11]. Kaolin is not stable under severe alkaline conditions and as such it is desirable to convert it into a more reactive form (metakaolin) by calcination at elevated temperatures. Because of their unique porous properties, zeolites could be applied in the removal of hardness in domestic water which is mainly due to calcium and magnesium ions. Water supplies with total hardness of more than 500 mg/L are not suitable for domestic consumption [12]. Hard water is responsible for the formation of deposits in boilers, cooling towers, water pipes, and household facilities, as well as diverse influences on the cleaning performance of detergents. Traditionally, water purification plants used lime and soda ash for the removal of hardness. One of the main drawbacks of this process is the generation of large amounts of liquid sludge as well as the need for recarbonation of the treated water [13]. The use of polyphosphates in removing water hardness is also practiced but results in massive discharge of phosphates in water bodies which lead to eutrophication [14].Various other methods including membrane precipitation, phytoextraction, flocculation, solvent extraction, ultrafiltration, reverse osmosis, electrodialysis, and adsorption have been studied for the removal of a wide variety of cations from water streams including magnesium and calcium [15–17]. Most of these are either inefficient or expensive and result in the generation of large amounts of sludge. Activated carbon is considered to be a particularly competitive and effective process for the removal of cations but has been hampered by the high costs associated with production and regeneration of spent carbon. The use of low-cost ion exchangers such as zeolites is an attractive method for the removal of metals from aqueous solutions. In this work, we report on the synthesis of zeolite-A from Zimbabwean kaolin and its application in the sorption of calcium ions from aqueous solutions. All the process independent variables have been optimized collectively by applying response surface methodology (RSM), a mathematical statistical technique which optimizes the process and evaluates the relationship between a set of independent variables [18–20]. Moreover, it evaluates the relative significance of the various independent variables even in the presence of complex factor-factor interactions [21]. The adsorbent was characterized using Fourier Transform Infrared (FTIR) Spectroscopy and XRD (X-Ray Diffraction) Spectroscopy.


## 2. Materials and Methods

### 2.1. Chemicals and Solutions

All chemicals used in this work were obtained from Skylabs (Zimbabwe) and were used as received without further purification. A pH meter (Az-8601, China) was employed for pH measurement and 0.1 M HCl and 0.1 M NaOH were used for pH adjustment. CaCl2 was used for the preparation of stock solution using double deionized water. All glassware used was soaked in 10% (v/v) nitric acid solution for 24 h and cleaned repeatedly with double deionized water.


### 2.2. Sample Collection and Pretreatment

The kaolin clay used in this study was collected from Chegutu, Zimbabwe. The kaolin clay sample was pulverized and sieved through a 90μm sieve. The pulverized kaolin clay material was digested in 6 M HCl to remove iron and washed with distilled water followed by drying overnight at 120°C. The treated kaolin clay was exposed to 900°C for 1 h where its structure was destroyed [22]. This removed all incorporated hydrocarbons and was dehydroxylated to form an activated amorphous material called metakaolin, a material which accepts and readily exchanges sodium as a guest in its structure.


### 2.3. Zeolitization Using the Hydrothermal Transformation Method

The zeolite gel was prepared by dissolving metakaolin in sodium hydroxide solutions [23]. Metakaolin (20 g) was refluxed and stirred in 100 mL of sodium hydroxide (1, 3, and 5 M) at a temperature of 100°C at specified reaction times (1, 2, and 4 h) [5]. The metakaolin-sodium hydroxide slurries were filtered by suction filtration and washed several times with deionized water to remove excess unreacted sodium hydroxide. The reaction products were dried at a temperature of 120°C in the oven for 24 h. Triplicate samples were prepared for each NaOH concentration and reaction time.


### 2.4. Characterization of the Zeolites

The Fourier Transform Infrared (FTIR) Spectroscopy spectra of the metakaolin zeolite (MZ) were obtained using a Thermo Fisher Scientific spectrometer (Nicolet 6700, USA) in the scanning range 4000–400 cm−1. A Bruker D8 Advance X-ray diffractometer (Germany) using nickel filtered Cu Kα radiation (40 kV, 40 mA) was used for identification of the structural phases.


### 2.5. Adsorption Batch Studies

All experiments were carried out in batch mode in 250 mL conical flasks. Several experimental parameters (solution pH: 2–10; contact time: 10–180 min; adsorbent dosage: 0.1–2.0 g; and initial metal ion concentration: 5–120 mg/L) were investigated following a central composite design (CCD). A predetermined adsorbent mass was added to 100 mL solution in a conical flask containing Ca2+ cations at a concentration according to CCD. The mixture was agitated on a shaker at 150 rpm for a specified time at room temperature. After agitation, the solid matrix was separated from the rest of the solution by filtration using Whatman number 42 filter paper followed by centrifugation to get the supernatant solution. The determination of Ca2+ ions in aqueous solution was done by complexometric titration using standardized 0.1 M EDTA (ethylenediaminetetraacetic acid) in the presence of Eriochrome Black T as an indicator. Typically, 100 mL of each supernatant solution was pipetted into a 250 mL conical flask, 4 mL of 1.0 M NH3 solution and 2-3 drops of Eriochrome Black T were added, and the mixture was titrated with 0.1 M EDTA solution until the color changed from pink to blue [12].The percentage removal (R) of Ca(II) ions from aqueous solutions was determined using the following equation:(1)R=Co-CeCo×100%.The equilibrium adsorption amount (qe) was calculated according to the mass balance equation:(2)qe=Co-CeVM,where qe is the equilibrium amount (mg g−1) of Ca(II) ions adsorbed per gram of metakaolin zeolite adsorbent, Co and Ce are the Ca(II) concentrations (mgL−1) in the solution initially and after adsorption, respectively, V is the volume (L) of the solution, and M is the mass (g) of the adsorbent used in the experiment.The experimental domain used is presented in Table1. Preliminary experiments were done to obtain the extreme levels of the independent input variables. Design Expert Version 5 (Stat-Ease, USA) was used to generate the CCD experiments, optimize the levels of the independent variables, and evaluate the interactions of the process parameters. In generating the CCD, the experimental domain for independent factors for high and low was entered in terms of alpha value of 2 to give 30 experiments with 6 center points. The percentage removal of Ca(II) ions was taken as the dependent variable. The Design Expert software was also used for statistical, regression, and graphical analysis of the obtained data. The general LogitR transformation quadratic model was proposed to be(3)LogitR=b0+b1A+b2B+b3C+b4D+b5A2+b6B2+b7C2+b8D2+b9AB+b10AC+b11AD+b12BC+b13BD+b14CD,where R is the percentage removal of Ca(II) ions, A is the pH, B is the contact time in min, C is the initial concentration in mg/L, and D is the dosage in g. The optimum values of the independent input variables were obtained by Excel Solver software applying the GRG function.Table 1
Experimental domain.
pH
Contact time
Initial concentration
Dosage
(min)
(mg L−1)
(g)
Min. point
2
10
5
0.1
Max. point
10
180
120
2


### 2.6. Desorption Studies

0.2 g of the adsorbent was left in contact with 100 mL of 30 mg/L of Ca(II) for 180 min at 150 rpm. The spent adsorbent was filtered, washed, and dried at 55°C for 24 h. The dried spent adsorbent was left in contact with different concentrations of NaOH (0.1, 0.5, 1.0, and 2.0 M) for 500 min and then filtered and washed several times with deionized water. The desorbed adsorbent was used for adsorption of the Ca(II) ions and the regeneration percentage was determined.


## 2.1. Chemicals and Solutions

All chemicals used in this work were obtained from Skylabs (Zimbabwe) and were used as received without further purification. A pH meter (Az-8601, China) was employed for pH measurement and 0.1 M HCl and 0.1 M NaOH were used for pH adjustment. CaCl2 was used for the preparation of stock solution using double deionized water. All glassware used was soaked in 10% (v/v) nitric acid solution for 24 h and cleaned repeatedly with double deionized water.


## 2.2. Sample Collection and Pretreatment

The kaolin clay used in this study was collected from Chegutu, Zimbabwe. The kaolin clay sample was pulverized and sieved through a 90μm sieve. The pulverized kaolin clay material was digested in 6 M HCl to remove iron and washed with distilled water followed by drying overnight at 120°C. The treated kaolin clay was exposed to 900°C for 1 h where its structure was destroyed [22]. This removed all incorporated hydrocarbons and was dehydroxylated to form an activated amorphous material called metakaolin, a material which accepts and readily exchanges sodium as a guest in its structure.


## 2.3. Zeolitization Using the Hydrothermal Transformation Method

The zeolite gel was prepared by dissolving metakaolin in sodium hydroxide solutions [23]. Metakaolin (20 g) was refluxed and stirred in 100 mL of sodium hydroxide (1, 3, and 5 M) at a temperature of 100°C at specified reaction times (1, 2, and 4 h) [5]. The metakaolin-sodium hydroxide slurries were filtered by suction filtration and washed several times with deionized water to remove excess unreacted sodium hydroxide. The reaction products were dried at a temperature of 120°C in the oven for 24 h. Triplicate samples were prepared for each NaOH concentration and reaction time.


## 2.4. Characterization of the Zeolites

The Fourier Transform Infrared (FTIR) Spectroscopy spectra of the metakaolin zeolite (MZ) were obtained using a Thermo Fisher Scientific spectrometer (Nicolet 6700, USA) in the scanning range 4000–400 cm−1. A Bruker D8 Advance X-ray diffractometer (Germany) using nickel filtered Cu Kα radiation (40 kV, 40 mA) was used for identification of the structural phases.


## 2.5. Adsorption Batch Studies

All experiments were carried out in batch mode in 250 mL conical flasks. Several experimental parameters (solution pH: 2–10; contact time: 10–180 min; adsorbent dosage: 0.1–2.0 g; and initial metal ion concentration: 5–120 mg/L) were investigated following a central composite design (CCD). A predetermined adsorbent mass was added to 100 mL solution in a conical flask containing Ca2+ cations at a concentration according to CCD. The mixture was agitated on a shaker at 150 rpm for a specified time at room temperature. After agitation, the solid matrix was separated from the rest of the solution by filtration using Whatman number 42 filter paper followed by centrifugation to get the supernatant solution. The determination of Ca2+ ions in aqueous solution was done by complexometric titration using standardized 0.1 M EDTA (ethylenediaminetetraacetic acid) in the presence of Eriochrome Black T as an indicator. Typically, 100 mL of each supernatant solution was pipetted into a 250 mL conical flask, 4 mL of 1.0 M NH3 solution and 2-3 drops of Eriochrome Black T were added, and the mixture was titrated with 0.1 M EDTA solution until the color changed from pink to blue [12].The percentage removal (R) of Ca(II) ions from aqueous solutions was determined using the following equation:(1)R=Co-CeCo×100%.The equilibrium adsorption amount (qe) was calculated according to the mass balance equation:(2)qe=Co-CeVM,where qe is the equilibrium amount (mg g−1) of Ca(II) ions adsorbed per gram of metakaolin zeolite adsorbent, Co and Ce are the Ca(II) concentrations (mgL−1) in the solution initially and after adsorption, respectively, V is the volume (L) of the solution, and M is the mass (g) of the adsorbent used in the experiment.The experimental domain used is presented in Table1. Preliminary experiments were done to obtain the extreme levels of the independent input variables. Design Expert Version 5 (Stat-Ease, USA) was used to generate the CCD experiments, optimize the levels of the independent variables, and evaluate the interactions of the process parameters. In generating the CCD, the experimental domain for independent factors for high and low was entered in terms of alpha value of 2 to give 30 experiments with 6 center points. The percentage removal of Ca(II) ions was taken as the dependent variable. The Design Expert software was also used for statistical, regression, and graphical analysis of the obtained data. The general LogitR transformation quadratic model was proposed to be(3)LogitR=b0+b1A+b2B+b3C+b4D+b5A2+b6B2+b7C2+b8D2+b9AB+b10AC+b11AD+b12BC+b13BD+b14CD,where R is the percentage removal of Ca(II) ions, A is the pH, B is the contact time in min, C is the initial concentration in mg/L, and D is the dosage in g. The optimum values of the independent input variables were obtained by Excel Solver software applying the GRG function.Table 1
Experimental domain.
pH
Contact time
Initial concentration
Dosage
(min)
(mg L−1)
(g)
Min. point
2
10
5
0.1
Max. point
10
180
120
2


## 2.6. Desorption Studies

0.2 g of the adsorbent was left in contact with 100 mL of 30 mg/L of Ca(II) for 180 min at 150 rpm. The spent adsorbent was filtered, washed, and dried at 55°C for 24 h. The dried spent adsorbent was left in contact with different concentrations of NaOH (0.1, 0.5, 1.0, and 2.0 M) for 500 min and then filtered and washed several times with deionized water. The desorbed adsorbent was used for adsorption of the Ca(II) ions and the regeneration percentage was determined.


## 3. Results and Discussion

### 3.1. Characterization of the Adsorbent

#### 3.1.1. FTIR

Zeolites were synthesized at different reaction times and different NaOH concentrations and the zeolite that was similar to zeolite-A was selected for use. Figure1 shows the FTIR spectra of the metakaolin zeolites synthesized at an optimum time of 4 h at different NaOH concentrations. The spectrum of the selected zeolite (C2, Figure 1) had a band at 3458.53 cm−1 corresponding to O-H vibration. There was structural T-O stretching and deformation at 1642.33 cm−1 and a peak at 1021.10 cm−1 that corresponded to internal tetrahedron asymmetrical vibration. A peak at 1421.37 cm−1 might be due to Si-O asymmetric stretching whilst bands at 723.79 and 1072.79 cm−1 were due to internal symmetrical stretching vibration of (Al-Si)-O. The 473.46 cm−1 band was due to internal vibration of (Al-Si)-O bending and the 558.95 cm−1 band corresponded to the formation of double four-membered rings by external linkages [5]. The zeolite-A framework possesses good exchange capacity, making it a good material as an ion exchange agent. It may thus be concluded that IR spectra of the C2 spectra are closely complementary to zeolite-A; therefore, the C2 zeolites were used for batch adsorption studies.Figure 1
FTIR spectra of metakaolin zeolites (C1, 4 h, 3 M NaOH zeolite; C2, 4 h, 5 M NaOH zeolite; and C3, 4 h, 1 M NaOH zeolite).


#### 3.1.2. XRD Analysis

The XRD data (Figure2) showed four crystallographic phases at 2θ degree values of 10.09 (ZON), and 12.69 (MER), 26.69 (Quartz), and 30.28 (CAN) are quite consistent with the two theta values of zeolite-A (LTA) showing that the pure phase of crystalline zeolite-A was produced.Figure 2
XRD pattern for metakaolin zeolite-A.


### 3.2. Adsorption Batch Studies

Adsorption studies using MZ were done on an aqueous Ca(II) solution applying a central composite design [24] developed from the experimental domain presented in Table 1. The investigation was carried out following a full central composite design consisting of 30 experiments, which included several replicate experiments to check for consistency of the adsorption procedure. The average Ca(II) removal from aqueous solutions using the prepared adsorbent over six replicate runs (midpoint experimental conditions) was 39.73±0.41% (at 95% confidence). The results obtained were consistent as evidenced by the small relative standard deviation (1.04%). The CCD batch method was therefore capable of providing consistent results and hence was suitable for use in the investigation of the adsorption of Ca(II) ions onto MZ.


#### 3.2.1. Response Surface Methodology Modeling

The experimental variable settings used for this investigation together with the actual experimental results are presented in Table2.Table 2
Experimental variables and results.
Run
A: pH
B: contact time
C: initial concentration
D: dosage
Ca(II) removal
(min)
(mgL−1)
(g)
(%)
1
2
95
62.5
1.05
32.0
2
4
52.5
33.75
0.575
57.8
3
4
52.5
33.75
1.525
62.2
4
4
52.5
91.25
1.525
26.8
5
4
52.5
91.25
0.575
24.7
7
4
137.5
33.75
0.575
74.1
8
4
137.5
33.75
1.525
78.5
9
4
137.5
91.25
1.525
28.5
10
4
137.5
91.25
0.575
25.8
11
6
10
62.5
1.05
36.0
12
6
95
62.5
1.05
39.2
13
6
95
62.5
1.05
39.2
14
6
95
62.5
1.05
40.0
15
6
95
62.5
2
42.4
16
6
95
62.5
1.05
40.0
17
6
95
62.5
0.1
36.0
18
6
95
62.5
1.05
40.0
19
6
95
62.5
1.05
40.0
20
6
95
120
1.05
22.9
21
6
180
62.5
1.05
43.2
22
8
52.5
33.75
0.575
66.7
23
8
52.5
33.75
1.525
72.6
24
8
52.5
91.25
1.525
30.1
25
8
52.5
91.25
0.575
26.8
26
8
137.5
33.75
1.525
75.6
27
8
137.5
33.75
0.575
59.3
28
8
137.5
91.25
1.525
34.5
29
8
137.5
91.25
0.575
32.3
30
10
95
62.5
1.05
47.2The proposed fullLogitR transformation model (see (3)) was fitted on the experimental data obtained in Table 2. The least squares regression results for the adsorption of Ca(II) after elimination of the insignificant terms (p>0.05) during stepwise multiple regression are summarized in Table 3.Table 3
Least squares regression data for Ca(II) removal.
Factor
Coefficient estimate
DF
Standard error
t for H0
P
r
o
b
>
t
VIF
Coeff. = 0
Intercept
2.16972
1
0.2366
A: pH
0.062119
1
0.0110
5.64648
<0.0001
1.01478
B: contact time
0.008357
1
0.0015
5.48405
<0.0001
8.79209
C: concentration
−0.0863
1
0.0065
−13.279
<0.0001
47.681
D: dosage
0.149761
1
0.0463
3.23304
0.0042
1.01478
C
2
0.0005
1
0.0000
10.147
<0.0001
44.4523
BC
-
8.10
E
-
05
1
0.0000
−3.6024
0.0018
14.1953
R
2
0.984All thep values associated with the coefficients of pH (A), contact time (B), initial concentration (C), dosage concentration (D), initial concentration squared term (C2), and the interaction between contact time and initial concentration term (BC) were smaller than 0.05 (Table 3), indicating a significant effect of these factors on the percentage removal of calcium by metakaolin zeolite. The interaction between contact time and initial concentration (BC) has an antagonistic effect on the removal of calcium as shown by the negative value of the associated coefficient. The final model obtained after elimination of the insignificant term was(4)LogitR=b0+b1A+b2B+b3C+b4D+b5C2+b6BC.The results of the analysis of variance for the regression model are presented in Table 4.Table 4
Results for ANOVA for the model.
Source
Sum of squares
DF
Mean square
F-value
P
r
o
b
>
F
Model
13.4078
6
2.23463
203.981
<0.0001
Residual
0.219102
20
0.010955
Lack of fit
0.21761
15
0.014507
48.6273
0.0002
Pure error
0.001492
5
0.000298
Cor. total
13.6269
26Thep value for the model was less than 0.05 (p<0.0001), indicating that the model was statistically significant. Moreover, a higher regression coefficient (R2=0.984) supported the significance of the model [25]. Model validity was evaluated by normal probability plot which was produced by the Design Expert software. Figure 3 shows that the residuals were close to the straight line and were scattered randomly around it with no particular pattern, showing no abnormal behavior [26].Figure 3
Normal plot of residuals.The plot of standard residuals versus predicted values showed a random distribution of residuals (difference between the experimental and the predicted values), with no particular pattern showing well behaved residuals (Figure4) [27]. Moreover, it showed no outliers supporting the statistical validity of the model.Figure 4
Plot of standard residuals versus predicted values.


#### 3.2.2. Model Interpretation

A 3-dimensional surface plot gives vital information on the behavior of the experimental design system. This aids the evaluation of the effects of the independent variables on the response factor. Figure5 shows the effect of pH and contact time on % removal of Ca(II) ions at constant dosage amount and initial Ca(II) concentration. An increase in both pH and contact time increased the percentage removal of Ca(II). Since the sorbent had abundant binding sites, the gradual occupancy of these sites over different times resulted in an increase in the uptake of Ca(II). The lower percentage removal observed in acidic pH medium is due to protonation of adsorbent functional groups or competition of H+ with Ca(II) ions to bind and occupy the active sites of the adsorbent. On the other hand, higher pH medium promotes formation of insoluble metal hydroxides such as Ca(OH)2 which are filtered off.Figure 5
3D surface plot for total hardness removal.The linear increase in adsorption efficiency of MZ with increasing adsorbent dosage indicated the accessibility of a larger number of sorption sites at higher dosage to adsorb Ca(II) ions (Figure6).Figure 6
Effect of adsorbent dosage.The effect of initial metal concentration on the removal efficiency of the zeolite adsorbent is illustrated in Figure7. The initial concentration-profile plot shows a remarkable decrease in removal efficiency as initial concentration is increased. At low concentration, most of the metal ions in the solution interact with active sites on the adsorbent, resulting in high percentage removal [28].Figure 7
Effect of initial concentration.


#### 3.2.3. Effect of Temperature

The amount of Ca(II) adsorbed on MZ as a function of solution temperature is shown in Figure8. The removal efficiency decreased as temperature was increased from 20 to 40°C, showing that low temperature favors Ca(II) removal from aqueous solutions. The decrease of Ca(II) removal may be attributed to the Ca(II) ions escaping from the solid phase with the rise in temperature of solutions [29]. The optimum temperature of 20°C was used for all further experiments.Figure 8
Effect of temperature.


#### 3.2.4. Adsorption Thermodynamics

Thermodynamic parameters such as standard Gibb’s free energy change (ΔGo), the entropy change (ΔSo), and the enthalpy change (ΔHo) were calculated from the following equations:(5)ΔGo=-RTln⁡Kd,Kd=qeCe,ΔGo=ΔHo-TΔSo,ln⁡Kd=ΔSoR+ΔHoRT,where R is the ideal gas constant, T is the temperature in K, and Kd is the thermodynamic equilibrium constant. The parameter qe is the amount of Ca(II) adsorbed at equilibrium in mg/L and Ce is the equilibrium concentration of Ca(II) ions in the solution. The intercept and the slope of the Van’t Hoff plots of ln⁡Kd versus 1/T were used to determine the ΔSo and ΔHo values, respectively. Table 5 shows the thermodynamic parameters. The calculated ΔHo value was positive, showing that the adsorption process was endothermic. A slightly positive ΔSo indicated some randomness at the solid/liquid interface during the sorption process. The ΔGo values were all positive, showing that the sorption of metals was not thermodynamically spontaneous.Table 5
Thermodynamic parameters.
Temperature (K)
Δ
G
o (kJmol−1)
Δ
H
o (kJmol−1)
Δ
S
o (kJmol−1)
293.15
+1.284
+3.953
+0.0091
303.15
+1.193
313.15
+1.102


#### 3.2.5. Adsorption Isotherms

Adsorption isotherms are useful in determining the nature of the interaction between the adsorbate and the adsorbent. In this study, the Freundlich [30] and Langmuir [31] adsorption isotherms were used to interpret the experimental data.The linearized form of the Langmuir isotherm model can be representedby(6)1qe=1qmax+1bqmax1Ce,where qe is the amount of metal ion adsorbed at equilibrium, qmax is the maximum adsorption capacity (mg g−1), Ce (mgL−1) is the equilibrium concentration, and b is the equilibrium Langmuir constant. A plot of 1/qe versus 1/Ce (Figure 9) gave a straight line with 1/qmax as intercept and 1/bqmax as slope, and hence qmax and b could be estimated (Table 6).Table 6
Equilibrium studies parameters.
Isotherm
Parameter
Value
Langmuir
q
m
a
x (mg g−1)
12.610
b (L mg−1)
0.764
χ
2
4.76
R
2
0.993
Freundlich
KF (mg g−1)
5.608
n
3.578
χ
2
37.91
R
2
0.933Figure 9
Langmuir isotherm model.Monolayer sorption with a heterogeneous energetic distribution of active sites, coupled by interaction between the adsorbed molecules, is assumed by the Freundlich isotherm. The linearized Freundlich isotherm equation is given by(7)ln⁡qe=ln⁡KF+1nln⁡Ce,where qe (mg g−1) is the amount of metal ion adsorbed at equilibrium by the adsorbent, KF (mg g−1) and n are constants representing the adsorption capacity and intensity of adsorption, respectively, and Ce (mgL−1) is the equilibrium concentration. A plot of ln⁡qe versus ln⁡Ce (Figure 10) gave a straight line, and KF and n were estimated from the intercept and slope, respectively (Table 6). The calculated values of n (3.578) were between 1 and 10 indicating favorability of the adsorption of Ca(II) ions on the adsorbent.Figure 10
Freundlich isotherm model.The Langmuir isotherm model correlation coefficient (R2=0.993) was significantly closer to unity relative to that of the Freundlich isotherm model (R2=0.933). Moreover, the Chi-square value for the Langmuir model (χ2=4.76) was lower than that of Freundlich model (χ2=37.91), indicating that the Freundlich model could not fit all the experimental data well.


#### 3.2.6. Adsorption Kinetics

In the current study, the pseudo-first-order and pseudo-second-order models were used for determining the mechanism of the adsorption process. The pseudo-first-order model which assumes that the rate of adsorption site occupation is proportional to the number of unoccupied sites is expressed by the Lagergren equation [32] (Lagergren, 1898) in the linear form as follows:(8)log⁡qe-qt=log⁡qe-t·k12.3,where qe and qt are the amount of Ca(II) adsorbed (mg g−1) onto MZ at equilibrium and at any time t, respectively, k1 (min−1) is the rate constant of pseudo-first-order model, and t is the time (min). A plot of log⁡(qe-qt) versus t (Figure 11) was used to estimate the values of k1 and qe from the slope and the intercept, respectively.Figure 11
Pseudo-first-order model.The second-order kinetic model can be expressed in the linear form as follows [33]:(9)tqt=tqe+1k2qe2,where k2 is the equilibrium rate constant of pseudo-second-order model (g mg-1min−1). The values of qe and k2 (Table 7) were determined from the slope and intercept of the plot of (t/qt) versus t, respectively (Figure 12). The pseudo-second-order kinetic model correlation coefficient was R2=0.991, suggesting the applicability of the model to the adsorption of Ca(II) by MZ. Furthermore, the qe,cal value (2.81 mg g−1) for the pseudo-second-order kinetic reaction was found to be in better agreement with the qe,exp value (2.77 mg g−1).Table 7
Kinetic parameters.
Experimental value
Pseudo-first-order kinetic model
Pseudo-second-order kinetic model
q
e (mg g−1)
q
e (mg g−1)
k
1 (min−1)
R2
q
e (mg g−1)
k
1 (g mg−1 min−1)
R
2
2.77
1.01
0.01
0.964
2.81
0.0318
0.991Figure 12
Pseudo-second-order kinetic model.


#### 3.2.7. Desorption Studies

The reusability of the spent adsorbent was studied by desorption/regeneration experiments, to evaluate the economical feasibility of the method. Regeneration percentage of the spent adsorbent versus NaOH is illustrated in Figure13. Maximum recovery of the adsorbed metal ions was achieved at 2 M NaOH concentration leading to 90% desorption of the adsorbed Ca(II).Figure 13
Desorption of Ca(II) ions from the spent adsorbent.


## 3.1. Characterization of the Adsorbent

### 3.1.1. FTIR

Zeolites were synthesized at different reaction times and different NaOH concentrations and the zeolite that was similar to zeolite-A was selected for use. Figure1 shows the FTIR spectra of the metakaolin zeolites synthesized at an optimum time of 4 h at different NaOH concentrations. The spectrum of the selected zeolite (C2, Figure 1) had a band at 3458.53 cm−1 corresponding to O-H vibration. There was structural T-O stretching and deformation at 1642.33 cm−1 and a peak at 1021.10 cm−1 that corresponded to internal tetrahedron asymmetrical vibration. A peak at 1421.37 cm−1 might be due to Si-O asymmetric stretching whilst bands at 723.79 and 1072.79 cm−1 were due to internal symmetrical stretching vibration of (Al-Si)-O. The 473.46 cm−1 band was due to internal vibration of (Al-Si)-O bending and the 558.95 cm−1 band corresponded to the formation of double four-membered rings by external linkages [5]. The zeolite-A framework possesses good exchange capacity, making it a good material as an ion exchange agent. It may thus be concluded that IR spectra of the C2 spectra are closely complementary to zeolite-A; therefore, the C2 zeolites were used for batch adsorption studies.Figure 1
FTIR spectra of metakaolin zeolites (C1, 4 h, 3 M NaOH zeolite; C2, 4 h, 5 M NaOH zeolite; and C3, 4 h, 1 M NaOH zeolite).


### 3.1.2. XRD Analysis

The XRD data (Figure2) showed four crystallographic phases at 2θ degree values of 10.09 (ZON), and 12.69 (MER), 26.69 (Quartz), and 30.28 (CAN) are quite consistent with the two theta values of zeolite-A (LTA) showing that the pure phase of crystalline zeolite-A was produced.Figure 2
XRD pattern for metakaolin zeolite-A.


## 3.1.1. FTIR

Zeolites were synthesized at different reaction times and different NaOH concentrations and the zeolite that was similar to zeolite-A was selected for use. Figure1 shows the FTIR spectra of the metakaolin zeolites synthesized at an optimum time of 4 h at different NaOH concentrations. The spectrum of the selected zeolite (C2, Figure 1) had a band at 3458.53 cm−1 corresponding to O-H vibration. There was structural T-O stretching and deformation at 1642.33 cm−1 and a peak at 1021.10 cm−1 that corresponded to internal tetrahedron asymmetrical vibration. A peak at 1421.37 cm−1 might be due to Si-O asymmetric stretching whilst bands at 723.79 and 1072.79 cm−1 were due to internal symmetrical stretching vibration of (Al-Si)-O. The 473.46 cm−1 band was due to internal vibration of (Al-Si)-O bending and the 558.95 cm−1 band corresponded to the formation of double four-membered rings by external linkages [5]. The zeolite-A framework possesses good exchange capacity, making it a good material as an ion exchange agent. It may thus be concluded that IR spectra of the C2 spectra are closely complementary to zeolite-A; therefore, the C2 zeolites were used for batch adsorption studies.Figure 1
FTIR spectra of metakaolin zeolites (C1, 4 h, 3 M NaOH zeolite; C2, 4 h, 5 M NaOH zeolite; and C3, 4 h, 1 M NaOH zeolite).


## 3.1.2. XRD Analysis

The XRD data (Figure2) showed four crystallographic phases at 2θ degree values of 10.09 (ZON), and 12.69 (MER), 26.69 (Quartz), and 30.28 (CAN) are quite consistent with the two theta values of zeolite-A (LTA) showing that the pure phase of crystalline zeolite-A was produced.Figure 2
XRD pattern for metakaolin zeolite-A.


## 3.2. Adsorption Batch Studies

Adsorption studies using MZ were done on an aqueous Ca(II) solution applying a central composite design [24] developed from the experimental domain presented in Table 1. The investigation was carried out following a full central composite design consisting of 30 experiments, which included several replicate experiments to check for consistency of the adsorption procedure. The average Ca(II) removal from aqueous solutions using the prepared adsorbent over six replicate runs (midpoint experimental conditions) was 39.73±0.41% (at 95% confidence). The results obtained were consistent as evidenced by the small relative standard deviation (1.04%). The CCD batch method was therefore capable of providing consistent results and hence was suitable for use in the investigation of the adsorption of Ca(II) ions onto MZ.


### 3.2.1. Response Surface Methodology Modeling

The experimental variable settings used for this investigation together with the actual experimental results are presented in Table2.Table 2
Experimental variables and results.
Run
A: pH
B: contact time
C: initial concentration
D: dosage
Ca(II) removal
(min)
(mgL−1)
(g)
(%)
1
2
95
62.5
1.05
32.0
2
4
52.5
33.75
0.575
57.8
3
4
52.5
33.75
1.525
62.2
4
4
52.5
91.25
1.525
26.8
5
4
52.5
91.25
0.575
24.7
7
4
137.5
33.75
0.575
74.1
8
4
137.5
33.75
1.525
78.5
9
4
137.5
91.25
1.525
28.5
10
4
137.5
91.25
0.575
25.8
11
6
10
62.5
1.05
36.0
12
6
95
62.5
1.05
39.2
13
6
95
62.5
1.05
39.2
14
6
95
62.5
1.05
40.0
15
6
95
62.5
2
42.4
16
6
95
62.5
1.05
40.0
17
6
95
62.5
0.1
36.0
18
6
95
62.5
1.05
40.0
19
6
95
62.5
1.05
40.0
20
6
95
120
1.05
22.9
21
6
180
62.5
1.05
43.2
22
8
52.5
33.75
0.575
66.7
23
8
52.5
33.75
1.525
72.6
24
8
52.5
91.25
1.525
30.1
25
8
52.5
91.25
0.575
26.8
26
8
137.5
33.75
1.525
75.6
27
8
137.5
33.75
0.575
59.3
28
8
137.5
91.25
1.525
34.5
29
8
137.5
91.25
0.575
32.3
30
10
95
62.5
1.05
47.2The proposed fullLogitR transformation model (see (3)) was fitted on the experimental data obtained in Table 2. The least squares regression results for the adsorption of Ca(II) after elimination of the insignificant terms (p>0.05) during stepwise multiple regression are summarized in Table 3.Table 3
Least squares regression data for Ca(II) removal.
Factor
Coefficient estimate
DF
Standard error
t for H0
P
r
o
b
>
t
VIF
Coeff. = 0
Intercept
2.16972
1
0.2366
A: pH
0.062119
1
0.0110
5.64648
<0.0001
1.01478
B: contact time
0.008357
1
0.0015
5.48405
<0.0001
8.79209
C: concentration
−0.0863
1
0.0065
−13.279
<0.0001
47.681
D: dosage
0.149761
1
0.0463
3.23304
0.0042
1.01478
C
2
0.0005
1
0.0000
10.147
<0.0001
44.4523
BC
-
8.10
E
-
05
1
0.0000
−3.6024
0.0018
14.1953
R
2
0.984All thep values associated with the coefficients of pH (A), contact time (B), initial concentration (C), dosage concentration (D), initial concentration squared term (C2), and the interaction between contact time and initial concentration term (BC) were smaller than 0.05 (Table 3), indicating a significant effect of these factors on the percentage removal of calcium by metakaolin zeolite. The interaction between contact time and initial concentration (BC) has an antagonistic effect on the removal of calcium as shown by the negative value of the associated coefficient. The final model obtained after elimination of the insignificant term was(4)LogitR=b0+b1A+b2B+b3C+b4D+b5C2+b6BC.The results of the analysis of variance for the regression model are presented in Table 4.Table 4
Results for ANOVA for the model.
Source
Sum of squares
DF
Mean square
F-value
P
r
o
b
>
F
Model
13.4078
6
2.23463
203.981
<0.0001
Residual
0.219102
20
0.010955
Lack of fit
0.21761
15
0.014507
48.6273
0.0002
Pure error
0.001492
5
0.000298
Cor. total
13.6269
26Thep value for the model was less than 0.05 (p<0.0001), indicating that the model was statistically significant. Moreover, a higher regression coefficient (R2=0.984) supported the significance of the model [25]. Model validity was evaluated by normal probability plot which was produced by the Design Expert software. Figure 3 shows that the residuals were close to the straight line and were scattered randomly around it with no particular pattern, showing no abnormal behavior [26].Figure 3
Normal plot of residuals.The plot of standard residuals versus predicted values showed a random distribution of residuals (difference between the experimental and the predicted values), with no particular pattern showing well behaved residuals (Figure4) [27]. Moreover, it showed no outliers supporting the statistical validity of the model.Figure 4
Plot of standard residuals versus predicted values.


### 3.2.2. Model Interpretation

A 3-dimensional surface plot gives vital information on the behavior of the experimental design system. This aids the evaluation of the effects of the independent variables on the response factor. Figure5 shows the effect of pH and contact time on % removal of Ca(II) ions at constant dosage amount and initial Ca(II) concentration. An increase in both pH and contact time increased the percentage removal of Ca(II). Since the sorbent had abundant binding sites, the gradual occupancy of these sites over different times resulted in an increase in the uptake of Ca(II). The lower percentage removal observed in acidic pH medium is due to protonation of adsorbent functional groups or competition of H+ with Ca(II) ions to bind and occupy the active sites of the adsorbent. On the other hand, higher pH medium promotes formation of insoluble metal hydroxides such as Ca(OH)2 which are filtered off.Figure 5
3D surface plot for total hardness removal.The linear increase in adsorption efficiency of MZ with increasing adsorbent dosage indicated the accessibility of a larger number of sorption sites at higher dosage to adsorb Ca(II) ions (Figure6).Figure 6
Effect of adsorbent dosage.The effect of initial metal concentration on the removal efficiency of the zeolite adsorbent is illustrated in Figure7. The initial concentration-profile plot shows a remarkable decrease in removal efficiency as initial concentration is increased. At low concentration, most of the metal ions in the solution interact with active sites on the adsorbent, resulting in high percentage removal [28].Figure 7
Effect of initial concentration.


### 3.2.3. Effect of Temperature

The amount of Ca(II) adsorbed on MZ as a function of solution temperature is shown in Figure8. The removal efficiency decreased as temperature was increased from 20 to 40°C, showing that low temperature favors Ca(II) removal from aqueous solutions. The decrease of Ca(II) removal may be attributed to the Ca(II) ions escaping from the solid phase with the rise in temperature of solutions [29]. The optimum temperature of 20°C was used for all further experiments.Figure 8
Effect of temperature.


### 3.2.4. Adsorption Thermodynamics

Thermodynamic parameters such as standard Gibb’s free energy change (ΔGo), the entropy change (ΔSo), and the enthalpy change (ΔHo) were calculated from the following equations:(5)ΔGo=-RTln⁡Kd,Kd=qeCe,ΔGo=ΔHo-TΔSo,ln⁡Kd=ΔSoR+ΔHoRT,where R is the ideal gas constant, T is the temperature in K, and Kd is the thermodynamic equilibrium constant. The parameter qe is the amount of Ca(II) adsorbed at equilibrium in mg/L and Ce is the equilibrium concentration of Ca(II) ions in the solution. The intercept and the slope of the Van’t Hoff plots of ln⁡Kd versus 1/T were used to determine the ΔSo and ΔHo values, respectively. Table 5 shows the thermodynamic parameters. The calculated ΔHo value was positive, showing that the adsorption process was endothermic. A slightly positive ΔSo indicated some randomness at the solid/liquid interface during the sorption process. The ΔGo values were all positive, showing that the sorption of metals was not thermodynamically spontaneous.Table 5
Thermodynamic parameters.
Temperature (K)
Δ
G
o (kJmol−1)
Δ
H
o (kJmol−1)
Δ
S
o (kJmol−1)
293.15
+1.284
+3.953
+0.0091
303.15
+1.193
313.15
+1.102


### 3.2.5. Adsorption Isotherms

Adsorption isotherms are useful in determining the nature of the interaction between the adsorbate and the adsorbent. In this study, the Freundlich [30] and Langmuir [31] adsorption isotherms were used to interpret the experimental data.The linearized form of the Langmuir isotherm model can be representedby(6)1qe=1qmax+1bqmax1Ce,where qe is the amount of metal ion adsorbed at equilibrium, qmax is the maximum adsorption capacity (mg g−1), Ce (mgL−1) is the equilibrium concentration, and b is the equilibrium Langmuir constant. A plot of 1/qe versus 1/Ce (Figure 9) gave a straight line with 1/qmax as intercept and 1/bqmax as slope, and hence qmax and b could be estimated (Table 6).Table 6
Equilibrium studies parameters.
Isotherm
Parameter
Value
Langmuir
q
m
a
x (mg g−1)
12.610
b (L mg−1)
0.764
χ
2
4.76
R
2
0.993
Freundlich
KF (mg g−1)
5.608
n
3.578
χ
2
37.91
R
2
0.933Figure 9
Langmuir isotherm model.Monolayer sorption with a heterogeneous energetic distribution of active sites, coupled by interaction between the adsorbed molecules, is assumed by the Freundlich isotherm. The linearized Freundlich isotherm equation is given by(7)ln⁡qe=ln⁡KF+1nln⁡Ce,where qe (mg g−1) is the amount of metal ion adsorbed at equilibrium by the adsorbent, KF (mg g−1) and n are constants representing the adsorption capacity and intensity of adsorption, respectively, and Ce (mgL−1) is the equilibrium concentration. A plot of ln⁡qe versus ln⁡Ce (Figure 10) gave a straight line, and KF and n were estimated from the intercept and slope, respectively (Table 6). The calculated values of n (3.578) were between 1 and 10 indicating favorability of the adsorption of Ca(II) ions on the adsorbent.Figure 10
Freundlich isotherm model.The Langmuir isotherm model correlation coefficient (R2=0.993) was significantly closer to unity relative to that of the Freundlich isotherm model (R2=0.933). Moreover, the Chi-square value for the Langmuir model (χ2=4.76) was lower than that of Freundlich model (χ2=37.91), indicating that the Freundlich model could not fit all the experimental data well.


### 3.2.6. Adsorption Kinetics

In the current study, the pseudo-first-order and pseudo-second-order models were used for determining the mechanism of the adsorption process. The pseudo-first-order model which assumes that the rate of adsorption site occupation is proportional to the number of unoccupied sites is expressed by the Lagergren equation [32] (Lagergren, 1898) in the linear form as follows:(8)log⁡qe-qt=log⁡qe-t·k12.3,where qe and qt are the amount of Ca(II) adsorbed (mg g−1) onto MZ at equilibrium and at any time t, respectively, k1 (min−1) is the rate constant of pseudo-first-order model, and t is the time (min). A plot of log⁡(qe-qt) versus t (Figure 11) was used to estimate the values of k1 and qe from the slope and the intercept, respectively.Figure 11
Pseudo-first-order model.The second-order kinetic model can be expressed in the linear form as follows [33]:(9)tqt=tqe+1k2qe2,where k2 is the equilibrium rate constant of pseudo-second-order model (g mg-1min−1). The values of qe and k2 (Table 7) were determined from the slope and intercept of the plot of (t/qt) versus t, respectively (Figure 12). The pseudo-second-order kinetic model correlation coefficient was R2=0.991, suggesting the applicability of the model to the adsorption of Ca(II) by MZ. Furthermore, the qe,cal value (2.81 mg g−1) for the pseudo-second-order kinetic reaction was found to be in better agreement with the qe,exp value (2.77 mg g−1).Table 7
Kinetic parameters.
Experimental value
Pseudo-first-order kinetic model
Pseudo-second-order kinetic model
q
e (mg g−1)
q
e (mg g−1)
k
1 (min−1)
R2
q
e (mg g−1)
k
1 (g mg−1 min−1)
R
2
2.77
1.01
0.01
0.964
2.81
0.0318
0.991Figure 12
Pseudo-second-order kinetic model.


### 3.2.7. Desorption Studies

The reusability of the spent adsorbent was studied by desorption/regeneration experiments, to evaluate the economical feasibility of the method. Regeneration percentage of the spent adsorbent versus NaOH is illustrated in Figure13. Maximum recovery of the adsorbed metal ions was achieved at 2 M NaOH concentration leading to 90% desorption of the adsorbed Ca(II).Figure 13
Desorption of Ca(II) ions from the spent adsorbent.


## 3.2.1. Response Surface Methodology Modeling

The experimental variable settings used for this investigation together with the actual experimental results are presented in Table2.Table 2
Experimental variables and results.
Run
A: pH
B: contact time
C: initial concentration
D: dosage
Ca(II) removal
(min)
(mgL−1)
(g)
(%)
1
2
95
62.5
1.05
32.0
2
4
52.5
33.75
0.575
57.8
3
4
52.5
33.75
1.525
62.2
4
4
52.5
91.25
1.525
26.8
5
4
52.5
91.25
0.575
24.7
7
4
137.5
33.75
0.575
74.1
8
4
137.5
33.75
1.525
78.5
9
4
137.5
91.25
1.525
28.5
10
4
137.5
91.25
0.575
25.8
11
6
10
62.5
1.05
36.0
12
6
95
62.5
1.05
39.2
13
6
95
62.5
1.05
39.2
14
6
95
62.5
1.05
40.0
15
6
95
62.5
2
42.4
16
6
95
62.5
1.05
40.0
17
6
95
62.5
0.1
36.0
18
6
95
62.5
1.05
40.0
19
6
95
62.5
1.05
40.0
20
6
95
120
1.05
22.9
21
6
180
62.5
1.05
43.2
22
8
52.5
33.75
0.575
66.7
23
8
52.5
33.75
1.525
72.6
24
8
52.5
91.25
1.525
30.1
25
8
52.5
91.25
0.575
26.8
26
8
137.5
33.75
1.525
75.6
27
8
137.5
33.75
0.575
59.3
28
8
137.5
91.25
1.525
34.5
29
8
137.5
91.25
0.575
32.3
30
10
95
62.5
1.05
47.2The proposed fullLogitR transformation model (see (3)) was fitted on the experimental data obtained in Table 2. The least squares regression results for the adsorption of Ca(II) after elimination of the insignificant terms (p>0.05) during stepwise multiple regression are summarized in Table 3.Table 3
Least squares regression data for Ca(II) removal.
Factor
Coefficient estimate
DF
Standard error
t for H0
P
r
o
b
>
t
VIF
Coeff. = 0
Intercept
2.16972
1
0.2366
A: pH
0.062119
1
0.0110
5.64648
<0.0001
1.01478
B: contact time
0.008357
1
0.0015
5.48405
<0.0001
8.79209
C: concentration
−0.0863
1
0.0065
−13.279
<0.0001
47.681
D: dosage
0.149761
1
0.0463
3.23304
0.0042
1.01478
C
2
0.0005
1
0.0000
10.147
<0.0001
44.4523
BC
-
8.10
E
-
05
1
0.0000
−3.6024
0.0018
14.1953
R
2
0.984All thep values associated with the coefficients of pH (A), contact time (B), initial concentration (C), dosage concentration (D), initial concentration squared term (C2), and the interaction between contact time and initial concentration term (BC) were smaller than 0.05 (Table 3), indicating a significant effect of these factors on the percentage removal of calcium by metakaolin zeolite. The interaction between contact time and initial concentration (BC) has an antagonistic effect on the removal of calcium as shown by the negative value of the associated coefficient. The final model obtained after elimination of the insignificant term was(4)LogitR=b0+b1A+b2B+b3C+b4D+b5C2+b6BC.The results of the analysis of variance for the regression model are presented in Table 4.Table 4
Results for ANOVA for the model.
Source
Sum of squares
DF
Mean square
F-value
P
r
o
b
>
F
Model
13.4078
6
2.23463
203.981
<0.0001
Residual
0.219102
20
0.010955
Lack of fit
0.21761
15
0.014507
48.6273
0.0002
Pure error
0.001492
5
0.000298
Cor. total
13.6269
26Thep value for the model was less than 0.05 (p<0.0001), indicating that the model was statistically significant. Moreover, a higher regression coefficient (R2=0.984) supported the significance of the model [25]. Model validity was evaluated by normal probability plot which was produced by the Design Expert software. Figure 3 shows that the residuals were close to the straight line and were scattered randomly around it with no particular pattern, showing no abnormal behavior [26].Figure 3
Normal plot of residuals.The plot of standard residuals versus predicted values showed a random distribution of residuals (difference between the experimental and the predicted values), with no particular pattern showing well behaved residuals (Figure4) [27]. Moreover, it showed no outliers supporting the statistical validity of the model.Figure 4
Plot of standard residuals versus predicted values.


## 3.2.2. Model Interpretation

A 3-dimensional surface plot gives vital information on the behavior of the experimental design system. This aids the evaluation of the effects of the independent variables on the response factor. Figure5 shows the effect of pH and contact time on % removal of Ca(II) ions at constant dosage amount and initial Ca(II) concentration. An increase in both pH and contact time increased the percentage removal of Ca(II). Since the sorbent had abundant binding sites, the gradual occupancy of these sites over different times resulted in an increase in the uptake of Ca(II). The lower percentage removal observed in acidic pH medium is due to protonation of adsorbent functional groups or competition of H+ with Ca(II) ions to bind and occupy the active sites of the adsorbent. On the other hand, higher pH medium promotes formation of insoluble metal hydroxides such as Ca(OH)2 which are filtered off.Figure 5
3D surface plot for total hardness removal.The linear increase in adsorption efficiency of MZ with increasing adsorbent dosage indicated the accessibility of a larger number of sorption sites at higher dosage to adsorb Ca(II) ions (Figure6).Figure 6
Effect of adsorbent dosage.The effect of initial metal concentration on the removal efficiency of the zeolite adsorbent is illustrated in Figure7. The initial concentration-profile plot shows a remarkable decrease in removal efficiency as initial concentration is increased. At low concentration, most of the metal ions in the solution interact with active sites on the adsorbent, resulting in high percentage removal [28].Figure 7
Effect of initial concentration.


## 3.2.3. Effect of Temperature

The amount of Ca(II) adsorbed on MZ as a function of solution temperature is shown in Figure8. The removal efficiency decreased as temperature was increased from 20 to 40°C, showing that low temperature favors Ca(II) removal from aqueous solutions. The decrease of Ca(II) removal may be attributed to the Ca(II) ions escaping from the solid phase with the rise in temperature of solutions [29]. The optimum temperature of 20°C was used for all further experiments.Figure 8
Effect of temperature.


## 3.2.4. Adsorption Thermodynamics

Thermodynamic parameters such as standard Gibb’s free energy change (ΔGo), the entropy change (ΔSo), and the enthalpy change (ΔHo) were calculated from the following equations:(5)ΔGo=-RTln⁡Kd,Kd=qeCe,ΔGo=ΔHo-TΔSo,ln⁡Kd=ΔSoR+ΔHoRT,where R is the ideal gas constant, T is the temperature in K, and Kd is the thermodynamic equilibrium constant. The parameter qe is the amount of Ca(II) adsorbed at equilibrium in mg/L and Ce is the equilibrium concentration of Ca(II) ions in the solution. The intercept and the slope of the Van’t Hoff plots of ln⁡Kd versus 1/T were used to determine the ΔSo and ΔHo values, respectively. Table 5 shows the thermodynamic parameters. The calculated ΔHo value was positive, showing that the adsorption process was endothermic. A slightly positive ΔSo indicated some randomness at the solid/liquid interface during the sorption process. The ΔGo values were all positive, showing that the sorption of metals was not thermodynamically spontaneous.Table 5
Thermodynamic parameters.
Temperature (K)
Δ
G
o (kJmol−1)
Δ
H
o (kJmol−1)
Δ
S
o (kJmol−1)
293.15
+1.284
+3.953
+0.0091
303.15
+1.193
313.15
+1.102


## 3.2.5. Adsorption Isotherms

Adsorption isotherms are useful in determining the nature of the interaction between the adsorbate and the adsorbent. In this study, the Freundlich [30] and Langmuir [31] adsorption isotherms were used to interpret the experimental data.The linearized form of the Langmuir isotherm model can be representedby(6)1qe=1qmax+1bqmax1Ce,where qe is the amount of metal ion adsorbed at equilibrium, qmax is the maximum adsorption capacity (mg g−1), Ce (mgL−1) is the equilibrium concentration, and b is the equilibrium Langmuir constant. A plot of 1/qe versus 1/Ce (Figure 9) gave a straight line with 1/qmax as intercept and 1/bqmax as slope, and hence qmax and b could be estimated (Table 6).Table 6
Equilibrium studies parameters.
Isotherm
Parameter
Value
Langmuir
q
m
a
x (mg g−1)
12.610
b (L mg−1)
0.764
χ
2
4.76
R
2
0.993
Freundlich
KF (mg g−1)
5.608
n
3.578
χ
2
37.91
R
2
0.933Figure 9
Langmuir isotherm model.Monolayer sorption with a heterogeneous energetic distribution of active sites, coupled by interaction between the adsorbed molecules, is assumed by the Freundlich isotherm. The linearized Freundlich isotherm equation is given by(7)ln⁡qe=ln⁡KF+1nln⁡Ce,where qe (mg g−1) is the amount of metal ion adsorbed at equilibrium by the adsorbent, KF (mg g−1) and n are constants representing the adsorption capacity and intensity of adsorption, respectively, and Ce (mgL−1) is the equilibrium concentration. A plot of ln⁡qe versus ln⁡Ce (Figure 10) gave a straight line, and KF and n were estimated from the intercept and slope, respectively (Table 6). The calculated values of n (3.578) were between 1 and 10 indicating favorability of the adsorption of Ca(II) ions on the adsorbent.Figure 10
Freundlich isotherm model.The Langmuir isotherm model correlation coefficient (R2=0.993) was significantly closer to unity relative to that of the Freundlich isotherm model (R2=0.933). Moreover, the Chi-square value for the Langmuir model (χ2=4.76) was lower than that of Freundlich model (χ2=37.91), indicating that the Freundlich model could not fit all the experimental data well.


## 3.2.6. Adsorption Kinetics

In the current study, the pseudo-first-order and pseudo-second-order models were used for determining the mechanism of the adsorption process. The pseudo-first-order model which assumes that the rate of adsorption site occupation is proportional to the number of unoccupied sites is expressed by the Lagergren equation [32] (Lagergren, 1898) in the linear form as follows:(8)log⁡qe-qt=log⁡qe-t·k12.3,where qe and qt are the amount of Ca(II) adsorbed (mg g−1) onto MZ at equilibrium and at any time t, respectively, k1 (min−1) is the rate constant of pseudo-first-order model, and t is the time (min). A plot of log⁡(qe-qt) versus t (Figure 11) was used to estimate the values of k1 and qe from the slope and the intercept, respectively.Figure 11
Pseudo-first-order model.The second-order kinetic model can be expressed in the linear form as follows [33]:(9)tqt=tqe+1k2qe2,where k2 is the equilibrium rate constant of pseudo-second-order model (g mg-1min−1). The values of qe and k2 (Table 7) were determined from the slope and intercept of the plot of (t/qt) versus t, respectively (Figure 12). The pseudo-second-order kinetic model correlation coefficient was R2=0.991, suggesting the applicability of the model to the adsorption of Ca(II) by MZ. Furthermore, the qe,cal value (2.81 mg g−1) for the pseudo-second-order kinetic reaction was found to be in better agreement with the qe,exp value (2.77 mg g−1).Table 7
Kinetic parameters.
Experimental value
Pseudo-first-order kinetic model
Pseudo-second-order kinetic model
q
e (mg g−1)
q
e (mg g−1)
k
1 (min−1)
R2
q
e (mg g−1)
k
1 (g mg−1 min−1)
R
2
2.77
1.01
0.01
0.964
2.81
0.0318
0.991Figure 12
Pseudo-second-order kinetic model.


## 3.2.7. Desorption Studies

The reusability of the spent adsorbent was studied by desorption/regeneration experiments, to evaluate the economical feasibility of the method. Regeneration percentage of the spent adsorbent versus NaOH is illustrated in Figure13. Maximum recovery of the adsorbed metal ions was achieved at 2 M NaOH concentration leading to 90% desorption of the adsorbed Ca(II).Figure 13
Desorption of Ca(II) ions from the spent adsorbent.


## 4. Conclusions

The present study shows that metakaolin zeolite has much potential as an adsorbent for the removal of Ca(II) from aqueous solutions. The influences of pH, adsorbent dosage, contact time, and initial concentration on adsorption of the metal ion and their interactions were investigated by a response surface methodology and ANOVA. The Excel Solver showed that optimum removal (87.70%) was obtained at a pH, contact time, adsorbent dosage, and initial Ca(II) concentration of 6, 180 min, 1.0 g, and 40.0 mg L−1, respectively. Confirmatory experimental analysis under the optimized conditions gave average Ca(II) removal of 87.26±0.31%. The adsorption process was found to be endothermic and not thermodynamically spontaneous. The Langmuir isotherm model best described the adsorption mechanism with maximum adsorption capacity of 12.61 mg g−1. The kinetic study was performed based on pseudo-first-order and pseudo-second-order equations and the adsorption followed pseudo-second-order kinetic model. The results obtained showed that metakaolin zeolite can be used as an effective adsorbent for removal of Ca(II) ions from aqueous solutions.



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