# Optimization of lead adsorption of mordenite by response surface methodology: characterization and modification

- Havva Turkyilmaz†
^{1}, - Tolga Kartal†
^{1}and - Sibel Yigitarslan Yildiz
^{2}Email author

**12**:5

**DOI: **10.1186/2052-336X-12-5

© Turkyilmaz et al.; licensee BioMed Central Ltd. 2014

**Received: **28 August 2012

**Accepted: **6 October 2013

**Published: **6 January 2014

## Abstract

### Background

In order to remove heavy metals, water treatment by adsorption of zeolite is gaining momentum due to low cost and good performance. In this research, the natural mordenite was used as an adsorbent to remove lead ions in an aqueous solution.

### Methods

The effects of adsorption temperature, time and initial concentration of lead on the adsorption yield were investigated. Response surface methodology based on Box-Behnken design was applied for optimization. Adsorption data were analyzed by isotherm models. The process was investigated by batch experiments; kinetic and thermodynamic studies were carried out. Adsorption yields of natural and hexadecyltrimethylammonium-bromide-modified mordenite were compared.

### Results

The optimum conditions of maximum adsorption (nearly 84 percent) were found as follows: adsorption time of 85-90 min, adsorption temperature of 50°C, and initial lead concentration of 10 mg/L. At the same optimum conditions, modification of mordenite produced 97 percent adsorption yield. The most appropriate isotherm for the process was the Freundlich. Adsorption rate was found as 4.4. Thermodynamic calculations showed that the adsorption was a spontaneous and an exothermic process.

### Conclusions

Quadratic model and reduced cubic model were developed to correlate the variables with the adsorption yield of mordenite. From the analysis of variance, the most influential factor was identified as initial lead concentration. At the optimum conditions modification increased the adsorption yield up to nearly 100 percent. Mordenite was found an applicable adsorbent for lead ions especially in dilute solutions and may also be applicable in more concentrated ones with lower yields.

### Keywords

Risk Environment Hazard Lead Adsorption## Background

Heavy metals are defined as those having higher density than 5000 g/L [1]. When their concentrations reach a certain level, they cause serious damage to the environment, animals and public health. Lead is one such extremely toxic element even at low concentrations that can damage to the nervous system, gastrointestinal tract, reproductive system, liver and brain [2, 3]. Major industries of lead pollution are mining, paint, chemical, textile etc. [4]. Lead discharge from them to the atmosphere is approximately 2000 kilotons/year; thus lead pollution is serious environmental problems of worldwide. There are conventional methods for removing lead from aqueous solution such as reverse osmosis, ion exchange, electrochemical treatment, solvent extraction, chemical precipitation, adsorption and biosorption [5, 6]. Among those, adsorption is a simple process with low cost and good performance [7]. High exchange capacity, high specific surface area and low cost make natural zeolites good adsorbents [8, 9]. Their adsorption capacity can also be further increased by modification with various agents, such as CTAB (cetyltrimethylammoniumbromide) and HDTMA (hexadecyltrimethylammonium-bromide) [9]. A special type of zeolite, mordenite is abundant in nature. Comparing to other zeolites, it has rather low Si/Al ratio (5:1) which may render the adsorption of lead [10]. Removal of heavy metal ions by using mordenite is very rare [11–14]. None of the studies investigated the effect of modification of mordenite on adsorption yield. Above studies have shown that lead removal by mordenite is strongly dependent upon the initial concentration of lead and adsorption conditions. In assessing the effect (single effect and interactive effects) of variables on quality attributes an adequate experimental design is required. Response Surface Methodology (RSM) has an important application for analyzing effects of several independent variables and also interactive effects among the variables on the response. Nevertheless, no study has been found in the literature for optimization of adsorption of lead ions by mordenite, neither modified nor unmodified. The objective of the present research was to optimize the adsorption conditions of lead ions by mordenite. It was thought that the level of adsorption may be further increased by modification of mordenite with HDTMA. The effects of variables including initial lead concentration, adsorption time and temperature on adsorption yield were investigated by three-variable-three-level Box-Behnken Design (BBD). Emprical model correlating response to the three variables was then developed. Langmuir and Freundlich isotherm models were investigated in terms of their appropriateness and fractional-life method was used to determine kinetic parameters. The thermodynamic parameters of the process were also calculated.

## Methods

### Chemicals and reagents

Mordenite, a type of zeolite, was selected for having high ion-exchange capacity, high surface area and low Si/Al ratio. Mordenite, analytical grades of lead nitrate (Pb(NO_{3})_{2}) and HDTMA were purchased from Sigma and used without further purification. Three stock lead nitrate solutions (10 mg/L, 1005 mg/L, and 2000 mg/L) were prepared and used in adsorption studies as working solutions.

### Analysis and measurements

Elemental analysis of natural mordenite was determined by Perkin-Elmer (2400 series) Elemental Analyzer. The surface area of mordenite was determined by BET analysis of Micromeritics (Gemini 2360). The concentrations of residual lead(II) ions in the supernatant solutions were determined using ICP-OES (Perkin-Elmer Optima 5300 DV) measurements.

### Design of experiments, model fitting and statistical analysis

_{i}is the dimensionless coded value of the ith independent variable, x

_{0}is the value of x

_{i}at the center point and ∆x is the step change value. The behavior of the system is explained by the following empirical second-order polynomial model (Eq. 2):

where Y is the predicted response, *x*_{
i
}, *x*_{
j
}, …, *x*_{
k
} are the input variables, which affect the response Y, ${x}_{i}^{2}$, ${x}_{j}^{2}$,…, ${x}_{k}^{2}$ are the square effects, β_{0} is the intercept term, *x*_{
i
}*x*_{
j
}, *x*_{
j
}*x*_{
k
} and *x*_{
i
}*x*_{
k
} are the interaction effects, β_{i} (i = 1, 2, …, k) is the linear effect, β_{ii} (i = 1, 2, …, k) is the squared effect, β_{ij} (j = 1, 2, …, k) is the interaction effect and ϵ is a random error [17–19].

**Experimental ranges and levels of the independent variables**

Independent variables | Range and level | ||
---|---|---|---|

-1 | 0 | +1 | |

Adsorption time, min (X | 30 | 75 | 120 |

Adsorption temperature, °C (X | 20 | 35 | 50 |

Initial lead ion concentration, mg/L (X | 10 | 1005 | 2000 |

Each experiment was repeated three times (average values were used in optimization) and the experimental sequence was randomized in order to minimize the effects of the uncontrolled factors.

### Lead adsorption studies

where R is the percentage of lead adsorbed by adsorbent, P_{0} is the initial concentration of metal ion in mg/L and P_{e} is the final concentration of metal ion in mg/L.

### Adsorption isotherms

_{e}is the equilibrium concentration (mg/L), Q is the amount of metal adsorbed (mg/g), b is sorption constant (L/mg) (at 35°C) related to the energy of sorption, and Q

_{0}is the maximum sorption capacity (mg/g). For Freundlich isotherm [20]:

where Q_{e} is the amount of metal adsorbed at the equilibrium (mg/g), K_{F} ((mg/g)(L/mg)^{1/n}) and n (dimensionless) are Freundlich constants related to the adsorption capacity and adsorption intensity, respectively. The regression analysis and calculation of constants of Eq. (4) and (5) were achieved by using the solver add-in function of MS Excel.

### Adsorption kinetics

where F is the fractional value (C_{A}/C_{A0}) in time t_{F}; n the reaction order; k reaction rate constant; and C_{A} the concentration of reactant A (mg/L) at time t (min). Kinetic parameters of adsorption were determined by plotting log t_{F} versus log C_{A0} and using MS Excel.

### Adsorption thermodynamics

^{-1}K

^{-1}), T is the temperature (K) and K

_{c}is the equilibrium constant at that temperature calculated by the equation:

where C_{a} is the concentration of the adsorbed material (mg/L), and C_{e} is the concentration of remaining material in solution (mg/L).

## Results

### Properties of natural and modified mordenite

Natural mordenite has a purity of 99.8 percent with impurity of magnesium. According to the chemical composition of the zeolite, the chemical formula was determined as K_{2.87}Ca_{1.43}Na_{1.27}Al_{7.98}Si_{40}O_{88}.25H_{2}O. This result showed that the major components of mordenite were silica and alumina and the ratio of Si/Al was 5.215. The surface area of the mordenite was determined as 53 m^{2}/g with BET analysis. HDTMA-modification was corrected with the elemental analysis [23]. The ratio of C/N for HDTMA-mordenite showed that 4.15 percent of modifying agent was transferred onto the surface of the zeolite.

### Regression model and optimization

**Experimental design matrix based on Box-Behnken and results**

Run no | Independent variables | Observed values | |||||
---|---|---|---|---|---|---|---|

Coded values | Real values | ||||||

1 | -1 | 0030 | -1 | 30 | 35 | 10 | 55.800 |

2 | 0 | +1 | -1 | 75 | 50 | 10 | 83.500 |

3 | +1 | 0 | -1 | 120 | 35 | 10 | 71.400 |

4 | 0 | +1 | +1 | 75 | 50 | 2000 | 49.350 |

5 | 0 | 0 | 0 | 75 | 35 | 1005 | 48.498 |

6 | -1 | +1 | 0 | 30 | 50 | 1005 | 47.190 |

7 | 0 | 0 | 0 | 75 | 35 | 1005 | 48.373 |

8 | +1 | 0 | +1 | 120 | 35 | 2000 | 48.900 |

9 | +1 | -1 | 0 | 120 | 20 | 1005 | 44.530 |

10 | 0 | 0 | 0 | 75 | 35 | 1005 | 48.385 |

11 | 0 | -1 | -1 | 75 | 20 | 10 | 45.200 |

12 | +1 | +1 | 0 | 120 | 50 | 1005 | 49.930 |

13 | -1 | -1 | 0 | 30 | 20 | 1005 | 42.915 |

14 | -1 | 0 | +1 | 30 | 35 | 2000 | 47.700 |

15 | 0 | -1 | +1 | 75 | 20 | 2000 | 44.800 |

**Observed and predicted values for the quadratic model**

Run no | Observed values | Predicted value | Residual |
---|---|---|---|

1 | 55.800 | 57.850 | -2.05 |

2 | 83.500 | 78.860 | 4.64 |

3 | 71.400 | 70.340 | 1.06 |

4 | 49.350 | 45.700 | 3.65 |

5 | 48.498 | 48.420 | 0.079 |

6 | 47.190 | 49.780 | -2.59 |

7 | 48.373 | 48.420 | -0.046 |

8 | 48.900 | 46.850 | 2.05 |

9 | 44.530 | 41.940 | 2.59 |

10 | 48.385 | 48.420 | -0.034 |

11 | 45.200 | 48.850 | -3.65 |

12 | 49.930 | 55.630 | -5.70 |

13 | 42.915 | 37.210 | 5.70 |

14 | 47.700 | 48.760 | -1.06 |

15 | 44.800 | 49.440 | -4.64 |

**Observed and predicted values for the reduced cubic model**

Run no | Observed values | Predicted value | Residual |
---|---|---|---|

1 | 55.800 | 55.800 | 0.000 |

2 | 83.500 | 83.500 | 0.000 |

3 | 71.400 | 71.400 | 0.000 |

4 | 49.350 | 49.350 | 0.000 |

5 | 48.498 | 48.420 | 0.078 |

6 | 47.190 | 47.190 | 0.000 |

7 | 48.373 | 48.420 | -0.047 |

8 | 48.900 | 48.900 | 0.000 |

9 | 44.530 | 44.530 | 0.000 |

10 | 48.385 | 48.420 | -0.035 |

11 | 45.200 | 45.200 | 0.000 |

12 | 49.930 | 49.930 | 0.000 |

13 | 42.915 | 42.920 | 0.005 |

14 | 47.700 | 47.700 | 0.000 |

15 | 44.800 | 44.800 | 0.000 |

**Analysis of variance (ANOVA) for the quadratic model**

Source of variations | Degrees of freedom | Sum of squares | Mean square | F-value | Probability (p) |
---|---|---|---|---|---|

Regression | 9 | 1560.78 | 173.42 | 5.46 | 0.0381 |

Main effects | 3 | 931.37 | 931.37 | 29.31 | 0.2419 |

Square effects | 3 | 279.68 | 279.68 | 8.80 | 0.7422 |

Interaction effects | 3 | 336.93 | 336.93 | 10.60 | 0.9244 |

Residual | 5 | 158.89 | 31.78 | ||

Total | 14 | 1719.67 |

**Analysis of variance (ANOVA) for the reduced cubic model**

Source of variations | Degrees of freedom | Sum of squares | Mean square | F-value | Probability (p) |
---|---|---|---|---|---|

Regression | 12 | 1719.66 | 143.30 | 30129.29 | <0.0001 |

Main effects | 3 | 828.02 | 828.02 | 174087.1 | <0.0001 |

Square effects | 3 | 279.68 | 279.68 | 58801.17 | 0.0012 |

Interaction effects | 3 | 336.93 | 336.93 | 70836.5 | 0.0147 |

Added terms | 3 | 158.88 | 158.88 | 33404.44 | 0.0024 |

Total | 14 | 1719.67 |

where Y is lead ion removal (response) in percentage, *x*_{1}, *x*_{2} and *x*_{3} are the coded values of variables; adsorption time in min (*x*_{1}), adsorption temperature in °C (*x*_{2}), and initial lead ion concentration in mg/L (*x*_{3}).

**Regression analysis for the reduced cubic model**

Model term | Coefficient estimate | Standart error | F-Value | p-Value |
---|---|---|---|---|

Intercept | +48.42 | 0.04 | 30129.29 | <0.0001 |

| +4.20 | 0.034 | 14834.96 | <0.0001 |

| +10.71 | 0.034 | 96509.35 | <0.0001 |

| -8.64 | 0.034 | 62742.79 | <0.0001 |

| +0.28 | 0.034 | 66.52 | 0.0147 |

| -3.60 | 0.034 | 10899.15 | <0.0001 |

| -8.44 | 0.034 | 59870.83 | <0.0001 |

${x}_{1}^{2}$ | -1.02 | 0.036 | 807.59 | 0.0012 |

${x}_{2}^{2}$ | -1.26 | 0.036 | 1227.48 | 0.0008 |

${x}_{3}^{2}$ | +8.55 | 0.036 | 56766.10 | <0.0001 |

${x}_{1}^{2}{x}_{2}$ | -8.29 | 0.049 | 28924.08 | <0.0001 |

${x}_{1}^{2}{x}_{3}$ | +0.99 | 0.049 | 410.05 | 0.0024 |

${x}_{1}{x}_{2}^{2}$ | -3.11 | 0.049 | 4070.31 | 0.0002 |

**Numerical optimization of the model obtained by desirability function**

Criteria | Solution | Desirability | |
---|---|---|---|

1 | Adsorption time: in range | 89.47 | 1.000 |

Adsorption temperature: in range | 49.68 | ||

Initial lead concentration: target = 10 | 10.00 | ||

Lead removal: maximize | 83.7369 | ||

2 | Adsorption time: in range | 85.29 | 0.968 |

Adsorption temperature: in range | 50.00 | ||

Initial lead concentration: target = 100 | 100.00 | ||

Lead removal: maximize | 81.0066 | ||

3 | Adsorption time: in range | 81.83 | 0.602 |

Adsorption temperature: in range | 50.00 | ||

Initial lead concentration: target = 1000 | 799.10 | ||

Lead removal: maximize | 61.8751 | ||

4 | Adsorption time: in range | 82.66 | 0.425 |

Adsorption temperature: in range | 50.00 | ||

Initial lead concentration: target = 2000 | 828.11 | ||

Lead removal: maximize | 61.2467 |

### Characterization of adsorption

^{2}so lower than 1, demonstrating that Langmuir isotherm is not applicable for describing the adsorption. The experimental data fitted well to Freundlich Model (R

^{2}= 0.993) which shows that mordenite has a form of surface heterogeneity [20].

**Isotherm model constants for the adsorption of lead on mordenite (T: 35°C, sorbent dosage: 0.5 g, initial lead concentration: 10–2000 mg/L)**

Langmuir model | Freundlich model | ||||
---|---|---|---|---|---|

Q | b (L/mg) | R | 1/n | K | R |

4.387 | 0.0006 | 0.571 | 0.876 | 0.0041 | 0.993 |

^{-14}min

^{-1}(mg/L)

^{-3.39}.

**Thermodynamical constants of lead adsorption at different temperatures**

T (°C ) | Kc | ΔG | ΔS | ΔH |
---|---|---|---|---|

20 | 0.791 | 571.44 | 15.91 | -4737 |

35 | 1.683 | -1333.70 | ||

50 | 3.55 | -3403.87 |

## Discussion

In order to develop an equation describing the relation between the adsorption yield and three adsorption variables shown in Table 2, a BBD was conducted. Quadratic model and reduced cubic model were developed to correlate the variables to the response. Predicted values for yield by using reduced cubic model (Table 4) were closer to observed values than those by using quadratic model (Table 3). In quadratic model (Table 5), F-value of the model 5.46 implied that the model was statistically significant. There was only a 3.81 percent chance that a model F-value this large could occur due to noise. The fit of the model was checked by the determination coefficient (R^{2}). In this case, the value of the determination coefficient (R^{2} = 0.9076) indicated that 9.24 percent of the total variable was not explained by the model. The value of adjusted determination coefficient (adjusted R^{2} = 0.7413) was low and it was not in reasonable agreement with the adjusted R^{2}. Negative predicted R^{2} implied that the overall mean was a better predictor of the response than the current model. Significant lacks of fit and high value of the coefficient of variation were found. Probability values (greater than 0.1000) indicated that some of the model terms are not significant. But, reduced cubic model (Table 6) produced the closest predicted values, predicted R^{2} and adjusted R^{2} equal to 1, no lack of fit and low coefficient of variance. The model F-value implied that the model was significant, and there was only a 0.01 percent chance occurs due to noise. Thus, as a result of the statistical analysis, reduced cubic model was found satisfactory for describing the process and useful for developing empirical relation.

Lead removal showed to be very sensitive to changes in the temperature both in dilute and in concentrated solutions. The removal capacity of mordenite was sharply increased when the adsorption temperature increased from 20 to 50°C in dilute solutions; as it was also reported by Wang [14] (from 20 to 40°C; in a solution of 40 mg lead/L). No comparison can be made with the research by Dai *et al*. [13] since the temperature set constant at 25°C. For moderately concentrated solutions (1005 mg/L) this increase in yield was only 5 percent. The increase in yield due to increase in adsorption temperature in diluted solutions was more dominated than one in concentrated solutions.

Initial lead ion concentration was another parameter that has high effect on the response. As can be seen on Figure 1, the concentration of the aqueous solution increases the removal of lead decreases. About 84 percent yield was obtained in diluted solutions (10 mg/L). When the initial lead concentration increased to 100 mg/L, the yield decreased to 81 percent. Dai *et al*. [13] also observed that increase in initial lead concentration from 3 to 200 mg/L decreased the lead removal down to 70 percent. Also (Figure 1), the results of the study showed that this yield could also be achieved up to 500 mg/L of initial lead concentrations.

Adsorption time has little effect on lead removal. It was found that nearly 80–90 minute was enough to obtain highest yield in both dilute and concentrated solutions. The results obtained were in agreement with the work done by Dai [13] which reported that optimum time required to reach the equilibrium was 100 min. Also Wang [14] reported that adsorption time has little effect on yield and that the adsorption required 90 min.

Optimum conditions for the adsorption process were searched by numerical optimization section of the software by choosing different targets for initial lead ion concentration. As shown in Table 8, for dilute solutions (initial lead ion concentration up to 10 mg/L), the best local maximum was found to be at adsorption time of 85–90 min, adsorption temperature of 50°C, lead removal of nearly 84 percent, and desirability of 1.000. High desirability shows that the estimated function may represent the experimental model and desired conditions. As the concentration increases, desirability and lead removal percentage were found to be decreasing (Table 8). Finally, 97 percent lead adsorption was achieved by using HDTMA-mordenite at the same optimum conditions of unmodified-mordenite; i.e. initial lead ion concentrations: 10–100 mg/L. It can be concluded that, modification of mordenite or adjustment of adsorption medium (lowering up to pH 3) [13] produce nearly the same adsorption yield. But lowering the pH of the medium was useful for solutions containing 3 mg lead /L [13], whereas modification of mordenite was applicable up to 100 mg/L of lead solutions.

Fitting of adsorption data showed that (Table 9), Langmuir isotherm, thus monolayer adsorption, solely, was not suitable for the process. Equilibrium adsorption data were best represented by the Freundlich isotherm. Heterogeneous adsorption of lead on mordenite was also stated in the literature before [14]. The obtained value of (1/n) (0.1 < 1/n < 1) demonstrated that favourable nature of both lead and the heterogeneity of the mordenite sites. The 1/n value of the present study was higher than those obtained (0.537 at 30°C; 0.555 at 40°C) [14] showing that higher adsorption intensity of the mordenite used. Negative Gibbs free energy (Table 10) indicated the spontaneous nature of adsorption at those temperatures. These results were well-matched with literature [14]. Also, negative ∆H˚ values showed the adsorption of lead ions was an exothermic process. A negative enthalpy values were also reported for the adsorption of lead ions onto wollastonite, bentonite and mordenite [14]. A positive ∆S˚ value corresponded to an increase in both the randomness at the solid-solution interface and the degree of freedom of the adsorbed species. Adsorption reaction rate was found 4.4 at 0°C (Figure 2). In a different study, lead adsorption data (at 20-40°C) onto a local mordenite were fitted well to several equations; pseudo-second order, parabolic diffusion and Elovich equations [14]. It seemed that the steps of adsorbate transport from the solution to the surface of mordenite; such as film diffusion, pore diffusion, surface diffusion and adsorption are strongly affected on temperature.

## Conclusions

A Box-Behnken Design was conducted to study the effects of three adsorption variables, namely adsorption time, temperature and initial lead ion concentration on the adsorption yield of lead. Quadratic model and reduced cubic model were developed to correlate the variables to the response. Through the analysis of response surfaces, adsorption temperature and initial lead ion concentration were found to have significant effects on adsorption yield, whereas initial ion concentration showed that most significant. Process optimization was carried out and the experimental values were found to agree satisfactorily with the predicted values. Mordenite was shown to be a promising adsorbent for removal of lead from aqueous solutions. Further increase in the adsorption yield obtained at the optimum conditions was achieved with HDTMA-modification. Adsorption isotherm, adsorption kinetic and adsorption thermodynamics were studied. Equilibrium adsorption data were best represented by the Freundlich isotherm model. Thermodynamic calculations indicated that the adsorption was exothermic and spontaneous process.

## Declarations

### Acknowledgements

The present research was funded under the code of 2635-YL-11 by Scientific Research Project Coordination Unit of Suleyman Demirel University (Turkey).

## Authors’ Affiliations

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