The present paper discusses response surface methodology as an efficient approach for predictive model building and optimization of As(V) adsorption on activated carbon derived from a food industry waste: peach stones. The objectives of the study are application of a three-factor 2^{3} full factorial and central composite design technique for maximizing As(V) removal by produced activated carbon, and examination of the interactive effects of three independent variables (i.e., solution pH, temperature, and initial concentration) on As(V) adsorption capacity. Adsorption equilibrium was investigated by using Langmuir, Freundlich, and Dubinin-Radushkevich isotherm models. First-order and second-order kinetic equations were used for modeling of adsorption kinetics. Thermodynamic parameters (ΔG °, ΔH °, and ΔS °) were calculated and used to explain the As(V) adsorption mechanism. The negative value of ΔH (−7.778 kJ mol^{−1}) supported the exothermic nature of the sorption process and the Gibbs free energy values (ΔG°) were found to be negative, which indicates that the As(V) adsorption is feasible and spontaneous.

## INTRODUCTION

Arsenic, a known carcinogen in humans, is generally found in contaminated groundwater as a result of weathering of rocks, industrial waste discharges, agricultural use of arsenical herbicides, and pesticides (Bilici Baskan & Pala 2010). Drinking arsenic-rich water over a long period can result in adverse health effects including various types of cancers (bladder, kidneys, and lungs) and diseases of the blood vessels of the legs and feet (Dong *et al*. 2009). There are many methods for dealing with arsenic pollution and among them, adsorption is a versatile treatment technique practised widely in fine chemical and process industries for wastewater. Activated carbon (AC) based systems can remove a wide variety of toxic pollutants with very high removal efficiencies due to their well-developed pore structure (ranging from micro-pores to macro-pores), high active surface area, high degree of surface reactivity, and good mechanical characteristics (Özdemir *et al*. 2011). AC can be produced from a number of precursor materials, such as coal, peat, shell, or peach, apricot and cherry stones, or any other inexpensive material with a high carbon content. However, the usefulness of the adsorption process lies in the operational simplicity and reuse potential of adsorbents during long-term applications (Wen & Wu 2012; Sahu *et al.* 2009). Wen & Wu (2012) have stated that the adsorption process is difficult to understand in terms of the effects of independent variables and it does not depict their interactions on the dependent variable. Response surface methodology (RSM) is one of the statistical methods available to evaluate the effective factors and to design chemical and to physical processes in respect of the interactions between the input parameters. The experimental design technique gives an approximate description of an experimental region around a center of interest with validity of interpolation with a minimum number of experiments. Therefore, examining the effects of process parameters by statistical models is a more useful approach in order to understand the phenomena of As(V) adsorption onto activated carbon. The objectives of the study are: application of a three-factor 2^{3} full factorial and central composite design technique for maximizing As(V) removal by activated carbon produced, and investigation of the interactive effects of three independent variables (i.e., solution pH, temperature, and initial concentration) on As(V) adsorption capacity.

## MATERIALS AND METHODS

### Materials

All the chemicals/reagents used in this work were of analytical reagent grade. As(V) stock solutions were prepared by dissolving Na_{2}HAsO_{4}·7H_{2}O (Sigma–Aldrich) in deionized water. Peach stones were obtained from a fruit juice factory in Bursa, Turkey.

### Preparation of adsorbent

The peach-stone-based activated carbon was prepared by the steam activation method as described in a previous study (Duranoğlu & Beker 2012). The carbonization experiments were conducted in a horizontal quartz tube reactor with a diameter of 6 cm and a length of 55 cm. The reactor was heated using a Protherm ASF tube furnace (Alserteknik, Turkey). The nitrogen flow rate was kept constant at 500 mL/min by using a Dwyer MMA flow meter (Dwyer MMA, MI, USA). Briefly, the pretreated peach stones were placed into the quartz tube reactor and steam activation was performed at 800 °C with the heating rate of 5 °C/min in nitrogen atmosphere. Steam/nitrogen flow was passed through the reactor for 2 h at 800 °C. Steam activated carbon was rinsed with distilled water until neutral pH. The sample was denoted as peach stone-based activated carbon (PSAC).

### Adsorption experiments

Arsenate (As(V)) adsorption experiments were conducted by varying amount of adsorbent of PSAC (2–500 mg) with different concentrations (0.5–8.5 mg L^{−1}) at various pHs (2.0–10.0) and temperatures (25, 45, and 65 °C). Thermodynamic studies were conducted at different temperatures (25, 45, and 65 °C) at pH 4.0 with 4.5 mg L^{−1} initial As(V) concentration. Samples were shaken at 130 rpm using water bath with orbital shaker (Memmert WB14-SV1422). The pH values of solutions were adjusted with HCl and NaOH twice a day. Equilibrium As(V) concentration was determined at 193.696 nm by atomic absorption spectrophotometer (Analytik Jena ContrAA 700 TR). Analysis were conducted at a wavelength of 193.7 nm by the graphite furnace system using Pd/Mg(NO_{3})_{2} as a matrix modifier.

### Statistical analysis

RSM is essentially a particular set of mathematical and statistical methods for designing experiments, building models, evaluating the effects of variables, and searching optimum conditions of variables to predict targeted responses (Song *et al.* 2011). RSM also offers a relationship between the controllable input parameters and response function. The three-factor, five-level central composite (CCD), and three-level 2^{3} full factorial design (FFD) techniques were used in order to examine the effects of parameters. The quadratic model was defined by three selected parameters namely, pH (*x*_{1}), initial As(V) concentration (*x*_{2}), and temperature (*x*_{3}). As(V) adsorption capacities (mg g^{−1}) of PSAC sample were designated as dependent variables (*Y _{i}*). The levels of each factor chosen for CCD and 2

^{3}FFD were shown in Tables 1 and 2, respectively. For the three variables, the FFD for each categorical variable that consists of eight factorial points and six replicates at the center points (pH: 6.0,

*C*

_{i}: 4.5 mg L

^{−1}, T: 45 °C) were employed. The center points are used to estimate the experimental error and the duplicability of the data.

Independent variables | |||
---|---|---|---|

Level | x_{1}, pH | x_{2}, C_{i} (mg L^{−1}) | x_{3}, T (°C) |

−2 | 2 | 0.5 | 25 |

−1 | 4 | 2.5 | 35 |

0 | 6 | 4.5 | 45 |

1 | 8 | 6.5 | 55 |

2 | 10 | 8.5 | 65 |

Independent variables | |||
---|---|---|---|

Level | x_{1}, pH | x_{2}, C_{i} (mg L^{−1}) | x_{3}, T (°C) |

−2 | 2 | 0.5 | 25 |

−1 | 4 | 2.5 | 35 |

0 | 6 | 4.5 | 45 |

1 | 8 | 6.5 | 55 |

2 | 10 | 8.5 | 65 |

Independent variables | |||
---|---|---|---|

Level | x_{1}, pH | x_{2}, C_{i} (mg L^{−1}) | x_{3}, T (°C) |

−1 | 4 | 2.5 | 35 |

0 | 6 | 4.5 | 45 |

1 | 8 | 6.5 | 55 |

Independent variables | |||
---|---|---|---|

Level | x_{1}, pH | x_{2}, C_{i} (mg L^{−1}) | x_{3}, T (°C) |

−1 | 4 | 2.5 | 35 |

0 | 6 | 4.5 | 45 |

1 | 8 | 6.5 | 55 |

STATISTICA (Ver. 8.0, StatSoft Inc., USA) package was used to improve the mathematical model and estimate the regression and graphical analyses.

## RESULTS AND DISCUSSION

### Response surface methodology and statistical analysis

Table 3 represents range of three variables employed and their levels of independent reaction conditions (−2, 0, +2) according to the CCD. As(V) adsorption capacities were in the range of 34–229 μg g^{−1}. Moreover, the matrix of independent variables and the observed response values for FFD are given in Table 4. The comparison of observed and predicted As(V) sorption capacities were found in good agreement for both statistical methods.

Run | x_{1} (pH) | x_{2} (C_{i}, mg L^{−1}) | x_{3} (T, °C) | q_{e},_{exp} (μg g^{−1}) | q_{e},_{model} (μg g^{−1}) |
---|---|---|---|---|---|

1 | 0 | 2 | 0 | 180.71 | 181.01 |

2 | 0 | 0 | 0 | 140.11 | 140.83 |

3 | −1 | −1 | 1 | 80.71 | 69.10 |

4 | −2 | 0 | 0 | 98.61 | 126.18 |

5 | −1 | 1 | 1 | 218.84 | 196.35 |

6 | 0 | 0 | 0 | 145.32 | 140.83 |

7 | 0 | 0 | 0 | 145.65 | 140.83 |

8 | 0 | 0 | −2 | 182.02 | 170.51 |

9 | 0 | 0 | 0 | 140.59 | 140.83 |

10 | 1 | 1 | −1 | 97.18 | 113.77 |

11 | 0 | −2 | 0 | 34.48 | 29.21 |

12 | −1 | 1 | −1 | 229.48 | 224.12 |

13 | 0 | 0 | 2 | 106.90 | 113.43 |

14 | 1 | −1 | 1 | 49.55 | 59.91 |

15 | 2 | 0 | 0 | 39.19 | 6.64 |

16 | 1 | −1 | −1 | 61.76 | 89.22 |

17 | 0 | 0 | 0 | 137.14 | 140.83 |

18 | −1 | −1 | −1 | 94.98 | 84.29 |

19 | 0 | 0 | 0 | 141.10 | 140.83 |

20 | 1 | 1 | 1 | 56.22 | 71.88 |

Run | x_{1} (pH) | x_{2} (C_{i}, mg L^{−1}) | x_{3} (T, °C) | q_{e},_{exp} (μg g^{−1}) | q_{e},_{model} (μg g^{−1}) |
---|---|---|---|---|---|

1 | 0 | 2 | 0 | 180.71 | 181.01 |

2 | 0 | 0 | 0 | 140.11 | 140.83 |

3 | −1 | −1 | 1 | 80.71 | 69.10 |

4 | −2 | 0 | 0 | 98.61 | 126.18 |

5 | −1 | 1 | 1 | 218.84 | 196.35 |

6 | 0 | 0 | 0 | 145.32 | 140.83 |

7 | 0 | 0 | 0 | 145.65 | 140.83 |

8 | 0 | 0 | −2 | 182.02 | 170.51 |

9 | 0 | 0 | 0 | 140.59 | 140.83 |

10 | 1 | 1 | −1 | 97.18 | 113.77 |

11 | 0 | −2 | 0 | 34.48 | 29.21 |

12 | −1 | 1 | −1 | 229.48 | 224.12 |

13 | 0 | 0 | 2 | 106.90 | 113.43 |

14 | 1 | −1 | 1 | 49.55 | 59.91 |

15 | 2 | 0 | 0 | 39.19 | 6.64 |

16 | 1 | −1 | −1 | 61.76 | 89.22 |

17 | 0 | 0 | 0 | 137.14 | 140.83 |

18 | −1 | −1 | −1 | 94.98 | 84.29 |

19 | 0 | 0 | 0 | 141.10 | 140.83 |

20 | 1 | 1 | 1 | 56.22 | 71.88 |

Run | x_{1} (pH) | x_{2} (C_{i}, mg L^{−1}) | x_{3} (T, °C) | q_{e},_{exp} (μg g^{−1}) | q_{e},_{model} (μg g^{−1}) |
---|---|---|---|---|---|

1 | 0 | 0 | 0 | 140.11 | 144.05 |

2 | −1 | −1 | 1 | 80.71 | 84.76 |

3 | −1 | 1 | 1 | 218.84 | 214.79 |

4 | 0 | 0 | 0 | 145.32 | 144.05 |

5 | 0 | 0 | 0 | 145.65 | 144.05 |

6 | 0 | 0 | 0 | 140.59 | 144.05 |

7 | 1 | 1 | −1 | 97.18 | 93.13 |

8 | −1 | 1 | −1 | 229.48 | 233.53 |

9 | 1 | −1 | 1 | 49.55 | 45.50 |

10 | 1 | −1 | −1 | 61.76 | 65.81 |

11 | 0 | 0 | 0 | 137.14 | 144.05 |

12 | −1 | −1 | −1 | 94.98 | 90.93 |

13 | 0 | 0 | 0 | 155.51 | 144.05 |

14 | 1 | 1 | 1 | 56.22 | 60.27 |

Run | x_{1} (pH) | x_{2} (C_{i}, mg L^{−1}) | x_{3} (T, °C) | q_{e},_{exp} (μg g^{−1}) | q_{e},_{model} (μg g^{−1}) |
---|---|---|---|---|---|

1 | 0 | 0 | 0 | 140.11 | 144.05 |

2 | −1 | −1 | 1 | 80.71 | 84.76 |

3 | −1 | 1 | 1 | 218.84 | 214.79 |

4 | 0 | 0 | 0 | 145.32 | 144.05 |

5 | 0 | 0 | 0 | 145.65 | 144.05 |

6 | 0 | 0 | 0 | 140.59 | 144.05 |

7 | 1 | 1 | −1 | 97.18 | 93.13 |

8 | −1 | 1 | −1 | 229.48 | 233.53 |

9 | 1 | −1 | 1 | 49.55 | 45.50 |

10 | 1 | −1 | −1 | 61.76 | 65.81 |

11 | 0 | 0 | 0 | 137.14 | 144.05 |

12 | −1 | −1 | −1 | 94.98 | 90.93 |

13 | 0 | 0 | 0 | 155.51 | 144.05 |

14 | 1 | 1 | 1 | 56.22 | 60.27 |

To determine the main and interaction effects of the independent variables on As(V) adsorption onto adsorbent, an analysis of variance (ANOVA) was performed. ANOVA results showed that interactions of pH, temperature, and concentration were highly significant according to the *p-*values. The coefficient of determination (*R*^{2}) values of the CCD and FFD models were found to be 0.931 and 0.992, respectively, indicating the accuracy and general availability of the proposed models. The ANOVA results of the response surface models for As(V) adsorption on PSAC showed that the effects and the interactions of pH, temperature, and concentration were highly significant according to the *p*-values (*P* < 0.05) (Tables 5 and 6).

Sum of squares (SS) | df | Mean square | F-value | p-value | |
---|---|---|---|---|---|

Model | 57482.05 | 9 | 6386.89 | 15.04 | 0.0001 |

Residual | 4246.391 | 10 | 424.64 | ||

Total SS | 61728.44 | 19 |

Sum of squares (SS) | df | Mean square | F-value | p-value | |
---|---|---|---|---|---|

Model | 57482.05 | 9 | 6386.89 | 15.04 | 0.0001 |

Residual | 4246.391 | 10 | 424.64 | ||

Total SS | 61728.44 | 19 |

Sum of squares | df | Mean square | F-value | p-value | |
---|---|---|---|---|---|

Model | 39827.92 | 7 | 5689.70 | 99.88 | <0.0001 |

Residual | 341.81 | 6 | 56.97 | ||

Total SS | 61728.44 | 13 |

Sum of squares | df | Mean square | F-value | p-value | |
---|---|---|---|---|---|

Model | 39827.92 | 7 | 5689.70 | 99.88 | <0.0001 |

Residual | 341.81 | 6 | 56.97 | ||

Total SS | 61728.44 | 13 |

*p*≤ 0.05 and the model equations of the CCD (Equation (1)) and FFD (Equation (2)) models were established as The linear term of the initial concentration shows a significant effect on the response compared to the quadratic term of the same parameter (Equation (1)). For the temperature term, while the linear term exhibits a negative effect, the quadratic term of that temperature indicated a positive and favorable effect on sorption capacity. Equation (1) revealed that the coefficient values of pH (−29.89/

*x*

_{1}) and initial concentration (+37.95/

*x*

_{2}) indicated the greatest impact on the sorption capacity of PSAC when compared to the coefficient value of temperature (−14.27/

*x*

_{3}). A similar phenomenon was also observed for FFD model. Three-dimensional (3-D) response surface plots are the best way to examine the relation between the main and the interaction effects of two factors by keeping another factor at a fixed level. As the FFD model was found to be more reliable than the CCD, the surface plots of As(V) adsorption were drawn according to the FFD model. As can be seen in Figure 1, the maximum sorption efficiency was observed when the solution pH was 4.0.

Moreover, the As(V) adsorption capacity of PSAC decreased with increasing temperature by virtue of the exothermic nature of the adsorption process. As(V) adsorption capacities were found to be 182.02 μg g^{−1} at 25 °C (Run #8) where it decreased to 145.65 μg g^{−1} at 45 °C (Run #7) (Table 3). In the studied initial As(V) concentration range, the maximum As(V) uptake capacity was obtained at the maximum As(V) concentration of 6.5 mg L^{−1} because of the availability of a higher number of As(V) ions in the solution for the sorption process (Shi *et al.* 2009). Higher initial concentrations provide faster transport with increasing diffusion or mass transfer coefficient, resulting in a higher possibility of collision between active sites of adsorbents and As(V) ions (Aksu & Gönen 2004). According to the results, the initial As(V) concentration and pH were found to be the most significant parameters affecting adsorption capacity. The initial arsenic concentration of 6.5 mg L^{−1}, pH of 4.0, and temperature of 35 °C were found to be optimum for maximum As(V) uptake (*q*_{e} = 233.5 μg g^{−1}) based on the 2^{3} FFD. The As(V) sorption capacity of PSAC – at 99% removal – was compared with other capacities of different types of activated carbons reported in the literature (Table 7).

Adsorbent | q_{max} (mg g^{−1}) | pH | Temperature (°C) | C_{i} (mg L^{−1}) | Reference |
---|---|---|---|---|---|

Char carbon | 34.4 | 2.0–3.0 | 25 | 157–737 | Pattanayak et al. (2000) |

AC prepared from oat hulls | 3.09 | 5.0 | 24 | 100 | Chuang et al. (2005) |

Fe loaded-AC | 0.020 | 3.0 | 24 | 0.05 | Payne & Abdel-Fattah (2005) |

GAC^{a} | 0.038 | 4.7 | 25 | 0.1–30 | Gu et al. (2005) |

GAC-Fe^{c} | 2.96 | 4.7 | 25 | 0.1–30 | Gu et al. (2005) |

GAC | ^{b} | 5–7 | 30 | 0.2 | Mondal et al. (2007) |

GAC | 51.3 | 6.0 | 20 | 20–22 | Chen et al. (2007) |

Commercial GAC | 2.3 | 8.0 | 55 | 1.0 | Natale et al. (2008) |

Carbon black | 46.3 | 5.0 | 20 | 50 | Borah et al. (2009) |

PH-H_{2}0^{d} | 2.82 | 6.0 | 20 | 0.1–5.0 | Torres-Perez et al. (2012) |

BP-H_{2}0^{e} | 0.69 | 6.0 | 20 | 0.1–5.0 | Torres-Perez et al. (2012) |

Fe(II)-loaded IAC | 2.02 | 3.0 | 25 | 4.5 | Avcı Tuna et al. (2013) |

Fe(III)-loaded IAC | 3.00 | 3.0 | 25 | 4.5 | Avcı Tuna et al. (2013) |

PSAC | 0.23 | 4.0 | 35 | 6.5 | Present study |

Adsorbent | q_{max} (mg g^{−1}) | pH | Temperature (°C) | C_{i} (mg L^{−1}) | Reference |
---|---|---|---|---|---|

Char carbon | 34.4 | 2.0–3.0 | 25 | 157–737 | Pattanayak et al. (2000) |

AC prepared from oat hulls | 3.09 | 5.0 | 24 | 100 | Chuang et al. (2005) |

Fe loaded-AC | 0.020 | 3.0 | 24 | 0.05 | Payne & Abdel-Fattah (2005) |

GAC^{a} | 0.038 | 4.7 | 25 | 0.1–30 | Gu et al. (2005) |

GAC-Fe^{c} | 2.96 | 4.7 | 25 | 0.1–30 | Gu et al. (2005) |

GAC | ^{b} | 5–7 | 30 | 0.2 | Mondal et al. (2007) |

GAC | 51.3 | 6.0 | 20 | 20–22 | Chen et al. (2007) |

Commercial GAC | 2.3 | 8.0 | 55 | 1.0 | Natale et al. (2008) |

Carbon black | 46.3 | 5.0 | 20 | 50 | Borah et al. (2009) |

PH-H_{2}0^{d} | 2.82 | 6.0 | 20 | 0.1–5.0 | Torres-Perez et al. (2012) |

BP-H_{2}0^{e} | 0.69 | 6.0 | 20 | 0.1–5.0 | Torres-Perez et al. (2012) |

Fe(II)-loaded IAC | 2.02 | 3.0 | 25 | 4.5 | Avcı Tuna et al. (2013) |

Fe(III)-loaded IAC | 3.00 | 3.0 | 25 | 4.5 | Avcı Tuna et al. (2013) |

PSAC | 0.23 | 4.0 | 35 | 6.5 | Present study |

^{a}Granular activated carbon.

^{b}Not indicated.

^{c}Fe-impregnated granular activated carbon.

^{d}Steam-activated carbon derived from peanut hulls.

^{e}Steam-activated carbon derived from sugar beet pulp.

### Adsorption isotherms

The equilibrium adsorption studies were carried out with different pH values (4.0–10.0) at an initial As(V) concentration of 4.5 mg L^{−1} and the adsorption isotherms are shown in Figures 2 and 3.

Freundlich and Dubinin-Radushkevich (DR) isotherm models fitted the equilibrium data better than the Langmuir isotherm. Chi-square values (χ^{2}) of DR and Freundlich isotherm models were equal to zero while they were found to be higher in the case of the Langmuir model. The dimensionless separation factor (*R*_{L}) of the Langmuir model can be used to predict the affinity between the adsorbent and adsorbate (Avcı Tuna *et al*. 2013). The *R*_{L} values of the PSAC adsorbent indicated that As(V) adsorption was favorable.

### Thermodynamic evaluation of the adsorption process

As can be seen in Figure 4, lower adsorption capacities were achieved with increasing temperature, indicating the exothermic behavior of the process. The adsorption capacities at 25, 45, and 65 °C were calculated as 243, 207.6, and 188 μg g^{−1}, respectively. The Gibbs free energy values were found to be negative, which indicates that the As(V) adsorption is feasible and spontaneous (Table 8). The negative value of ΔH (−7.778 kJ mol^{−1}) supported the exothermic nature of the sorption process.

Temperature, K | ΔG°, kJ mol^{−1} | ΔH°, kJ mol^{−1} | ΔS°, kJ mol^{−1}K^{−1} | R^{2} |
---|---|---|---|---|

295 | −10.651 | − 7.778 | 0.0096 | 0.991 |

305 | −10.796 | |||

318 | −11.39 |

Temperature, K | ΔG°, kJ mol^{−1} | ΔH°, kJ mol^{−1} | ΔS°, kJ mol^{−1}K^{−1} | R^{2} |
---|---|---|---|---|

295 | −10.651 | − 7.778 | 0.0096 | 0.991 |

305 | −10.796 | |||

318 | −11.39 |

The value of ΔS (0.0096 kJ mol^{−1} K^{−1}) was found to be positive, reflecting the increase in the randomness on the solid–liquid interface during the process, and the higher affinity of As(V) toward the PSAC adsorbent (Bilgin Simsek *et al*. 2013).

### Adsorption kinetics

^{−1}As(V) solution (pH 4.0) and a defined amount of the PSAC adsorbent were mixed in a polyethylene bottle, and the experiments were carried out at 25 °C. The removal percentage in the first hour was calculated to be 17% and at the end of 8 h, 90% of As(V) was removed by the PSAC adsorbent. To analyze the controlling mechanism of the adsorption process, kinetic models were applied to test the experimental data. The adsorption rate of As(V) onto the PSAC was determined using two kinetic models, i.e., the pseudo-first-order and pseudo-second-order models. The Lagergren's rate equation is the most widely used model for the sorption of a solute from a liquid solution (Ho 2004) and it called the ‘pseudo-first-order model’ where ‘

*q*’ and ‘

_{e}*q*’ are the amounts of As(V) adsorbed (μg g

_{t}^{−1}) at equilibrium and at time

*t*, respectively, and

*k*

_{1}is the pseudo-first-order rate constant. Figure 5(a) shows a plot of the linear form of the pseudo-first-order model. Judging from the regression coefficient (

*R*

^{2}= 0.753), it was observed that the kinetic data are not satisfactorily correlated by the pseudo-first-order model (Table 9). Moreover, the theoretical value calculated for the pseudo-first-order model (

*q*

_{e,cal}= 12.373 μg g

^{−1}) did not give reasonable values with regard to the experimental uptake value (

*q*

_{e,exp}= 24.629 μg g

^{−1}), suggesting that the adsorption was not a pseudo-first-order reaction.

Pseudo-first-order | q_{e,exp} (μg g^{−1}) | q_{e,cal} (μg g^{−1}) | k_{1} (min^{−1}) | R^{2} |

24.629 | 12.373 | 0.0067 | 0.753 | |

Pseudo-second-order | q_{e,exp} (μg g^{−1}) | q_{e,cal} (μg g^{−1}) | k_{2} (g μg^{−1} h^{−1}) | R^{2} |

24.629 | 24.610 | 0.1499 | 0.994 |

Pseudo-first-order | q_{e,exp} (μg g^{−1}) | q_{e,cal} (μg g^{−1}) | k_{1} (min^{−1}) | R^{2} |

24.629 | 12.373 | 0.0067 | 0.753 | |

Pseudo-second-order | q_{e,exp} (μg g^{−1}) | q_{e,cal} (μg g^{−1}) | k_{2} (g μg^{−1} h^{−1}) | R^{2} |

24.629 | 24.610 | 0.1499 | 0.994 |

*k*

_{2}is the pseudo-second-order rate constant. The pseudo-second-order model assumes that the rate-determining step might be chemical sorption involving valence forces through sharing or exchange of electrons between the adsorbent and adsorbate (Ho 2006; Chen

*et al.*2008). The present data were tested in the light of the pseudo-second-order model. The plot between

*t*/

*q*versus

_{t}*t*was drawn and is shown in Figure 5(b). The pseudo-second-order rate equation showed the correlation coefficient (

*R*

^{2}) of 0.994 for As(V), indicating that the process can be better described by the second-order reaction kinetics. Furthermore, the theoretical values (

*q*

_{e,cal}= 24.610 μg g

^{−1}) were found to be in accord with the experimental uptake values (

*q*

_{e,exp}= 24.629 μg g

^{−1}), confirming that the present adsorption system follows pseudo-second-order kinetics.

## CONCLUSIONS

The As(V) adsorptive properties of PSAC have been systematically studied. The proposed mathematical methodology provided a critical analysis of the interactive effects of the independent variables: initial pH of the solution, initial concentration, and temperature, to gain a better understanding of As(V) removal onto PSAC. The response surfaces derived from the models revealed that initial pH and initial As(V) concentration showed the greatest effect on the As(V) adsorption capacity. Lower adsorption capacities were achieved with increasing temperature, indicating the exothermic behavior of the process. The initial arsenic concentration of 6.5 mg L^{−1}, pH of 4.0, and temperature of 35 °C were found to be optimum for maximum As(V) uptake based on the 2^{3} FFD. The empirical equation of As(V) adsorption capacity was established and it could be further employed in the chosen range to find the adsorption capacity without any further experimental study. The adsorption data conformed best to the Freundlich and DR models. The kinetic data were analyzed in the light of pseudo-first-order and pseudo-second-order models. It was found that As(V) adsorption on PSAC can be defined more favorably by the pseudo-second-order kinetics model.