Introduction

Industrial activities such as electroplating, welding, leather tanning, mining, dyeing, fertilizer, photography, and chromate painting processes discharge heavy metals like hexavalent chromium (Cr(VI)) into the environment through their effluents [1, 2]. Cr(VI) is one of the 17 humans threating chemicals identified by the U.S. Environmental Protection Agency (USEPA) due to its high toxicity, carcinogenicity, mutagenicity, solubility, and mobility in aqueous solutions [3,4,5]. US.EPA has set a maximum contaminant level of 10 μg L−1 for Cr(VI) in the drinking water and a range of 0.1–0.5 mg L−1 in the wastewater discharge [6, 7]. Thus, it is necessary to remove Cr(VI) from the wastewater before discharge into the environment. Recently, some methods including adsorption [8,9,10,11,12], biosorption [13], precipitation [14], electrocoagulation [15], photocatalytic reduction [16] and ion exchange [17, 18] have been developed for Cr(VI) removal from aqueous solutions. In the past decades, several studies showed that the combining the properties (characteristics) of the two methods, i.e. ion exchange with solvent extraction, led to the development of extractant-impregnated resins, which is a promising and suitable technique for adsorption of pollutants from aquatic environments [19, 20] . Amberlite XAD series, as part of the available commercial resins, are widely used for the impregnation process. This type of resin has interested researchers for its good physical properties such as high porosity, uniform pore size distribution, large surface area, and durability as well as a chemically homogeneous nonionic structure. So far, modification of Amberlite resins with various compounds, i.e. metal oxides, has been reported for separation of heavy metals from aqueous solutions [21,22,23,24,25]. Among different types of metal oxides used for removal of pollutants and heavy metals from wastewater, TiO2 has shown promising results [26, 27]. Non-toxicity, low costs, inertness, flexibility in combination with other materials, and biocompatibility have made Titania compounds (TiO2) an attractive material in various purification systems [28, 29]. In this regards, Zhang et al. [30] investigated the effect of titania loading on carbon black for Cr(VI) removal from aqueous solutions and reported that impregnation of titanium dioxide on carbon black can improve the performance of the adsorption process. According to the above, this study was conducted to evaluate impregnation of TiO2 nanoparticles onto the Amberlite XAD7 resin and its characterization, to examine the efficiency of Ti-XAD7 nanocomposite in Cr(VI) adsorption considering the effects of operating parameters including adsorbent dose, contact time, pH, and initial Cr(VI) concentration using response surface methodology (RSM) as statistical approach, to predict and optimize the parameters affecting Cr(VI) adsorption by central composite design (CCD), and to evaluate the kinetics and the adsorption isotherms of Cr(VI).

Materials and methods

Chemicals and instruments

All chemicals, including Amberlite XAD-7 resin (mean particle size: 20–60 mesh), potassium dichromate (K2Cr2O7, MW = 294.18), and titanium tetraethoxide, were purchased from Sigma-Aldrich (St. Louis, MO) and used without further purification. Double distilled water was used to prepare the Cr(VI) stock solution and dilution. Other required Cr(VI) concentrations for adsorption experiments were obtained by diluting the stock solution. Inductively coupled plasma optical emission spectrometry (ICP-OES) (ARCOS, SPECTRO®, Analytical Instrument, Kleve, Germany) was used for measurement of Cr(VI) absorbance. The prepared Ti-XAD7 was characterized by Scanning Electron Microscopy (SEM) (MIRA III, TESCAN®, Czech), Fourier Transform Infrared Spectroscopy (FTIR) (Avatar, Thermo®, USA), and XRD (PW1730, Philips®, Netherlands) techniques. pH was adjusted using a MITEC-965 (micra®, India) pH meter. A thermostatic shaker (Innova 4340, Eppendorf, Germany) was used for appropriate mixing of samples.

Preparation of Ti-XAD7

Prior to the impregnation process, Amberlite XAD-7 resin was washed with double distilled water and dried in an oven at 200 °C for 120 min [31]. Ti-XAD7 was synthesized using Amberlite XAD-7 impregnated with titanium tetraethoxide. For this purpose, 21 g of dried resin was added to 21 g titanium tetraethoxide and mixed vigorously for 15 min until titanium tetraethoxide completely penetrated into the resin structure. Then, 200 mL of 1 M ammonium hydroxide was added to the mixture and the reflux operation was performed at 70 °C for 5 h. In the next step, the resin was washed with double distilled water until the solution pH approached 7. Finally, the prepared composite resin was dried overnight in a vacuum oven at 65 °C [25].

Batch experiments

The batch experiments were performed to determine the sorption behavior of Cr(VI) onto the Ti-XAD7 adsorbent. For this purpose, 100 mL Cr(VI) solutions at different concentrations from 500 to 5000 ppb were prepared in 250 mL beakers and 0.1–10 g adsorbent was added. pH was adjusted to the desired level by addition of 0.1 M NaOH and 0.1 M H2SO4. Then, the solution was mixed in a rotary shaker at 130 rpm and sampling was done at predetermined intervals (Table 1). in the next step, the solutions were passed through cellulose acetate filter with a diameter of 0.22 μm, and residual chromium was measured using the ICP-OES. The Cr(VI) adsorption capacity and removal efficiency were calculated according to the Eqs. [1 and 2]:

$$ \mathrm{qe}\ \left(\mathrm{mg}/\mathrm{g}\right)=\frac{\left({\mathrm{C}}_0-{\mathrm{C}}_{\mathrm{e}}\right)\times \mathrm{V}}{\mathrm{w}} $$
(1)
$$ \mathrm{Removal}\ \mathrm{efficiency}\%=\frac{\left({\mathrm{C}}_0-{\mathrm{C}}_{\mathrm{e}}\right)}{{\mathrm{C}}_0}\times 100 $$
(2)
Table 1 CCD Matrix for adsorption experiments of Cr(VI) onto the Ti-XAD7
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Where qe is the adsorption capacity of the absorbent (mg/g), w is the weight of adsorbent (g), V is the solution volume (mL), and Ce and C0 are the final and initial concentration of Cr(VI) (mg/L).

Multivariate experimental design

RSM is an attractive technique for modeling and optimizing parameters affecting the adsorption process. In the present study, RSM based CCD was applied to investigate the effect of the optimization of vital factors, i.e. pH (X1), adsorbent dose (X2, g/L), contact time (X3, min), and initial Cr concentration (X4, mg/L), on adsorption [32]. A five-level-four-factor central composite design (CCD) with 38 runs of experiments was employed to study the effect of the factors on the response (Table 1). Also the number of total samples for comparison between efficiency of XAD7 and Ti-XAD7 for Cr(VI) adsorption were 76 samples (38 samples for each adsorbent). Eq. (3) illustrates the formula for converting original values of variables to their coded values:

$$ \mathrm{X}\mathrm{i}=\frac{{\mathrm{X}}_{\mathrm{i}}-{\mathrm{X}}_0}{{\Delta \mathrm{X}}_{\mathrm{i}}} $$
(3)

Where Xi is the coded value of the independent variable, X0 is the center point value of Xi, and ΔX is the step change value. After developed the experiments, empirical second-order polynomial model was applied to describe the effect of variables on the response (adsorption rate) [32]:

$$ \mathrm{Y}={\upbeta}_0{\sum}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{a}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}+{\sum}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{a}}_{\mathrm{i}\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}^2+{\sum}_{\mathrm{i}=1}^{\mathrm{n}-1}{\sum}_{\mathrm{j}=2}^{\mathrm{n}}\ {\mathrm{a}}_{\mathrm{i}\mathrm{j}}{\mathrm{x}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{j}}+\upvarepsilon $$
(4)

Where Y is the predicted response, β0 is the constant coefficient, Xi and Xj indicate the independent variables in the form of coded values, ai, aii and aij are the regression coefficients, and ε is the random error. The R software (version 3.3.1) was used for CCD design and the related statistical analysis [33].

Adsorption isotherms

Nonlinear regression

Nonlinear regression can be a powerful alternative to linear regression because it offers the most flexible curve-fitting functionality. For nonlinear models, the sum of square must be minimized by an iterative method. The nonlinear regression line is the line that minimizes the sum of squared deviations of prediction (also called the sum of squares error). In nonlinear regression, goodness of fitness (GooF) is used after error analysis. The best set of parameters for each isotherm is selected using the sum of normalized error (SNE). In this research, four isotherms with two parameter (TWP), i.e. the Temkin, Langmuir, Dubinin-Radushkevich, and Freundlich, and four isotherms with three parameters (THP), i.e. Toth, Khan, Redlich-Peterson, and Sips, were fitted to explain adsorption processes at the equilibrium point (Table 2). Moreover, minimization of the eight different non-linear error functions (see Table 3) was done to determine isotherm parameters and examine different isotherm models. The solver add-in of Microsoft Excel® (version 2013) was employed to maximize the coefficient of determination to produce the best fitness to experimental data and minimize the error functions to estimate the coefficients of isotherm models. Goodness of fitness (GooF) was applied in order to recognize the optimum isotherm. Error functions values were taken into account to classify isotherm models from the best to the worst.

Table 2 Non-linear forms of adsorption isotherm and kinetic models
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Table 3 Equations of error functions
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Sum of the normalized error (SNE)

A various set of parameters can be generated for each isotherm by various error functions [52]. In the current study, a normalization method was established to select the best set of parameters for each isotherm. In this regard, the selected parameters were obtained by calculating the sum of the normalized error (SNE) according to the following steps:

  1. I)

    one isotherm and one error function were selected and the isotherm parameters were determined based on the trial and error method so that the obtained parameters minimized the selected error function.

  2. II)

    the values of other error functions for obtained parameters of the selected isotherm were calculated.

  3. III)

    the steps I and II were repeated for individual isotherms and other error functions.

  4. IV)

    the ratio of associated error functions related to each parameter set to the largest associated error function were computed.

  5. V)

    the obtained ratios for that parameter set were summed.

  6. VI)

    the parameter set with the minimum SNE was designated as the best set of parameters for that isotherm.

Adsorption kinetics

Nonlinear regression

Four kinetic models, including Elovich, Intraparticle diffusion, pseudo-first order, and pseudo-second order, were applied to fit the experimental data and obtain the best results. The nonlinear equations of kinetic models are presented in Table 2. The R-squared (R2) was maximized to obtain the nonlinear kinetic models and select the best fitted model to the experimental data. The R2 value was calculated as follows:

$$ \mathrm{R}2=\frac{\sum_{i=1}^n\ {\left({q}_{e, calc}-{\overline{q}}_{e,\mathit{\exp}}\right)}_i^2}{\sum_{i=1}^n\ {\left({q}_{e, calc}-{\overline{q}}_{e,\mathit{\exp}}\right)}_i^2+{\sum}_{i=1}^n\ {\left({q}_{e, calc}-{\overline{q}}_{e,\mathit{\exp}}\right)}_i^2} $$
(25)

Where qe,ccalc is the calculated adsorption capacity, \( \overline{q} \)e,exp is the average of qe,exp, and qe,exp is the experimental adsorption capacity.

Results and discussions

Comparison of adsorption efficiency

Figure 1 and Table 4 present the efficiency of XAD7 and Ti-XAD7 samples for chromium adsorption. The Ti-XAD7 was more efficient than Amberlite XAD7 in Cr(VI) removal. The Wilcoxon test results (see Table 5) also confirmed that the Ti-XAD7 had a better performance (about 98%) compared to the XAD7 (nearly 80%) for Cr(VI) removal from aqueous solution. Therefore, due to the higher efficiency of Ti-XAD7, this adsorbent was used in the future section (Statistical analysis and model development) of this study.

Fig. 1
figure 1

Box plot of Cr (VI) removal efficiency by XAD7 and Ti-XAD7

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Table 4 Comparison of Cr (VI) removal efficiency for XAD7 and Ti-XAD7
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Table 5 Comparison of Cr (VI) removal efficiency for XAD7 and Ti-XAD7
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Characterization of Ti-XAD7

The scanning electron microscope (SEM) images of the XAD7 Amberlite and Ti-XAD7 at 50.0 Kx magnification are shown in Fig 2 (a) and (b). The SEM images of XAD7 Amberlite resin indicated irregular morphological aggregation with large amounts of inter-particle voids, whereas Ti-XAD7 images showed that the degree of aggregation increased with loading TiO2 on Amberlite [53]. It was observed that synthesized Ti-XAD7 had a porous and heterogeneous structure with a size range of 130-200 nm. The images indicated that the surface of the adsorbents was rough and had a decent porosity. This feature developed the contact between the Cr (VI) and Ti-XAD7 adsorbent, which resulted in the improvement of the adsorption performance.

Fig. 2
figure 2

SEM image of (a) Amberlite XAD7 and (b) Ti-XAD7, (c) FTIR images of Amberlite XAD7 and Ti-XAD7 and (d) XRD image Ti-XAD7

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Fourier-transform infrared spectroscopy (FTIR) of the original and TiO2-loaded Amberlite XAD7 resin in the range of 4000–400 cm-1 is presented in Fig. 2.C. In both spectra, the hydroxyl group appeared at a broad band around 3420 cm-1. The presence of strong bands at ⁓1260 cm-1 and ⁓1730 cm-1 in all samples was attributed to C–O stretching in ester and H-O-H bending in water molecules on the surface, respectively [54]. The peaks in the Ti-XAD7 spectrum at around 522 cm-1 and 605 cm-1 were attributed to the Ti-O-Ti (Ti-O) and theoretical frequencies of Ti (OC2H5)4 (600 to 623 cm-1), respectively. The bands at 2971.62 cm−1 were related to the stretching and bending vibration of the C–H group in the resin structure. The bands at 1639.04 and 1384.68 cm−1 are usually attributed to the –OH bending vibrations of water molecules and/or the bond between oxygen in TiO2 and hydrogen in the physical adsorbed water molecules. The above-mentioned results confirmed the proper loading of TiO2 onto the Amberlite XAD-7 resin [22, 55].

X-ray diffraction (XRD) patterns of Ti-XAD7 in the range of 2θ=10–80° are shown in Fig. 2.d. The diffraction peaks at 27.46° for (1 0 1), 31.71° for (0 0 4), 45.45° for (2 0 0), 56.46° for (2 1 1), 66.31° for (116) and 75.26° for (220) based on JCPDS no. 21-1272 indicated the presence of TiO2 with an anatase structure. The presence of other peaks, i.e. a broad peak at 15.11°, was attributed to XAD7 resin. Moreover, sharp peaks at 31.71° and 45.45° could be due to the overlapping of the iron in the resin structure and TiO2 NPs [56].

Statistical analysis and model development of Cr(VI) adsorption on Ti-XAD7

It should be noted that 38 run were considered for the experiment. After performing the lab test for XAD7 it was shown that that quadratic model is the best choice. As there was not any indication for three or four ways interaction, the fractional CCD was considered for Ti-XAD7; to reduce the number of laboratory runs without any problem in the outcomes of modeling for two ways interactions. So, to investigate the effect of independent variables, including Cr(VI) concentration, contact time, pH, and adsorbent dosage, on adsorption of Cr(VI) by Ti-XAD7, 28 experiments were suggested using the CCD approach. According to Table 6, the highest and the lowest removal efficiency for Ti-XAD7 was around 98%, and 23%, respectively.

Table 6 Results of experimental design matrix for Cr(VI) adsorption by Ti-XAD7
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The results of RSM analysis, including standard error, t-value, and the significance of input variables for Cr(VI) removal by Ti-XAD7, are presented in Table 7. The impact of contact time on Cr(VI) removal by Ti-XAD7 was not statistically significant, while other factors (adsorbent dosage, pH, and Cr(VI) initial concentration) were effectively associated with Cr(VI) removal (p < 0.05). The p value, R2, and adjusted R2 (R2adj) were used to investigate the accuracy of the model. The model was found to be statistically significant (p value = 5.221 × 10−05) and had a high R2 value of 0.7251. Additionally, a small difference (0.0786) was found between the R2 and R2adj, indicating a reasonable consistency of the quadratic model with the experimental data. As shown in Table 8, the model terms are divided into two categories: first order or linear terms (FO) and pure quadratic (PQ) terms. The results of ANOVA (Table 8) indicated that all first order parameters and pure quadratic terms included in the model were statistically significant. Model validation was also evaluated using the lack-of-fit parameter (LOF). The results showed a P value of 0.0519 for LOF, indicating a non-significant correlation (larger than 0.05) between the factors and the response.

Table 7 Regression analysis for the reduced quadratic model of Cr(VI) removal by Ti-XAD7
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Table 8 Variance analysis (ANOVA) of the adsorption of Cr(VI) by Ti-XAD7
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Response surface and contour plots of parameters

The interaction between all investigated factors and Cr(VI) adsorption is shown in Fig. 3. An increase of the adsorbent dosage from 0.1 to 10 g/L increased the adsorption efficiency by increasing the pH from 3 to 12, as shown in Fig. 3a. When the adsorbent dosage and Cr(VI) initial concentration was fixed at 5.05 g/L and 2750 ppb respectively, the removal efficiency increased with an increase in pH to 9 for a determined contact time (for example 50 min) [Fig. 3b]. However, at a higher pH [9,10,11,12], an opposite effect was seen. At a contact time of 40 min, the removal efficiency was 70% and 60% at pH = 9 and 11, respectively. The results showed that the removal efficiency of Cr(VI) by Amberlite XAD7 resin loaded with titanium dioxide improved markedly when pH increased from 3 to 9. Figure 3c presents the interaction between the adsorbent dose and Cr(VI) initial concentrations. With a decrease in the Cr(VI) concentration from 5000 to 500 ppb, the adsorption efficiency improved by increasing the adsorbent dosage from 0.1 to 10 g/L. Figure 3d shows increased removal efficiency by increasing the contact time for a specified absorbent dosage (for example, 5 g/L) when pH and Cr(VI) initial concentration are fixed at their centerpoints.

Fig. 3
figure 3

Contour plots used to display the effects of, a: pH and adsorbent dose, b: time and pH, c: adsorbent dose and concentration, and d: time and adsorbent dose, for Ti-XAD7

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Optimization of Cr(VI) adsorption process

The optimal parameters of the Cr(VI) adsorption by Ti-XAD7 were found based on mathematical equations. The Solver software was employed for maximization of the Cr(VI) adsorption to produce the optimum value for each factor. The optimum conditions of the four factors are shown in Table 9.

Table 9 Optimization of factors based on the response surface modeling
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Adsorption isotherms

Selecting the best isotherm model

The results of the isotherm models ranking are shown in Tables 10, 11 and 12. The first rank belonged to the isotherm with the lowest error function. According to Table 10, according to the RMSE, ERRSQ, APE and ARE error functions, the best isotherm model was the Langmuir followed by Freundlich, Tempkin, and Dubinin-Radushkevich. According to χ2, HYBRID and MPSD error functions, the best model was the Dubinin-Radushkevich followed by Langmuir, Freundlich and Tempkin. Based on the EABS error function, Freundlich was the best model followed by Tempkin, Dubinin-Radushkevich, and Langmuir. In the overall ranking (highlighted column), the Langmuir, Freundlich, Tempkin, and Dubinin-Radushkevich models ranked 1st to 4th based on the highest frequency of each isotherm in each row. Finally, the Langmuir isotherm model was selected as the best fitted nonlinear model for the data.

Table 10 Ranking of two-parameter isotherm models for different error functions
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Table 11 Ranking of three-parameter isotherm models for different error functions
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Table 12 Ranking of TWP and THP isotherm models for different error functions
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According to Table 11, based on the RMSE, χ2, ERRSQ, and MPSD error functions, Sips was the best isotherm model followed by Redlich-Peterson, Toth, and Khan in order. According to ARE, EABS, and APE error functions, Sips was the best model followed by Redlich-Peterson, Khan, and Toth. Based on the HYBRID error function, Redlich-Peterson was the best model followed by Toth, Khan, and Sips. In overall ranking (highlighted column), the Sips, Redlich-Peterson, Khan, and Toth models ranked 1st to 4th based on the highest frequency of each isotherm in each row. Finally, the Sips isotherm model was selected as the best fitted nonlinear model for the data.

According to Table 12, as for overall ranking (highlighted column), Sips was the best isotherm model followed by Redlich-Peterson, Toth, Khan, Langmuir, Freundlich, Tempkin, and Dubinin-Radushkevich models based on the highest frequency of each isotherm in each row. Finally, the Sips isotherm model was selected as the best fitted nonlinear model for the data.

Determination of optimal parameter values by SNE method

Tables 13 and 14 show the coefficients of fitted TWP and THP isotherm models of the Cr(VI) adsorption on Ti-XAD7, which were obtained by minimizing various error functions. The optimal values of the parameters for each isotherm obtained from the standardized normal error method are shown in highlighted columns. According to Tables 13 and 14, as for Dubinin-Radushkevich (Kad = 1.8E-08, qs = 1.39) and Langmuir (q0 = 2.5, b = 1) for TWP and Redlich-Peterson (kr = 2.85, ar = 1.46,β = 0.79) and Sips (ks = 1.86, qs = 0.88, ms = 0.59) for THP adsorption isotherms, the optimal parameters were obtained by minimizing the MPSD error function. As for Tempkin (bT = 7519, aT = 31.2), adsorption by χ2 error function yielded optimal parameters. Regarding Freundlich (k = 0.98, n = 1.69) for TWP and Toth (kT = 1.73,aT = 0.6, t = 1.28) and Khan (bk = 1.66, qs = 1.55, ak = 0.78) for THP adsorption isotherms, optimal parameters were derived from the HYBRID error function. The Langmuir constant, b, which denotes adsorption energy, was 1 Lmg−1. The high R2 (near 1) obtained indicated a good agreement between the experimental values and isotherm parameters and also confirmed the monolayer adsorption of Cr(VI) onto the adsorbent surface. RL, a dimensionless constant known as a quality determination factor of Langmuir isotherm, is presented in Eq. 26 [57].

$$ \mathrm{RL}=\frac{1}{1+{K}_L\ {C}_0} $$
(26)

where KL (b) and Co are the Langmuir constant and the initial concentration of Cr(VI) ions in mg L−1. The adsorption process was favorable within the range 0 < RL < 1, unfavorable when RL > 1, became linear when RL = 1, and was irreversible when RL = 0. According to Table 12, the adsorption process was favorable for Ti-XAD7 because RL ranged from 0 to 1. The strong interaction between the Cr(VI) molecules and the adsorbent can be explained by low relative factor of RL [57].

Table 13 The constants of two-parameter isotherm obtained by different error function
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Table 14 The constants of three-parameter isotherm obtained by different error function
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In the Freundlich constant, n > 1 indicates favorable adsorption conditions [58]. On the other hand, the coefficient of determination obtained from the Freundlich isotherm model was 0.981, which was lower than the coefficient obtained from the Langmuir isotherm model (R2 = 0.998), indicating that the equilibrium data were not fitted well with the Freundlich isotherm model.

The Langmuir isotherm model has been also used to present the best fit for the sorption of heavy metals, i.e. chromium ions onto/by a magnetic ion exchange resin [59], Lewatit FO36 nano ion exchange resin [60], Ulmus leaves and their ash [61], titan yellow-impregnated XAD-7 resin beads [22], and Amberlite IRA 410 [42].

Figures 4 and 5 present the plots of different nonlinear isotherm models with optimized values of the constants for defining the parameters of the isotherm models. According to these curves, the Langmuir model had the best fit on the experimental data among the four TWP isotherms. The lowest consistency was related to the Dubinin-Radushkevich isotherm. Regarding the three-parameter models in Fig. 5, the non-linear regression curves and laboratory data were very compatible. Typically, if the number of model parameters is increased, the error of the fitting is decreased because the model fits better. Therefore, in the three-parameter models it is expected that the predicted values be more close to the experimental values. This causes these models to have a high coefficient of determination (R2).

Fig. 4
figure 4

Non-linear plot of two-parameter isotherm models fitted to the experimental data (T = 293 K, pH = 8.7, Ti-XAD7 dosage = 5.05 g/L, time = 120 min)

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Fig. 5
figure 5

Non-linear plot of three-parameter isotherm models fitted to the experimental data (T = 293 K, pH = 8.7, Ti-XAD7 dosage = 5.05 g/L, time = 120 min)

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Adsorption kinetics

In this study, four different kinetic models (Elovich, Intraparticle diffusion, pseudo-first-order, and pseudo-second-order) were applied to test the kinetic data. The best fitted equation was identified by applying the R-squared (R2). The model with the highest R2 value was selected as the best model. Table 15 shows the kinetic constants and R2 values obtained by the nonlinear method.

Table 15 Kinetic parameters for the Cr(VI) removal via Ti-XAD7 (T = 293 K, pH = 8.7, Ti-XAD7 dosage = 5.05 g/L)
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As a result, when the initial concentration of Cr(VI) was 2.75 mg/L, the Elovich model was the best model. On the other hand, the pseudo-first-order model with the lowest R2 value was selected as the worst model (see Fig. 6). The significant difference between the q0 value obtained from the Langmuir model (2.7 mg/g) and qe value obtained from the pseudo-second order and pseudo-first order (0.285 and 0.245 mg/g, respectively) can indicate that chromium adsorption onto Ti-XAD7 is not controlled by the perfect pseudo-second or pseudo-first order reaction [62]. The assumption of the Elovich model is based on the presence of the heterogeneous active sites on the adsorbent that are related to the activation energy for chemisorption [62]. The adsorption kinetics at this initial concentration of Cr(VI) followed the Elovich model with a high correlation coefficient (0.978). The kinetic results of this study were consistent with adsorption of Cr ions onto various adsorbents such as the powder of potato peelings as a low cost sorbent [63], and aluminosilicate minerals in their Pb-exchanged forms [64].

Fig. 6
figure 6

Plot of adsorption kinetic equations for sorption of Cr(VI) onto Ti-XAD7 (T = 293 k, pH = 8.7, dosage = 5.05 g/L)

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Conclusions

According to the results, Cr(VI) was successfully removed from aqueous solution by Ti-XAD7. CCD and RSM were used for process modeling and optimization. The optimum conditions of initial Cr(VI) concentration, contact time, pH, and Ti-XAD7 dosage for the adsorption process were 2750 ppb, 51.53 min, 8.7, and 5.05 g/L, respectively. According to the results, chromium can be removed by this adsorbent at pH >7. Thus, the adsorbent can remove Cr(VI) without pH change. In summary, Ti-XAD7 is efficient compared with XAD7 for Cr(VI) removal from aqueous solutions.