Modelling and optimization of hexavalent chromium removal from aqueous solution by adsorption on low-cost agricultural waste biomass using response surface methodological approach

In this study, response surface methodology (RSM) approach using central composite design (CCD) was investigated to develop mathematical model and to optimize the effects of pH, adsorbent amount and temperature related to the hexavalent chromium removal by biosorption on peanut shells (PSh). The highest removal percentage of 30.28% was found by the predicted model under the optimum conditions (pH of 2.11, 0.73 g of PSh and 37.2 °C) for a 100 mg/L initial Cr (VI) concentration, which was very near to the experimental value (29.92%). The PSh was characterized by SEM, EDX, FTIR, BET, XRD analysis. Moreover, Langmuir isotherm ﬁ tted well ( R 2 ¼ 0.992) with the experimental data, and the maximum adsorption capacity was discovered to be 2.48 and 3.49 mg/g respectively at 25 and 45 °C. Kinetic data was well foreseen by pseudo second order. Thermodynamic study depicted that biosorption of Cr(VI) onto PSh was spontaneous and endothermic. Regeneration of the PSh using NaOH showed a loss , 5% in the Cr (VI) removal ef ﬁ ciency till three recycle runs. In summary, the Cr (VI) removal onto economic, sensitive and selective biosorbent (PSh) optimized using CCD to study biosorption behaviors. hexavalent chromium ions removal (Mondal et al. 2017). The agricultural products enclose some compounds, including lignin, pectin, cellulose, hemicellulose, which possess effective functional groups with great af ﬁ nity to Cr (VI) ions (Ali et al. 2016). In addition, they have been used owing to their low cost, renewability, sustainability, rich surface with functional groups and biodegradability (Dai et al. 2018). Several studies were focused on the ef ﬁ ciency of various biosorbents for Cr(VI) removal such as potato peels (Mutongo et al. 2014), peapod (Sharma et al. 2016), rice straw (Gao et al. 2008), barks of acaciaalbida (Gebrehawaria et al. 2015), teff straw (Tadesse et al. 2014). Recently, agricultural wastes such as pineapple core (Rosales et al. 2019), tea (Çelebi 2020), sugarcane bagasse (Karri et al. 2020), mango kernel (Akram et al. 2017), phragmites australis and ziziphus spin-christi (Mahmoud et al. 2020), fruit peel (Ben Khalifa et al. 2019; Wang et al. 2020) showed good results in the adsorption of Cr (VI) ions. Nag et al. have studied the ef ﬁ cients of diverse natural biomaterials including mango, jackfruit, bamboo leaves, onion and garlic peel, coconut shell and acid-treated rubber leaf for Cr(VI) removal from aqueous solution. Their results showed maximum capacity of 35.7 mg/g for mango leaf and the sequence of adsorption capacity was found to be mango leaf . jackfruit leaf . acid-treated rubber leaf . onion peel . bamboo leaf . garlic peel . coconut shell, at a lower pH solution (Nag et al. 2020). Another study done by Rambabu et al. showed Cr (VI) removal ef ﬁ ciency of 58.02% using date palm empty fruit bunch wastes (Rambabu et al. 2020). and by using Boehm and pH zero charge methods. The signi ﬁ variables (pH, adsorbent and temperature (°C)) affecting Cr (VI) were studied and using with CCD according to the Function kinetics and studies This work reports recovery after necessary for sustainable application of peanut shells in treatment.


Adsorbent preparation
The peanut shells (PSh) were collected from a local center of preparation of shell-removed peanut in Kelibia, Tunisia. The raw feed stocks were washed three times with tap water to remove all the adhering dirt. Then, they were washed three times with distilled water. The wet material was dried in the oven at 80°C for 24 hours and was ground using a mortar. The resulting powdered PSh was sieved to obtain a particle size less than 250 μm. Table 1 shows some physical and chemical proprieties of peanut shells powder.

Characterization of the PSh
In this study, the morphology and structure of PSh were carefully investigated through various measurements. The surface functional groups of PSh were estimated by the Boehm method (Valentín-Reyes et al. 2019). This method is based on the neutralization of oxygenated functions by three bases having different strengths, sodium carbonate (Na 2 CO 3 ), sodium bicarbonate (NaHCO 3 ) and sodium hydroxide (NaOH) in order to determine the nature and amounts of surface functionalities among carboxylic, phenolic and lactonic groups (Kim et al. 2012). 0.5 g of PSh was added to 50 mL of the three mentioned basis and HCl (0.1 mol/L). After 24 h, the basic functions were titrated with HCl (0.1 mol/L) and the acidic with NaOH (0.1 mol/L).
The pH of zero charge (pH pzc ) was determined by mixing 0.15 g of PSh with a solution 0.01 mol/L NaCl. The pH of each sample was adjusted to different values from 2 to 12 (2 units increment) using HCl (1 and 0.1 mol/L) and NaOH (1 and 0.1 mol/L). After 24 h the final pH of solutions was measured and the point of intersection of pH final versus pH initial was noted as pH pzc of PSh. The pH pzc of a material refers to the pH value for which the net charge on the surface of the material is zero (Norouzi et al. 2018).
Fourier transform infrared spectroscopy (FTIR) of the PSh was conducted by Bruker Vertex 70 model, in a spectral range of 400-4,000 cm À1 . The PSh was also characterized by X-ray Diffraction (XRD Model: PANalytical X-ray diffractometer) to identify the surface groups and phase identification. Microstructure and morphology of the native PSh was carried out using Hitachi S-4800 scanning electron microscope (SEM) operating at 20 kV. The elemental composition of PSh was determined using Energy Dispersive X-ray Spectrometer (EDX). The surface area and pore size of the biosorbent was determined using nitrogen adsorption isotherms at 77 K recorded with a Micrometrics Surface Area Analyzer (ASAP 2020, Micrometrics Inc, USA) after degassing at 100°C overnight.

Batch biosorption experiments
The adsorption experiments were performed to study the effect of various operating parameters on adsorption. Batch biosorption of Cr (VI) on PSh was carried out in erlenmeyer conical flask with constant time of 45 min and constant agitation speed of 125 rot/min. Adsorption tests were conducted to investigate the effects of solution pH (2.11-9.22), adsorbent amount (0.07-0.73 g) and temperature (12.70-37.20°C) on the optimization of Cr (VI) adsorption on PSh. Solutions with different concentrations of hexavalent chromium in the range of 10-250 mg/L Uncorrected Proof were prepared from the stock solution (1,000 mg/L). 50 mL of each solution was shaken at the same speed using a shaking water bath 'OLS 200 Grant'. After filtration, the Cr(VI)concentration in the filtrate was determined by the 1, 5 diphenylcarbazide method using ″VWR UV-1600PC″ spectrophotometer at 540 nm. The percentage removal of Cr (VI) and the amount of adsorbed Cr (VI) qe (mg/g) were respectively computed using the Equations (1) and (2): where q e (mg/g)refers tothe Cr(VI) adsorption capacity, C 0 and C e (mg/L) are, the initial and equilibrium Cr(VI) concentrations respectively. Moreover, V (L) is the solution volume and m (g) is the adsorbent weight.

Statistical design of experiments
Experimental designs grant maximum efficiency using the smallest number of trials and, consequently the minimum cost. It is usually suitable for concurrent optimization of the effect of variables to improve the efficiency attributes and decrease errors with the least possible number of runs (Adio et al. 2017). Central Composite Design (CCD) as a broadly appropriate optimization method allows the approximation of coefficients in a mathematical form and predicts the reaction and the validation of method (de Carvalho et al. 2016). In this study, three factors pH (X 1 ), adsorbent amount (X 2 ) and temperature (X 3 ) were applied for hexavalent chromium removal percentage at five levels utilizing the STATISTICA 10.0 with 20 runs. Table 2 illustrates the experimental design points with the coded values of variables used in the matrix of experiments (À1.68(α), À1, 0, þ1, þ1.68(α)) having of 2 k axial points, 2 k factorial points and six central points. The central points were used to evaluate the data reproducibility and the experimental error. The second order polynomial model can be used to estimate the mathematical relation between the three independent variables by Equation (3) (Melliti et al. 2021): where Y refers to the predicted response (the percentage of Cr(VI) removal), while b 0 is the constant coefficient, b i shows the linear coefficient, bii represents the quadratic, and bij shows the interactive coefficient. Moreover, X i and X j correspond to the independent variables; ɛ and k respectively represent the residual error and the number of the independent variables. The design was arbitrarily performed to reduce the effect of non-controlled variables. Furthermore, this design enables approximating quadratic effects and the main interaction. The Response Surface Methodology (RSM) was utilized to allow the considerable specification and assessment of the relative factors and resolve multivariate equation to acquire an optimum response. The modeling was conducted by adjusting the first or second order polynomial equations to the experimental reactions. Then, the variance analysis (ANOVA) was investigated to identify the essential effects of the variables and their interactions on the chromium removal process. Plotting tridimensional graph was performed to make the surface response used for predicting the optimum working conditions based on the p-value and F-value. After the generation of polynomial model (Equation (3)), the desirability function (DF) was found to optimize the Cr (VI) adsorption process. The main advantages of DF are its ability to obtain qualitative and quantitative responses by simple and quick transformation of different responses for one measurement (Asfaram et al. 2015). The experimental response was converted to DF values, it is in the range of 0-1. The 1 indicates the maximum desirability and 0 the minimum desirability. Based on the study of S. Harbi et al., the DF equation can be expressed as follows (Harbi et al. 2016): α and β are the lowest and highest obtained values for the response U i (i ¼ 1, 2, 3…, n) respectively, and w i is the weight. The individual desirability scores for each predicted response are then combined on a single overall DF, which is calculated to find the optimum set of input variables as following: where df i indicates the desirability of the response U i and v i represents the importance of responses.

Regeneration
Reusability of the biosorbent is very essential factor that influences the process economics of the biosorption system, precisely towards the operational costs of the process . 0.73 g of PSh was treated with 100 mg/L of Cr (VI) solution for 45 min at the optimum conditions (pH (2.11) and temperature (37.2°C)). Cr (VI) loaded adsorbent was filtered, dried overnight at 80°C and transferred into a series of flasks containing 0.1 M of sodium hydroxide, 0.1 M of sodium chloride and distilled water. Saturated adsorbent was then agitated at 125 rot/min for 45 min with all desorption solutions. The temperature of 25°C was chosen

Adsorbent characterization
The intersection of the curve final pH ¼ f (initial pH) with the bisector corresponds to the pH pzc of PSh as shown in Figure 1 was equal to 4.6. Therefore, when the pH of the solution is lower than4.6, the adsorbent surface is charged positively. On the contrary, for pH values above 4.6,the surface is charged negatively (Raza et al. 2015). The amounts of basic and acidic groups found in PSh are presented in Table 3. Obtained results proved that the adsorbent had more acidic functional groups at the surface. The distribution of the acidic functional groups differs: the carboxylic functions represent 31.03%, the phenolic functions 6.90% and the lactones 62.07%. These results are perfectly consistent with the pH of zero charge found previously (4.6). Omorogie et al. was found quit similar value for Nauclea Diderrichii seed biomass waste equal to 4.9 (Omorogie et al. 2016).
The FTIR spectrum of peanut shells is shown in Figure 2(a). The broad peak at 3,313 cm À1 is an indicator of O-H group suggesting the presence of phenols and alcohols which proves the presence of cellulose and lignin in the PSh sample (Tasar et al. 2014). The peak observed at 2,922 cm À1 is attributed to C-H stretching vibration of lignocellulosic components proving the presence of methyl and methylene groups (Ding et al. 2012). The peak situated at 1,724 cm À1 was ascribable to carbonyl group C ¼ O stretching vibrations of hemicelluloses. The absorbance peak at 1,627 cm À1 is characteristics of aromatic C ¼ O stretching vibrations in associated carbonyl of lignin. The peak around 1,509 cm À1 may be attributed to C ¼ C vibration of an aromatic cycles of lignin (Bayuo et al. 2019). The peak appearing in 1,030 cm À1 indicates the presence of C─O bonds. The phenol (OH), Carbonyl (C ¼ O) and carboxylic (COOH) groups are essential sorption sites (Lugo-Lugo et al. 2012). The existence of -OH group coupled to carbonyl group, confirms the presence of carboxylic acid groups in the biomass (Chigondo et al. 2013). The slight shifting of bands after adsorption of Cr (VI) ions is due to the chemical interaction confirming the sorption of PSh to chromium ions from wastewater (Banerjee et al. 2019). Zhao et al. (2020) reported a FTIR spectrum of peanut shells presenting similar bands.
XRD patterns of the material was determined by X-ray diffraction using a PANalytical X-ray diffractometer applying CoKα irradiation (λ ¼ 1.79 Å) operated at 40 kV and 30 mA. The scanning scope and scanning speed were 10°-120°. The XRD pattern (Figure 2(b)) of peanut shells showed typical spectrum of cellulosic material having main and secondary peaks at 2θ of 24°and 16°, respectively. The major peak is an indicator of the presence of highly organized crystalline cellulose, while the minor rather weak peak is an indicator of a less organized polysaccharide structure (Zhu et al. 2009). The intensity of these peaks depends on the amount of cellulose present in the biomaterials (Prithivirajan et al. 2016). The conclusion is accordant with that of the FT-IR analysis.

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The SEM micrographs of peanut shells at different magnifications were shown in Figure 3. As presented in Figure 3(a), the surface of PSh is porous, irregular and has different shapes. Inside the peanut shells matrix, a great numbers of pores were observed at higher magnification (Figure 3(c)). A variety of shapes were also observed, for example spiral tubes shapes ( Figure 3(b-1)) and cavities ( Figure 3(b-2)). These biomasses formed a unique and natural porous arrangement during plant growth. The surface of the PSh after the adsorption of Cr (VI) (Figure 3(d)) turned to be less porous on the PSh surface, indicating successful loading of Cr (VI) molecules on the PSh surface (Jawad et al. 2020a).
The EDX spectra results and the weight percentages (wt. %) of PSh are given in Figure 2(c). The amounts of C and O loaded on the surface with weight percentages of 68.68% and 30.01% respectively are rather high compared to Na, Mg, Cl and Ca loading. The Nitrogen adsorption-desorption isotherms of PSh was also obtained and shown in Figure 2(d), The isotherm is type-IV with broad H3 hysteresis loop as defined by the International Union of Pure and Applied Chemistry (IUPAC) classification (Thommes et al. 2015), which is characteristic of mesoporous materials. The specific surface areas pore volume and pore size of PSh was calculated to be 0.8126 m 2 /g, 0.0020 cm 3 /g and 8.9339 nm, respectively. Tasar et al. was studied the removal of lead (II) on peanut shells and was found similar surface area of 0.8444 m 2 /g, and average pore diameter of 20.72 Å using a Micromeritics ASAP 2020 apparatus. The pore volume was calculated as 0.000471 cm 3 /g (Tasar et al. 2014).

Effect of contact time
Contact time was evaluated as one of the most essential factors affecting the biosorption efficiency. The Figure 4(a) showed that the Cr (VI) adsorption increased over time until reaching equilibrium after 45 minutes. The fast adsorption in the beginning is due to the availability of a high number of empty sites, and then the saturation is due to the saturation of adsorbent sites. Therefore, the optimum contact time was chosen as 45 min for

Effect of adsorbent amount
The effect of adsorbent amount was studied to get an idea about the range which is used for the experimental design. It can be seen in Figure 4(b) that the % Cr (VI) removal increased gradually from 4.05 to 22.33% with the increase in the mass of the adsorbent from 0.05 to 0.7 g and remained practically constant at adsorbent quantities higher than 0.7 g. This is due to the increase in the contact area and the number of adsorption sites and thus making easier penetration of Cr (VI) to the adsorption sites. Since the quantity of hexavalent chromium ion is stable, a raise in the amount of adsorbent over a quantity that can completely adsorb the available Cr (VI) had no clear effect on further enhance of percent adsorption. In addition, the Lack of Fit (LOF) is the difference of the values around the model fitted to experimental values. LOF is an exacting experiment for adequacy of model fit with no influences of extra higher-order terms. The inefficiency of this model for fitting the data results in significant value. The P-value of LOF is 4.2 10 À5 (Table 4), verifying the fitting applicability of this method for well-fitting of the response. The validity of the polynomial model was checked by completing the coefficient of determination (R 2 ). The large values of R 2 ¼ 0.972 and adjusted R 2 ¼ 0.947 indicate that the data predicted by the model correlated well with what is found experimentally. The Equation (4) was used to estimate the influence of the factors studied on the removal of chromium by adsorption on PSh: R% Cr(VI) ¼ 6, 736 À 5, 143 X 1 þ 1, 689 X 2 þ 1, 856 X 3 þ 3, 059 X 2 1 þ 0, 003 X 2 2 þ 0, 188 X 2 3 þ 0, 273 X 1 X 2 À 0, 288 X 1 X 3 À 0, 231 X 2 X 3 (6)  where X 1 , X 2 and X 3 respectively refer to the real values of the independent variables related to pH, adsorbent amount and temperature. A Pareto chart was used mainly to recognize the factors that have the most cumulative effect on the system and thus abandon the less significant factors (Figure 5(a)). The frequency or impact of parameter is indicated by the length of each bar in the diagram. The positive coefficients indicate a desirable effect on the efficiency of Cr (VI) removal while the negative coefficients for the model indicate an undesirable effect. It can be seen from Figure 5(a) that the pH was the most influencing factor on the removal of chromium followed by the temperature and the adsorbent amount (Mahmoud et al. 2016). The signs of coefficients showed that the adsorbent amount and the temperature had positive effects, while the pH had a negative effect on the chromium removal.
The adequacy graph of the model (Figure 5(b)) prove that the experimental results (R %) are very close to the values calculated by the model, insuring an accuracy of the model for favorable and real prediction of the results. It is clear that there is no obvious pattern followed in the observed values versus the residuals (Figure 5(c)). Figure 5(d) presents the histogram of raw residual, in which the arbitrary template of the residuals as well, announces the adequacy of the model.

The effects of variables on Cr(VI) adsorption efficiency
To make easy the determination of the interactions between the factors and the identification of the main factors influencing the response, we resorted to the use of 3D surface plots (Fakhri 2014). The factors were taken in our case two by two in each figure while the third variable is maintained at level zero (in coded term). These plots are presented in Figure 6. From these interaction plots, it is noticed that there are very slight curvatures between the factors studied (pH, adsorbent amount and temperature) which affirm that there are very slight interactions between these factors, as it had already been shown by the statistical analysis of Pareto. Figure 6(a) shows the interaction connecting pH and adsorbent amount in the adsorption process of chromium on PSh. As shown, the removal percentage of Cr (VI) sharply increases by decreasing pH (from 10.0 to 2.0). For pH less than 2.5 ( Figure 6(a)), the adsorption efficiency was maximum. This can be explained by chromium species distribution and the pH of zero charge (pH PZC ) of the biomass. At lower pH (pH , pH PZC ) , the HCrO 4 À and Cr 2 O 7 2À ions are the predominant chromium species and the surface of biosorbent gets positively charged (Haroon et al. 2016). Therefore, the improvement of the Cr (VI) uptake at lower pH could be due to the electrostatic attraction between the biosorbent surface and the chromium species in solution. In contrary at higher pH(pH . pH PZC ), there is an electrostatic repulsion between the CrO 4 2À ions present mainly in the solution and the surface of the adsorbent charged negatively. Similarly, Figure 6(c) presents the effect of adsorbent amount and temperature on Cr (VI) removal while pH is constant. A grow in both adsorbent mass and temperature increased the percentage of Cr (VI) removal awaiting the optimum conditions were reached. Indeed, the number of abundant bonding sites on the PSh surface increased when adsorbent was added which caused the improvement of the chromium adsorption efficiency. The removal yield was better for the higher temperatures (Figure 6(b) and 6(c)). This result indicates that the Cr (VI) uptake on PSh is an endothermic in nature The increasing in removal yield of Cr (VI) at high temperature can be attributed to the effect of temperature on the internal structure of the PSh, thus facilitation the diffusion of Cr (VI) ions in the PSh interspaces structure (Jawad et al. 2020a). Ben Ali et al. (2017) outlined that the biosorption on pomegranate peels was endothermic. The increase of adsorption efficiency with temperature suggests that active sites at the surface of the adsorbent available for adsorption increased with temperature. It may possibly also lead to some changes of the pore size which becomes larger and to a relative increase in the diffusion of the chromium ions due to the solution viscosity decreasing.

Optimum conditions
Maximum adsorption efficiency for Cr (VI) by PSh and the corresponding optimal experimental conditions were determined by the desirability function (Asfaram et al. 2017) (Figure 7). The profile for predicted values and DF developed by STATISTICA 10.0 software. The measure in the range of 0.0 (unpleasant) to 1.0 (very pleasant) was employed to obtain a global function (D) which must be maximized based on the efficient optimization and selection of the considered variables. As claimed by the results of the CCD design matrix in Table 2, the minimum and maximum Cr (VI) removal are respectively are equal to 1.94% and26.29%. In conformity with these values, desirability function (DF) settings for each removal percentage as dependent factor are shown on the right side of Figure 7. The optimal conditions for chromium removal are a pH equal to 2.11, an adsorbent mass of 0.73 g and temperature of 37.2°C. The maximum chromium removal percentage obtained from DF is 30.28%.
To verify the results given by the model, the experiment was repeated three times using the optimal conditions given by the software. The results showed an average Cr(VI) adsorption efficiency of 29.49 + 0.8% which is near to the predicted value as revealed in Figure 7.

Mechanism of the biosorption of Cr (VI) on PSh
The biosorption mechanism of Cr (VI) ions on PSh surface associated perplexing adsorption chemistry with coexistence of several interactions. Generally, four main steps explain the mechanism of the biosorption of Cr (VI) ions at the surface of biosorbents rich in lignocellulose and hemicellulose. These steps are: (1) adsorption coupled reduction, (2) an anionic adsorption, (3) reduction and cationic adsorption and (4) cationic and anionic adsorption (Fan et al. 2017). Based on the PSh characterizations and the biosorption experiments obtained, a possible biosorption mechanism for the Cr (VI) ions removal by PSh could be planned through the adsorption-coupled reduction pathway. Figure 8 describes the hexavalent chromium biosorption mechanism on PSh surface. The different surface functionality of PSh which contained various functional groups such as -OH, -NH 2 , -COO, -COC, C ¼ C (as showed through FTIR analysis) played a main role in the adsorption-coupled reduction mechanism. The mechanism suggested three main steps for the capture of Cr (VI) ions from the bulk phase to the solid phase. Thus, the Uncorrected Proof first step implicated the rapid adsorption of the Cr (VI) ions on these functional sites on the PSh surface by electrostatic attraction, following a surface protonation of PSh sites (Islam et al. 2019). Moreover, surface complexation facilitated the Cr (VI) ions uptake by the PSh sorbent owing to the presence of carboxyl groups. Besides, the adsorbed Cr (VI) ions on the PSh sustained a heterogeneous redox reaction to form Cr (III) ions, as represented by the Equation (7) (Fan et al. 2017): The strongly acidic medium provided an excess of H þ ions for the reduction of chromium from its Cr (VI) nature to the Cr (III) state. Lastly, the reduced Cr (III) was more efficiently attracted to functional sites by electrostatic attractions and surface complexation. The greater affinity of Cr (III) ions for active anionic sites on the surface of the PSh improved the anchoring of chromium ions on the PSh biosorbent (Islam et al. 2019).

Adsorption equilibrium modeling
Adsorption isotherms were employed using four different models in order to elucidate the biosorption performance. Generally, adsorption isotherms including Langmuir, Freundlich, Dubinin-Radushkevich and Temkin present precious information about adsorption process, surface properties and adsorbent tendency. The adsorption experiments were conducted at four temperatures 283, 298, 308 and 318 K and for chromium concentration in the range of 10-250 mg/L. The Cr (VI) adsorption isotherms on peanut shells provided by the origin Pro version 8 software are represented in Figure 9. The non-linearized equations with the corresponding constants presented in the literature (Surip et al. 2020) are summarized in Table 5.
The chi-square test χ 2 is a statistical tool used to recognize well between the adopted models because of the small difference between their regression coefficients was calculated according to the Equation (8) (Appa et al. 2019): According to the values of R 2 and χ 2 in Table 5, Langmuir model was the model which had the highest values of correlation coefficients R 2 which represents an excellent regression; in addition it had the lowest values of the chi-square χ 2 at different temperatures. Therefore, Langmuir model was the most suitable model to describe the bioadsorption phenomenon of hexavalent chromium on PSh. This proved that the biosorption of Cr (VI) on PSh involved monolayer adsorption on the active sites of the material (Khammour et al. 2021).

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In order to predict whether the adsorption process is favorable or unfavorable, the separation factor R L was calculated by Equation (9) (Rangabhashiyam et al. 2019): were C 0 (mg/L) refers to the initial concentration of chromium and K L (L/mg) represent the Langmuir constant. The R L values allowed a prediction of the shape of the isotherm and the nature of the adsorption process. For a favorable adsorption (Mahmoud 2020), 0 , RL , 1, while RL . 1, RL ¼ 1 and RL ¼ 0 represent unfavorable monolayer adsorption process, linear [51], and irreversible adsorption process, respectively (Ali et al. 2019). According to the calculated results of separation factor in Table 6, it can be seen that the values of R L are between 0 and 1, which proved that the adsorption of chromium on the peanut shells was favorable. Besides, the R L values decreased with the increase of the initial concentration, which showed that the adsorption was favorable for high initial concentrations.
The values of the Freundlich constant n F shown in Table 6 decreased with the increase of temperature, which implied a decrease in adsorption intensity. Moreover, the values of 1/n F were less than unity, indicating favorable adsorption of chromium under the conditions studied. The value of the adsorption energy E (kJ/mol) determined by the model D-A can be used to expect the adsorption process nature; it is given as follows by Equation (10):

Uncorrected Proof
Physisorption occurs in the range of 1-8 kJ/mol, while for values more than 8 kJ/mol, chemisorption is ruling (Touihri et al. 2021). The values of E in Table 5 indicated the physical adsorption of Cr (VI) on PSh. In addition, the values of the heterogeneity factors n D were higher than 3 proved the homogenization of the adsorbent sites. On the other hand, as seen from Table 5, the adsorption heat b T of the Temkin model increased with the increase of temperature from 283 to 318 K proving that Cr (VI) adsorption on PSh was endothermic.
The performance of different adsorbents and their maximum Cr (VI) adsorption capacity is presented in Table 7. The Tunisian peanut shells have a relatively high adsorption capacity (3.489 mg/g) compared to other biomasses, confirming the suitability of the suggested use of PSh for the removal of Cr(VI). PSh proved a good adsorption capacity compared to some activated biomasses such as banana peel (Ali & Saeed 2015), barks of Acacia albida (Gebrehawaria et al. 2015) and leaves of Eucleas Chimperi (Gebrehawaria et al. 2015). The present biosorbent was able to remove 30.28 mg/L of Cr (VI) from wastewater which is a high concentration removal compared to other biomasses.
Many connections for binding Cr (VI) to the surface of PSh might be explained by one or more of these bonds as follows: (I) Electrostatic interaction of the chromium metal with charged surfaces on the PSh, (II) Surface area, total pore volume and pore size obtained by such kind of biomass, and active sites including and -OH and -COOH groups in PSh play an important role in chromium removal process.  The kinetic experiments of Cr (VI) removal were analyzed using the non-linear form of the pseudo-first-order, pseudo-second-order and Elovich models (Huynh et al. 2020;Mohammed et al. 2020). The kinetics of PSh data obtained from the experiments of concentration of 100 mg/Lat various contact times, and optimum conditions obtained previously along with the equations and constants are shown in Table 8. In addition the nonlinear plots of the three models are illustrated in Figure 10. As shown in Table 8, the pseudo second order kinetic model has the lowest chi-square value χ 2 and the highest correlation coefficient R 2 comparing with the other models (first order and Elovich). So the pseudo second order model indicated excellent applicability for describing the chromium (VI) adsorption process on peanut shells. In addition, the values of the calculated qe from the pseudo second order model was close to the values of the experimental q e,exp suggesting that the Cr (VI) adsorption may be due to electrostatic attraction between the positively   Yi et al. (2017) proved that the adsorption of chromium on litchi peels follows the pseudo second order.

Adsorption thermodynamic study
The thermodynamic parameters were calculated using Equations (11)-(13): where DG T is Gibbs free energy (kJ/mol), DS T is the standard entropy (J/mol K), DH T is the standard enthalpy (kJ /mol), Kc is the thermodynamic equilibrium constant (L/g), R the universal gas constant (8.314 J/mol K), T is temperature (K), C a and C e are respectively the equilibrium concentrations of metal ions on the adsorbent (mg/g) and the equilibrium concentrations of metal ions in the solution (mg/L). The curve relating Ln (K c ) to 1/T ( Figure 11) allows the resolve of the thermodynamic parameters presented in Table 9.
The decrease in ΔG o values with an increase in temperature proves that better biosorption occurred at high temperatures (Aditya et al. 2012).Moreover, the positive value of ΔH o proved that the adsorption process was endothermic (Iftekhar et al. 2017).This conclusion is in agreement with the results proving the increase in Cr (VI) removal yield with temperature. In addition, the positive value of ΔS ○ indicated an increase in the disorder between the solid and solution interface during the adsorption process. Hlihor et al. (2017) have found similar  results saying that the adsorption of Cr (VI) on dead and living Arthrobacter viscosus biomass is endothermic due to the positive value of ΔH o . A positive value of ΔS ○ reflects the affinity of biomass towards chromium ions in aqueous solution.

PSh reusability and Cr (VI) recovery
Desorption is required to manage the biosorbent waste to avoid the generation of secondary waste and recovery of valuable materials. As low pH (pH ¼ 2.0) was favorable for Cr(VI) uptake, recovery of consumed PSh was performed using 0.1 M NaOH solvent as a basic desorbent, 0.1 M NaCl and deionized water as a neutral desorbents. Figure 12 showed the outcomes of the PSh biosorbent reusability. From the different regenerants studied, it was detected that NaOH provided the best regenerability outcomes for the PSh biosorbent as shown in Figure 12. The biosorbent suffered a friendly loss of ,5% in chromium ions recovery efficiency till 3 recycle runs when washed with NaOH solvant. Desorption of Cr (VI) from the PSh biosorbent surface at strong basic pH environment can occur due to the exchange of CrO 4 2À (the dominant species of Cr (VI) in alkaline solution) with hydroxyl ions (Ye et al. 2019). Daneshvar et al. was found similar results studying Cr (VI) desorption by NaOH solution at pH 12 (Daneshvar et al. 2019). They assured that attacking on adsorption sites by OH À ions led to Cr (VI) desorption. In another work, the maximum desorption efficiency of Cr(VI) was noted as 98.45% by 0.8 M NaOH solution (Akram et al. 2017).They explained that by the electrostatic repulsion, due to negatively charged sites of sorbent, increases Cr(VI) desorption from the adsorbent. To make the desorption process more environmental friendly, desorption of Cr (VI) efficiency was also investigated using NaCl and deionized water. However, the loss in Cr (VI) removal efficiency by the regenerated biosorbent was .5% after the first recycle run.. In agreement with our results, Cheng et al. found extremely low Cr(VI) efficiency desorption using deionized water (.3%) and high desorption efficiency (,84%) using NaOH solution (Cheng et al. 2011). They concluded that desorption of Cr (VI) by chemical adsorption and ion exchange mechanisms is more efficient than desorbed during washing by deionized water. Uncorrected Proof

CONCLUSION
Hexavalent chromium removal from aqueous solution is a worldwide environmental concern. Studies have used diverse processes to attain a Cr(VI) free environment or achieve the stringent guidelines of governmental rules. In this study, a response surface methodology (RSM) with Central Composite Design (CCD) was used to develop mathematical model and optimize process conditions (pH, adsorbent amount and temperature) for Cr (VI) removal from wastewater by biosorption on PSh with a less number of experiments. The value of the adjusted coefficient of determination R 2 ¼ 0.972 showed that the % removal of Cr (VI) predicted by the model is correlated with that found experimentally. ANOVA study shows the significance of generated models and depicts that pH has the most significant effect on response which has substantial effect on the removal efficiency of Cr (VI). Temperature and adsorbent amount have comparatively less significant effects on the response of Cr (VI) removal yield. The optimal parameters to remove Cr (VI) from aqueous solution at constant short time of 45 min and constant initial Cr (VI) concentration of 100 mg/L using PSh were found to be pH 2.11, biosorbent amount 0.73 g and temperature of 37.2°C. At these conditions maximum chromium removal (29.49%) was achieved, which was rather near to the predicted value (30.28%) obtained from RSM model. Peanut shells were characterized by SEM, EDX, FTIR, BET, XRD, Boehm method and pH zero charge analyses. The isotherm and kinetic data were described by Langmuir and the pseudo-second order models, while maximum adsorption capacity attributed to Langmuir model was 3.49 mg/g for 0.73 g PSh at 318 K. This biosorbent was an efficient material despite its low specific area. The thermodynamic analysis also demonstrated that the biosorption process was endothermic as did the positive heat of enthalpy ΔH o , accompanied by a positive value of entropy change ΔS o . The PSh waste biomass proved good regeneration potential, precisely with NaOH washing, up to three successive biosorption runs. The results of this study proved that the reported material is efficient to remove 30.28% from 100 mg/L of Cr (VI) from aqueous solutions. The material has advantages such as shortest sorption time, easy to use, economic, sensitive and selective for the removal of hexavalent chromium from wastewater samples.