Introduction

Toxic heavy metals are often released into the ecosystem through agricultural and industrial activities and spread into the natural environment, and their presence in the environment may be harmful to people, plants and animals. These inorganic micro-pollutants are nonbiodegradable, extremely toxic and have a carcinogenic consequence and other health-related problems (Cimino et al. 2000). Heavy metal ions are present in the biosphere and industrial wastewater and owing to their kinesis in the aquatic environment and toxicity; their presence in water media had turned out to be a main inorganic pollution problem. Discharge and treatment of aqueous solution containing poisonous metals and specific identification of the main sources of their pollution of water resources are imperative, because the acute, severe and persistent effects of these contaminants on the health of living species and on the sustainability of ecosystems are essential concerns in environmental protection (Bayuo et al. 2018).

Chromium is a common contaminant released into water media from various industrial wastewaters including those from the electroplating, tanning of leather, dyeing of textile and metal finishing industries (Ahalya et al. 2005; Faisal and Hasnain 2004). Chromium exists in different oxidation states. Trivalent Cr(III) and the hexavalent Cr(VI) species are the most common and stable forms, which exhibit quite distinct chemical properties such as bioavailability, mobility and toxicities (Lim and Aris 2014). Cr(VI) regarded to be the most lethal of chromium is readily mobile, a strong oxidizing agent, and has the ability to be absorbed via the skin (Park and Jung 2001). It is also capable of being accumulated in water, soil, plants and living tissues, consequently becoming concentrated throughout the food chain (Bayuo et al. 2019a, b, c).

Ion exchange, chemical precipitation, evaporation, solvent extraction, reverse osmosis, lime coagulation and electrolysis are conventional metal elimination techniques. However, these conventional procedures have some inherent restrictions including lower efficiency, sensitive operating conditions and secondary sludge production (Zarubica and Purenovic 2011) or other waste products, which require cautious disposal in further steps (Pandey et al. 2007). The most proficient and significant technology is the sorption of toxic metals from domestic to industrial wastewaters using activated carbon (Zarubica and Purenovic 2011). However, the expensive nature of the commercial activated carbon and its loss during regeneration limits its application (Sud et al. 2008).

Recently, alternative biosorbents for the decontamination of heavy metals from aqueous media have been considered with dependence on the adsorption capacities of waste materials, both organic and inorganic (Pandey et al. 2007). The materials that have been explored as biosorbents include agricultural and industrial waste materials such as groundnut shells (Bayuo et al. 2019a), Lagenaria vulgaris shell (Zarubica and Purenovic 2011) and peanut skins (Cimino et al. 2000). The major benefits of biosorption over conventional techniques include high efficiency, low cost, minimization of secondary sludge and the possibility to regenerate the biosorbent (Cimino et al. 2000). Agricultural waste materials with or without any modification have all been found to complex and sequester heavy metals (Bayuo et al. 2019a; Sud et al. 2008). This is attributable to their structural composition (cellulose, hemicellulose, lignin, proteins, lipids, simple sugars, hydrocarbons) and numerous functional groups such as carboxyl, carbonyl, hydroxyl, phenyl, ester, acetamido, amido, amino and sulphydryl found on the surfaces of biosorbents (Bayuo et al. 2019a).

In this work, the prepared unmodified adsorbent from Arachis hypogea shell was studied as a low-cost biosorbent for depolluting Cr(VI) from aqueous media. Statistical optimization of independent variables influencing the sorption process was examined with central composite design (CCD), a subset of response surface methodology (RSM) in Design-Expert software 12.0.0. Furthermore, three-parameter adsorption isotherm and kinetic models were explored to determine the models that best represent the equilibrium data.

Materials and method

Materials

The Arachis hypogea (groundnut) husks were collected from Kologo in Navrongo Municipal in the Upper East region of Ghana and use naturally as a biosorbent for the biosorption of Cr(VI) from water media. Arachis hypogea (groundnut) is a variety of leguminous crop which is a very essential legume found in Africa (Sellscope 1962). The types of Arachis hypogea are classified into a bunch and runner types. In the current study, the bunch type (Fig. 1a) was used and it has a well-built taproot with many lateral roots that outspread several inches into the soil. Most of the roots have nodules but bearing insufficient root hairs (Icrist 2005). The whole seed of Arachis hypogea is referred to as pod while the shell or husk (Fig. 1b) is the outer cover of Arachis hypogea. Groundnuts are an important plant in Ghana and are currently grown in temperate and tropical climates. Groundnut is an annual dicotyledon legume with a low growing plant and upright stem. In the whole of West Africa, Ghana has become the major groundnuts producer with the mainstream production coming from the North. Every year the northern parts of Ghana produce about 94% of groundnuts, and since 2004, groundnut production ranges between 400,000 and 450,000 MT (Owusu-adjei et al. 2017).

Fig. 1
figure 1

Arachis hypogea plant (a) and Arachis hypogea husks (b)

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All the chemicals used in the study, including potassium dichromate (K2Cr2O7), sodium hydroxide (NaOH), hydrochloric acid (HCl) and 1, 5-diphenylcarbazide, were of analytical grade obtained from Applied Chemistry and Biochemistry Laboratory of the University for Development Studies, Navrongo Campus, Ghana.

A 1000 mg/L Cr(VI) stock solution was prepared by dissolving 2.83 g of K2Cr2O7 in 200 mL of deionized water in a 1000-mL volumetric flask and toping up to the mark with deionized water. Various aqueous solutions of initial Cr(VI) concentrations were also prepared as required through the dilution of the stock solution to the desired volume using deionized water.

Preparation of adsorbent

The husks were locally collected and treated with distilled water to get rid of the attached dust and any other contaminations. The washed husks were dried in an oven at 105 °C for 24 h to constant mass and ground to form a powder using a mechanical grinder. Standard mesh size was used to sieve the powder into a size fraction ranged between 250 and 300 µm and utilized in all the adsorption experiments.

Physicochemical parameters of Arachis hypogea husk

The physicochemical parameters of the Arachis hypogea husk that were determined in the current study include moisture content, bulk density, surface area, pH and point of zero charge pH (\({\text{pH}}_{pzc}\)) of the biosorbent.

Characterization of adsorbent

The characterization of Arachis hypogea husk had been carried out in our previous study (Bayuo et al. 2019c) by way of Fourier transform infrared spectrometer to examine the surface functional groups of the adsorbent operating in the range 4000–400 cm−1. The characterization of the husk was done before and after the adsorption of  Cr(VI) ions. Additionally, a Quantachrome analyzer was applied to determine the BET surface area and pore size distributions of the obtained unmodified adsorbent.

Experimental design and statistical analysis

Central composite design (CCD) was applied as an optimization tool of RSM, to explore the impact of the independent variables on the sorption process. To determine the optimum conditions, three process independent variables were considered: Contact time (A), pH of the aqueous solution (B), initial Cr(VI) concentration (C) and their influences on the uptake capacity of Cr(VI) were investigated.

The CCD involves 2n factorial runs, 2n axial runs and nc center runs. The center points determine the experimental error and how well the data can be reproduced. The axial points are taken in a way to ensure ratability, and the model prediction variance is constant at every point equidistant from the center of design (Mourabet et al. 2017).

The total experimental runs conducted are computed by Eq. (1) (Owolabi et al. 2018):

$$\begin{aligned} N & = 2^{n} + 2n + n_{c} \\ N & = 2^{3} + 2\left( 3 \right) + 6 = 8 + 6 + 6 = 20 \\ \end{aligned}$$
(1)

where n is number of independent variables (factors), nc is number of center points and N is the overall total of experimental runs. This indicated that 20 experimental runs comprising 8 factorial runs, 6 axial runs and 6 center runs were prerequisites for the modeling and optimization process.

The experimental data obtained were studied by means of Design-Expert 12.0.0 software. The level of the considered independent variables and their experimental ranges for Cr(VI) adsorption capacity (Y) are presented in Table 1.

Table 1 Levels of the sorption process variables considered
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The purpose of the current study is to explore the optimum operating conditions for adsorption of Cr(VI) from aqueous media onto unmodified Arachis hypogea husk. However, the dependent variable (response) which is the adsorption capacity (Y) was determined through the batch technique and was used to develop an empirical mathematical model. The model relates the response (Y) to the three independent factors with a second-order polynomial expression as given in Eq. (2) (Bayuo et al.  2019b; Auta 2012)

$$Y = b_{0} + \mathop \sum \limits_{i = 1}^{n} b_{i} X_{i} + \mathop \sum \limits_{i = 1}^{n} b_{ii} X_{i}^{2} + \mathop \sum \limits_{i = 1}^{n - 1} \mathop \sum \limits_{j = i + 1}^{n} b_{ij} X_{i} X_{j}$$
(2)

where Y represents the response predicted, b0 is the coefficient constant, bi signifies linear coefficient, bij is the coefficient of interaction, bii connotes quadratic coefficient and \(X_{i}\), \(X_{j}\) mean, coded values of factors.

Batch adsorption studies

The batch experiments of the unmodified Arachis hypogea husk were conducted in a set of each 250-mL Erlenmeyer conical flasks containing 100 mL of the required concentration of an adjusted pH of Cr(VI) solution. The flasks were later capped and agitated at a constant stirring speed of 120 rpm. The experiments were carried out according to the experimental conditions obtained with experimental design (Table 5) for the required time intervals using magnetic stirrers until equilibrium operating conditions were achieved. Upon equilibrium attainment, the suspension of each sample was allowed to settle and filtered using Whatman 42 filter paper. The concentration of the Cr(VI) ions in the filtrate was determined spectrophotometrically (UV–Vis Spectrophotometer) by diphenyl-carbazide method (Bayuo et al. 2019c).

The Cr(VI) removal efficiency, RE(%) and amount of Cr(VI) adsorbed at equilibrium, \(q_{e}\) (Y), mg/g, were determined as given in Eqs. (3, 4) (Bayuo et al. 2019a):

$${\text{Removal}}\,{\text{efficiency}} \left( \% \right) = \left( {C_{O} - {\raise0.7ex\hbox{${C_{e} }$} \!\mathord{\left/ {\vphantom {{C_{e} } {C_{o} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${C_{o} }$}} } \right) \times 100$$
(3)

where Co is the initial Cr(VI) concentration (mg/L) and Ce is the equilibrium Cr(VI) concentration (mg/L).

$$q_{e} = \left( {C_{o} - {\raise0.7ex\hbox{${C_{e} }$} \!\mathord{\left/ {\vphantom {{C_{e} } m}}\right.\kern-0pt} \!\lower0.7ex\hbox{$m$}} } \right) \times V$$
(4)

where qe represents the equilibrium mass of the adsorbed substance per unit mass of adsorbent, V is the volume of solution (mL) and m is the mass of the adsorbent (g).

Equilibrium adsorption isotherm

The potentiality of three-parameter adsorption isotherm models (Redlich–Peterson and Jossens) was tested with the purpose of choosing the most suitable model that would best describe and predict the biosorption of Cr(VI) onto the unmodified Arachis hypogea husk.

Redlich–Peterson isotherm model

This model is experiential in nature consisting of three parameters and combines Langmuir and Freundlich models (Toth 1971). The model is a mix-type that joins elements from Langmuir and Freundlich isotherm models, and the mechanism of adsorption is hybrid in nature; hence, ideal monolayer sorption does not take place (Foo and Hameed 2009). Through the Langmuir isotherm, the numerator of the equation is obtained and with the potential of reaching Henry’s model through infinite dilution (Khan and Al-Haddad 1996). In addition, it shows linearized dependence on the concentration in the numerator and an exponential function in the denominator all denoting sorption equilibrium over vast solute concentration that is capable of being applied in homogeneous or else heterogeneous surfaces due to its versatility (Maximova and Koumanova 2008). The model can be expressed as in Eq. (5).

$$q_{e} = \frac{{AC_{e} }}{{1 + BC_{e}^{\beta } }}$$
(5)

where \(C_{e}\) denotes equilibrium concentration of the solute (mg/L), \(q_{e}\) represents equilibrium uptake capacity (mg/g), \(A\) (L/g), \(B\) (L/mg) connote the constants of the Redlich–Peterson model and \(\beta\) signifies an exponent positioned between 0 and 1. At a very high solute concentration in the liquid phase, Eq. (6) becomes the Freundlich model.

$$q_{e} = \frac{A}{B}C_{e}^{1 - \beta }$$
(6)

where \({\raise0.7ex\hbox{$A$} \!\mathord{\left/ {\vphantom {A B}}\right.\kern-0pt} \!\lower0.7ex\hbox{$B$}} = K_{\text{F}}\) and \(\left( {1 - \beta } \right) = \frac{1}{n}\) of the Freundlich model, and when \(\beta = 1\), Eq. (6) becomes the Langmuir isotherm with \(b = B\) [Langmuir constant (L/mg) that is interrelated to the adsorption energy]. \(A = bq_{m}\), but \(q_{m}\) refers to Langmuir’s optimum uptake capacity of the solid (mg/g).

When \(\beta = 0\), Eq. (6) becomes Henry’s model having \(\frac{A}{{B}}\) as Henry’s constant (\(K_{HE}\)). The linearized expression of the Redlich–Peterson model is expressed as in Eq. (7):

$$\ln \left( {\frac{{C_{e} }}{{q_{e} }}} \right) = \beta \ln C_{e} - \ln A$$
(7)

By plotting \(\ln \left( {\frac{{C_{e} }}{{q_{e} }}} \right)\) against \(\ln C_{e}\) (Fig. 2), \(\beta\) and \(A\) are obtained through the slope and intercept correspondingly.

Fig. 2
figure 2

Redlich–Peterson isotherm plot of Cr(VI) onto Arachis hypogea husk

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Jossens n isotherm model

The Jossens model is an expression established due to the energy dissemination of solute-solid interactions at adsorbent adsorption sites (Dilekoglu 2016). The model posits the solid surface to be heterogeneous regarding the interactions between the solute. The Jossen model is presented in Eq. (8).

$$C_{e} = \frac{{q_{e} }}{H}\exp \left( {Fq_{e}^{p} } \right)$$
(8)

where \(C_{e}\) refers to equilibrium solute concentration (mg/L), \(H\) and \(F\) are Jossens isotherm constant and \(p\) denotes a constant that is typical of the adsorbent regardless of temperature and the solid nature. Equation (8) becomes Henry’s law at small capacities but upon rearranging Eq. (8) (Juang et al. 1996) yields Eq. (9):

$$\ln \left( {\frac{{C_{e} }}{{q_{e} }}} \right) = - \ln \left( H \right) + Fq_{e}^{p}$$
(9)

The Jossens constants, \(H\) and \(F\), are obtained from the plot of \(\ln \left( {\frac{{C_{e} }}{{q_{e} }}} \right)\) against \(q_{e}\) (Fig. 3).

Fig. 3
figure 3

Jossens isotherm plot of Cr(VI) onto Arachis hypogea husk

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Equilibrium Kinetic modeling

The equilibrium data attained were applied to pseudo-first-order and pseudo-second-order kinetic models to gain insight into the controlling mechanism of the biosorption of Cr(VI) on Arachis hypogea husk. The linearized forms of the pseudo-first-order (Lagergren 1898) and pseudo-second-order (Ho 2006) models are expressed in Eqs. (10) and (11), respectively, as follows:

$$\log \left( {q_{e} - q_{t} } \right) = \log q_{e} - \frac{{k_{{p_{1} }} }}{2.303}t$$
(10)
$$\frac{t}{{q_{t} }} = \frac{1}{{k_{{p_{2} }} q_{{e^{2} }} }} + \frac{1}{{q_{e} }}t$$
(11)

where \(k_{{p_{1} }}\) (min−1) and \(k_{{p_{2} }}\) (\({\text{gmg}}^{ - 1} \,\min^{ - 1}\)) are pseudo-first-order rate and pseudo-second-order rate constants and \(q_{e}\) and \(q_{t}\) (mg/g) are the sorption capacities at equilibrium and time t (min), respectively.

By plotting \(\log \left( {q_{e} - q_{t} } \right)\) versus t (Fig. 4) and \(\frac{t}{{q_{t} }}\) versus t (Fig. 5), the constants \(k_{{p_{1} }}\), \(k_{{p_{2} }}\) and \(q_{e}\) can be obtained.

Fig. 4
figure 4

Pseudo-first-order plot of Cr(VI) onto Arachis hypogea husk

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Fig. 5
figure 5

Pseudo-second-order plot of Cr(VI) onto Arachis hypogea husk

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Results and discussions

Physicochemical parameters of groundnut husk

The results of the physicochemical properties of the adsorbent are reported in Table 2.

Table 2 Physicochemical parameters of the adsorbent (Arachis hypogea husk)
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The quality of a produced biosorbent can be enriched by reducing the adsorbent moisture content. The Arachis hypogea husk low moisture content (8.41 percent) indicated better yield and biosorbent quality. The Arachis hypogea husk moisture level was lower than the percentage moisture content obtained from Osakwe et al. (2014) and Okuofu and Osakwe (2012) using raw and carbonized baobab fruit shells and Theobroma cacao pods, and Borrassus Aethiopium and Cocos Nucifera, respectively. This implied that the Arachis hypogea husk used for the decontamination of Cr(VI) was of quality and there was no interference of moisture with the process, hence the higher the Cr(VI) uptake onto the Arachis hypogea husk.

As suggested by Amuda et al. (2007), the bulk density (0.46 g/cm3) was found to be greater than 0.25 g/cm3, and this showed better biosorbent filterability.

In most adsorption tests, the point of zero charge pH (\({\text{pH}}_{pzc}\)) should be related to the pH of the adsorption system as \({\text{pH}}_{pzc}\) established the limitations of the adsorbent pH (Abas et al. 2014). In the present work, the \({\text{pH}}_{zpc}\) (5.5) of the biosorbent was found to be lower than the pH (6.0) of the adsorption media, which produced a more negative charge on the Arachis hypogea husk surface. An upsurge in the negative charge density on the Arachis hypogea husk surface improved the decontamination of Cr(VI) (Ofudje et al. 2015). Similar findings had been recounted in the literature (Abdullah et al. 2014 and Yu et al. 2011).

Using the Saers’ method (Dada et al. 2012; Shawabkeh and Tutunji 2003 and Saer 1956), the specific surface area of the adsorbent was obtained as 432.60 m2/g signifying high surface area and porous nature of the Arachis hypogea husk. Abudaia et al. (2013) in a study discovered that the adsorption capacity of the adsorbent exhibited dependence largely on the surface area available for the adsorbate interaction. Generally, the greater the surface area, the higher the number of metal ions adsorbed on the surface of the adsorbent. This could be due to an increase in the number of binding sites on the biosorbent surface for the adsorptive removal of the metal ions (Oboh et al. 2009).

Furthermore, the raw sample (Arachis hypogea husk) was digested (by wet digestion) to determine the background concentration of Cr(VI) (Table 3). The background concentration of the Cr(VI) in the Arachis hypogea husk was found to be below the detection limit (BDL) of the UV–Vis spectrophotometer (Cary 60) which implied that the Arachis hypogea husks were initially free from Cr(VI) ions contamination.

Table 3 Background concentration of chromium (VI) in Arachis hypogea husk
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Characterization of the adsorbent

The FTIR analysis conducted in our previous study (Bayuo et al.  2019c) showed that the Arachis hypogea husk has surface functional groups (carboxyl, carbonyl, hydroxyl, phenyl, amino, and ester) that were accountable for the biosorption of Cr(VI) from the aqueous media.

Furthermore, the BET surface area of the unmodified Arachis hypogea husk was found to decline after loading with Cr(VI) ions. Moreover, the total pore volume of the biosorbent decreases significantly after the removal of Cr(VI) onto the surface of the Arachis hypogea husk (Bayuo et al.  2019c).

Central composite design (CCD) model and data analysis

The 3-factor CCD design matrix produced by the software and the experimental data attained in the batch adsorption of Cr(VI) by Arachis hypogea husk are summarized in Table 5.

A quadratic model that relates the adsorption capacity (response) and the independent parameters were chosen by the CCD (Table 4) and described in terms of the coded parameters by the second-order polynomial equation as given in Eq. (12):

$$\begin{aligned} Y & = 1.33 - 0.0612 A + 0.4162 B + 0.6251 C + 0.0015 AB - 0.0052AC \\ & \quad + \,0.2347 BC - 0.1322 A^{2} - 0.1676 B^{2} - 0.0049 C^{2} \\ \end{aligned}$$
(12)
Table 4 Model summary statistics for adsorption capacity (response Y) of Cr(VI) ion
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The predicted Cr(VI) adsorption capacity (mg/g) obtained by Eq. (12) is shown in Table 5. The residuals between the predicted and experimental (actual) values were found to be low implying that both the predicted and experimental responses had strong agreements (Mohammad et al. 2014). The correlation coefficient (\(R^{2}\)) used to determine the relationship between the experimental (actual) and predicted responses was 0.9873 as established by the model. This suggests that the process parameters analyzed explain 98.73% of the adsorption capacity variability and that the model could not explain only 1.27% of the variation of the response (Garba et al. 2016).

Table 5 Design matrix for Cr(VI) adsorption factors and corresponding responses from the experiment
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Furthermore, the analysis of variance (ANOVA) was used to determine the adequacy of the model. Table 6 presents the results of the quadratic response surface model fitting in the form of ANOVA. According to Yusuff (2018), ANOVA divides the complete variation of the results into two variations: one associated with the model and the other with experimental errors so as to determine whether the variation from the model is significant or not. This is calculated by evaluating the F-value expressed as the square-to-residual error ratio of the mean model. If the calculated F-value is found to be greater than that of the tabulated F-value, then the model is a strong experimental data predictor (Ani et al. 2015). The F-value obtained in the present study was 77.67, which suggested the fitness of the response surface model. More so, the significance of each of the model terms was evaluated using the probability of error value (Prob > F). In Table 6, the values of Prob > F less than 0.0500 showed that the terms are significant (Garba et al. 2016). It is found that B, C, A2, B2 and C2 were the significant model terms, whereas \(A, AB, AC\) and \(BC\) were the insignificant terms for adsorption capacity of Cr(VI). Hence, based on the F-value (Table 6), the three process variables studied had a significant effect on the Cr(VI) adsorption capacity. The initial Cr(VI) concentration (C) had the highest F-value of 423.95 implying that it had the most significant influence on the adsorption of Cr(VI) in comparison with contact time (A) and pH of the solution (B) (Gottipati et al. 2012). However, only quadratic effects of contact time (A) and pH of solution (B) on adsorption capacity of Cr(VI) were significant. In Table 6, the lack of fit F-value of 0.1109 showed the lack of fit is not significant relative to the pure error. Nonsignificant lack of fit, however, is good because the model is geared toward perfect fitness (Bayuo et al.  2019b).

Table 6 ANOVA for quadratic model for adsorption capacity (response Y) of Cr(VI)
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The second-order polynomial Eq. (12) in terms of coded parameters after removing the nonsignificant model terms is given in Eq. (13).

$$Y = 1.33 + 0.4162 B + 0.6251 C + 0.2347 BC - 0.1322 A^{2} - 0.1676 B^{2}$$
(13)

Figure 6 represents the 3D surface plot of Cr(VI) adsorption capacity at a constant initial Cr(VI) concentration (C) as a function of contact time (A) and pH of the solution (B). The Arachis hypogea husk adsorption capacity of Cr(VI) was found to be rapid at the initial stage as shown in Fig. 6. The improvement in the adsorption capacity at the start of the adsorption cycle could be attributable to the availability of large surface area for bulk adsorption of the Cr(VI) ions onto the husk (Bayuo et al. 2019a). The maximum adsorption of Cr(VI) was nearly accomplished at a constant initial Cr(VI) concentration of 50 mg/L at about 90 min of contact time. However, a further increase in contact time led to a rise in Cr(VI) uptake capacity until optimum removal of Cr(VI) by Arachis hypogea husk was accomplished at 120 min of equilibrium time.

Fig. 6
figure 6

Combined effect of factors A–B on adsorption capacity (response Y) of Cr(VI) onto Arachis hypogea husk

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Figure 7 is a 3D surface plot indicating the combined effects of contact time (A) and initial Cr(VI) concentration (C) on the adsorption capacity (Y) of Cr(VI) at constant pH of the solution (B). At the constant pH of the solution, it was observed that the variation of contact time and initial Cr(VI) concentration had a reasonably joint impact on the adsorption capacity (Y). At higher values of the two parameters, the collective effect was greater. In addition, it was discovered that by increasing initial Cr(VI) concentration, the uptake capacity generally increased. This is because higher concentration levels provide an improved concentration gradient, an essential driving force that helps to resolve the mass transfer resistance of the Cr(VI) ions between the liquid and solid phases (Futalan et al. 2012).

Fig. 7
figure 7

Combined effect of factors A–C on adsorption capacity (response Y) of Cr(VI) onto Arachis hypogea husk

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Figure 8 depicts the 3D surface plot representing the mutual effects of the solution pH (B) and initial Cr(VI) concentration (C) at constant contact time (A). Figure 8 revealed that Cr(VI) adsorption capacity increased with decreasing initial pH of the solution. This is attributable to the point of zero charge \({\text{pH}}\) (\({\text{pH}}_{\text{zpc}}\)) of the Arachis hypogea husk as a biosorbent (Bayuo et al.  2019c). It has been established that when the \({\text{pH}}\) of the solution is less than that of the \({\text{pH}}_{\text{zpc}}\) of the biosorbent, a positive charge is usually created on its surface, thereby decreasing the uptake capacity of the cations (Yusuff 2018; Mourabet et al. 2017). In the present study, the pH of the aqueous media (\({\text{pH}} = 8.0\)) was greater than that of the point of zero charge \({\text{pH}}\) (\({\text{pH}}_{\text{zpc}}\)) of the Arachis hypogea husk (\({\text{pH}} = 5.5\)). Thus, \({\text{pH}} > {\text{pH}}_{\text{zpc}}\) signifying that the surface of the Arachis hypogea husk turns out to be negatively charged and upsurges the decontamination Cr(VI) from the aqueous media (Bayuo et al.  2019c).

Fig. 8
figure 8

Combined effect of factors B–C on adsorption capacity (response Y) of Cr(VI) onto Arachis hypogea husk

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Optimization of the adsorption process

In the optimization analysis, a goal criterion was set as maximum values for the three independent factors and one dependent factor (response) for the adsorption of Cr(VI) by the Arachis hypogea husk. For the independent factors, the goal was to obtain optimum values for which optimum response would be achieved (Fig. 9).

Fig. 9
figure 9

Point of zero charge pH of the adsorbent (Arachis hypogea husk)

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Therefore, by applying the desirability function, the optimum response (adsorption capacity) was found to be 2.234 mg/g at a contact time of 120 min, pH of 8.0 and initial Cr(VI) concentration of 50 mg/L with good desirability of 0.969. At this optimum process condition, the residual between the predicted response (2.234 mg/g) and the experimental response (2.355 mg/g) was found to be only 0.11 mg/g indicating that the regression quadratic model was valid and accurate in predicting the response (Y) (Bayuo et al.  2019b).

The high optimum adsorption capacity of 2.355 mg/g obtained at the maximum values of the factors suggests that the unmodified Arachis hypogea husk as a non-conventional adsorbent has the potential of depolluting contaminants especially heavy metals from aqueous media (Bayuo et al. 2019a).

Adsorption equilibrium isotherm

From the three-parameter isotherm models investigated, it was found that Redlich–Peterson isotherm (Fig. 2) fitted well to the experimental data with good correlation coefficient of 0.9756 as compared to Jossens’ model.

The fitness of the experimental data to Redlich–Peterson isotherm suggested that the adsorption mechanism is a mixed type and did not necessarily follow the ideal monolayer adsorption (Toth 1971). This is because the Redlich–Peterson isotherm is a blend of the Langmuir and Freundlich models, and therefore, the adsorption of the metal ions could occur on homogeneous and heterogeneous surfaces of the adsorbent (Foo and Hameed 2009). The relative high values of \(\beta\) and A for both metal ions further confirmed the fitness of the experimental data of Cr(VI) to the Redlich–Peterson isotherm model (Table 7).

Table 7 Calculated values of the various isotherm models constants and their correlation coefficients (R2) for the adsorption of Cr(VI) onto Arachis hypogea husk
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Equilibrium adsorption kinetics

The adsorption kinetics was carried out by studying the adsorptive removal of the Cr(VI) at different time intervals. Two different models were applied to the experimental data to determine the mechanisms of adsorption and sole rate-limiting steps. The linear plots of the kinetic models are given in Figs. 4 and 5 while the calculated values of their constants and correlation coefficients (R2) are presented in Table 8.

Table 8 Calculated values of the various kinetic models’ constants and their correlation coefficients (R2) for the adsorption of Cr(VI) onto Arachis hypogea husk
Full size table

The results in Table 8 showed that the experimental data of both metal ions fitted the two kinetic models analyzed. The plots of pseudo-first- and pseudo-second-order models showed that the uptake of Cr(VI) onto Arachis hypogea husk followed both pseudo-first- and pseudo-second-order reaction with good correlation coefficients as shown in Figs. 4 and 5, respectively. However, it was found that the pseudo-second-order model of Cr(VI) showed outstanding linearity with good correlation coefficients (\(R^{2} = 0.9803\)) in contrast to the pseudo-first-order model (\(R^{2} = 0.9682\)) tested, hence the best fit.

The fitness of the experimental data to pseudo-first- and pseudo-second-order models could be implied that the removal of Cr(VI) by the Arachis hypogea husk was due to physisorption and chemisorption processes (Bayuo et al. 2019a), respectively. The higher uptake capacities (\(q_{e}\)) and rate constants of the pseudo-first-order- (\({\text{Kp}}_{1}\)) and pseudo-second-order (\({\text{Kp}}_{2}\)) models (Table 8) of both metal ions confirmed that the experimental data agreed with these models.

Conclusion

The optimization of Cr(VI) adsorption from aqueous solution by the unmodified Arachis hypogea husk showed that contact time, pH of the solution and initial Cr(VI) concentration had a significant effect on adsorption capacity of Cr(VI). As discovered by RSM, the interaction among the process variables studied improved the adsorption of Cr(VI). At the following optimum operation conditions: 120 min contact time, 8.0 pH of solution and 50 mg/L initial Cr(VI) concentration, the maximum Cr(VI) uptake of 2.355 mg/g was achieved. Redlich–Peterson isotherm provided the best fit to the experimental data, indicating that the adsorption mechanism of Cr(VI) by Arachis hypogea husk adsorbent is a mixed type and did not necessarily follow ideal monolayer adsorption but could occur on both homogeneous and heterogeneous surfaces of the adsorbent. The experimental data were well predicted by the pseudo-second-order kinetic model. It can, therefore, be concluded that the adsorbent from Arachis hypogea husk is highly efficient for the elimination of Cr(VI) from any water media.