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Article

Statistical Modelling of Biosorptive Removal of Hexavalent Chromium Using Dry Raw Biomasses of Dioscorea rotundata, Elaeis guineensis, Manihot esculenta, Theobroma cacao and Zea mays

by
Angel Villabona-Ortíz
1,
Candelaria Tejada-Tovar
1 and
Ángel Darío González-Delgado
2,*
1
Process Design and Biomass Utilization Research Group (IDAB), Chemical Engineering Department, Universidad de Cartagena, Avenida del Consulado St. 30, Cartagena de Indias 130015, Colombia
2
Nanomaterials and Computer Aided Process Engineering Research Group (NIPAC), Chemical Engineering Department, Universidad de Cartagena, Avenida del Consulado St. 30, Cartagena de Indias 130015, Colombia
*
Author to whom correspondence should be addressed.
Sustainability 2023, 15(12), 9156; https://doi.org/10.3390/su15129156
Submission received: 27 April 2023 / Revised: 29 May 2023 / Accepted: 5 June 2023 / Published: 6 June 2023
(This article belongs to the Special Issue Prevention and Control of Heavy Metal Water Pollution)

Abstract

:
Hexavalent chromium [Cr (VI)] is a highly toxic and hazardous contaminant that poses serious health risks to both humans and the environment. Its presence in water sources can lead to severe health issues, including various types of cancer and respiratory ailments. Therefore, developing efficient and effective methods for Cr (VI) removal is crucial in ensuring safe and clean water supplies. The aim of this research is the environmentally responsible elimination of hexavalent chromium by bioadsorption using corn residues (CR), palm fiber (PF), and the peels of yam (YP), cassava (CP), and cocoa (CH). The study was conducted with varying levels of pH, bioadsorbent quantity, temperature, and adsorbent particle size at 200 rpm, with an initial concentration of 100 mg/L and 24 h of contact time to improve the adsorption efficiency. The process variables were evaluated and optimized using the statistical technique response surface methodology (RSM). The SEM-EDS analysis revealed that the predominant elements in the structure of the bioadsorbents were carbon and oxygen. Furthermore, the adsorption process led to the incorporation of Cr (VI) into the structure of the biomaterials, as indicated by their EDS spectra. The maximal adsorption efficiency of 99.11% was obtained at pH 2, bioadsorbent dose of 0.03 mg, 30 °C, and 0.5 mm of particle size. Various equilibrium isotherms were utilized to fit and analyze the adsorption data. The assessed maximum adsorption capacities were 38.84, 56.88, 52.82, 138.94, and 240,948.7 mg/g for YP, PF, CP, CH, and CR, respectively. The adsorption data exhibited conformity with the Freundlich and Redlich–Peterson isotherm models (R2 = 0.95), indicating that the phenomenon occurs in a multilayer. Pseudo-second order and Elovich kinetic models adjusted the kinetics of chromium (VI), suggesting that the mechanism could be controlled by chemisorption. Therefore, the residual biomasses evaluated can serve as a cost-effective adsorbent for Cr (VI) removal, and the use of RSM enables efficient modeling and prediction of the adsorption process.

1. Introduction

Chromium exists naturally and can be found in rocks, soil, and water. It appears in two primary forms: Cr (III) and Cr (VI) [1]. While trivalent chromium [Cr (III)] is an essential nutrient for humans, hexavalent chromium [Cr (VI)] is toxic and poses significant health risks since it is classified as a human hazard by the International Agency for Research on Cancer (IARC) [2]. Chromium pollution is a major environmental concern, and its sources include industrial discharges, mining operations, and agricultural practices [3]. Cr (VI) is frequently utilized in diverse industrial sectors, including electroplating, textile manufacturing, and leather tanning. Improper handling and disposal of Cr (VI) waste can lead to its release into the environment, where it can contaminate soil, water, and air [4]. Contact with Cr (VI) through contaminated water, food, and air can cause lung cancer, nasal and sinus cancer, and cancer of the gastrointestinal tract, as well as respiratory irritation, asthma, allergic dermatitis, liver damage, nausea, vomiting, and diarrhea [5,6]. It has been established that concentrations exceeding 0.05 mg/L of Cr (VI) and 5 mg/L of Cr (III) can have toxic effects on living organisms, and a maximum concentration of chromium total of 100 μg/L is recommended in drinking water by US Environmental Protection Agency (US EPA) [7].
The effective and economical way to eliminate Cr (VI) from contaminated environments is a critical research area. The development of capable and renewable methods for the removal of Cr (VI) is essential to mitigate the health risks associated with exposure to this toxic metal. The process of removing heavy metals using biological materials (bioadsorption) has become an affordable and eco-friendly alternative for eliminating Cr (VI) from polluted water and soil [8]. Thus, research in this area has the potential to provide sustainable solutions for the management of chromium pollution.
Lignocellulosic biomasses have been investigated as probable bioadsorbents for the clearing of heavy metals from wastewater, particularly for the elimination of Cr (VI) from the aqueous medium, including chromium six. The cost-effective, renewable nature and high availability of these biomasses make them an attractive option as adsorbents [9]. Different types of lignocellulosic biomasses have been evaluated as adsorbents for chromium (VI), including agricultural wastes, forestry residues, and aquatic plants [10,11,12]. Agricultural wastes such as rice husk [13], wheat straw [14], sugarcane bagasse [15], and corn cob [16] have shown promising results as adsorbents for Cr (VI). These materials contain high amounts of cellulose and hemicellulose, which provide attachment points for the metal ions [17]. Forestry residues, such as sawdust and wood chips, are also effective adsorbents for chromium six due to their high surface area and permeability [18].
Taking the above into account, the aim of this article is to explore the bioadsorption of chromium (VI) using dry biomass obtained from corn residues (CR), palm fiber (PF), peels of yam (YP), cassava (CP), and cocoa (CH), which were selected due to the large quantity of post-harvest waste generated as a result of cultivating these species in the Bolivar department (Colombia) [19]. The effect of pH was established, and a central composite experimental design (CCD) was followed to analyze the impact of temperature, particle size, and adsorbent dosage. The influence of the initial concentration and the time was analyzed by adjusting the data to equilibrium and kinetic models.

2. Materials and Methods

2.1. Reagents

Potassium dichromate (K2Cr2O7) was used to prepare the synthetic solutions, following the ASTM D1687-17 standard method [20]. The initial pH of the solutions was adjusted until the desired values (2, 4, and 6) were reached by adding 1N HCl or 1N NaOH solutions. The chemical reagents employed in this investigation were produced by Merck. In addition, deionized water was used for all analyses.

2.2. Pretreatment of the Biomasses

Palm fiber (PF) was acquired from Bolivar-Colombia; PF is produced as waste during the process of palm oil extraction. YP, CP CH, and CR were obtained after post-harvest handling. The most suitable biomasses were selected to ensure their effectiveness as adsorbents. Subsequently, the biomasses were washed with distilled water four times to remove impurities. Then, biomasses were dried for 24 h in an oven at 60 °C until constant weight. Subsequently, biomasses were size-reduced using an Oster electric mill and sieved for 10 min, selecting particle sizes of 0.14–0.15, 0.315–0.355, 0.45–0.5, 0.9–1.0, and 1.12–1.18 mm, using the sieves Nº 100, 45, 35, 18, and 16, respectively.

2.3. Characterization of Bioadsorbents

The bioadsorbents prepared were characterized through Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray (EDX) analyses to investigate their microstructure and surface chemistry using a TESCAN scanning electron microscope coated with gold, 10 kV voltage, and 500× enlargement. The compositional analysis of the bioadsorbents was performed using the methods shown in Table 1.

2.4. Batch Adsorption

2.4.1. Adsorption Essays

The impact of pH on the Cr (VI) removal was initially investigated using values of 2, 4, and 6. The adsorption tests were carried out at the best pH value obtained, using a CCD experimental design with three independent factors: temperature, particle size, and dose of biomass. Specific quantities of bioadsorbent and 100 mL of Cr solution were combined in Erlenmeyer flasks for each adsorption test. The blend was stirred on a rotary shaker at 200 rpm for 24 h, at a concentration of 100 mg/L.

2.4.2. Chromium Analysis

After completion of the essays, the bioadsorbent and supernatant were separated through filtration using a microfiber glass filter. A colorimetric method was used to determine the final Cr (VI) quantity in the liquid [21]. The pink complex resulting from the reaction between the Cr (VI) and 1.5-diphenylcarbazide was measured at 540 nm using distilled water as the blank in a Shimadzu UV-Vis UV 1700 spectrophotometer.
The Cr removal percentage from the solution and the amount of chromium adsorbed by the biomass were determined using Equation (1), which considers the initial concentration (Ci) and final concentration (Cf) of Cr (VI) in each test. The adsorption capacity (q) of Cr (VI) in the bioadsorbent was calculated using Equation (2), which considers the initial and final Cr (VI) amounts in the liquid phase, the volume of the liquid phase (100 mL), and the amount of bioadsorbent used in each test (m). The bioadsorption capacity was reported in mg of Cr (VI)/g of biomass.
% E = C i C f C i × 100
q t = ( C i C f ) × V m

2.4.3. Central Composition Design

Table 2 shows the CCD experimental design implemented to investigate the impact of the factors on the uptake of Cr (VI) in the studied bioadsorbents. The design consists of both real and coded variables. The CCD was set in 16 experiments, which were performed at predetermined levels of the variables (as listed in Table 3). To assess the error related to the procedure and analysis, repeated tests were conducted at the central point (0, 0, 0) for the variables under study (essays 5 and 16 in Table 3). The statistical analysis was conducted using Statgraphics Centurion XIX software (Plains, VA, USA).

2.4.4. Thermodynamic Analysis

A graphical technique derived from the Van ’t Hoff equation was employed to calculate the thermodynamic parameters. The determination of these parameters will provide insight into the probability of the adsorption process and the impact of temperature and pH on it. Specifically, this study aimed to estimate the changes in standard Gibbs free energy (ΔG°), standard enthalpy (ΔH°), and standard entropy (ΔS°). Adsorption capacity tests were conducted on the samples, with temperatures ranging from 29 to 81 °C, according to the conditions outlined in the experimental design. Using this information, a graph of ln(Kc) versus 1/T was plotted, and the thermodynamic parameters were estimated [21]. For the estimation of the thermodynamic parameters, Equations (3)–(7) were used, where CT is the final adsorbate concentration on the surface of the adsorbent in mg/L, and Qt is the adsorption capacity of the adsorbent in mg/g [22].
Δ G ° = R × T × lnKc
Δ G ° = Δ H ° T × Δ S °
ln   ( K C ) = Δ H ° R   ×   T + Δ S ° R
K C = Q T C T  

2.5. Adsorption Isotherms Study

The isotherm studies were performed using solutions of K2Cr2O7 with concentrations from 25 to 500 mg/L and a volume of 100 mL. The essays were made at the best conditions of adsorbent dose, particle size, and temperature obtained after the experimentation following the CCD at 250 rpm. Thereafter, the samples were centrifugated at 10,000 rpm for 10 min, and bioadsorbents were separated from the supernatant; final concentration was determined for the liquid phase. The collected experimental data points were plotted and fitted to non-linear Langmuir, Freundlich, Sips, and Redlich–Peterson adsorption isotherms. The variance, σ2, was defined according to Equation (7).
σ 2 = i = 1 N ( y i , e y i , m ) 2 N p
where yi,e is the experimental data, yi,m is the predicted data by each model, N is the number of data, and p is the sum of parameters for each model.

2.6. Adsorption Kinetic Analysis

The reaction rate analysis was carried out under the best conditions obtained for temperature, particle size, and adsorbent dose. Samples were taken at 5, 10, 15, 20, 25, 30, 60, 120, 240, 360, 960, and 1440 min. The estimation of the remaining Cr (VI) was carried out following the procedure presented in Section 2.4.2. The obtained data were fitted to the Lagergren pseudo-first-order, pseudo-second order, Elovich, and intraparticle diffusion kinetic models.

3. Results and Discussion

3.1. Surface Characterization of Bioadsorbents

The morphological and compositional properties of the bioadsorbents were studied, and Figure 1, Figure 2, Figure 3, Figure 4 and Figure 5 show their characteristics before and after the adsorption process using SEM-EDS. The predominant component of the five bioadsorbents is carbon, which is followed by oxygen. This can be attributed to the lignocellulosic nature of the material [23,24]. Before adsorption, the presence of elements such as Fe, Cu, Ca, Si, and S are noted, which are part of the structure of plants because of their function during photosynthesis, respiration, and synthesis of lignin, enzymes, and proteins [25]. Minerals such as calcium, magnesium, and potassium are necessary for plant growth and development, as they are involved in the formation of cell walls, cell division, and the regulation of water and nutrient uptake [26]. In SEM micrographs before adsorption, the presence of white particles, attributed to metallic cations such as Ca2+, Mg2+, K+, Si+, and Fe+, are observed, which are retained in the active centers of the materials due to the electrostatic attraction of the carboxylic groups. YP, CP, and CH are the bioadsorbents with the most diverse structure, while the structures of CR and PF are less complex, which can be attributed to the agro-industrial utilization of these prior to their disposal and their use as adsorbent material. These results align with our previously reported surface area values of the adsorbents YP (0.946 m2/g), PF (2.732 m2/g), CP (2.051 m2/g) [27], CH (1.45 m2/g) [28], and CR (0.979 m2/g) [29].
After the removal process, the formation of complexes on the surface of the bioadsorbents is noted. Regarding the SEM and EDS analyses of the biomaterials, it is observed that after removal, more white granular crystals are formed, which are loaded with Cr (VI); EDS analysis confirms the presence of Cr (VI) ions due to the characteristic high-density peak at 0.573 and 5.411 keV, which appears after the biosorption. These results are consistent with those previously reported by Chen et al. [30] when using powdered activated carbon for the removal of Cr (VI). Hence, the increase in the number of particles that precipitated on the surface of the five bioadsorbents can be explained by the formation of micro-complexes. This happens when the metal is retained in the active centers of the biomaterials as a result of cation exchange [31]. For more clarity, EDS images are shown in Supplementary Files (Supplementary Files: S1–S5).
Results from the bromatological analysis shown in Figure 6 confirm that the biomasses are mostly composed of cellulose, and carbon is the main constituent of the biomasses, followed by hydrogen. The above makes the bioadsorbents under study also attractive for their use as a fuel material. In addition, the existence of lignin, cellulose, and hemicellulose in each bioadsorbent has been directly related to a substantial removal effectiveness because these polymers contain numerous hydroxyl groups, and in the case of lignin, phenolic groups, which can promote metal adsorption [32,33,34]. Likewise, it is observed that YP has a lower presence of lignin compared to the other biomasses, so lower performance is expected in its efficiency as an adsorbent of Cr (VI) ions. Biomass has the capability to adsorb Cr (VI) through several mechanisms, including micro-precipitation, ion exchange, coordination, and complexation. The existence of OH, COOH, and amide reactive groups in lignocellulosic materials facilitates these mechanisms, which have been previously reported for the biomasses under study [35]. Nonetheless, the research mentioned the importance of cation exchange and microprecipitation mechanisms in the process by the assessed bioadsorbents.

3.2. Effect of the pH

The pH of the solution has a significant impact on the bioadsorption capacity, mainly due to the phenomenon of protonation that occurs at low pH values and its effect on the chemistry of the solutions [36]; therefore, the adsorption capacity can be influenced by the pH [37]. The binding sites in bioadsorbents are carboxyl, amine, phosphate, sulfate, and hydroxyl groups; the rise in the disposal of these binding sites depends on the displacement of protons, which is pH-dependent [38].
In Figure 7, the influence of pH on the removal of Cr (VI) is presented with an average deviation of the data of 0.0138 and 0.0251 for the five bioadsorbents under study. In all cases, the best adsorption was observed under a pH of 2. According to the speciation diagram of Cr (VI) [39], it is found that adsorption increases as the pH decreases since the stability of the ionic species of chromium HCrO4, Cr2O72−, and CrO42− highly depends on the pH value. At lower pH values, the active sites of the adsorbents are protonated, and then, anionic species can be linked to the adsorbent due to electrostatic forces. On the other hand, the dominant form of Cr (VI) between pH 1 and 4 is HCrO4 [40], so this is the one that is mainly accommodated on the surface of the adsorbent. At higher pH values, the concentration of OH- ions increases, inducing changes in the surface of the adsorbent and preventing the adsorption of Cr (VI) ions.
The implementation of an acidic pH level, such as 2, on an industrial scale appears to be impractical due to the large volumes involved. However, the authors are currently exploring an alternative approach that involves combining different wastewater treatment technologies. This consideration stems from the fact that industrial effluents contaminated with chromium, such as those from tanneries, typically exhibit pH ranges between 3 and 5.5 [41,42]. Within this range, the use of various bioadsorbents has demonstrated a removal efficiency of over 70% (as shown in Figure 7). Therefore, technologies such as electrocoagulation or advanced oxidation technologies, despite being more expensive, exhibit excellent performance when dealing with low concentrations.

3.3. Optimization of Cr (VI) Adsorption by RSM

Table 4 shows the results of the CCD experiments for Cr (VI) removal by the adsorbents under study. The adsorbed amount of Cr (VI) was determined by utilizing Equations (1) and (2) after the adsorption essays to determine the residual Cr (VI) in the aqueous solution. Different statistical designs can assist in evaluating the impact of factors and determining their optimal values for the elimination of Cr (VI) [43]. Based on the surface response method, a model was created based on the experimental data presented in Table 4, which established the trend within a range of 33.70–99.70% (as shown in Table 5). Other studies have also investigated the removal of chromium using waste tires [44], orange peel [45], and Teff husk-based activated carbon, wherein the removal percentages were 79.6%, 97%, and 95.597%, respectively. The results of the removal efficiency of Cr (VI) in terms of coded variables (Table 1) were presented as polynomial equations for each bioadsorbent (Table 5). The coefficients indicate the influence of each factor on the equation, and their signs indicate whether the contribution is positive or negative.
In order to ensure a good adjustment, the regression equation and statistical parameters underwent significance testing through ANOVA [46] from the data presented in Table 4, and the results are summarized in Supplementary Files (Supplementary Files: S1–S5). The significance of the coefficients and model terms were evaluated based on their p-values at a confidence level of 95%. Typically, model terms are considered significant if their p-value is less than 0.05. From ANOVA, it can be said that the bioadsorbent dose (factor C) is the variable with the stronger influence when using CH and CR as Cr (VI) bioadsorbents. When the bioadsorbents are PF, YP, and CP, there is no significant evidence of the influence of the variables in the evaluated range. Overall, it can be concluded that the adsorption percentage of Cr (VI) over CH and CR is favored at a higher bioadsorbent quantity with a low influence of temperature and particle size. Figure 8 shows the normal distribution of residuals for the data, with a single outlier falling outside the range of residuals without transforming the response variable, which affects the accuracy of the equation (left). Additionally, the trend of externally standardized residuals plotted against predicted removal efficiencies is shown on the right of the figure. The plots suggest that the model’s predictions and residual precision do not follow any discernible pattern, as indicated by the distance line at zero, confirming the randomness of the residuals.
The equations in Table 5 can be utilized to anticipate the adsorption removal efficiency of Cr (VI) in the tested bioadsorbents within the chosen experimental scope. The visual depiction of the equations is provided in Figure 9. It is observed that at 30 °C, pH 2, and 24 h of contact time, the adsorption removal percentage is higher when the particle size decreases, and the evaluated mean value of the adsorbent dose is employed.

3.4. Thermodynamic Study

For determining the spontaneity and the influence of the temperature on the adsorption for each of the systems evaluated, the values of adsorption entropy (ΔS°), adsorption enthalpy (ΔH°), and Gibbs free energy (ΔG°) were obtained by calculating the adsorption capacity and equilibrium constants (KC). To achieve this, the Van ’t Hoff approach was utilized, which relates the alteration in free energy to the variation in enthalpy and adsorption entropy at different temperatures. This enabled us to determine the regression line of −ΔS° and obtain ΔH° through intercepting, as shown in the equation [47]. Results are shown in Table 6.
Based on these thermodynamic findings, it can be inferred that energy needs to be provided to the system, given the endothermic nature of the process of removing Cr (VI) using YP, CR, and CP bioadsorbents. This is supported by the positive and increasing values of ΔH° [48,49]; however, data in Table 6 indicate that the ions exhibit higher adsorption efficiency at intermediate and low temperature values. The adsorption process using PF and CH is suggested to be exothermic based on the negative values of enthalpy. This indicates that the system releases energy, resulting in potential energy frugality when scaling up the process [47,50]. A different behavior for the bioadsorbents based on the sign of ΔH° is observed, thus, might be related to the origin of the biomasses; for example, PF is a residue of the oil palm industry, and it was previously treated with chemicals such as NaOH; meanwhile, the husk and peels (CH, CP, CR, and YP) are agro-residues. The level of processing and degradation of each biomass are different, and this was evidenced in the SEM-EDS shown in Figure 1, Figure 2, Figure 3, Figure 4 and Figure 5. The above will influence the adsorbate–adsorbent interactions.
The negative values of ΔS° observed for YP, PF, CP, and CR suggest a strong binding between Cr (VI) and the active centers in the biomass, indicating high affinity and selectivity of the biosorbents towards the metal ion. Additionally, the low randomness at the interface suggests a low possibility of reversibility, resulting in an energetically stable adsorption process [51,52], and the biomass could be inactivated by thermal or physical methods with a low possibility of desorption of the heavy metal, resulting in the immobilization of the pollutant. Cr (VI) has been previously immobilized in orange peel as part of brick matrices, resulting in a release of the metallic ion between 0.21 and 0.25 mg/L after acid treatments under constant agitation conditions for 18 h [53]. Concentrations below the environmental limit have been reported for Pb (II) and Ni (II) when yam peels are used as bioadsorbents in conjunction with cement-based solidification/stabilization techniques [54]. Successful immobilization of heavy metals through thermal treatment has been reported by incinerating dredged sediments functionalized with phosphate at 700 °C [55]. The low leaching of heavy metals using immobilization techniques is justified by their conversion into more evenly distributed and less soluble metal-bearing phases, reducing their toxic potential [56].
For all the evaluated temperatures, it was observed that when using CR, ΔG° is negative, indicating that the process of adsorption occurs spontaneously, is feasible, and is advantageous. The increase in Gibbs free energy in temperature suggests that spontaneity behaves inversely proportional to the temperature [47,48,50]. Alternatively, when using YP, PF, CP, and CH, ΔG° is positive and rises with increasing temperature, suggesting a decrease in spontaneity and an unfavorable characteristic of the process [11]. As the temperature increases, the magnitude of ΔG° also increases, indicating that the system evolves spontaneously and becomes more favorable for the removal process.

3.5. Effect of the Contact Time

Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14 show the fitting of the pseudo-first order, pseudo-second order, Elovich, and intraparticle diffusion models of Cr (VI) adsorption kinetics in the five assessed bioadsorbents, respectively. The results indicate that rapid adsorption happens within the first 40 min of the process, with equilibrium being achieved after 90 to 150 min of contact between the ion and the adsorbent. The rapid adsorption observed initially during the removal process is ascribed to the presence of unoccupied active sites on the surface of the bioadsorbent, which are gradually filled by the ions as time progresses [57].
Based on Figure 10 and Table 7, the pseudo-first order kinetic model is the most appropriate for describing the kinetic data of Cr (VI) removal by CP and PF. This suggests that the rate of adsorption at the surface of the adsorbent is mainly influenced by the disposal of active sites on the adsorbent [58]. The high correlation coefficient (R2) and low residual errors between the experimental data and the model prediction further support the validity of the model. A similar result was found when using mosambi peel at pH 2, 5 g/L of adsorbent dose, and 125 rpm [59]. Mondal et al. [60] reported that the Cr (VI) kinetic adsorption of Cr (VI) by banana peel dust adjusted to the pseudo-first order model.
The experimental kinetic data of Cr (VI) removal of the five evaluated bioadsorbents were fitted to the pseudo-second order model, as shown in Figure 11. The data in Table 7 and the plot indicate that the model accurately describes the kinetic behavior of PF, CP, and CH. This suggests that the rate of adsorption of chromium (VI) at the adsorbent surface is principally controlled by the chemical exchanges between the metal and the binding sites on the adsorbent [61], as well as the strength of these interactions [62]. Consequently, as time progresses, the number of active sites on the adsorbent surface decreases, resulting in a decrease in the rate of adsorption [63]. This adjustment also suggests that the rate of adsorption eventually becomes negligible when the concentration of metal ions in the solution approaches zero, indicating that the process reaches equilibrium. The magnitude of the equilibrium constant (k2) suggests that the rate of adsorption follows this order CH > PF > CP. Furthermore, the calculated qe values align with the experimental results when using the pseudo-second order kinetic model. Similar data were found when using sawdust modified with formaldehyde [64] and Luffa cylindrica activated carbon [65].
Elovich’s kinetic model is another widely used model for describing the adsorption kinetics of heavy metal ions by adsorbents, including chromium (VI). In this model, the rate of adsorption is assumed to be limited by the number of active sites available on the adsorbent surface, as well as the surface coverage of adsorbed metal ions [66]. Based on the data presented in Table 7 and Figure 12, it can be inferred that the Elovich model provides a good fit for describing the kinetics of Cr (VI) adsorption by the five bioadsorbents evaluated. The results suggest that the disposal of active sites and the surface coverage of adsorbed metal ions are the primary factors that control the adsorption process. Additionally, the rate of adsorption is influenced by both the availability of active sites on the adsorbent surface and the strength of the chemical interactions between the metal ions and the adsorbent [67]. In the first stages of the process, a high number of active sites are available, resulting in rapid adsorption of metal ions. As the adsorption process continues, the availability of active sites decreases, leading to a decrease in the rate of adsorption. The constant β in the Elovich model represents the initial rate of adsorption, while the constant α is the extent of surface coverage of adsorbed metal ions. Similar results were found when using rice husk ash [67] and pea peel activated carbon modified with ZnCl2 [68].
The ID kinetic model is another widely used model for describing the adsorption kinetics of heavy metal ions by adsorbents, including chromium (VI). In this model, the kinetics of adsorption are assumed to be controlled by the diffusion of metal to the interior of the adsorbent particles [69]. Figure 13 and Table 7 give evidence that the adsorption kinetics of Cr (VI) of the five evaluated bioadsorbents is not described by the intraparticle diffusion model, suggesting that the rate of adsorption is not controlled by the diffusion of metal ions from the bulk solution into the interior of the adsorbent particles. These results are consistent with those reported by Pabithra et al. [70], where the metal adsorption process is non-linear, and the intra-particle diffusion model did not provide evidence of the metal ion adsorption mechanism.
The experimental kinetic data show good fitting using the pseudo-second order, pseudo-first order, and Elovich models, indicating that the adsorption is mainly controlled by chemisorption. This implies that there is an exchange of Cr (VI) cations with the functional groups present on the biomass surface, such as COO and OH groups of cellulose and hemicellulose [71]. The reason for this is the creation of chemical bonds between the adsorbent and the adsorbate at the surface [72].

3.6. Equilibrium Analysis: Adsorption Isotherms

In Figure 14, the equilibrium adsorption of the ion concentration in water and adsorbent material is presented after 24 h of contact time at 30 °C. The adsorption isotherms are fitted to various models, including Langmuir, Freundlich, Redlich–Peterson, Temkin, and Sips models, which are shown in the figure.
The Langmuir isotherm model is frequently employed to analyze the adsorption characteristics of heavy metal ions, such as chromium (VI), by adsorbents. The model is based on the assumption that the surface of the solid features a finite amount of identical sites, and the adsorption of metal ions at these sites follows a monolayer coverage mechanism [73]. Based on Table 8, it can be inferred that the equilibrium adsorption data of Cr (VI) in YP, CP, and PF are well-described by the Langmuir model, indicating that the adsorption occurs through a monolayer coverage mechanism and the bioadsorbent surface possesses a finite number of identical sites for the adsorption of metal ions [74]. The maximum adsorption capacity, qmax, indicates the maximum amount of metal ions that can be adsorbed by the adsorbent surface under ideal conditions when all the available adsorption sites are occupied by metal ions; the obtained qmax for each adsorbent follows this order: CH > PF > CP > YP. The Langmuir constant KL represents the affinity of the adsorbent for the metal ions and is related to the energy of adsorption [75], having YP with the highest affinity with the ion. The RL parameter is the separation factor and indicates the reversibility (RL = 0), favourability (0 < RL < 1), linearity (RL = 1), and unfavorability (RL > 1) of the adsorption process; from the found values for this parameter, it can be said that the Cr (VI) adsorption by the evaluated adsorbents is favourable.
From the data in Table 8, it can be suggested that the Cr (VI) adsorption by YP occurs on a heterogeneous surface with a distribution of active sites and that the adsorption capacity varies with the surface coverage, considering the good adjustment to the Freundlich’s isotherm model [76]. In addition, the adsorption capacity varies with the surface coverage. The value of n > 1 suggests that the intensity of adsorption is high and is affected by the initial concentration of the heavy metal [77].
The Temkin model assumes that the process involves a reduction in the adsorption energy as the surface coverage increases due to the interactions between the adsorbate and the adsorbent surface [78]. Good fitting between the experimental results of Cr (VI) by PF, CP, CH, and CR and the Temkin isotherm model suggests that the adsorption involves a decrease in the adsorption energy as the surface coverage increases, due to the interactions between the adsorbate and the adsorbent surface [79]. The Temkin constant A is related to the heat of adsorption, which represents the energy released or absorbed during the adsorption process following the order CR > CP > PF > CH. The Temkin constant B is related to the adsorption energy, which indicates the strength of the interactions between the adsorbate and the adsorbent surface, having CR and CH the strongest interaction with the adsorbate, which could enhance the retention of the metal in the structure of the adsorbent and it could be easily immobilized by carbonization or in concrete [80], for example.
The Sips model described the adsorption of Cr (VI) by YP, PF, CP, and CR, suggesting that the adsorption occurs through multilayer adsorption on a heterogeneous surface and that the adsorbent surface contains varying degrees of affinity for the metal ions [81]. The values of the maximum adsorption capacity (qms) are similar to the Langmuir model’s results, which is common, taking into account that the structure of both equations is alike, considering the Sips model, the heterogeneity of the adsorbent surface across the ms parameter. The Redlich–Petersen isotherm model fitted the equilibrium adsorption of Cr (VI) by YP, PF, CP, and CH, suggesting that the adsorption of the adsorbate occurs through a combination of monolayer and multilayer adsorption mechanisms, and the adsorption sites on the adsorbent surface have a distribution of energies [82].
Table 9 compares the results obtained in previous studies that use lignocellulosic-based adsorbents for the removal of Cr (VI). The table shows that when the pH was not acidic, the adsorption capacity decreased. This is because at low pH levels, the surface of the adsorbents becomes protonated, and the existing chromium species are anions such as chromates and dichromates. These anions can be easily attached to the adsorbent due to electrostatic forces [40].

3.7. Future Approach and Practical Applications

Lignocellulosic adsorbents have shown great potential for the removal of contaminants from water due to their low cost, availability, and eco-friendliness [84]. Although bioadsorption is a technology studied in different countries, it still is in its developing phases, and efforts are needed to improve its performance and cost-effectiveness, considering its advantages over conventional adsorbents. The use of bioadsorbents for removing heavy metals has been a topic of great interest due to the rising demand for high-quality water. This demand has prompted researchers to focus on wastewater recovery and reuse, as well as the recovery of the ion and the final disposition of the exhausted adsorbent at the end of its useful life [85].
Industrial wastewater contains a wide range of organic and inorganic pollutants that can have a significant impact on water quality. Although the use of biosorbents for heavy metal removal has been studied extensively, there is still much to explore in terms of addressing the complex challenges presented by industrial wastewater. This represents a promising opportunity for researchers to develop new and effective solutions to the problem of heavy metal contamination [86]. In addition, there is a need to explore not only the reusability of adsorbents through cycles of adsorption–desorption, but also to determine how they are affected by microorganisms, which are also present in wastewater, due to the risk of releasing the contaminants retained in their lignocellulosic matrix. Based on these findings, actions must be taken to increase their lifespan against pathogenic agents and find suitable techniques for immobilizing and stabilizing the remaining contaminants retained in the biomass.
While small-scale studies have shown that biosorbents can be effective and practical for removing heavy metals, their applicability in the field may be limited. Pilot studies and field implementation are crucial for understanding the performance and potential performances of different biosorbents. While many laboratory experiments have been conducted on biosorption technology, implementation remains a challenge due to the need to assess the behavior of the process under dynamic conditions, which differ from those of batch systems. In this sense, from a phenomenological point of view, there is a big gap in the research field, and this could lead to the development of a standardized model for the kinetic and adsorption rates in the equilibrium conditions for water–solid systems, considering the models used until today are based on gas–solid interactions.
For scaling up the adsorption process, the use of Computed Aided Process Engineering (CAPE) as a tool for studying the effect of difficult-to-determine variables, such as mass transfer coefficients, on the process in packed bed systems, simulation in software such as Aspen adsorption can be used to design processes and find behaviors that approach reality, especially when there is not much budget for experimental research before building the prototype equipment. The above, considering the scale-up of the process, is necessary to make it applicable for large-scale water treatment. Further research is needed to study the feasibility and cost-effectiveness of the scale-up process using computational tools and analysis under economic, exergy, and environmental parameters in order to establish sustainability from an integral perspective [87].
There is a growing effort to explore novel materials, enhance the efficacy of current biosorbents, and develop hybrid technologies that target multicomponent biosorption, incorporating methods such as electrocoagulation [88], ozonation [89], and photocatalysis [90] as a second phase for degrading the pollutants. Research efforts are also underway to explore the potential of hybrid biosorbents derived from a variety of agricultural waste materials. In addition, the use of nanocomposites is emerging as a promising approach for the efficient removal of toxic pollutants and heavy metals from aqueous solutions, although there is still a considerable distance to cover before reaching on-site applications. Biosorbents are considered eco-friendly, biodegradable, and cost-effective adsorbents, representing a smart technology concept that continues to evolve in response to growing demands.

4. Conclusions

This study evaluates five dried lignocellulosic bioadsorbents prepared from corn waste, palm fiber, and the peels of yam, cassava, and cocoa for removing Cr (VI) from a synthetic aqueous solution. The SEM-EDS analysis revealed that the predominant elements in the structure of the bioadsorbents were carbon and oxygen, and the mechanism might be controlled by the incorporation of Cr (VI) into the structure of the biomaterials. The adsorption efficiencies of the metal were strongly dependent on pH and adsorbent dosage. The maximal adsorption efficiency of 99.11% was obtained at pH 2, bioadsorbent dose of 0.03 mg, 30 °C, and 0.5 mm of particle size. Adsorption equilibrium data fitted well in the Redlich–Peterson and Temkin models (R2 = 0.95), indicating that the phenomenon occurs in a multilayer. Pseudo-second order and Elovich kinetic models adjusted the kinetics of chromium (VI) at the evaluated conditions. The assessed maximum adsorption capacities were 38.84, 56.88, 52.82, 138.94, and 240,948.7 mg/g for YP, PF, CP, CH, and CR, respectively. The results demonstrated that the evaluated lignocellulosic bioadsorbents could be utilized as an economical and environmentally benign adsorbent at a low cost, and the combination with other technologies would allow for the diminution of the concentration of Cr (VI) in the treated waters more efficiently.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/su15129156/s1, Figure S1: EDS spectra of YP: (upper) before and (lower) after Cr (VI) adsorption; Figure S2: EDS spectra of PF: (upper) before and (lower) after Cr (VI) adsorption; Figure S3: EDS spectra of CP: (upper) before and (lower) after Cr (VI) adsorption; Figure S4: EDS spectra of CH: (upper) before and (lower) after Cr (VI) adsorption; Figure S5: EDS spectra of CR: (upper) before and (lower) after Cr (VI) adsorption; Table S1: Model fitting and regression analysis of Cr (VI) adsorption process og PF; Table S2: Model fitting and regression analysis of Cr (VI) adsorption process by YP; Table S3: Model fitting and regression analysis of Cr (VI) adsorption process by CP; Table S4: Model fitting and regression analysis of Cr (VI) adsorption process by CH; Table S5: Model fitting and regression analysis of Cr (VI) adsorption process by CR.

Author Contributions

Conceptualization, C.T.-T., A.V.-O. and Á.D.G.-D.; methodology, C.T.-T.; software, Á.D.G.-D.; validation, C.T.-T. and Á.D.G.-D.; formal analysis and investigation, C.T.-T.; resources, C.T.-T.; data curation, Á.D.G.-D.; writing—original draft preparation, C.T.-T.; writing—review and editing, Á.D.G.-D.; visualization, A.V.-O.; supervision, C.T.-T.; project administration, A.V.-O. and Á.D.G.-D.; funding acquisition, C.T.-T. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Acknowledgments

The authors thank the Universidad de Cartagena for providing the materials, equipment, and laboratory facilities required to successfully conclude this research project.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. (Left) SEM photograph ×500 and (right) EDS spectra of YP: (upper) before and (lower) after Cr (VI) adsorption.
Figure 1. (Left) SEM photograph ×500 and (right) EDS spectra of YP: (upper) before and (lower) after Cr (VI) adsorption.
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Figure 2. (Left) SEM photograph ×500 and (right) EDS spectra of PF: (upper) before and (lower) after Cr (VI) adsorption.
Figure 2. (Left) SEM photograph ×500 and (right) EDS spectra of PF: (upper) before and (lower) after Cr (VI) adsorption.
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Figure 3. (Left) SEM photograph ×500 and (right) EDS spectra of CP: (upper) before and (lower) after Cr (VI) adsorption.
Figure 3. (Left) SEM photograph ×500 and (right) EDS spectra of CP: (upper) before and (lower) after Cr (VI) adsorption.
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Figure 4. (Left) SEM photograph ×500 and (right) EDS spectra of CH: (upper) before and (lower) after Cr (VI) adsorption.
Figure 4. (Left) SEM photograph ×500 and (right) EDS spectra of CH: (upper) before and (lower) after Cr (VI) adsorption.
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Figure 5. (Left) SEM photograph ×500 and (right) EDS spectra of CR: (upper) before and (lower) after Cr (VI) adsorption.
Figure 5. (Left) SEM photograph ×500 and (right) EDS spectra of CR: (upper) before and (lower) after Cr (VI) adsorption.
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Figure 6. Characterization of bioadsorbents on a wet basis. The deviation of the data is +/− 0.01.
Figure 6. Characterization of bioadsorbents on a wet basis. The deviation of the data is +/− 0.01.
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Figure 7. Effect of the pH on Cr (VI) adsorption of bioadsorbents at room temperature, 250 rpm, and 24 h of contact time.
Figure 7. Effect of the pH on Cr (VI) adsorption of bioadsorbents at room temperature, 250 rpm, and 24 h of contact time.
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Figure 8. Analytic plots: (left) normal probability plot of the residuals and (right) externally studentized residuals plot for Cr (VI) removal using (a) PF, (b) YP, (c) CP, (d) CH, and (e) CR.
Figure 8. Analytic plots: (left) normal probability plot of the residuals and (right) externally studentized residuals plot for Cr (VI) removal using (a) PF, (b) YP, (c) CP, (d) CH, and (e) CR.
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Figure 9. Response surface plots of Cr (VI) efficiency removal % as a function of temperature, particle size, adsorbent dose, and its interaction effects for Cr (VI) removal using (a) PF, (b) YP, (c) CP, (d) CH, and (e) CR.
Figure 9. Response surface plots of Cr (VI) efficiency removal % as a function of temperature, particle size, adsorbent dose, and its interaction effects for Cr (VI) removal using (a) PF, (b) YP, (c) CP, (d) CH, and (e) CR.
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Figure 10. Adjustment of the Cr (VI) adsorption data to the pseudo-first order (PFO) kinetic model.
Figure 10. Adjustment of the Cr (VI) adsorption data to the pseudo-first order (PFO) kinetic model.
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Figure 11. Adjustment of the Cr (VI) adsorption data to the pseudo-second order (PSO) kinetic model.
Figure 11. Adjustment of the Cr (VI) adsorption data to the pseudo-second order (PSO) kinetic model.
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Figure 12. Adjustment of the Cr (VI) adsorption data to Elovich’s kinetic model.
Figure 12. Adjustment of the Cr (VI) adsorption data to Elovich’s kinetic model.
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Figure 13. Adjustment of the Cr (VI) adsorption data to the Intraparticle Diffusion (ID) kinetic model.
Figure 13. Adjustment of the Cr (VI) adsorption data to the Intraparticle Diffusion (ID) kinetic model.
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Figure 14. Adjustment of the Cr (VI) adsorption equilibrium data of the bioadsorbents from (a) YP, (b) PF, (c) CP, (d) CH, and (e) CR to the isotherm models.
Figure 14. Adjustment of the Cr (VI) adsorption equilibrium data of the bioadsorbents from (a) YP, (b) PF, (c) CP, (d) CH, and (e) CR to the isotherm models.
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Table 1. Methods for the analysis of the composition of the biomasses.
Table 1. Methods for the analysis of the composition of the biomasses.
ParametersMethod
Cellulose (%)Digestion-thermogravimetry
Hemicellulose (%)Digestion-thermogravimetry
Lignin (%)Photocolorimetry
Pectin (%)Acid digestion-thermogravimetry
Carbon (%)AOAC 949.14
Hydrogen (%)AOAC 949.14
Nitrogen (%)AOAC 949.13-Kjeldahl
Table 2. CCD for the Cr (VI) adsorption in the lignocellulosic bioadsorbents under study.
Table 2. CCD for the Cr (VI) adsorption in the lignocellulosic bioadsorbents under study.
Independent VariableSCodeFactor Level and Variable Value
−α−10+1
Temperature (°C)A3040557080
Particle size (mm)B0.1350.3550.67711.22
Adsorbent dose (g)C0.0310.150.3250.50.619
Table 3. Adsorption tests of the CCD.
Table 3. Adsorption tests of the CCD.
TestTemperature, °CParticle Size, mmAdsorbent Dose, g
140.01.00.5
240.01.00.15
355.01.2190.325
455.00.67750.03
555.00.67750.325
670.00.3550.5
780.220.67750.325
870.00.3550.15
940.00.3550.15
1070.01.00.15
1140.00.3550.5
1229.770.67750.325
1355.00.1350.325
1470.01.00.5
1555.00.67750.619
1655.00.67750.325
Table 4. CCD experimental design and its response for Cr (VI) removal using palm fibrillates, peels of yam, cassava and cocoa, and corn residues.
Table 4. CCD experimental design and its response for Cr (VI) removal using palm fibrillates, peels of yam, cassava and cocoa, and corn residues.
RunAdsorption Process VariablesCr (VI) Removal, %
PFYPCPCHCR
ABCERSMPERSMPERSMPERSMPERSMP
140.01.00.599.99910090.08510091.78210099.75110098.638100
240.01.00.1596.54187.77351.31574.41253.57867.7179.66272.93681.75275.556
355.01.2190.32599.99910099.99949.29498.78968.70999.01110098.152100
455.00.67750.0347.93167.21397.76378.54996.43277.42434.03351.82238.78255.872
555.00.67750.32595.85195.00895.80597.12496.45696.97899.49099.04198.72397.946
670.00.3550.599.99910099.99996.49598.98489.08899.49110098.76499.428
780.220.67750.32599.99910099.99980.78799.89796.82799.03210098.153100
870.00.3550.1599.99990.54999.99996.49599.47490.81499.36380.60997.46588.271
940.00.3550.1599.99990.00957.54445.09556.45659.91379.41075.75882.72375.009
1070.01.00.1599.99990.00923.73257.48946.15672.53599.36288.71799.53689.144
1140.00.3550.599.99910099.99976.93899.89777.75410010098.763100
1229.770.67750.32599.99910081.94986.04286.15683.23599.02198.19197.00397.541
1355.00.1350.32599.99910023.22459.93337.15661.32799.01310098.153100
1470.01.00.599.99910023.47846.62289.15689.93699.36210096.24898.429
1555.00.67750.61998.80689.26592.19996.24994.15698.0799.03189.00197.32587.939
1655.00.67750.32595.85295.00995.80597.10396.47396.97899.01298.56598.51297.946
E is the experimental data, and RSMP is the predicted results by Response Surface Method.
Table 5. Statistical analysis of experimental data for determining optimal conditions.
Table 5. Statistical analysis of experimental data for determining optimal conditions.
BiomassEquation
PF Y = 126.686 1.70139 A 53.7905 B + 166.658 C + 0.0155568 A 2 + 0.0893539 A B 0.164667 A C + 33.6544 B 2 + 7 . 65891 B C -   193 . 144 C 2 (8)
YP Y = 247.68 + 5.91523 A + 386.304 B + 321.945 C 0.0215131 A 2 3.53087 A B 3.87998 A C 146.353 B 2 8.72738 B C 111.798 C 2 (9)
CP Y = 92.2692 + 2.9888 A + 200.686 B + 130.56 C 0.0109166 A 2 1.34762 A B 1.86357 A C 108.783 B 2 + 84.7243 B C 54.0263 C 2 (10)
CH Y = 26.317 + 0.0591254 A 19.6269 B + 380.75 C + 0.00691135 A 2 0.00361757 A B 1.93143 A C + 14.9515 B 2 1.4175 B C 324.249 C 2 (11)
CR Y = 32.6509 + 0.0729527 A 17.5524 B + 346.157 C + 0.00556871 A 2 + 0.0168217 A B 1.66262 A C + 13.9998 B 2 8.28571 B C 299.935 C 2 (12)
where Y is chromium efficiency removal (%) and A, B, and C denotes values of temperature (°C), particle size (mm), and adsorbent dose (g), respectively.
Table 6. Thermodynamic parameters for adsorption of Cr (VI) in the bioadsorbents under study.
Table 6. Thermodynamic parameters for adsorption of Cr (VI) in the bioadsorbents under study.
YP
T (K)ΔG (kJ/mol)ΔH (kJ/mol)ΔS (kJ/mol·k)
306.91.4390.057−0.0465
328.22.611
349.43.783
PF
T (K)ΔG (kJ/mol)ΔH (kJ/mol)ΔS (kJ/mol·k)
306.9−0.549−2.121−0.143
328.20.782
349.412.837
CP
T (K)ΔG (kJ/mol)ΔH (kJ/mol)ΔS (kJ/mol·k)
306.91.2160.727−0.186
328.22.341
349.45.876
CH
T (K)ΔG (kJ/mol)ΔH (kJ/mol)ΔS (kJ/mol·k)
306.92.468−1.908−0.354
328.24.397
349.413.465
CR
T (K)ΔG (kJ/mol)ΔH (kJ/mol)ΔS (kJ/mol·k)
2981.24646.7720.153
323−2.572
348−6.391
Table 7. Adjustment parameter of Cr (VI) adsorption data to the evaluated kinetic models.
Table 7. Adjustment parameter of Cr (VI) adsorption data to the evaluated kinetic models.
ModelEquationParameterYPPFCPCHCR
Pseudo-first order q t = q e ( 1 e k 1 t ) qe1 (mg/g)21.702 ± 130.298 ± 0.0159.634 ± 114.46 ± 0.76516.663 ± 0.5
k1 (min−1)83.2316.366 ± 2.2481.046 ± 0.8549.05913877.719
R20.8120.9990.9950.7830.807
Reduced Chi-Square10.9870.00210.045.8614.442
σ20.7360.0380.0450.8930.757
Pseudo-second order q t = t ( 1 q e 2 k 2 ) + ( t q e ) qe2 (mg/g)21.702 ± 130.3399.6673 ± 0.07311.508 ± 1.4316.663 ± 0.54
k2 (g/mg.min)6.0152.977 ± 1.290.896 ± 0.9048.749 ± 1.4372.437 × 1019
R20.8120.9990.9960.9990.807
Reduced Chi-Square10.9877.116 × 10−40.03915.5444.442
σ20.7360.00050.0410.0040.747
Elovich q t = 1 β ln ( α β ) + 1 β ln ( t ) β (g/mg)0.504 ± 2.1573.5797.633 ± 2.1570.698 ± 0.0610.596 ± 0.05
α (mg/g min)1.242.464 ± 84.248 × 10441.205 × 1029389.198 ± 31212.943 ± 17
R20.9920.9980.9970.9860.979
Reduced Chi-Square0.4480.1850.0330.3770.482
σ20.0490.0400.0410.0530.068
Intraparticle diffusion q t = k 3 t 0.5 k31.1781.5000.4810.7880.925
R21.4333.1593.0271.3170.951
Reduced Chi-Square128.225347.79234.09556.25241.939
σ215.87310.98710.74615.94617.457
Table 8. Fitting parameters of Cr (VI) adsorption by YP, PF, CP, CH, and CR to isotherm models.
Table 8. Fitting parameters of Cr (VI) adsorption by YP, PF, CP, CH, and CR to isotherm models.
ModelEquationParameterYPPFCPCHCR
Freundlich q e = K F C e 1 / n KF 8.631 ± 0.83310.244 ± 2.45312.428 ± 2.9772.949 ± 1.1720.376 ± 0.226
n2.216 ± 0.2221.949 ± 0.3972.372 ± 0.5811.096 ± 0.220.681 ± 0.10
R20.9770.8920.8360.8780.935
Reduced Chi-Square1.89921.82532.45710.1527.149
σ20.8937.4566.8987.4647.149
Sips q e = q ms K s C e ms 1 + K s C e ms qms36.842 ± 5.35556.879 ± 10.12752.819 ± 7.282138.936 ± 8.32136.123
Ks0.203 ± 0.0740.158 ± 0.0640.201 ± 0.0670.0219.94 × 10−5
ms0.4560.3980.4510.4763.573
R20.9550.9360.9430.8910.977
Reduced Chi-Square4.53317.34015.03711.4111.565
σ26.65416.45619.45620.4561.877
Langmuir q e = ( Q max K L C e ) 1 + K L C e qmax38.842 ± 4.78956.879 ± 8.76952.819 ± 6.306138.936 ± 6.650240,948.7
KL0.203 ± 0.0660.159 ± 0.0550.202 ± 0.0580.021 ± 0.0295.65 × 10−6
RL0.0470.0590.0470.3230.999
R20.9550.9360.9430.8900.003
Reduced Chi-Square3.62613.00511.2789.129
σ25.45610.6647.5621.05416.076
Redlich –
Peterson
q e = ( AC e ) 1 + BC e g A278,317.865 ± 2.7376.759 ± 2.1727.045 ± 0.8542.663 ± 0.2061.477
B32,244.602 ± 3.180.019 ± 0.0670.018 ± 0.0195.099 ± 1.3900.087
g0.5491.631 ± 1.1241.644 ± 0.29312.4970
R20.9770.9490.9860.9480.853
Reduced Chi-Square2.37413.6553.8215.39520.093
σ213.05410.4560.4560.89810.046
Temkin q e = RT b T ln ( A T C e ) AT8.999 ± 5.6591.261 ± 0.2871.564 ± 0.4290.445 ± 0.051198.549
bT492.759 ± 83.969183.041 ± 20.771198.486 ± 25.191153.057 ± 15.609144.926
B5.11513.76912.69816.46717.399
R20.8740.9510.9400.9510.988
Reduced Chi-Square10.1759.86411.8694.087
σ225.0566.45610.45612.46520.091
Table 9. Maximum adsorption capacity comparison of different adsorbent materials.
Table 9. Maximum adsorption capacity comparison of different adsorbent materials.
BiomassBetter Adjustment ModelLangmuir’s qmax (mg/g)Reference
Activated carbon prepared from apple peelsFreundlich36.01[83]
Wheat branFreundlich4.2[14]
Wheat bran calcinated at 500 °C7.6
Wheat bran calcinated at 1000 °C29.3
Sawdust modified with formaldehydeFreundlich8.84[64]
Luffa cylindrica activated carbonFreundlich188.5[65]
Rice husk ashTemkin and Dubinin-Radushkevich4.1[67]
Pea peel activated carbon modified with ZnCl2Langmuir, Freundlich and Temkin306.75[68]
Banana peel dustLangmuir20.46[60]
Yam peelLangmuir, Freundlich, Sips and Redlich–Peterson38.842This study
Palm fibrillates Langmuir, Temkin, Sips and Redlich–Peterson56.879
Cassava peel52.819
Cocoa huskRedlich–Peterson and Temkin138.936
Corn residuesFreundlich, Sips, Langmuir y Temkin240,948.7
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Villabona-Ortíz, A.; Tejada-Tovar, C.; González-Delgado, Á.D. Statistical Modelling of Biosorptive Removal of Hexavalent Chromium Using Dry Raw Biomasses of Dioscorea rotundata, Elaeis guineensis, Manihot esculenta, Theobroma cacao and Zea mays. Sustainability 2023, 15, 9156. https://doi.org/10.3390/su15129156

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Villabona-Ortíz A, Tejada-Tovar C, González-Delgado ÁD. Statistical Modelling of Biosorptive Removal of Hexavalent Chromium Using Dry Raw Biomasses of Dioscorea rotundata, Elaeis guineensis, Manihot esculenta, Theobroma cacao and Zea mays. Sustainability. 2023; 15(12):9156. https://doi.org/10.3390/su15129156

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Villabona-Ortíz, Angel, Candelaria Tejada-Tovar, and Ángel Darío González-Delgado. 2023. "Statistical Modelling of Biosorptive Removal of Hexavalent Chromium Using Dry Raw Biomasses of Dioscorea rotundata, Elaeis guineensis, Manihot esculenta, Theobroma cacao and Zea mays" Sustainability 15, no. 12: 9156. https://doi.org/10.3390/su15129156

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