## Abstract

In this work, malachite green dye was removed from an aqueous effluent using acerola seed as an adsorbent. The adsorbent was characterized by Fourier transform infrared (FTIR), X-ray diffraction, zero charge potential, and acid group concentration techniques. The findings revealed that the adsorbent has a characteristic composition of lignocellulosic materials, as described by the FTIR data, besides having a pH-PZC of 3.5 and a concentration of acid groups of 0.2313 mmol g^{−1}. The central composite design was used for batch experiments, and the effects of three variables were analysed. The optimum conditions (pH, particle size, and adsorbent mass) were 10.0, 600 μm, and 0.8 g, respectively, for 97.52% dye removal. Redlich–Peterson isotherm fitted well to the experimental data (*R*^{2} = 0.997 and root-mean-square error (RMSE) = 1.168). From the Langmuir isotherm, the maximum adsorption capacity obtained for dye was 103.50 mg g^{−1}. As for the adsorption kinetics, it was found that the pseudo-second-order model sufficiently describes the experimental data (*R*^{2} = 0.999 and RMSE = 0.018). Thus, the acerola seed has excellent properties as an adsorbent, demonstrating a remarkable performance and a great capacity to be used in the treatment of aqueous effluents contaminated by dyes.

## HIGHLIGHTS

Biosorption has been investigated as a solution for malachite green dye from wastewater.

Optimization of dye removal on acerola seed was studied through three factors central composite design.

The highest removal yield was for adsorbent mass 0.8 g, pH 10.0, and particle size 600 μm.

From the Langmuir isotherm, the maximum adsorption capacity was 103.5 mg/g. The kinetic data were well fitted by the pseudo-second-order model.

## INTRODUCTION

Water is used in almost all human functional operations. It is a crucial factor for both domestic and industrial activities. However, it is common to find water bodies contaminated with plastic waste, toxic products, and other materials that pose a risk to the aquatic balance.

One of the main causes of water pollution is effluents from industrial activities, including toxic chemicals and pollutants, which are improperly disposed of in the environment, in water bodies such as rivers, lakes, aquifers, wells, and oceans.

Dyes are among the most common hazardous environmental pollutants in contaminated water, and they are improperly disposed of due to various industrial activities such as textiles, tanning, pulp and paper, paints, and pigments (Sridhar *et al.* 2022).

Currently, more than 10,000 commercial dyes are available, with an estimated production of 10^{6} tons per year (Bulgariu *et al.* 2019). However, a significant amount (>15%) is lost due to the dyeing process, which is discharged as effluent, posing a major threat to living beings and the environment (Dutta *et al.* 2014). This loss corresponds to approximately 280 kilotons of dyes lost in wastewater annually (Mishra *et al.* 2021).

The presence of dyes in water bodies causes distinct changes in water colour with a sudden reduction in oxygen content, harming flora and fauna (Bulgariu *et al.* 2019), impeding light penetration, and slowing photosynthetic activity. Due to their stable chemical structure containing aromatic rings, it is challenging to degrade such complex compounds (Hynes *et al.* 2020). Thus, there is a pressing need for the effective removal of these hazardous compounds to address environmental safety and toxicity.

Dye remediation techniques can be classified into four categories: physical, chemical, physicochemical, and biological. Numerous technologies have been proposed for the treatment of effluents contaminated with dyes: membrane filtration (the physical method) (Song *et al.* 2019); oxidation/Fenton process (the chemical method) (Patel *et al.* 2020); ozonation (Suryawan *et al.* 2018); photocatalytic methods (Kuvarega *et al.* 2018); coagulation/flocculation (Rodrigues *et al.* 2013) and adsorption (Madan *et al.* 2019) (physicochemical methods); and enzymes/microorganisms (Liu *et al.* 2020) and biosorption/biodegradation (Geed *et al.* 2019) (biological techniques). However, most of these dye removal techniques have challenges and drawbacks in terms of cost, generation of hazardous by-products, high energy consumption, efficiency, sustainability, and use of toxic chemicals.

Notably, adsorption procedures are an alternative to treat wastewater containing dyes, which, in turn, have gained prominence among the physicochemical procedures, as it is the one that allows the recovery of the material used, has high efficiency, and is relatively lower cost compared to other technologies.

The application of natural, ecological, and low-cost adsorbents to remove dyes and pigments from aqueous effluents through adsorption has been presented as a promising alternative for the problems generated by these wastes. The use of agro-industrial residues to remove these contaminants has been investigated, considering that these by-products of the agri-food sector represent an abundant, effective, and low-cost source to solve the problem of colour removal in contaminated effluents.

Thus, the production of alternative adsorbent materials has been explored, and among the raw materials used, fruit peels, flowers, seeds, or vegetable parts can be highlighted, mainly because they are reused waste from agricultural activities without any added economic value, which includes *Moringa oleifera* seed (Çelekli *et al.* 2019), mango leaf powder (Uddin & Rahman 2017), pineapple peel (Chaiyaraksa *et al.* 2019), and coffee husk (Murthy *et al.* 2019).

Acerola (*Malpighia emarginata*) is a fruit native to tropical Americas, also called Antilles cherry, and of great economic interest due to its high content of vitamin C. Brazil is the leading country in its production, consumption, and exportation. Acerola fruits are primarily used in the food industry to produce juice, ice cream, liqueur, soft drinks, gum, fruit conserve, jelly, yogurt, and others. With the increase in production, a great amount of fruit waste is generated, reaching up to 40% of the total volume processed, commonly consisting of peel, seed, and bagasse waste rejected during the process. The disposal of these residues is costly for companies, often being discharged or underused, thereby representing significant losses of feedstock and energy resources (Silva *et al.* 2018, 2020).

This article aims to study the use of acerola (*M. emarginata*) seeds in the removal of malachite green dye from aqueous effluents through adsorption in a finite batch, investigating kinetic and equilibrium aspects and the influence of process variables.

## METHODS

### Materials

Acerola seeds were obtained from the pulping of fruits collected from plants in Lagoa Seca, Paraíba State, Brazil. Analytical grade Malachite Green Oxalate, C.I. 42000 (molecular formula: C_{46}H_{50}N_{4}·2 C_{2}HO_{4}·C_{2}H_{2}O_{4}; molecular weight: 927.03 g/mol and *λ*_{max}: 617 nm), sodium hydroxide, hydrochloric acid, and sodium chloride (Neon, Brazil) solutions were prepared in deionized water. The standard dye solution used in the experiments was prepared after stepwise dilution of 1,000 mg L^{−1} stock solution. To determine the dye concentration, a straight-line calibration curve was used, previously prepared by plotting absorbance versus malachite green concentration. The absorbance was measured with a VIS spectrophotometer (WebLaborSP, WUV-M51) at 617 nm wavelength.

### Preparation of adsorbent

Acerola seeds were manually cleaned to remove foreign materials and dried in the sunlight for 8 h to remove moisture. Dried acerola seeds were ground in a knife mill and sieved to obtain uniform-sized particles. Grounded acerola seeds were washed repeatedly with distilled water until neutral pH and dried at 60 °C for 12 h.

### Point of zero charge and acid group concentrations

The experiments to determine the point of zero charge (PZC) were carried out with 0.1 M NaCl solutions in Erlenmeyer flasks, whose pH values were previously adjusted to 2 and 12, with intervals of 2 units by adding 0.1 M HCl or NaOH solutions. In each flask, 0.1 g of adsorbent was added under stirring at 120 rpm. After 24 h of contact, the samples were decanted, and the pH was measured in the final liquid phases with a Simpla PH-140 pH meter. The PZC was determined by plotting (pH_{initial} – pH_{final}) against pH_{initial}.

To determine the acid group concentrations, 0.5 g of adsorbent was put in contact with 25 mL of 0.025 M NaOH solution and stirred for 24 h at 100 rpm and 25 °C. Then, the samples were decanted, and the excess base in the final liquid phases was titrated with 0.025 M HCl to determine the surface acidity. The tests were performed in duplicate.

### X-ray diffractions

X-ray diffraction (XRD) powder diffraction pattern was obtained from a Bruker – D2 Phaser X-ray diffractometer operated with a voltage of 30 kV, X-ray source Cu k*α* radiation (*λ* = 1.5418 Å), and emission current of 10 mA. The diffractogram was recorded in terms of 2*θ* in the range of 3.0–70.0° with a step size of 0.02°.

### Infrared spectroscopy

The infrared (IR) spectra in the 4,000–500 cm^{−1} range were obtained for the adsorbent at room temperature using a Bruker VERTEX-70 Fourier transform infrared (FTIR), with a resolution of 4 cm^{−1}. The samples were prepared using the standard KBr pellet method.

### Adsorption isotherms

^{−1}). The contents were agitated on an orbital shaker at 100 rpm for 30 min at room temperature. Afterwards, 10-mL samples of the solution were filtered through filter paper, and the residual dye concentration was measured by visible spectrophotometry at 617 nm. The dye removal efficiency was given by the percentage of dye removal and adsorption capacity, calculated using Equations (1)–(3):where %Rem is the percentage of dye removal, and

*C*

_{0},

*C*, and

_{t}*C*are the initial concentration, at time

_{e}*t*, and final concentration (mg L

^{−1}) of malachite green dye in the solution, respectively.

*q*and

_{t}*q*are the adsorption capacities (mg g

_{e}^{−1}) at time

*t*or equilibrium time, respectively.

*V*is the volume (L) of the solution, and

*m*is the mass (g) of the adsorbent used.

*et al.*(2014), using nonlinear regression, from Equations (4)–(6), respectively:where

*q*is the maximum adsorptive capacity (mg g

_{m}^{−1}),

*k*is the Langmuir constant (L mg

_{L}^{−1}),

*k*is the Freundlich constant ((mg g

_{F}^{−1}) (mg L

^{−1})

^{−1/nF}), 1/

*nF*is the heterogeneity factor (dimensionless),

*k*

_{RP}(L mg

^{−1}) and

*a*

_{RP}(L mg

^{−1})

*are the constants for the Redlich–Peterson model, and*

^{β}*β*is the exponent of the Redlich–Peterson model (dimensionless).

### Adsorption kinetics

Kinetic removal of malachite green dye by acerola seed adsorbent was performed by batch experiments. Samples of 1.5 g of adsorbent, with 850 μm average particle size, and 100 mL aliquot of a 100 mg L^{−1} solution (pH 5.5) were placed in an Erlenmeyer flask and agitated on an orbital shaker at 120 rpm and room temperature (298.15 K). At different time periods (0, 60, 120, 180, 240, 300, 360, 420, 480, 540, and 600 s), aliquots of the supernatant solution were taken, and the malachite green concentration was determined using a visible spectrophotometer (*λ* = 617 nm).

*et al.*(2014), through nonlinear regression, represented by Equations (7)–(10), respectively:where

*q*is the adsorption capacity at equilibrium (mg g

_{e}^{−1}) and

*k*

_{1}(min

^{−1}), and

*k*

_{2}(g mg

^{−1}min

^{−1}) are the constants of the pseudo-first-order and pseudo-second-order models, respectively.

*q*

_{1},

*q*

_{2},

*q*

_{3}, and

*q*

_{4}are the theoretical values of adsorption capacity (mg g

^{−1}) at any time,

*t*.

*α*is the initial adsorption rate (mg g

^{−1}min

^{−1}), and

*β*is the desorption rate (mg g

^{−1}).

*k*

_{id}is the IPD rate constant (mg/(g.min

^{0.5}), and

*C*is the initial adsorption (mg g

^{−1}).

Regression analysis of the experimental data was performed using Microsoft Excel (2016) by the nonlinear least square method using the SOLVER tool based on the generalized reduced gradient method. The accuracy of the data fit was measured by evaluating the statistical parameters coefficient of determination (*R*^{2}), residual sum of squares (RSS), and root-mean-square error (RMSE).

### Experimental design

The adsorption process parameters, i.e., adsorbent mass (*X*_{1}), pH (*X*_{2}), and average particle size (*X*_{3}) were evaluated using a full factorial design, a central composite design (CCD). A total of 11 trials were conducted, comprising 8 factorial runs and 3 central runs (Table 1).

Run . | Adsorbent mass (g), X_{1}
. | pH (dimensionless), X_{2}
. | Average particle size (μm), X_{3}
. |
---|---|---|---|

1 | 0.2 ( − 1) | 4.0 ( − 1) | 600 ( − 1) |

2 | 0.8 ( + 1) | 4.0 ( − 1) | 600 ( − 1) |

3 | 0.2 ( − 1) | 10.0 ( + 1) | 600 ( − 1) |

4 | 0.8 ( + 1) | 10.0 ( + 1) | 600 ( − 1) |

5 | 0.2 ( − 1) | 4.0 ( − 1) | 850 ( + 1) |

6 | 0.8 ( + 1) | 4.0 ( − 1) | 850 ( + 1) |

7 | 0.2 ( − 1) | 10.0 ( + 1) | 850 ( + 1) |

8 | 0.8 ( + 1) | 10.0 ( + 1) | 850 ( + 1) |

9 | 0.5 (0) | 7.0 (0) | 725 (0) |

10 | 0.5 (0) | 7.0 (0) | 725 (0) |

11 | 0.5 (0) | 7.0 (0) | 725 (0) |

Run . | Adsorbent mass (g), X_{1}
. | pH (dimensionless), X_{2}
. | Average particle size (μm), X_{3}
. |
---|---|---|---|

1 | 0.2 ( − 1) | 4.0 ( − 1) | 600 ( − 1) |

2 | 0.8 ( + 1) | 4.0 ( − 1) | 600 ( − 1) |

3 | 0.2 ( − 1) | 10.0 ( + 1) | 600 ( − 1) |

4 | 0.8 ( + 1) | 10.0 ( + 1) | 600 ( − 1) |

5 | 0.2 ( − 1) | 4.0 ( − 1) | 850 ( + 1) |

6 | 0.8 ( + 1) | 4.0 ( − 1) | 850 ( + 1) |

7 | 0.2 ( − 1) | 10.0 ( + 1) | 850 ( + 1) |

8 | 0.8 ( + 1) | 10.0 ( + 1) | 850 ( + 1) |

9 | 0.5 (0) | 7.0 (0) | 725 (0) |

10 | 0.5 (0) | 7.0 (0) | 725 (0) |

11 | 0.5 (0) | 7.0 (0) | 725 (0) |

*Source*: Elaborated by the authors.

A 50 mL aliquot of malachite green solution (200 mg L^{−1}) was mixed with an adsorbent dosage (Table 1) in a 125 mL Erlenmeyer flask and shaken for 30 min at 120 rpm using an orbital shaker at room temperature. Then, the solutions were filtered through Whatman filter paper No. 41. To determine the malachite green concentration in the final solution, the absorbance of each sample was measured with a VIS spectrophotometer at 617 nm. The response variable was evaluated as the percentage of dye removal (%Rem), shown in Equation (1).

*p*-values,

*F*-values, and coefficient of determination (

*R*

^{2}). The Statistica software (version 10.0) was used to generate the regression model, the response surface, and the Pareto chart.where

*Y*is the response variable (percentage of dye removal);

*X*

_{1},

*X*

_{2}, and

*X*

_{3}are the independent variables, i.e., the process parameters (adsorbent mass, pH, and particle size);

*β*

_{0}is the average response in all runs;

*β*

_{1},

*β*

_{2}, and

*β*

_{3}are the linear coefficients of the model;

*β*

_{12},

*β*

_{13}, and

*β*

_{23}are the second-order interaction coefficients; and

*β*

_{123}is the third-order interaction coefficient.

## RESULTS AND DISCUSSION

### Point of zero charge and acid groups concentration

*et al.*(2019), when pH < pH(PZC), the solid surface is predominantly positive charge and repels dye particles (cationic). In turn, when pH > pH(PZC), the surface has a negative charge, which increases the adsorption rate due to the strong electrostatic force between the adsorbent and the dye molecules, thus favouring the dye adsorption process.

Referring to acid group concentration (AGC) on the acerola seed surface, an amount of 0.2313 mmol g^{−1} of adsorbent was obtained. The principal surface acid groups in lignocellulosic materials are the phenolic (-OH), lactone (-C = O), and carboxylic (-COOH) functional groups, responsible for the adsorption of dye molecules, metal ions, etc. Similar results are presented by Nogueira *et al.* (2019), who report that these groups promote interactions between the adsorbate and the adsorbent, making surface complexes, π-bonds, and supporting adsorption.

### X-ray diffractions

### IR spectroscopy

According to Silverstein & Webster (1998), the bands in the region of 1,570–1,645 cm^{−1} are characteristic of the carboxylate ion (COO^{−}); the first intense band comes from the asymmetric axial strain, while the other is weaker and comes from the symmetric axial strain. In this work, these bands are observed at 1,531 and 1,629 cm^{−1}.

Nakamoto (1997) found that the hydroxyl group (OH^{−}) exhibits a metal-OH bonding mode that appears at approximately 1,100 cm^{−1}. In this study, this band appears at 1,034 cm^{−1}, and this displacement occurs due to interactions with other groups and/or bonds.

The broad and intense band 3,280 cm^{−1} can be attributed to the O-H stretching vibration. The two bands located at 2,921 and 2,852 cm^{−1} can be attributed to asymmetric and symmetric -CH_{2} stretching vibration, respectively. IR absorption bands at 1,238, 1,325, and 1,369 cm^{−1} can be attributed to the N-H stretching vibration emitted by some aromatic compounds found in the material composition (Silva *et al.* 2020).

The biomass associated with alkali and alkaline earth metals is usually found in bands with high energy, as in this region stretching and bending vibrations can be assigned on the surface of hydroxyl groups. It is not clear from Figure 3 whether a band or shoulder is formed at 488 cm^{−1}.

Analysing the adsorbent spectra, before and after the dye adsorption, it is possible to notice that the broad and intense band 3,280 cm^{−1} suffered a small increment due to the contact with the solution. After adsorption, the peak at 2,852 cm^{−1} merges into a broadband formation at 2,919 cm^{−1}, which is also attributed to the asymmetric and symmetric stretching vibration –CH_{2}.

The peak 1,531 cm^{−1}, characteristic of the carboxylate ion (COO^{−}), originating from the asymmetric axial strain, disappears after adsorption, while the symmetric axial strain band widens and shifts to 1,601 cm^{−1}. Other smaller bands, due to the N-H stretching vibration (1,238, 1,325, and 1,369 cm^{−1}), also undergo smoothing, forming wider shoulders. These cited modifications do not constitute a visible change in the spectrum profile, making it clear that the structure of the material, at medium range, remains stable.

### Adsorption isotherms

Knowing the adsorption, equilibrium provides a basis for evaluating the adsorption process, characterizing the adsorbent/adsorbent interaction, selecting adsorption conditions, and designing the batch.

The adsorption isotherm data were analysed using the Langmuir, Freundlich, and Redlich–Peterson models, described by Equations (4)–(6), respectively. Nonlinear regression analysis, using the nonlinear least square method, was performed to estimate the model parameters, depicted in Table 2.

Model . | Temperature (K) . | Model constants . | . | Statistical parameters . | |||
---|---|---|---|---|---|---|---|

. | R^{2}
. | RSS . | RMSE . | ||||

Langmuir | k_{L} | q_{L} | |||||

298.15 | 0.046 | 103.507 | 0.995 | 14.580 | 1.559 | ||

Freundlich | k_{F} | n | |||||

298.15 | 7.957 | 1.696 | 0.992 | 20.742 | 1.859 | ||

Redlich–Peterson | k_{RP} | a_{RP} | β | ||||

298.15 | 6.036 | 0.189 | 0.588 | 0.997 | 8.179 | 1.168 |

Model . | Temperature (K) . | Model constants . | . | Statistical parameters . | |||
---|---|---|---|---|---|---|---|

. | R^{2}
. | RSS . | RMSE . | ||||

Langmuir | k_{L} | q_{L} | |||||

298.15 | 0.046 | 103.507 | 0.995 | 14.580 | 1.559 | ||

Freundlich | k_{F} | n | |||||

298.15 | 7.957 | 1.696 | 0.992 | 20.742 | 1.859 | ||

Redlich–Peterson | k_{RP} | a_{RP} | β | ||||

298.15 | 6.036 | 0.189 | 0.588 | 0.997 | 8.179 | 1.168 |

*Source*: Elaborated by the authors.

Table 2 shows that the *R*^{2} values of the Redlich–Peterson model are closer to unity than the *R*^{2} values of the Langmuir and Freundlich models. Nevertheless, the *R*^{2} values of the three models are greater than 0.99, thus confirming that these models can be applied to explain the malachite green adsorption onto acerola seed. The lower RSS and RMSE values of the Redlich–Peterson model compared to that of the Langmuir and Freundlich models also evidence that the first one better describes the experimental data.

According to Nascimento *et al.* (2014), the empirical Redlich–Peterson equation combines characteristics of the Langmuir and Freundlich models, approaching the former at low concentrations, when *β* tends to 1, and assuming the form of the latter in systems under high concentrations, when *β* tends to zero. In this case, as the *β* value is closer to 1 (*β* = 0.588), the Redlich–Peterson statistical parameters are closer to those of the Langmuir model.

In addition, Freundlich isotherms with 1/*n* > 1 show relatively high adsorbent loadings at low concentrations. Therefore, they are referred to as favourable isotherms, whereas isotherms with 1/*n* < 1 are characterized as unfavourable. This result also indicates that the adsorption process occurs in multilayers.

^{−1}. In comparison, Murthy

*et al.*(2019) reported values of adsorptive capacity for different adsorbents: H

_{2}SO

_{4}-treated coffee husk (264.812 mg g

^{−1}), NaOH-modified grapefruit peel (314.90 mg g

^{−1}), EDTA-modified sugarcane bagasse (157.2 mg g

^{−1}). Furthermore, Mishra

*et al.*(2021) showed adsorptive capacities for other materials:

*M. oleifera*seed husk (91.74 mg g

^{−1}) and

*Theobroma grandiflorum*seed shell (64.1 mg g

^{−1}).

### Adsorption kinetics

According to Murthy *et al.* (2019), the kinetics of the adsorption process allows to describe the rate of uptake of adsorbent, which, in turn, determines the contact time of the adsorption required for reaching equilibrium.

The experimental data obtained were fitted to four different kinetic models, i.e., pseudo-first-order, pseudo-second-order, second-order (Elovich), and Weber–Morris IPD models, described by Equations (7)–(10), respectively.

Kinetic and statistical parameters obtained by nonlinear regression using the least squares method are summarised in Table 3.

Model . | Concentration (g L^{−1})
. | Model constants . | Statistical parameters . | |||
---|---|---|---|---|---|---|

R^{2}
. | RSS . | RMSE . | ||||

Pseudo-first order | | q_{1} | k_{1} | | | |

100.0 | 6.240 | 0.036 | 0.998 | 0.064 | 0.077 | |

Pseudo-second order | | q_{2} | k_{2} | | | |

100.0 | 6.426 | 0.017 | 0.999 | 0.004 | 0.018 | |

Second order | | α | β | | | |

100.0 | 698.293 | 3.289 | 0.996 | 0.053 | 0.070 | |

Weber–Morris IPD | | k_{id} | C | | | |

100.0 | 0.197 | 2.479 | 0.607 | 13.745 | 1.118 |

Model . | Concentration (g L^{−1})
. | Model constants . | Statistical parameters . | |||
---|---|---|---|---|---|---|

R^{2}
. | RSS . | RMSE . | ||||

Pseudo-first order | | q_{1} | k_{1} | | | |

100.0 | 6.240 | 0.036 | 0.998 | 0.064 | 0.077 | |

Pseudo-second order | | q_{2} | k_{2} | | | |

100.0 | 6.426 | 0.017 | 0.999 | 0.004 | 0.018 | |

Second order | | α | β | | | |

100.0 | 698.293 | 3.289 | 0.996 | 0.053 | 0.070 | |

Weber–Morris IPD | | k_{id} | C | | | |

100.0 | 0.197 | 2.479 | 0.607 | 13.745 | 1.118 |

*Source*: Elaborated by the authors.

The *R*^{2} values for all three models are very close to unity, which shows that they all explain the experimental data satisfactorily well. However, the pseudo-second-order model still presents a higher value than the other models, which implies that it fits better with the experimental kinetic data. The lower RSS and RMSE values of the pseudo-second-order model compared to that of the pseudo-first-order and Elovich models also demonstrate that the first one better describes the experimental data.

The pseudo-second-order model assumes that there is more than one controlling step in the adsorption process, such as external and internal diffusion, in addition to diffusion at the active site itself. In this case, the rate constant *k*_{2} is equal to 0.017 g/mg s. It also considers that adsorption occurs at localized sites and does not involve interaction between adsorbate particles. Moreover, the maximum adsorption corresponds to a saturated monolayer of adsorbate on the surface of the adsorbent.

*q*and

*t*fitting the experimental and Weber–Moris IPD equation.

Internal diffusion models assume that mass transfer into the interior of the particle is the slowest step in the adsorption process. When the adsorption process is controlled only by the intraparticle diffusion mechanism, the line should pass through the origin. In this work, the intercept of the plot occurs above the origin, which implies multi-linearity, thus indicating that the adsorption process is controlled by multiple steps, i.e., the intraparticle diffusion is not the only rate-limiting step.

### Experimental design

*X*

_{1}), pH (

*X*

_{2}), and average particle size (

*X*

_{3}) were statistically evaluated using a CCD to investigate their effects on the response of interest, the percentage of dye removal (%Rem). A first-order polynomial model was fitted to the experimental results of malachite green removal using Statistica 10.0 software. The model obtained is shown in Equation (12):

The experimental and predicted results (using Equation (10)) for dye removal of each experimental trial are listed in Table 4.

Run . | Adsorbent mass (g), X_{1}
. | pH (dimensionless), X_{2}
. | Average particle size (μm), X_{3}
. | Dye removal (%) . | |
---|---|---|---|---|---|

Predicted . | Experimental . | ||||

1 | 0.2 ( − 1) | 4.0 ( − 1) | 600 ( − 1) | 90.97 | 90.44 |

2 | 0.8 ( + 1) | 4.0 ( − 1) | 600 ( − 1) | 97.72 | 97.19 |

3 | 0.2 ( − 1) | 10.0 ( + 1) | 600 ( − 1) | 92.90 | 92.38 |

4 | 0.8 ( + 1) | 10.0 ( + 1) | 600 ( − 1) | 98.05 | 97.52 |

5 | 0.2 ( − 1) | 4.0 ( − 1) | 850 ( + 1) | 82.13 | 81.60 |

6 | 0.8 ( + 1) | 4.0 ( − 1) | 850 ( + 1) | 94.42 | 93.90 |

7 | 0.2 ( − 1) | 10.0 ( + 1) | 850 ( + 1) | 84.15 | 83.63 |

8 | 0.8 ( + 1) | 10.0 ( + 1) | 850 ( + 1) | 94.84 | 94.31 |

9 | 0.5 (0) | 7.0 (0) | 725 (0) | 91.90 | 93.62 |

10 | 0.5 (0) | 7.0 (0) | 725 (0) | 91.90 | 93.09 |

11 | 0.5 (0) | 7.0 (0) | 725 (0) | 91.90 | 93.20 |

Run . | Adsorbent mass (g), X_{1}
. | pH (dimensionless), X_{2}
. | Average particle size (μm), X_{3}
. | Dye removal (%) . | |
---|---|---|---|---|---|

Predicted . | Experimental . | ||||

1 | 0.2 ( − 1) | 4.0 ( − 1) | 600 ( − 1) | 90.97 | 90.44 |

2 | 0.8 ( + 1) | 4.0 ( − 1) | 600 ( − 1) | 97.72 | 97.19 |

3 | 0.2 ( − 1) | 10.0 ( + 1) | 600 ( − 1) | 92.90 | 92.38 |

4 | 0.8 ( + 1) | 10.0 ( + 1) | 600 ( − 1) | 98.05 | 97.52 |

5 | 0.2 ( − 1) | 4.0 ( − 1) | 850 ( + 1) | 82.13 | 81.60 |

6 | 0.8 ( + 1) | 4.0 ( − 1) | 850 ( + 1) | 94.42 | 93.90 |

7 | 0.2 ( − 1) | 10.0 ( + 1) | 850 ( + 1) | 84.15 | 83.63 |

8 | 0.8 ( + 1) | 10.0 ( + 1) | 850 ( + 1) | 94.84 | 94.31 |

9 | 0.5 (0) | 7.0 (0) | 725 (0) | 91.90 | 93.62 |

10 | 0.5 (0) | 7.0 (0) | 725 (0) | 91.90 | 93.09 |

11 | 0.5 (0) | 7.0 (0) | 725 (0) | 91.90 | 93.20 |

*Source*: Elaborated by the authors.

The ANOVA shown in Table 5 was used to assess the significance and adequacy of the model. Statistical analysis of data variance was performed using Fisher's *F*-test.

Source . | Sum of squares (SS) . | Degrees of freedom . | Mean square . | F-value
. | p-value
. |
---|---|---|---|---|---|

Adsorbent mass (X_{1}) | 152.07 | 1 | 152.07 | 1,974.43 | 0.0005* |

pH (X_{2}) | 2.76 | 1 | 2.76 | 35.83 | 0.0268* |

Particle size (X_{3}) | 72.58 | 1 | 72.58 | 942.33 | 0.0011* |

X_{1}X_{2} | 1.30 | 1 | 1.30 | 16.86 | 0.0545 |

X_{1}X_{3} | 15.36 | 1 | 15.36 | 199.40 | 0.0049* |

X_{2}X_{3} | 0.004 | 1 | 0.004 | 0.05 | 0.8393 |

Lack of fit | 8.16 | 2 | 4.08 | 52.98 | 0.0185* |

Pure error | 0.15 | 2 | 0.08 | ||

Total SS | 252.39 | 10 |

Source . | Sum of squares (SS) . | Degrees of freedom . | Mean square . | F-value
. | p-value
. |
---|---|---|---|---|---|

Adsorbent mass (X_{1}) | 152.07 | 1 | 152.07 | 1,974.43 | 0.0005* |

pH (X_{2}) | 2.76 | 1 | 2.76 | 35.83 | 0.0268* |

Particle size (X_{3}) | 72.58 | 1 | 72.58 | 942.33 | 0.0011* |

X_{1}X_{2} | 1.30 | 1 | 1.30 | 16.86 | 0.0545 |

X_{1}X_{3} | 15.36 | 1 | 15.36 | 199.40 | 0.0049* |

X_{2}X_{3} | 0.004 | 1 | 0.004 | 0.05 | 0.8393 |

Lack of fit | 8.16 | 2 | 4.08 | 52.98 | 0.0185* |

Pure error | 0.15 | 2 | 0.08 | ||

Total SS | 252.39 | 10 |

*** p**-Value < 0.05 indicates that the model terms are significant.

*Source*: Elaborated by the authors.

To evaluate the significance of the regression model, the determination coefficient, *R*^{2}, was used. When *R*^{2} assumes values closer to 1, this indicates a better model prediction. In this case, the ANOVA shows that the adequacy between the experimental and the predicted values is high, with an *R*^{2} value of 0.9671 for dye removal onto acerola seed. This result indicates that 96.71% of the total data variance can be explained by the three independent variables analysed, showing the high degree of fit of the model.

*et al.*(2022), the model and its terms can be considered statistically significant when the

*p*-value is less than 0.05 with a larger

*F*-value. The finds revealed that the linear terms, adsorbent mass (

*X*

_{1}), pH (

*X*

_{2}), and particle size (

*X*

_{3}) showed the most significant effect with

*p*-value < 0.05 and higher values for

*F*. The interactive term between adsorbent mass and particle size (

*X*

_{1}

*X*

_{3}) was also significant (

*p*< 0.05), while the other two interactive terms adsorbent mass and pH (

*X*

_{1}

*X*

_{2}) and pH and particle size (

*X*

_{2}

*X*

_{3}) were not significant in the range analysed. This is corroborated by the Pareto chart presented in Figure 7, which shows the standardized effects for each term in the model.

Thus, a slight variation (independent variables) in the operational conditions promotes a significant alteration in the response, malachite green removal. In this case, the lack of fit of the model appears to be significant. However, this is due to the small value found for the pure error, with which the lack of fit is quantified.

To determine the optimal values for dye removal, the regression model equation was illustrated by 3D response surface and 2D contour plots for the studied variables within the experimental ranges.

However, as described by ANOVA and the Pareto chart, the effect of pH on dye removal is less than the influence of adsorbent mass, as shown in Figure 8.

## CONCLUSIONS

Locally, acerola seeds were investigated as an adsorbent for the removal of malachite green dye from synthetic wastewater. The adsorbents were characterized by XRD, FTIR spectroscopy, pH-PZC, and AGC techniques. The kinetic adsorption of malachite green onto acerola seeds follows the pseudo-second-order model. The intraparticle diffusion mechanism indicates the adsorption process is controlled by multiple steps, showing that the intraparticle diffusion is not the only rate-limiting step. The Redlich–Peterson isotherm model better fitted the equilibrium data. Adsorbent mass, pH, and average particle size were evaluated as process parameters for dye adsorption onto acerola seed. These independent variables were investigated by a statistical experimental design (CCD), and all three were statistically significant, with particle size and adsorbent mass having the greatest effects on dye removal. The optimal conditions (pH, particle size, and adsorbent mass) were 10.0, 600 μm, and 0.8 g, respectively, for 97.52% dye removal. The results suggest that grounded acerola seed has a good adsorption capacity and is a promising and low-cost adsorbent material for dye removal from industrial effluents. A possible way of concentrating and recovering malachite green dye adsorbed on acerola seed would be through dye solubilization in an organic solvent, such as methanol. This proposal involves drying the adsorbent solid containing the adsorbed dye, mixing it with methanol under stirring for a certain period, filtration to recover the dye-free adsorbent. Finally, the methanol containing the dissolved dye is separated by vacuum evaporation, regenerating the dye.

## DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

## CONFLICT OF INTEREST

The authors declare there is no conflict.

## REFERENCES

*Malphigia emarginata*D.C.). (2019 Characterization and application of hydrocarbon obtained from hydrothermal carbonization of acerola (

*Malphigia emarginata*D.C.) residue)