A solution of Fe(II) ions at a concentration of 1000 mg/L was prepared by dissolving 4.977 g of ferrous sulfate hepta-hydrate salt (Fe₂SO₄·₇H₂O, Labosi, purity: 100%) in a 1000 mL volumetric flask. For adsorption experiments in static and dynamic conditions, solutions with concentrations of 10, 50, 70, 90, 100, 150, and 200 mg/L were prepared by dilution from the 1000 mg/L Fe(II) solution.

Palm nut shells collected in the city of Franceville in the Haut-Ogooué region of Gabon, were used as raw material for the preparation of activated carbons (ACs) using a chemical activation process ( Amola et al., 2020 ). The palm nut shells were cleaned, ground, washed with distilled water, and then dried in an oven for 24 hours (h) at 110˚C. Afterward, 80 g of pre-treated shells were impregnated (1:1 ratio) in a 1 M potassium hydroxide solution (KOH, Acros Organics, purity: 98.5%) for 30 minutes (min), 1 h, and 24 h and then dried again for 24 h at 110˚C. After drying, the impregnated shells were calcined at 400˚C for 1 h and 30 min. with a heating rate of 5˚C/min. The ACs obtained were cooled, washed with distilled water until the pH of the residual water reached 6.5, dried for 48 h at 110˚C and sieved to obtain powdered activated carbon and granular activated carbon with particle sizes (x) of 0.04 mm < x and 0.04 mm < x < 0.1 mm, respectively (sieves: TAMISAR, Standard: AFNOR_NF-X11-501). The activated carbons obtained with impregnation times of 30 min, 1 h, and 24 h were indexed AC-i_30min, AC-i_1h, and AC-i_24h.

The methylene blue number (I_BM) was determined using the European Chemical Industry Council method ( CEFIC & EDFDLCECOCMF, 1986 ). 100 mg of activated carbon was mixed with 25 mL of a methylene blue solution (MB, Alp Osmose, purity: >98.5%) at 120 mg/L in a 50 mL beaker and stirred at 200 rpm for 20 min. The mixture was then filtered using a Büchner and the residual concentrations of MB were determined in colorimetry using a Thermo Electron Corporation Biomate 5 UV spectrophotometer at a wavelength λ = 664 nm. The methylene blue number (I_BM) is calculated using the following equation:

$I_{BM}=\frac{\left(C_0-C_f\right)V}{m_{AC}}$ (1)

where, I_BM is the methylene blue number (mg·g⁻¹); C₀ is the initial concentration of methylene blue (mg·L⁻¹); C_f is the residual concentration of methylene blue (mg·L⁻¹); m_AC is the activated carbon mass (g) and V is the volume of the methylene blue solution (L).

The iodine number ( $I_{I_2}$) was determined according to the ASTM D4607-94 method ( Balogoun et al., 2015 ). 100, 300, and 500 mg of prepared AC were stirred in 10 mL of 1 N hydrochloric acid solution (HCl, Emsure, purity: 33%) for 30 seconds in 150 mL beakers. After cooling at room temperature, 50 mL of iodine solution of 0.02 N (I₂, Fisher Scientific) solution was added to the mixture and stirred vigorously for 30 seconds, then filtered. After filtration, 25 mL of the filtrate was titrated with 0.1 N sodium thiosulfate (Na₂S₂O₃, Labosi, purity: 99%) until the filtrate turned pale yellow. Then, 2 mL of a starch solution (1 g/L) was added as color indicator and titration was continued with sodium thiosulfate until the solution became colorless. The iodine number ( $I_{I_2}$) is calculated as follows:

$I_{I_2}\left(\text{mg}/\text{g}\right)=\frac{A-\left(DF\times B\times V_{thiosulfate}\right)}{m_{AC}}$ (2)

where, A is the concentration of I₂ (mol·L⁻¹) x Molar mass of iodine (g·mol⁻¹); B is the concentration of Na₂S₂O₃ (mol·L⁻¹) x Molar Mass of Iodine (g·mol⁻¹), DF is the dilution factor ( $\frac{V_{I_2}+V_{HCl}}{V_{Filtrate}}$) and m_AC is activated carbon mass (g). By plotting the curve $Q_{I_2}={\displaystyle \int \left(C_r\right)}$, the iodine number is then the value of $Q_{I_2}$ (mg·g⁻¹) corresponding to a residual iodine concentration of 0.04 N. The residual concentration of iodine is given by the following relationship:

$C_r=\frac{C\cdot V_{eq}}{V}$ (3)

With C_r: residual concentration of I₂ (N); C: concentration of Na₂S₂O₃ (N); V_eq: volume of Na₂S₂O₃ (mL) and V: volume of titrated filtrate (mL). The residual concentration of I₂ should be between 16 × 10⁻⁴ N and 8 × 10⁻³ N.

A theoretical study of the specific surface areas was performed to estimate the specific surface areas of prepared ACs using iodine and methylene blue numbers. The method used was developed by Nunes et al. ( Nunes et al., 2011 ). It is based on modeling the relationship between the specific surface area, the iodine and the methylene blue number using multiple regression analysis. The model used to estimate (calculate) the specific surface area is described by the following equation:

$\begin{array}{c}S\left({\text{m}}^{\text{2}}/\text{g}\right)=2.28\times {10}^2-1.01\times {10}^{-1}\times I_{BM}+3\times {10}^{-1}\times I_{I_2}\\ +1.05\times {10}^{-4}\times I_{BM}^2+2\times {10}^{-4}\times I_{I_2}^2+9.38\times {10}^{-4}\times I_{BM}\times I_{I_2}\end{array}$ (4)

where S is the calculated specific surface area (m²/g), I_BM and $I_{I_2}$ are respectively the methylene blue index and the iodine number (mg/g).

Surface functional groups were determined using Boehm titration ( Boehm, 1966 ). 200 mg of activated carbon was stirred at 200 rpm in 25 mL of sodium hydroxide (NaOH, Emesure, purity: 99%), sodium bicarbonate (NaHCO₃, Mercek, purity: 99%), hydrochloric acid (HCl, Emsure, purity: 33%), and sodium carbonate (Na₂CO₃, Mercek, purity: 99.5%) at concentrations ranging from 0.05 to 0.1 M for 24 hours. The mixtures were filtered, and 10 mL of each filtrate was titrated with HCl or NaOH at 0.1 M to determine acidic and basic functions, respectively. The number of equivalents (m_eq·g⁻¹) or concentrations (mmol·g⁻¹) of acid or basic surface functional groups were determined by the following formula [33] [34]:

$n\left(\text{mmol}\cdot {\text{g}}^{-1}\right)=\frac{C\times \left(V_b-V_s\right)\times 1000}{m_{AC}}$ (5)

where C is the concentration of NaOH or HCl (mol·L⁻¹); V_b and V_s are the equivalent volumes of the blank and sample (L), respectively; m is the mass of activated carbon (g) and 1000 is the conversion factor (mmol).

The pH at the point of zero charge (pH_pzc) of prepared ACs was determined according to the method described by Amola et al. ( Amola et al., 2020 ). 40 mg of AC was placed in Erlenmeyer flasks and stirred at 200 rpm for 24 h in 20 mL of 0.1 M potassium chloride solutions (KCl, VWR Chemicals, purity: 99.5%) at different initial pH values (pH_i): 2; 5; 7 and 9. The pH of each solution was adjusted by adding either 0.1 M HCl or 0.1 M NaOH. After mixing, the solutions were left to decant, and the final pH (pH_f) was measured. The pH_pzc is obtained from the intersection point between the experimental curve and the theoretical curve of pH_f as a function of pH_i.

Static adsorption experiments were conducted at room temperature (24˚C - 27˚C) in five Erlenmeyer of 50 mL, each containing 20 mL of a Fe(II) ion solution at 50 mg/L and 0.05 g of prepared ACs. The mixtures were stirred at 200 rpm and the experiments were stopped at agitation times of 10, 20, 40, 60, and 80 minutes. The solutions were then filtered and a few drops of phenanthroline were added to the filtrates. The residual concentrations of Fe(II) in each Erlenmeyer flask were determined by colorimetry using a Thermo Electron Corporation Biomate 5 UV spectrophotometer at a wavelength of 512 nm based on a pre-established calibration curve for Fe(II).

The adsorption capacities at saturation (Q_sat) of Fe(II) for the prepared activated carbons were determined using the following expression:

$Q_{sat}=\frac{C_0-C}{m_{AC}}\cdot V$ (6)

With, Q_sat: adsorption capacity at saturation of activated carbon (mg/g), C₀: concentration of the solution initial of Fe(II) (mg/L), C: concentration residual of Fe(II) (mg/L), V: Volume of the Fe(II) solution (L) and m_AC: mass of activated carbon (g).

Percentages of Fe(II) elimination (%E) of prepared ACs were calculated as follows:

$\%E=\frac{C_0-C}{C_0}\times 100$ (7)

Dynamic adsorption experiments on a fixed-bed column of Fe(II) ions adsorption were conducted in a 55 cm long, 1.4 cm diameter glass column (Pyrex brand). The protocol and schematic of the experimental setup were described in a recent study ( Mve Mfoumou et al., 2022 ). The experiments were carried out at room temperature (24˚C - 27˚C) using a Fe(II) solution at pH 6.5 with a concentration of 50 mg/L and a flow rate of 2 mL/min. The height of the adsorbent bed was 1 cm and the particle size ranged between 0.04 < x < 0.1 mm. The experiments were stopped when the residual concentration (C) at the reactor outlet was equal to the concentration at the column inlet (C/C₀ = 1). A few drops of phenanthroline were added to solutions collected at the column outlet (every 4 minutes) in test tubes. Fe(II) concentrations in each tube (C) were determined by colorimetry using a Thermo Electron Corporation Biomate 5 UV-visible spectrophotometer at a wavelength of 512 nm.

The breakthrough curves were established by varying the ratio C/C₀ versus time (t). Exploitation of curve data $C/C_0={\displaystyle \int \left(t\right)}$ gives an area (A) in minutes obtained by integration according to the trapeze method ( Mve Mfoumou et al., 2022 ; Mve Mfoumou et al., 2024 ):

$A\left(\min \right)=\underset{n}{{\displaystyle \sum }}\frac{\left(1-\frac{C_{t_n}}{C_0}\right)+\left(1-\frac{C_{t_{n+1}}}{C_0}\right)}{2}\times \left(t_{n+1}-t_n\right)$ (8)

where C₀ and C are the inlet and outlet concentrations (mg/L) at times t_n and t_n+1, respectively.

Adsorbed quantities (q_ads) and adsorption capacities at saturation (Q_sat) of Fe(II) of prepared activated carbons were calculated using the following formulas ( Mve Mfoumou et al., 2022 ):

$q_{ads}\left(\text{mg}\right)=D\cdot C_0\cdot A$ (9)

$Q_{sat}\left(\text{mg}/\text{g}\right)=\frac{D\cdot C_0\cdot A}{m_{AC}}$ (10)

With D, C₀, A, and m_AC corresponding to the flow rate (mL/min), the concentration at the inlet of the column (mg/L), the surface area (min) corresponding to the amount of Fe(II) adsorbed and the activated carbon mass used (g) respectively.

Removal percentages of Fe(II) on prepared adsorbents (%E) were determined the following equation ( Mve Mfoumou et al., 2022 ):

$E\left(\%\right)=\frac{A}{t_{sat}}\times 100$ (11)

With t_sat: the saturation time (min).

Adsorption kinetic studies provide information on the transfer mode of the solute from the liquid phase to the solid phase. To evaluate these parameters, the pseudo-first-order kinetic model developed by Lagergren ( Belaid et al., 2011 ; Goertzen et al., 2010 ) and the pseudo-second-order kinetic model developed by Blanchard and linearized by Ho ( Blanchard et al., 1984 ; Ho et al., 1999 ) were applied to the experimental data obtained from the static and dynamic adsorption of Fe(II) on prepared ACs.

The rate law of a pseudo-first-order reaction is expressed by the following equation ( Belaid et al., 2011 ):

$\frac{\text{d}{q}_t}{\text{d}t}=k_1\left(q_e-q_t\right)$ (12)

By integration between t = 0 (q_t = 0) and t, the following linear form is obtained:

$\log \left(q_e-q_t\right)=\log \left(q_e\right)-\frac{k_1}{2.3}\cdot t$ (13)

where q_t and q_e correspond to maximum adsorption capacities at time t and equilibrium (mg/g) respectively and k₁ is the adsorption rate constant of the pseudo-first-order kinetic model (min^–1).

For the pseudo-second-order kinetic model, the rate law is expressed as follows ( Ho et al., 1999 ):

$\frac{\text{d}q}{\text{d}t}=k_2{\left(q_e-q_t\right)}^2$ (14)

After integration between t = 0 and t, and between Q_t = 0 and Q_t, the following linear form is obtained:

$\frac{t}{q}=\frac{1}{k_2\cdot q_e^2}+\frac{1}{q_e}\cdot t$ (15)

where q_t and q_e correspond to maximum adsorption capacities at time t and equilibrium (mg/g) respectively and k₂ is the adsorption rate constant of the pseudo-second-order kinetic model (g/(mg·min)).

The determination of thermodynamic parameters is based on the study of the Langmuir isotherm equation ( Mve Zue et al., 2016 ). This isotherm allows for the investigation of the adsorption of molecules in the gas or liquid phase and is based on several assumptions, such as the limitation of the number of adsorption sites on the surface, the homogeneity of active sites, the occurrence of monolayer adsorption and the absence of lateral interactions between adsorbed molecules on the surface ( Mve Zue et al., 2016 ). The Langmuir isotherm is represented by the following equation:

$\frac{C_e}{Q_e}=\frac{1}{K_L{Q}_m}+\frac{C_e}{Q_m}$ (16)

where Q_m is the maximum quantity of solute adsorbed (mg/g), Q_e: the quantity of solute adsorbed at equilibrium (mg/g), C_e: the residual concentration of the solute at equilibrium in the solution (mg/L), K_L: the Langmuir constant related to the adsorption energy (L/mg).

The plot of $C_e/Q_e={\displaystyle \int \left(C_e\right)}$ gives a straight line, where the parameters $1/Q_m$ and $1/K_L{Q}_m$ represent the slope and intercept respectively. The Langmuir constant K_L is used to determine the Gibbs free energy of reaction (ΔG˚), which represents the degree of spontaneity of the adsorption process and indicates an energetically favorable adsorption ( Mve Zue et al., 2016 ).

$\Delta G°=-RT\ln K_L$ (17)

where ΔG˚ is the Gibbs free energy (KJ/mol), R: perfect gas constant (8.314 J/mol·K) and T: the temperature (K).

The thermodynamic parameters such as entropy (ΔS˚) and enthalpy (ΔH˚) were calculated using the Van’t Hoff equation ( Aksu & Kabasakal, 2004 ; Mohan et al., 2001 ):

$\ln K_d=\frac{\Delta S°}{R}-\frac{\Delta H°}{RT}$ (18)

With, ΔH˚: the standard molar enthalpy (KJ/mol), ΔS˚: the standard molar entropy (J/mol·K) and K_d: the equilibrium constant.

The plot of $\ln K_d={\displaystyle \int \left(1/T\right)}$ gives a straight line, where the parameters ΔH˚ and ΔS˚ are the slope and intercept respectively.

The structural and chemical properties of prepared activated carbons (ACs) were evaluated in determining the methylene blue (I_MB) and iodine indices ( $I_{I_2}$), pH of the point of zero charge (pH_pzc) and in quantifying the surface functional groups. Additionally, a theoretical calculation of specific surface areas was conducted.

The methylene blue number (I_MB) assesses the capacity of prepared ACs to adsorb or trap large-sized molecules ( CEFIC & EDFDLCECOCMF, 1986 ). The I_MB results obtained for prepared ACs ( Table 1 ) indicate that the methylene blue number ranges from 22.83 to 24.57 mg/g. Regardless the impregnation time of the activation agent, the I_MB values of prepared ACs appear similar. Moreover, these values are relatively low, indicating that prepared ACs have developed a negligible mesoporous surface volume within their pore structures ( Mamane et al., 2016 ).

The iodine number ( $I_{I_2}$) evaluates the capacity of ACs to adsorb or trap small molecules and thereby estimating the microporous structure of the solid ( Balogoun et al., 2015 ). Iodine numbers obtained range from 580 to 920 mg/g ( Table 1 ). Compared to values of I_MB, the $I_{I_2}$ of prepared ACs are higher. It appears that the prepared adsorbents have developed micropores within their structures, especially the AC-i_24h adsorbent (920 mg/g), which shows a higher $I_{I_2}$ than AC-i_30min and AC-i_1h (580 and 560 mg/g respectively). In our experimental conditions, it seems that the longer the impregnation time of the activating agent (KOH), the better the development of the microporous structure in prepared ACs. These results are in agreement with those of Jia Guo et al. ( Guo & Lua, 1999 ) on the textural and chemical characterization of ACs prepared from palm nut shells using KOH as the chemical activating agent. The literature also reports that the typical iodine number of ACs ranges between 500 and 1200 mg/g ( Ozdemir et al., 2014 ). Based on the results obtained ( Table 1 ), the prepared ACs exhibit iodine numbers that fall within these characteristics.

S_{BET cal}: Calculated Specific surface area (m²/g) using the method by Nunes et al. (Nunes et al., 2011) . I_MB: Methylene blue number (mg/g). $I_{I_2}$: Iodine number (mg/g). pH_pzc: pH at the point of zero charge.

Results of calculated specific surface areas (S_{BET cal}) on prepared ACs are summarized in Table 1 . The values obtained indicate that AC-i_24h (691.57 m²/g) has a S_BET higher than AC-i_30min and AC-i_1h (480.23 and 468.46 m²/g respectively). These results confirm the hypothesis of a greater microporous surface area on AC-i_24h. Similar results were observed in the works of Ubago-Pérez et al. ( Ubago-Pérez et al., 2006 ), in studies on preparation of granular and monolithic activated carbons from olive pits using KOH as a chemical activating agent.

The pH at point of zero charge (pH_pzc) determines the net charge of an adsorbent ( Amola et al., 2020 ). The net charge of activated carbons is positive below pH_pzc and negative above it ( Amola et al., 2020 ).

Figure 1 shows the values of pH_pzc obtained on prepared ACs. The pH_pzc values of prepared ACs become more basic as the impregnation time of KOH increases ( Table 1 ). In general, the ACs prepared using KOH activation exhibit basic pH_pzc values ( Jawad et al., 2021 ; El-Hendawy, 2009 ). As a result, the surfaces of the prepared adsorbents will be negative or positive charged when the pH of the media is below or above pH_pzc.

The results of concentrations of acidic (carboxylic, lactonic, and phenolic groups) and basic surface functional groups are summarized in Table 1 . According to the results, basic functional groups predominate on the surface of prepared ACs, except for AC-i_30min, which presents more acidic functional groups ( Table 1 ). These results are consistent with the pH_pzc results of prepared ACs. Prepared adsorbents exhibit primarily basic characteristics. Similar results were observed in the studies by Baudu et al. ( Julien et al., 1998 ), which examined the chemical properties of activated carbons using KOH as the activating agent. However, it appears that KOH promotes the formation of basic functional groups on the surface of prepared ACs as the impregnation time increases.

Results of adsorption of Fe(II) ions in static conditions indicate that prepared adsorbents (AC-i_30min, AC-_i1h and AC-i_24h) have an affinity for Fe(II). Indeed, adsorption capacities at saturation (Q_sat) obtained on AC-i_30min, AC-i_1h and AC-i_24h are 13.89; 14.92 and 17.85 mg/g respectively, with removal percentages (%E) of 69.48%, 74.60%, and 89.27% respectively. The results also show that adsorption equilibria were reached after 60 min with AC-i_24h exhibiting the best Q_sat and %E values compared to AC-i_30min and AC-i_1h ( Table 2 ). These results seem to be related to the specific surface areas ( Table 1 ). As the S_BET increases, both Q_sat and %E improve. The adsorption and removal capacities of Fe(II) on ACs seem to be linked to the higher proportion of active sites formed due to surface modification ( Rahman et al., 2023 ).

Results of adsorption capacities at saturation (Q_sat), adsorbed quantities (q_ads) and removal percentages (%E) obtained from dynamic adsorption experiments using a fixed-bed column for Fe(II) adsorption on AC-i_30min, AC-i_1h, and AC-i_24h are shown in Table 2 . As in the static adsorption, the prepared ACs exhibit an affinity for Fe(II). The prepared ACs possess adsorption sites and/or surface functional groups capable of interacting with Fe(II) in dynamic conditions. Additionally, the dynamic adsorption results ( Table 2 ) indicate that the bed composed of AC-i_24h is more effective in removing Fe(II). The breakthrough and saturation times (t_sat), adsorbed quantities (q_ads), and capacities at saturation (Q_sat) obtained on AC-i_24h (20 and 88 minutes, 5.17 mg and 10.38 mg/g respectively) are higher than those obtained on AC-i_30min (8 and 52 minutes, 2.75 mg and 5.54 mg/g respectively) and on AC-i_1h (12 and 72 minutes, 4.28 mg and 8.64 mg/g respectively). These results are in agreement with those obtained in the S_BET ( Table 1 ) and confirm that adsorption is indeed a surface phenomenon ( Angin, 2014 ). Indeed, as the S_BET increases, the adsorbed quantities and saturation capacities improve. Dilek Angin ( Angin, 2014 ) demonstrated that the development of specific surface areas and pore volumes plays a crucial role in the removal of metallic ions from aqueous media when using activated carbons prepared from cherry stones.

Figure 3 shows breakthrough curves of Fe(II) adsorption on prepared ACs. These curves provide information about the evolution of the ratio of the outlet (C) to inlet (C₀) concentrations of the column as a function of time. The analysis of data from breakthrough curves allows for insights into the efficiency of the bed in trapping Fe(II), based on the breakthrough and saturation times, adsorbed quantities and adsorption capacities at saturation when C/C₀ = 1, also on the adsorption mechanism (kinetics, type of diffusion, etc.) of Fe(II) on adsorbents studied ( Mve Mfoumou et al., 2024 ).

The breakthrough curves obtained confirm that prepared ACs have an affinity with Fe(II). Breakthrough times for AC-i_30min, AC-i_1h, and AC-i_24h (8; 12 and 20 min respectively) and saturation times (52, 72 and 88 min respectively) confirm this. These curves indicate also a multi-step adsorption process (two types of adsorption) of Fe(II) with different adsorption kinetics, as indicated by the varying slopes of each Fe(II) adsorption zone on prepared ACs ( Figure 3 ) ( Mve Mfoumou et al., 2024 ). The first zones, between 8 - 32, 16 - 56 and 24 - 68 min for AC-i_30min, AC-i_1h and AC-i_24h respectively, indicate rapid adsorption compared to the second zones (36; 60 and 72 minutes respectively until saturation) which exhibit slower adsorption rates. The steeper slopes in the first zones suggest rapid diffusion of Fe(II) containing aqueous phase to the surface or into the micropores and/or weak interactions between Fe(II) and the adsorbent surface or adsorption sites. Stronger interactions appear to occur in the second zones, as indicated by the flatter slopes ( Figure 3 ) ( Mve Mfoumou et al., 2024 ).

The results of Fe(II) adsorption indicate that the removal of Fe(II) is more effective on AC-i_24h, regardless of the adsorption mode (static or dynamic) as shown in Table 2 . However, for adsorption in static conditions, the saturation capacities obtained are higher than those in dynamic conditions, regardless the adsorbents used ( Table 2 ). The difference in adsorption capacities between the two modes seems to be related to the availability of adsorption sites ( Li et al., 2011 ; Azoulay et al., 2020 ). In static adsorption mode, all adsorption sites (surface functional groups, pores, crevices, etc.) are utilized because the mixture is agitated and the ACs are dispersed in the solution. In contrast, in dynamic fixed-bed column adsorption, some ACs sites may not be accessible due to the overlapping of particles in the column, preventing access to all available sites ( Li et al., 2011 ; Azoulay et al., 2020 ).

Thus, in our experimental conditions, static adsorption appears to be more effective in the removal of Fe(II) in aqueous media.

Kinetic studies of Fe(II) adsorption on prepared ACs were carried out using the experimental data obtained from both static and dynamic adsorption experiments. The values of the rate constants (k), correlation coefficients (R²), and theoretical adsorption capacities (Q_theo) were obtained from the plots of the linear kinetic models for pseudo-first-order and pseudo-second-order kinetics.

Figure 4 shows the linear plots for the pseudo-first-order and pseudo-second-order kinetic models applied to experimental data of the Fe(II) adsorption in static mode. According to the results, the experimental points are in agreement with the linear pseudo-second-order kinetics model ( Figure 4(b) ). Indeed, the regression coefficients (R²) are close to unity ( Table 3 ). Furthermore, the experimental (Q_exp) and theoretical (Q_theo) adsorption capacities are comparable ( Table 3 ). Consequently, the kinetics of Fe(II) adsorption on prepared ACs can be described by the pseudo-second-order kinetic model, involving chemisorption, i.e. the covalent bonds between Fe(II) and the ACs on the surface of materials ( Ho et al., 1999 ). Similar results were observed in the study of Ho et al. ( Ho et al., 1999 ) which applied the pseudo-second-order kinetic model to the adsorption of metal ions (Cu(II), Zn(II), Pb(II), Cr(VI),and Cd(II)) on activated carbons in aqueous media.

Contrary to results of the static adsorption, in dynamic conditions the pseudo-first-order kinetic model is the model that best describes the adsorption mechanisms of Fe(II) on prepared adsorbents. Indeed, the Q_theo obtained are comparable with those obtained experimentally. This is not the case for the Q_exp obtained with the pseudo-second-order kinetic model ( Table 3 ). However, regardless of the model applied, the experimental points are in agreement with both models, as shown in Figure 5 . Moreover, the R² values are close to 1 in both cases ( Table 3 ). In dynamic fixed-bed column adsorption, both weak interactions (physisorption) and covalent bonds (chemisorption) between Fe(II) and ACs occur at the surface of the solids. These adsorption mechanisms (interactions) are due to the acidic and basic functional groups present on the surface of activated carbons (ACs). The carboxyl (-COOH) and hydroxyl (-OH) groups are those that form hydrogen bonds between Fe(II) and the ACs ( Suo et al., 2020 ), responsible for reversible interactions (physisorption) on the surface of ACs. On the other hand, the chemisorption reactions observed are due to nitrogenous functional groups (-NH₂, -NH, -C=N and C-N) or Lewis bases (-COO⁻) ( Suo et al., 2020 ; Yang et al., 2019 ), which form covalent bonds or complexes with the metal ions in solution. However, reversible reactions (physisorption) are dominant. These results correspond to those of Mve Mfoumou et al. ( Mve Mfoumou et al., 2024 ) on the study of adsorption kinetics of Cu(II) on activated carbons in aqueous media in dynamic conditions.

The thermodynamic study of Fe(II) adsorption was carried out using data from static adsorption experiments at different temperatures (298, 333 and 373 K) and applying the Langmuir model to experimental points to determine the Langmuir constant (K_L). The study focused therefore solely on the adsorbent AC-i_24h, which exhibited the best surface properties and Fe(II) removal percentage in our experimental conditions.

The thermodynamic curve of the Fe(II) adsorption in static conditions on AC-i_24h is shown in Figure 6 and the Langmuir parameters (Q_sat and K_L) as well as the thermodynamic parameters (ΔG˚, ΔH˚ and ΔS˚) are summarized in Table 4 . The results of Table 4 show negative values for the Gibbs free energy (ΔG˚ < 0), indicating the feasibility and spontaneity of Fe(II) adsorption on AC-i_24h, which becomes more spontaneous as temperature increases ( Kumar & Gayathri, 2009 ). The results also show positive values of entropy (ΔS˚ > 0) and standard molar enthalpy (ΔH˚ > 0) with values of 7.37 J/mol·K and 503.54 KJ/mol respectively. The positive value of ΔS˚ reflects the affinity of AC-i_24h for Fe(II) and indicates an increase in randomness at the solid-solution interface during the adsorption process ( Hameed et al., 2009 ; Thajeel et al., 2013 ). The positive value of ΔH˚ suggests that the adsorption of Fe(II) on AC-i_24h is endothermic, favoring chemical adsorption with the formation of covalent bonds between AC-i_24h and Fe(II) ( Netpradit et al., 2004 ; Cantu et al., 2018 ). This result confirms the hypothesis of chemisorption at the surface of the prepared ACs, as suggested by the pseudo-second-order kinetic model.

Similar results were observed in studies by Cantu et al. ( Cantu et al. 2018 ) and Thajeel et al. ( Thajeel et al., 2013 ), which investigated the thermodynamic parameters of metal ion adsorption (Cu(II), Pb(II), etc.) on activated carbon adsorbents in batch adsorption.