Adsorption Kinetics and Isotherms of Cd (II), As (III), and Pb (II) on Green Zn-Mn Ferrite Soft Magnetic Material

Abstract

In this study, a Zn-Mn ferrite soft magnetic material (Mn_0.6Zn_0.4Fe₂O₄) was successfully prepared from a spent Zn-Mn battery using a novel multi-step process involving bioleaching, co-precipitation, and boiling reflux. The green Zn–Mn ferrite exhibited optimal magnetic properties, with Ms, Mr, and Hc values of 68.9 emu/g, 4.7 emu/g, and 53.6 Oe, respectively. The adsorption kinetics and isotherms of Cd (II), As (III), and Pb (II) in wastewater on Mn_0.6Zn_0.4Fe₂O₄ were subsequently investigated. The sorption dosages of Cd (II), As (III), and Pb (II) were 22.9 mg/g, 8.7 mg/g, and 33.9 mg/g, respectively. The pseudo-second-order kinetic model provided a fitting correlation with the experimental data. The adsorption process exhibited a good correlation with the Langmuir model, with R² = 0.997, and the q_m and b values were 33.44 mg/g and 2.43 L/mg, respectively. The sorption rates followed the sequence Pb (II) > Cd (II) > As (III). On increasing the temperature, the saturated adsorption capacity of the Cd (II), As (III), and Pb (II) increased, thus indicating that the adsorption reaction was endothermic, with the corresponding activation energy (Ea) values determined to be 9.5 KJ/mol, 32.2 KJ/mol, and 1.4 KJ/mol, respectively.

1. Introduction

Heavy-metal contamination represents a critical anthropogenic threat to ecosystems and human health, driving substantial scientific efforts toward developing effective remediation strategies [1,2]. The battery industry, as a critical heavy-metal-intensive sector, faces significantly more stringent environmental regulations compared to other manufacturing industries. This heightened regulatory scrutiny stems from the substantial concentrations of toxic metals—including zinc, manganese, nickel, lead, cobalt, cadmium, and mercury—embedded in battery manufacturing processes. The improper disposal and unregulated discharge of spent batteries have consequently emerged as predominant contributors to anthropogenic heavy-metal contamination in ecosystems.

China dominates global battery production and consumption, accounting for over 60% of worldwide output and 55% of demand. At present, the battery output is increasing at a rate of about 10% per year; however, the recycling effort is less than 2% [1]. Moreover, the current state of waste-battery recycling and processing is not optimistic. The main reason is the lack of an effective battery recycling system. On the other hand, the key issues associated with the waste battery processing technology have not been fundamentally resolved [3]. As the world’s largest developing country, China’s battery production and consumption are dominated primarily by zinc–manganese batteries (ZMBs), accounting for more than 90% of the total battery consumption. In this respect, the zinc–manganese batteries with the lowest price, the shortest lifespan, and the largest extent of use have become the main source of the pollution hazards [2]. Therefore, the development of cost-effective, efficient, environmentally benign, and energy-efficient recycling technologies for spent zinc–manganese batteries (ZMBs) is imperative. Among emerging strategies, the synthesis of high-value Zn-Mn ferrite soft magnetic materials—derived from waste ZMBs via a multi-step process involving reductive strong-acid leaching followed by controlled co-precipitation—represents a particularly promising approach [4].

Heavy-metal pollution represents one of the most pressing environmental challenges, posing significant ecological and health risks globally. The electroplating, mineral-processing, and metallurgical industries constitute primary anthropogenic sources of heavy-metal emissions [5,6]. Over recent decades, the remediation of toxic heavy metals from aqueous systems has emerged as a critical research focus within environmental science and engineering [7]. Currently, the commonly used wastewater treatment methods to remove heavy metals are mainly classified as physical membrane filtration, chemical methods including chemical precipitation, ion exchange, electrochemical removal, etc., and biological adsorption [8,9,10]. However, these technologies also suffer from many limitations. The chemical precipitation process produces a large amount of sludge, and the generated sludge is classified as hazardous waste under international protocols due to elevated concentrations of leachable heavy metals. Meanwhile, membrane filtration systems face prohibitive cost barriers compounded by irreversible fouling and particulate clogging [9]. The adsorption method is a relatively economical and practical method for treating wastewater contaminated with heavy metals [7,11,12,13]. However, wastewater heavy-metal adsorption has long faced two fundamental constraints: (i) inherently slow sorption kinetics resulting in suboptimal capacity (<200 mg/g for most sorbents), and (ii) inefficient solid–liquid separation requiring energy-intensive centrifugation (typically >3000 rpm for 15 min) that impedes scale-up [14,15,16].

A large number of studies have reported that iron oxides, including Fe₃O₄ and ɣ-Fe₂O₃, are effective heavy-metal ion adsorbents due to their affinity and magnetic separation characteristics [17,18]. Recently, the research on Zn-Mn ferrites has mainly focused on the preparation of nanomaterials by mixing Mn-Zn ferrites in silicon-based materials with their photocatalytic properties [19,20], and the preparation of multi-metal ferrites, such as Ni-Mn-Zn ferrites and Mn-Mg-Cu-Zn ferrites [21,22]. Yao-Jen Tua et al. used the industrial copper slag CuFe₂O₄ for the adsorption of Cd (II). In addition, the effect of pH on the adsorption efficiency and adsorption kinetics was studied. Under optimal conditions, the Cd (II) adsorption capacity reached 17.5 mg/g [20]. A sol–gel process was used to prepare the porous MnFe₂O₄ structure. Subsequently, the adsorption of Pb (II) and Cu (II) was studied using a cyclic use performance analysis. Under optimal conditions, the adsorption capacity of Pb (II) and Cu (II) reached 333.3 umol/g and 952.4 umol/g, respectively. Further, the removal efficiency remained high even after five cycles [23]. Overall, the ultimate metal adsorption capacity is the focus of research interest [24]. The rate of separation of the adsorbents from the aqueous solutions is of even higher significance than their ultimate adsorption capacity.

The objective of this study was to investigate the adsorption kinetics and isotherms of Cd (II), As (III), and Pb (II) in wastewater on the Zn-Mn ferrite soft magnetic material (Mn_0.6Zn_0.4Fe₂O₄), manufactured from a spent Zn-Mn battery by a combination of bioleaching, co-precipitation, and boiling reflux processes. Adsorbent characterization, including particle size, crystalline phases, saturation magnetization, residual magnetization, and coercivity, was carried out in detail. A series of batch experiments were conducted to explore the influence of pH, adsorbent concentration, temperature, and adsorption time with respect to the adsorption equilibrium, as well as the adsorption kinetics and isotherms of Cd (II), As (III), and Pb (II) on the Mn_0.6Zn_0.4Fe₂O₄. Moreover, the reuse of the Zn-Mn ferrite with a high removal efficiency was presented.

2. Materials and Methods

2.1. Manufacturing of the Zn-Mn Ferrite Soft Magnetic Material

The Mn_0.6Zn_0.4Fe₂O₄ was manufactured from a spent Zn-Mn battery utilizing a combination of bioleaching, co-precipitation, and boiling reflux processes. The detailed process of preparing the Mn_0.6Zn_0.4Fe₂O₄ has been listed in our previous article [4]. Briefly, after the waste zinc–manganese battery was manually disassembled, it was ground into powder. The bioleachate enriched with Zn²⁺ and Mn²⁺ was employed as a precursor for Zn-Mn ferrite synthesis, with systematic variation of the Mn:Zn:Fe molar ratio to optimize spinel formation, with ZnSO₄, MnSO₄, Fe₂(SO₄)₃ adjusting in the bioleachate Zn:Mn:Fe = 4:6:20. The Mn_0.6Zn_0.4Fe₂O₄ manganese–zinc ferrite was prepared using the co-precipitation-boiling reflux method [25,26]. The manufactured Zn-Mn ferrite soft magnetic material was washed several times with deionized water, followed by drying in an oven at 105 °C for 2 h for subsequent characterization.

2.2. Characterization of the Adsorbent

Phase identification via powder XRD (Bruker D8 Advance, Berlin, Germany) confirmed the single-phase cubic spinel structure of the Mn_0.6Zn_0.4Fe₂O₄. Magnetic properties, including saturation magnetization (M_s), remanence (M_r), and coercivity, were measured using a vibrating sample magnetometer (VSM; Lake Shore 7407, LAKE SHORE Company, Westerville, OH, USA).

2.3. Effect of pH on Zn-Mn Ferrite

Chemical stability under extreme pH conditions is a critical performance metric for adsorbents, as protonation/deprotonation reactions directly govern adsorbent–adsorbate interactions. The Zn-Mn ferrite’s spinel structure demonstrates exceptional acid resistance (≤5% mass loss in pH 1–3 for 24 h). However, prolonged exposure to strongly acidic media (pH < 1) induces structural collapse via Mn/Fe leaching, necessitating pre-assessment of pH tolerance limits prior to adsorption studies [27]. Thus, the effect of pH on the Zn-Mn ferrite (0.5, 1.0, 1.5, 2.0) was studied in detail. The pH values of the solutions were adjusted by adding HCl or NaOH solutions. The samples were taken after 24 h via magnetic separation to monitor the concentration of Zn and Mn by using inductively coupled plasma atomic emission spectrometry (ICP-OES, Perkin Elmer Optima 8300, Waltham, WA, USA).

2.4. Zeta Potential of Zn-Mn Ferrite

The adsorbent suspensions with varying concentrations were obtained by dispersing the Zn-Mn ferrite in the aqueous solutions at different pH levels. The Zeta potential measurement of the suspensions was carried out using Zetasizer equipment supplied by Nano-Horiba SZ-100Z, Ogaki, Japan. The Zeta potential of each sample was measured nine times. The corresponding isoelectric point (IEP) provided a theoretical basis for the adsorption of the heavy-metal ions.

2.5. Adsorption of Cd (II), As (III), and Pb (II)

In a 250 mL flask, 0.1–1.0 g Zn-Mn ferrite was added to a solution containing 100 mL Cd (II), As (III), or Pb (II) of known concentration. Subsequently, the flask was shaken in a controlled shaker at 25 °C and 200 rpm for 90 min. The experiment was conducted in the following sequence: pH experiment (3.0–9.0); kinetic experiment (t: 0–90 min, pH: 3.0 or 5.0) and adsorption isotherm experiment (concentration of Cd (II): 2–50 mg/L; concentration of As (III): 2–50 mg/L; then concentration of Pb (II): 2–50 mg/L, pH: 3.0 or 5.0). For the accuracy of the experimental studies, three parallel experiments were set up for each group of experiments to ensure the error was within ±5%.

2.6. Adsorption Kinetics

The adsorption kinetics were studied at 298 K (25 °C), 303 K (30 °C), and 308 K (35 °C). Following end-over-end agitation for prescribed durations, the suspensions underwent magnetic separation followed by vacuum filtration through 0.22 μm mixed cellulose ester membranes. The concentrations of the Cd (II), As (III), and Pb (II) were determined by ICP-OES. The adsorption kinetics curves were obtained by plotting the adsorption amount q_t (mg/g) with respect to time t (min) [28,29]. The well-known kinetic model, the pseudo-second-order model, was used to fit the data [23].

2.6.1. The Pseudo-Second-Order Model

The batch adsorption was conducted in order to evaluate the adsorption mechanism, and the adsorption amount q_t (mg/g) and time t (min) data were used in the pseudo-second-order model. The pseudo-second-order equation assumes that the adsorbable capacity of the adsorbent is directly proportional to the surface activity of the adsorbent, as follows:

$${\displaystyle \frac{d{q}_t}{dt}}=k_2{\left(q_e-q_t\right)}^2$$

(1)

where q_e (mg/g) is the saturated adsorption capacity, q_t(mg/g) is the adsorbed amount at time t, and k₂ is the adsorption rate constant of the pseudo-second-order model. With the separation of variables for the above formula, the integrand becomes the following formula:

$${\displaystyle \frac{t}{q_t}}={\displaystyle \frac{k_2}{{q_e}^2}}+{\displaystyle \frac{1}{q_e}}t$$

(2)

The linear regression was applied to analyze the data. In case the pseudo-second-order model is fitted, a straight line can be obtained, and the reciprocal of the slope represents the saturated adsorption capacity of q_e. The intercept allows the calculation of the adsorption rate constant K₂. The greater the K₂ value, the faster the adsorption rate.

2.6.2. Adsorption Reaction Activation Energy

A batch technique was utilized for exploring the effect of temperature on the adsorption rate. By calculating the adsorption rate constants k₂ and k₂′ at 298 K and 303 K, the Arrhenius equation was used to calculate the adsorption activation energy, as follows:

$$k=k_0{e}^{-E_a/RT}$$

(3)

where E_a (kJ/mol) is the reaction activation energy and k₀ is the pre-exponential factor. The logarithmic form of Equation (3) is as follows:

$$\ln \left\{k\right\}=\ln \left\{k_0\right\}-{\displaystyle \frac{E_a}{RT}}$$

(4)

The k value at the two different temperatures is

$$\begin{array}{l}25 °\mathrm{C}, \ln \left\{k_2\right\}=\ln \left\{k_0\right\}-{\displaystyle \frac{E_a}{298R}}\\ 30 °\mathrm{C}, \ln \left\{{k_2}^{\prime }\right\}=\ln \left\{k_0\right\}-{\displaystyle \frac{E_a}{303R}}\end{array}$$

Subtracting the two equations yields

$$\ln {\displaystyle \frac{{k_2}^{\prime }}{k_2}}={\displaystyle \frac{E_a}{R}}\left({\displaystyle \frac{1}{298}}-{\displaystyle \frac{1}{303}}\right)$$

2.7. Adsorption Isotherms

The adsorption isotherms were attained using a batch adsorption approach, as mentioned earlier. The adsorption isotherms were evaluated at the Cd (II), As (III), and Pb (II) concentrations, controlled in the range 2–50 mg/L. The Langmuir and Freundlich adsorption isothermal models were used to evaluate the adsorption of Cd (II), As (III), or Pb (II) [30].

2.7.1. Langmuir Adsorption Isotherm Model

The Langmuir adsorption isotherm model was established by using the following assumptions: 1> the adsorbent material is uniform and has the same adsorption energy, 2> the adsorption of a single molecular layer on the adsorbent surface represents the maximum adsorption dosage, and 3> no mass transfer takes place between the adsorption sites of the adsorbent. According to the following equation:

$${\displaystyle \frac{C_e}{q_e}}={\displaystyle \frac{C_e}{q_m}}+{\displaystyle \frac{1}{b{q}_m}}$$

(5)

where q_e (mg/g) is the adsorption amount, q_m (mg/g) is the saturated adsorption capacity, C_e (mg/L) is the concentration of the residual heavy metals in wastewater, and b (L/mg) is the adsorption equilibrium constant.

2.7.2. Freundlich Adsorption Isotherm Model

The Freundlich adsorption isotherm model can be used to describe the nonlinear adsorption on a heterogeneous surface. It can be described as follows:

$$q_e=K_F{C_e}^{{\displaystyle \frac{1}{n}}}$$

(6)

where K_F is the Freundlich adsorption coefficient (related to the adsorbent properties and temperature), and n is the Freundlich constant.

2.8. Apparatuses and Conditions

The pH value of the media was determined using a pH meter (Hana HI2221, Padua City, Italy). The released concentrations of valuable metals were determined by inductively coupled plasma atomic emission spectrometry (ICP-OES, Perkin Elmer Optima 8300). The morphology change in the materials was analyzed with a scanning electron microscope (SEM, Hitachi S-4800, Tokyo, Japan) at an accelerating voltage of 20 kV. Zeta potentials were measured at pH 3.0–9.0 (Zetasizer Nano-Horiba SZ-100Z, Kyoto City, Japan). The magnetic properties, including saturation magnetization (M_s), remanence (M_r), and coercivity, were measured using a vibrating sample magnetometer (VSM; Lake Shore 7407).

3. Results and Discussion

3.1. Adsorbent Characterization

The adsorption efficiency has a significant correlation with the crystal structure. It can be noted that the peaks of the Zn–Mn ferrite are consistent with the characteristic peaks of the standard spinel Zn–Mn ferrite (JCPDS cards No. 74-2401), thus indicating the cubic spinel structure of Mn_0.6Zn_0.4Fe₂O₄. According to Scherrer’s formula,

$$D={\displaystyle \frac{K\lambda }{\beta \cos \theta }}$$

(7)

where constant (K) = 0.89, wavelength (λ) = 0.154178 nm, β is the half-width, and θ is the diffraction angle, the average particle size of Mn_0.6Zn_0.4Fe₂O₄ is determined to be about 42.6 nm (Figure 1). The magnetic performance parameters directly obtained from the hysteresis loop are as follows: the saturation magnetization Ms is 97.9 emu/g, the residual magnetization Mr is 15.5 emu/g, and the coercive force Hc is 6.6 mT. Compared with the manganese–zinc ferrite prepared by the other methods using the waste batteries, the manganese–zinc ferrite prepared by the co-precipitation-boiling reflux process using the leachate of the waste zinc–manganese battery exhibits superior magnetic properties. Figure 2 shows that the magnetic nanoparticles can be swiftly separated by the magnet. Overall, >99.9% nanoparticles can be recovered from the solution by using a strong magnet. On removing the external magnetic field, the nanoparticles can be redispersed by physical shaking.

3.2. Effect of pH Level on Zn-Mn Ferrite

Acid and alkali resistance is a very important property for adsorbents. pH is an important influencing factor affecting the adsorption effect. Before studying the influence of pH on adsorption performance, it is necessary to first determine the pH tolerance range of the adsorbent, that is, to conduct acid dissolution experiments on manganese–zinc ferrite. As shown in

Table 1. Fe, Mn, and Zn dissolution rates over 24 h under the different pH values.

pH	Mn Dissolution Rate (%)	Zn Dissolution Rate (%)	Fe Dissolution Rate (%)
0.5	14.23	18.82	6.72
1.0	6.88	12.70	2.46
1.5	1.96	3.43	0.51
2.0	0.08	0.21	0.00

, for the solution of Mn²⁺, Zn²⁺, and Fe³⁺, with the calculated dissolution rate at pH 2.0, Zn-Mn ferrite exhibits high stability. Under strongly acidic conditions, with a decline in the pH value, Mn, Zn, and Fe exhibit different degrees of dissolution. The dissolution rate of Zn is noted to be the fastest. It could be achieved at 99.7% of Zn-Mn ferrite at pH 2.0. As an adsorbent, the operative pH is in more alkaline conditions (pH > 2.0).

3.3. Zeta Potential of Zn-Mn Ferrite

The Zeta potential measurements of Zn-Mn ferrite suspensions across varying pH values revealed an isoelectric point (IEP) at pH 4.4 (Figure 3). The isoelectric point of the Zn-Mn ferrite is noted at pH 4.4. It indicates that at pH > 4.4, the Zn-Mn ferrite surface is negatively charged, and the surface material contains the hydroxyl groups contributing to the adsorption of heavy-metal ions.

3.4. Effect of pH on Adsorption of Cd (II), As (III), and Pb (II)

The heavy-metals adsorption on the Zn-Mn ferrite as a function of pH (pH 3.0–9.0) is shown in Figure 4. At pH 5.0, the Zn-Mn ferrite exhibits a high rate of Cd (II) removal, with the extent of removal reaching >98%. At pH 3.0, the rate of removal of Cd (II) is observed to be significantly reduced, to 54.5%. At a low pH (pH ≤ 3), Cd (II) exists as Cd²⁺ in the solution with a positive charge on the surface. This is due to the competitive adsorption not being conducive to the adsorption of Cd (II). On increasing the pH, the Cd (II) in the solution mainly exists as Cd(OH)₂. The negatively charged surface of the Zn-Mn ferrite is more conducive to the adsorption of Cd (II). Therefore, the adsorption of Cd (II) is suitably attained at pH 5.0. As shown in Figure 4, the removal rate of As (III) does not change significantly as the solution pH varies between 3.0 and 9.0. At a pH of 3.0, the rate of As (III) removal reaches > 97.3%. As the solution pH increases from 3.0 to 9.0, the removal efficiency of As (III) is noted to decrease gradually from 97.3% to 84.3%. Due to the surface H⁺, the combination with AsO₂⁻ is noted to be swift; thus, the adsorption equilibrium is faster compared to alkaline conditions. Under alkaline conditions, the solution of As (III) exists as AsO₂⁻. Thus, owing to competitive adsorption, the adsorption of As (III) is not conducive [31,32]. At pH 5.0, the Zn-Mn ferrite exhibits superior Pb (II) adsorption, with the Pb (II) removal rate reaching > 98% (Figure 4). At a lower pH (pH ≤ 3.0), Pb (II) exists in the solution as Pb²⁺. As the pH value is changed from 5.0 to 7.0, Pb(OH)⁻, as the main form, replaces Pb²⁺, and Pb(OH)⁻ is gradually replaced by Pb(OH)₂.

3.5. Effect of Concentration on Adsorption of Cd (II), As (III), and Pb (II)

Different amounts of the Cd (II), As (III), and Pb (II) solutions were added to the flasks at 25 °C to attain the final concentrations in the range 0.1–1 g/L. As shown in Figure 5, the concentration has a significant influence on the adsorption behavior. At pH 5.0, as the concentration increases from 0.3 g/L to 0.5 g/L, the efficiency of Cd (II) removal gradually enhances from 78.4% to 98.9%. On increasing the concentration, the rate of Cd (II) removal does not change significantly. Based on the economic considerations, the optimum concentration is noted to be 0.5 g/L. At pH 3.0, the As (III) removal efficiency gradually grows from 11.2% to 97.3%, with the concentration increasing from 0.1 g/L to 1.0 g/L. At pH 5.0, as the concentration is raised from 0.1 g/L to 0.3 g/L, the Pb (II) removal efficiency gradually grows from 35.8% to 95.7%. On increasing the concentration, the rate of Pb (II) removal is noted to remain unchanged. Thus, the optimal concentration for the Pb (II) adsorption is 0.3 g/L. Compared with previous studies, under the optimal conditions, the Cd (II) adsorption capacity reached 17.5 mg/g [20]. The sol–gel process was used to prepare the porous MnFe₂O₄ structure. Subsequently, the adsorption of Pb (II) and Cu (II) was studied using a cyclic use performance analysis. Under optimal conditions, the adsorption capacity of Pb (II) and Cu (II) reached 333.3 umol/g and 952.4 umol/g, respectively [31,32]. For Zn-Mn ferrite, the sorption dosages of Cd (II), As (III), and Pb (II) were 22.9 mg/g, 8.7 mg/g, and 33.9 mg/g, respectively. The adsorption efficiency for various metals was improved by approximately 30%.

3.6. Adsorption Kinetics

The adsorption of Cd (II) was studied as a function of temperature and time at pH 5.0, as well as the Zn-Mn ferrite and Cd (II) concentrations of 0.5 g/L and 10 mg/L, respectively (Figure 6). Temperature significantly influences Cd (II) adsorption capacity, with the saturated uptake increasing from 22.9 mg/g at 25 °C to 28.3 mg/g at 35 °C (Δq_m = +5.4 mg/g), indicating an endothermic adsorption process. Meanwhile, the duration to reach the adsorption equilibrium is shortened from 60 min to 30 min. The kinetics of the Cd (II) adsorption were adjusted by applying the adsorption amount q_t (mg/g) and time t (min) data to the pseudo-second-order model, along with plotting t/q_t with respect to time (t). Figure 6 demonstrates that the experimental kinetic data of the Cd (II) adsorption exhibit a superior fitting degree with the pseudo-second-order model, with R² = 0.998. Further, the theoretical (24.1 mg/g, 25 °C) and actual equilibrium adsorption (22.9 mg/g, 25 °C) capacity values are noted to be close. Therefore, the pseudo-second-order model can describe the adsorption phenomenon well [23]. Based on the Arrhenius equation, the activation energy for Cd (II) adsorption (E_a) is determined to be 9.46 kJ/mol.

At a pH value of 3.0, as well as the Zn-Mn ferrite and As (III) concentrations of 1.0 g/L and 10 mg/L, the saturated adsorption capacity of As (III) is noted to increase from 8.7 mg/g to 9.7 mg/g on raising the temperature from 25 °C to 35 °C. Simultaneously, the duration to reach the adsorption equilibrium is shortened from 12 h to 8 h. Figure 7 exhibits a superior linearity in the plot, with R² = 0.999. The theoretical equilibrium adsorption capacity (8.78 mg/g, 25 °C) is noted to be very close to the actual equilibrium adsorption capacity (8.12 mg/g, 25 °C). These results indicate that the pseudo-second-order model fits the data well [33]. Subsequently, the activation energy for As (III) adsorption (E_a) is determined to be 32.2 kJ/mol.

The adsorption kinetics of Pb (II) were evaluated further. At a pH value of 5.0, as well as the Zn-Mn ferrite and Pb (II) concentrations of 0.3 g/L and 10 mg/L, respectively, the saturated adsorption capacity of Pb (II) is noted to increase from 33.9 mg/g to 41.1 mg/g as the temperature is raised from 25 °C to 35 °C. In addition, the time required to reach the adsorption equilibrium is determined to be 60 min. The kinetic experimental data for the Pb (II) adsorption are noted to have a superior fitting degree with the pseudo-second-order model, with R² = 0.997 (Figure 8). The theoretical equilibrium adsorption capacity (37.3 mg/g, 25 °C) is observed to be very close to the measured value of 33.9 mg/g at 25 °C. By applying the Arrhenius equation, the activation energy for Pb (II) adsorption (E_a) is 1.4 kJ/mol. These results indicate that the pseudo-second-order kinetic model yields a better fit, thus concluding that the Cd (II), As (III), and Pb (II) adsorption on the Zn-Mn ferrite can be effectively described by the pseudo-second-order model. Consistent with prior studies [34,35], the adsorption kinetics of Cd (II), As (III), and Pb (II) on Zn-Mn ferrite exhibit superior alignment with the pseudo-second-order model (R² > 0.99) compared to alternative models, indicating chemisorption-dominated mechanisms. Further, during the Cd (II), As (III), and Pb (II) adsorption, the rate-controlling steps are driven by chemical adsorption.

3.7. Adsorption Isotherms

Adsorption isotherms play a pivotal role in elucidating adsorption processes under equilibrium conditions. These isotherms quantitatively characterize the adsorption capacity of an adsorbent, thereby providing critical insights into the underlying adsorption mechanism, such as monolayer/multilayer formation, surface heterogeneity, and adsorbate–adsorbent interactions. The analysis of isotherm models further enables the determination of thermodynamic parameters and the prediction of adsorbent performance across varying operational conditions. The isotherms for the Cd (II) adsorption were evaluated at a pH of 5.0 and a Zn-Mn ferrite concentration of 0.5 g/L. The adsorption process was evaluated using the Langmuir and Freundlich isotherm models, with Cd (II) concentrations ranging from 2 to 50 mg/L. As can be observed, the adsorption process does not correlate well with the Freundlich model, with R² = 0.95. However, a superior correlation is noted with the Langmuir model, with R² =0.999, q_m = 23.9 mg/g, and b = 3.4 L/mg (Figure 9a,b). As the adsorption of a single molecular layer is assumed, the main mechanism of Cd (II) adsorption is a chemical process.

The As (III) adsorption performance was obtained at a pH value of 3.0 and a Zn-Mn ferrite concentration of 1.0 g/L, with the As (III) concentration ranging from 2 to 50 mg/L. As shown in Figure 9c,d, the adsorption process does not correlate well with the Freundlich model, with R² = 0.764. However, a superior correlation is noted with the Langmuir model, with R² = 0.999, q_m = 8.8 mg/g, and b = 6.3 L/mg.

The Pb (II) adsorption thermodynamics was evaluated at a pH of 5.0 and a Zn-Mn ferrite concentration of 0.3 g/L, with the Pb (II) concentration ranging from 2 to 50 mg/L. The adsorption process is noted to ineffectively correlate with the Freundlich model, with R² = 0.915. Meanwhile, the Langmuir model displays a superior correlation, with R² = 0.997, q_m = 33.4 mg/g, and b = 2.4 L/mg (Figure 9e,f). Thermodynamic analysis demonstrates superior correlation of the Langmuir model (R² > 0.98) compared to the Freundlich model (R² < 0.92) for all three metals (Cd²⁺, As³⁺, and Pb²⁺) adsorbed on the Zn-Mn ferrite soft magnetic material across the studied temperature range (298–318 K), indicating dominant monolayer chemisorption behavior.

4. Conclusions

This study successfully prepared magnetic Mn_0.6Zn_0.4Fe₂O₄, which can effectively and rapidly remove Cd (II), As (III), and Pb (II) ions from aqueous solutions. The results indicate that Mn_0.6Zn_0.4Fe₂O₄ is sensitive to operating conditions such as pH, temperature, and density. The prepared Mn_0.6Zn_0.4Fe₂O₄ also exhibits the best magnetic properties, with Ms, Mr, and Hc values of 68.9 emu/g, 4.7 emu/g, and 53.6 Oe, respectively. Magnetic nanoparticles can be instantly separated from the magnet. Mn0.6Zn0.4Fe₂O₄ has excellent acid resistance. The optimal adsorption performance is at 25 °C, pH 3.0 or 5.0. The saturated adsorption values for Cd (II), As (III), and Pb (II) are 22.9 mg/g, 8.8 mg/g, and 33.9 mg/g, respectively. The pseudo-second-order kinetic model and the Langmuir model have a good relationship with adsorption. The corresponding activation energies, Ea, are 9.5 KJ/mol, 32.2 KJ/mol, and 1.4 KJ/mol, respectively. This proves that the reaction conforms to the pseudo-second-order reaction kinetics and the Langmuir isotherm model. The results of this study indicate that the development of cost-effective adsorbents for immobilizing cadmium, arsenic, and lead-based pollutants has great potential.