*2.1. Biosorbent*

The acorns of the oak *Quercus crassipes* Humb. and Bonpl. were collected from the town of El Durazno de Cuauhtémoc, located in the municipality of Jilotepec de Molina Enríquez, in the state of Mexico, Mexico. The acorns were washed under running water, rinsed with distilled deionized water, and then dried in an oven at 60 ◦C for 24 h. Thereafter, the shells were separated from the acorns and grounded in a Glen Creston® laboratory mill (Glen Creston, Ltd., London, England, UK). The resulting powder was sieved using American Society for Testing and Materials (ASTM) sieves (ASTM International, West Conshohocken, PA, USA), and the fraction with particle sizes ranging between 180–212 μm was used in all the experiments carried out in this study.

### *2.2. Stock and Test Solutions*

Stock solutions of NiSO4, KCl, NaNO3, Na2SO4, CaCl2, MgSO4, and MgCl2 with a concentration of 20 mM and 2000 mM NaCl were prepared by dissolving a precisely weighed amount of chemical compounds in 1 L distilled deionized water. All reagents were of analytical grade (JT Baker®, Monterrey, Mexico). The test solutions were prepared by diluting the stock solutions with distilled deionized water.

### *2.3. Biosorption Experiments*

The kinetic experiments were carried out using batch systems to assess the influence of ionic strength and background electrolytes on the biosorption of Ni2<sup>+</sup> from aqueous solutions by the acorn shell of *Quercus crassipes* Humb. & Bonpl. (QCS). The biosorption studies were performed in 500 mL Erlenmeyer flasks containing 110 mL Ni2<sup>+</sup> solution at an initial concentration of 1.97 mM and a QCS biomass at a concentration of 1 g/L. The flasks were shaken at a constant speed of 120 rpm in a Cole-Parmer® linear shaking water bath (Cole-Parmer®, Vernon Hills, IL, USA) for 120 h at 25 ± 1 ◦C. The pH of each test solution was measured regularly over the course of the experiments and then adjusted to 8.0 ± 0.1 using 0.1 M NaOH and/or HCl solutions when necessary.

Ni2<sup>+</sup> solutions containing some of the anions and cations that have been frequently found in industrial effluents were used to assess the influence of ionic strength and background electrolytes on the biosorption of Ni2<sup>+</sup> by QCS [24]. The effect of ionic strength was tested using NaCl as the background electrolyte at concentrations ranging from 0.2 to 2000 mM. To assess the effect of background electrolytes, chemical compounds (KCl, NaNO3, Na2SO4, CaCl2, MgSO4, and MgCl2) consisting of monovalent and divalent anions and cations were used at concentrations of 0.2, 2, and 20 mM. Control experiments that only contained QCS biomass at a concentration of 1 g/<sup>L</sup> and Ni2<sup>+</sup> solution at an initial concentration of 1.97 mM with no background electrolytes were conducted simultaneously.

Additionally, control experiments with no QCS biomass were performed using the same operating conditions of the Ni2<sup>+</sup> biosorption experiments to determine whether there was loss of Ni2<sup>+</sup> because of precipitation or adsorption onto the glass. Statistically, there were no significant differences between the Ni2<sup>+</sup> concentrations in the control experiments with no QCS biomass at different experimental times. Thus, the decrease in the Ni2<sup>+</sup> concentration observed in the experiments with QCS biomass was caused by QCS.

Samples were taken at different experimentation times, and then they were filtered through a Whatman® grade 42 filter paper (Whatman®, St. Louis, MI, USA). The collected filtrates were analyzed to determine their residual Ni2<sup>+</sup> concentration.

The Ni2<sup>+</sup> biosorption capacity (qt, mmol/g) at any time t was calculated using Equation (1):

$$\mathbf{q}\_{\mathbf{t}} = \frac{(\mathbf{C}\_{\mathbf{i}} - \mathbf{C}\_{\mathbf{t}})}{\mathbf{C}\_{\mathbf{b}}} \tag{1}$$

where Ci (mmol/L) is the initial concentration of Ni2<sup>+</sup> at time t = 0 h, Ct (mmol/L) is the residual concentration of Ni2<sup>+</sup> at time t = t, and Cb is the concentration of the QCS biosorbent (g/L).

The effect of background electrolytes and ionic strength on the biosorption of Ni2<sup>+</sup> by QCS was quantitatively assessed using the global performance index of the Ni2<sup>+</sup> biosorption (ξ, %), which was calculated using Equation (2) [26]:

$$\pounds = 100 \frac{\left(\int\_{t=0}^{t=t\_l} \mathbf{q}\_t \mathbf{dt}\right)\_{\text{problem}} - \left(\int\_{t=0}^{t=t\_l} \mathbf{q}\_t \mathbf{dt}\right)\_{\text{control}}}{\left(\int\_{t=0}^{t=t\_l} \mathbf{q}\_t \mathbf{dt}\right)\_{\text{control}}} \tag{2}$$

where (qtdt)problem and (qtdt)control are the time courses of the Ni2<sup>+</sup> biosorption capacity in the experiments carried out with (test experiments) and without (control experiments) background electrolytes, respectively, and tf is the total contact time between the Ni2<sup>+</sup> solution and the QCS biomass (120 h).

Integration of the (qtdt)problem and (qtdt)control functions from t = 0 to t = t was performed using Mathematica version 7.0 (Wolfram Research, Champaign, IL, USA). The biosorption of Ni2<sup>+</sup> by QCS is not affected by the ionic strength or background electrolytes if ξ = 0%. There is an improvement in the biosorption of Ni2<sup>+</sup> compared to the control if ξ > 0%, thus, the ionic strength or background electrolytes have a positive or synergistic effect on the metal biosorption. Finally, if ξ < 0%, the biosorption of Ni2<sup>+</sup> is decreased compared to the control, thus, the ionic strength or background electrolytes have a negative or antagonistic effect on the metal biosorption [26].

### *2.4. Determination of the Ni2*+ *Concentration*

The Ni2<sup>+</sup> concentration in the liquid phase was determined using the dimethylglyoxime method [27]. The absorbance of the chemical complex with a color ranging from red wine to brown that is formed during the reaction of Ni2<sup>+</sup> ions with dimethylglyoxime was measured in a Thermo Scientific™ Evolution 201 spectrophotometer (Thermo Fisher Scientific, Whaltman, MA, USA) at a wavelength of 465 nm.

### *2.5. Biosorption Kinetic Modeling*

The biosorption kinetics describes the rate of biosorption of the adsorbate and, therefore, controls the time required to reach dynamic equilibrium [28]. This study used the pseudo-first order, pseudo-second order, Elovich, intraparticle diffusion, and fractional power models to analyze the kinetics of the Ni2<sup>+</sup> biosorption process.

The pseudo-first order and pseudo-second order models can be described using Equations (3) and (4), respectively [29]:

$$\mathbf{q}\_{\rm t} = \mathbf{q}\_{\rm e1} \left( \mathbf{1} - \mathbf{e}^{-k\_{\rm l}} \, \mathbf{t} \right) \tag{3}$$

$$\mathbf{q}\_{\mathbf{t}} = \frac{\mathbf{t}}{\frac{1}{k\_2 \mathbf{q}\_{\mathbf{q}2}^2} + \frac{\mathbf{t}}{\mathbf{q}\_{\mathbf{t}^2}}} \tag{4}$$

where qe1 and qe2 are the equilibrium biosorption capacities (mmol/g) predicted by the pseudo-first order and pseudo-second order models, respectively, qt is the biosorption capacity (mmol/g) at time t = t (h), and k1 (1/h) and k2 (g/mmol·h) are the rate constants of the pseudo-first order and pseudo-second order models, respectively.

The Elovich kinetic model is given by Equation (5) [30]:

$$\mathbf{q}\_{\mathbf{t}} = \frac{1}{\mathbf{B}\_{\mathbf{t}}} \ln(\mathbf{1} + \mathbf{A}\_{\mathbf{e}} \mathbf{B}\_{\mathbf{e}} \mathbf{t}) \tag{5}$$

where Ae (mmol/g·h) and Be (g/mmol) are the initial biosorption rate and the desorption constant, respectively.

The fractional power kinetic model is given by Equation (6) [31]:

$$\mathbf{q}\_{\rm tr} = \mathbf{k}\_{\rm tp} \,\mathrm{t}^{\rm v} \tag{6}$$

where kfp (mmol/g) is the fractional power model constant and v (1/h) is the rate constant of the fractional power model. The product of these constants (kfp·v, mmol/g·h) is known as the specific biosorption rate at unit time, that is, when t = 1.

The intraparticle diffusion model can be described by Equation (7) [32]:

$$\mathbf{q}\_{\rm t} = \mathbf{k}\_{\rm id} \,\mathrm{t}^{0.5} + \mathbf{c} \tag{7}$$

where c (mmol/g) is the intercept of the model that is related to the thickness of the boundary layer and kid (mmol/g·<sup>h</sup>0.5) is the intraparticle diffusion rate constant.

### *2.6. Determination of the Parameters of the Kinetic Models and Statistical Analysis*

All the experiments of the study were carried out at least twice and the results reported herein are the average values ± mean standard deviation. Statistical analysis of the Ni2<sup>+</sup> biosorption data and estimation of the parameters of the tested kinetic models were performed using the GraphPad Prism version 8.0 (GraphPad Software, Inc., San Diego, CA, USA).

The analysis of variance (ANOVA) was performed using the Tukey's test for group comparisons to determine whether there were statistically significant differences in the Ni2<sup>+</sup> biosorption data. A significance level (α) of 0.05 was used. Probability values (*p*) lower than α indicate that the evaluated groups differ significantly.

The kinetic models parameters were obtained via non-linear regression analysis of the experimental data. Various error functions, such as root mean squared error (RMSE), sum of squared error (SSE), Akaike information criterion (AIC), coefficient of determination (r2), and 95% confidence intervals were used to determine the accuracy and adequacy of the tested kinetic models fit. Small RMSE, SSE, and AIC values, r2 values close to one, and narrow 95% confidence intervals indicate that the models describe the experimental Ni2<sup>+</sup> biosorption data more accurately [22].

### **3. Results and Discussion**

### *3.1. Influence of Ionic Strength on the Biosorption of Ni2*+ *by Acorn Shell of Quercus Crassipes Humb. & Bonpl. (QCS)*

The ionic strength of an aqueous solution is an environmental parameter that significantly affects the biosorption of heavy metal ions at the interface between the solid biosorbent and the liquid phase [24]. Thus, this study investigated its effect on the kinetics of biosorption of Ni2<sup>+</sup> by QCS.

Figure 1 shows the variation in Ni2<sup>+</sup> biosorption capacity as a function of the biosorption time at NaCl ionic strengths ranging from 0.2 to 2000 mM. The kinetic profile of the Ni2<sup>+</sup> biosorption at an ionic strength of 0.2 mM is similar to that of the control experiment (0 mM NaCl). There were no significant differences between the Ni2<sup>+</sup> biosorption capacities (*p* > 0.05) for the control experiment and at an ionic strength of 0.2 mM at different experimental times, which indicates that the Ni2<sup>+</sup> biosorption is not affected by a NaCl ionic strength of 0.2 mM.

**Figure 1.** Effect of the NaCl ionic strength on the biosorption of Ni2<sup>+</sup> by acorn shell of *Quercus crassipes* Humb. & Bonpl. (QCS).

In contrary, the Ni2<sup>+</sup> biosorption capacity decreased gradually as the ionic strength increased from 0.2 to 200 mM (*p* < 0.05). However, the Ni2<sup>+</sup> biosorption capacities were very similar and there were no significant differences between them (*p* > 0.05) at different biosorption times and at very high ionic strengths of 200 and 2000 mM. These results indicate that the biosorption of Ni2<sup>+</sup> is negatively affected by NaCl ionic strengths equal to or greater than 2 mM.

The global performance indexes for the biosorption of Ni2<sup>+</sup> at the different ionic strengths are summarized in Table 1.


**Table 1.** Effect of the NaCl ionic strength on the global performance index of the biosorption of Ni2<sup>+</sup> by acorn shell of *Quercus crassipes* (QCS).

The global performance index revealed that a NaCl ionic strength of 0.2 mM had a negligible negative effect on the biosorption of the metal (ξ = −4%). However, as the ionic strength increased from 2 to 200 mM, the global performance index decreased from −17 to −55%, which indicates that the adverse effect of the ionic strength on the biosorption of Ni2<sup>+</sup> increases with an increase in ionic strength (*p* < 0.05). Moreover, the global performance index for the biosorption of Ni2<sup>+</sup> at NaCl ionic strengths of 200 and 2000 mM were similar, thus, the adverse effects on the biosorption of the metal were similar under these conditions (*p* > 0.05). These results are in agreemen<sup>t</sup> with the negative effects observed in the kinetic studies of the Ni2<sup>+</sup> biosorption.

The decrease in Ni2<sup>+</sup> biosorption with increasing NaCl ionic strengths from 0.2 to 2000 mM can be attributed to the fact that the aqueous solution contain more positively charged Na<sup>+</sup> ions, which competed with the Ni2<sup>+</sup> cations for the available biosorption active sites on the QCS surface [24,33]. Moreover, changes in the ionic strength of a solution can make the reactive functional groups on the surface of the biosorbent less accessible to Ni2<sup>+</sup> ions [20,34]. Furthermore, Na<sup>+</sup> ions can reduce the concentration of other electrostatically bound counterions that balance the negative charge of the biomass, thus, Na<sup>+</sup> ions affect the intraparticle ion concentration and the binding of other ions, such as the Ni2<sup>+</sup> ions [33]. Additionally, it has been reported that high Cl− ion concentrations (present in NaCl) favor the formation of the nickel chloride (NiCl−) complex, thus decreasing the number of free Ni2<sup>+</sup> ions in the aqueous solution, which results in a lower number of interactions between Ni2<sup>+</sup> ions and biosorption active sites and consequently, a decrease in the heavy metal biosorption capacity [35].

Additionally, it has been reported that the NaCl ionic strength negatively a ffects the biosorption of Ni2<sup>+</sup> by grape stalks wastes [35], filamentous fungi such as *Rhizopus* sp., *Mucor* sp., and *Penicillium* sp. [36], and barley straw [37]. Moreover, the NaCl ionic strength decreased the sorption capacity of other heavy metals, such as Cu2+ by HNO3-pretreated newspaper scraps, HNO3-pretreated-maize spatha [38], and by an exopolysaccharide of *Wangia profunda* [39]; also Cd2+ by an exopolysaccharide of *Wangia profunda* [39] and by magnetic graphene oxide-supported sulfanilic acid [24], Pb2+ by *Sargassum filipendula* [40], and Cr6+ by lignin [28]. Likewise, the increase of NaCl ionic strength inhibited the biosorption of organic adsorbates, such as Methylene Blue and Rhodamine B dyes by *Phellinus igniarius* and *Fomes fomentarius* [41], and benzene and toluene by *Macrocystis pyrifera* [42].

Analysis of the kinetic model for biosorption study is crucial for understanding dynamics, mechanism, and reaction pathway of the biosorption process. It also helps in determining mass transfer, rate-controlling steps, and physicochemical interaction in the biosorption process. Additionally, knowledge about kinetics of metal biosorption is useful for determining optimum conditions for biosorption processes [43]. In the present work, the experimental kinetic data of the biosorption of Ni2<sup>+</sup> by QCS at di fferent ionic strengths were analyzed using the pseudo-first order, pseudo-second order, Elovich, fractional power, and intraparticle di ffusion models. These models have been used previously to analyze and understand biosorption kinetics of Ni2<sup>+</sup> ions in single metal systems by di fferent biosorbents [7,11,26,44] but to the best knowledge of the authors, the kinetic process of Ni2<sup>+</sup> biosorption from aqueous solutions containing NaCl or other background electrolytes has not been mathematically modeled. The parameters of the kinetic models are presented in Table 2.

The highest r2 values and the lowest SSE, RMSE, and AIC values were obtained using the pseudo-second order, Elovich, and fractional power models. Therefore, these models represent the kinetic profiles of the biosorption of Ni2<sup>+</sup> by QCS most adequately under the studied conditions.

The equilibrium Ni2<sup>+</sup> biosorption capacities obtained using the pseudo-second order model (qe2) were similar to those obtained experimentally (qe exp). Furthermore, as the NaCl ionic strength increased from 0 to 2000 mM, the rate constant of the pseudo-second order model (k2) decreased from 0.166 to 0.133 g/mmol·h. A similar behavior was observed in the studies of the biosorption of total chromium by QCS at di fferent ionic strengths [20]. A previous study that analyzed the kinetics of the biosorption of Ni2<sup>+</sup> by QCS at di fferent pH conditions, initial metal concentrations, and temperatures using the pseudo-first order and pseudo-second order models established that the pseudo-second order model described the biosorption kinetics of the heavy metal more satisfactorily than the pseudo-first order model [9]. The present study demonstrates that the pseudo-second order model can also describe the kinetics of the biosorption of Ni2<sup>+</sup> by QCS at di fferent ionic strengths.

Furthermore, it was observed that higher ionic strengths lead to higher rate constants of the fractional power model (v) and lower initial biosorption rates (Ae), as predicted by the Elovich model, as well as lower constants (kFP) and specific biosorption rates (kFP·v) of the fractional power model. The decrease in k2, Ae, and kFP·<sup>v</sup> with increasing ionic strengths indicates that the interactions between the QCS biomass and the Ni2<sup>+</sup> cations decrease with increasing NaCl ionic strengths, which prevents the binding of Ni2<sup>+</sup> ions to biosorption active sites and decreases the heavy metal biosorption capacity.

Notably, even though NaCl ionic strengths equal to and greater than 200 mM significantly a ffected the biosorption of Ni2<sup>+</sup> by QCS, this can be ignored in the present study since the ionic strength of industrial wastewater is lower than 100 mM [45].



### *3.2. Influence of Coexisting Ionic Species on the Biosorption of Ni2*+ *by Acorn Shell of Quercus Crassipes Humb. & Bonpl. (QCS)*

Generally, there are various types of background electrolytes in industrial wastewater at varying concentrations, which can affect the biosorption of the heavy metal of interest. This study investigated the effect of coexisting ionic species on the biosorption of Ni2<sup>+</sup> by QCS using different cations and anions at three different concentrations, namely 0.2, 2.0, and 20 mM.

Figure 2 shows the kinetic profiles of the biosorption of Ni2<sup>+</sup> by QCS at the different concentrations of background electrolytes. There was a small variation in the Ni2<sup>+</sup> biosorption capacity over the course of the experiments for background electrolyte concentration of 0.2 mM compared to the control experiment (with no background electrolytes) (Figure 2a). However, there were no statistically significant differences in all cases (*p* > 0.05), thus, it is concluded that a background electrolyte concentration of 0.2 mM has no negative effect on the biosorption of Ni2+. Moreover, the global performance indexes for the biosorption of Ni2<sup>+</sup> at a background electrolyte concentration of 0.2 mM were small and ranged from −7 to −5% (Table 3), which confirms that background electrolytes at a concentration of 0.2 mM have a negligible effect on the biosorption of Ni2+.

**Table 3.** Effect of background electrolytes at concentrations of 0.2, 2, and 20 mM on the global performance index of the biosorption of Ni2<sup>+</sup> by QCS.


Increasing the concentration of background electrolytes to 2 mM led to a further decrease in the Ni2<sup>+</sup> biosorption capacity. However, as shown in Figure 2b, the different background electrolytes influenced the biosorption of Ni2<sup>+</sup> at varying degrees. The decreases in Ni2<sup>+</sup> biosorption capacity were more significant in the presence of salts with divalent cations (CaCl2, MgSO4, and MgCl2) and, to a lesser extent, with monovalent cations (KCl, NaNO3, and Na2SO4). The statistical analysis revealed that there were significant differences in Ni2<sup>+</sup> biosorption capacities between the control and the experiments carried out in the presence of compounds with divalent cations (*p* < 0.05). However, there were no statistically significant differences in the maximum Ni2<sup>+</sup> biosorption capacities between the control and the experiments performed with monovalent cation salts (KCl, NaNO3, and Na2SO4) (*p* > 0.05). The global performance indexes corroborated that the compounds containing divalent cations (CaCl2, MgSO4 and MgCl2) affected the biosorption of Ni2<sup>+</sup> more negatively (from −24% to −20%) compared to the compounds containing monovalent cations (KCl, NaNO3 and Na2SO4) (from −12% to −8%).

The background electrolytes at a concentration of 20 mM caused an even greater decrease in the Ni2<sup>+</sup> biosorption capacity compared to that obtained at 2 mM (Figure 2c). The statistical analysis revealed that the differences between the Ni2<sup>+</sup> biosorption capacities of the control and the experiments carried out with all the background electrolytes were statistically significant (*p* < 0.05). For all the experiments, the lowest Ni2<sup>+</sup> biosorption capacities were obtained when MgSO4, CaCl2, and MgCl2 salts were present in the aqueous solutions (Figure 2c). Additionally, the global performance indexes showed that the biosorption of Ni2<sup>+</sup> was more negatively affected at the highest concentration (20 mM) of background electrolytes and that the negative effect of the background electrolytes followed the order: MgSO4 > CaCl2 > MgCl2 > Na2SO4 > NaNO3 ≈ KCl.

**Figure 2.** Effect of background electrolytes at a concentration of (**a**) 0.2 mM, (**b**) 2 mM, and (**c**) 20 mM on the biosorption of Ni2<sup>+</sup> by QCS.

These results clearly show that the Mg<sup>2</sup>+ and Ca2+ cations have a more pronounced effect on the biosorption of Ni2<sup>+</sup> from aqueous solutions by QCS compared to the Na<sup>+</sup> and K<sup>+</sup> cations. This could be attributed to the following reasons: First, the divalent Mg<sup>2</sup>+ and Ca2+ cations competed more efficiently with the Ni2<sup>+</sup> ions for the biosorption active sites present on the QCS surface compared to the monovalent Na<sup>+</sup> and K<sup>+</sup> cations. Second, the divalent Mg<sup>2</sup>+ and Ca2+ cations biosorb more easily on the QCS surface compared to the monovalent Na<sup>+</sup> and K<sup>+</sup> cations because of the higher electrostatic attraction. Finally, a Na<sup>+</sup> or K<sup>+</sup> ion biosorbed on the QCS surface occupies only one biosorption active site, whereas a Mg<sup>2</sup>+ or Ca2+ ion could occupy two sites, thus resulting in a greater decrease in the

biosorption of Ni2<sup>+</sup> in the presence of MgCl2, MgSO4, and CaCl2 [24,35,46]. These reasons indicate that the biosorption active sites present on the surface of the QCS are not specific to Ni2<sup>+</sup> ions.

Additionally, the decrease in Ni2<sup>+</sup> biosorption can be owing to the presence of the Cl- and SO42- ions, which could increase the formation of nickel chloride and nickel sulfate complexes, respectively, thus decreasing the free Ni2<sup>+</sup> ions in solution [46]. It was observed that the SO4<sup>2</sup>− ion had a more negative effect on the biosorption of Ni2<sup>+</sup> by QCS compared to the Cl- and NO3− ions.

Okoronkwo et al. [46] reported that the Ca2+ and Mg<sup>2</sup>+ cations and the SO4<sup>2</sup>− anion cause a decrease in the ability of the Mexican sunflower (*Tithonia diversifolia*) stems to bind the Ni2<sup>+</sup> ions in aqueous solutions. Ca2+ and Mg<sup>2</sup>+ cations also decreased the biosorption capacity of *Phellinus igniarius* and *Fomes fomentarius* for Methylene Blue and Rhodamine B dyes [41]. Moreover, Mn2<sup>+</sup> and Ag+ ions decreased the Cu2+ removal efficiency of granular activated carbon [47]. Likewise, an important decrease in biosorption capacity of *Macrocystis pyrifera* for benzene and toluene was observed, when an artificial seawater solution (Instant Ocean®, Blacksburg, VA, USA) was used, probably because this solution contains different ions [42].

Table 4 presents the equilibrium Ni2<sup>+</sup> biosorption capacity (qe exp) for the control experiment (without background electrolytes) and at the different concentrations of background electrolytes. From Table 4, it is evident that the highest biosorption capacity was obtained in the absence of background electrolytes. Moreover, the heavy metal biosorption capacity decreased as the concentration of background electrolytes increased, and the lowest equilibrium Ni2<sup>+</sup> biosorption capacities were obtained in the presence of MgSO4, CaCl2, and MgCl2 at a concentration of 20 mM. The Elovich, fractional power, and pseudo-second order kinetic models described the kinetic profiles of the biosorption of Ni2<sup>+</sup> at the three different concentrations of background electrolytes more adequately, as evidenced by the lower SSE, RMSE, and AIC values and the higher r2 values (Tables 4–6).

The equilibrium Ni2<sup>+</sup> biosorption capacities predicted by the pseudo-second order model were close to the values obtained experimentally, and they decreased as the concentration of the background electrolytes increased. It is also evident that background electrolytes affected the parameters of all the tested kinetic models, and this occurred to a greater extent at a concentration of 20 mM. Among the observed changes, the decrease in the specific biosorption rate of the fractional power model with increasing concentrations of background electrolytes should be noted.

The goodness of fit between Ni2<sup>+</sup> biosorption kinetics and pseudo-second order, Elovich, and fractional power models suggests that the biosorption process of Ni2<sup>+</sup> by QCS from aqueous solutions, containing different types and concentrations of background electrolytes, has a chemical process (chemisorption) as the rate-limiting step of the overall rate of heavy metal biosorption [18,29].

To our knowledge, the effect of ionic strength and background electrolytes on the parameters of kinetic models of the biosorption of Ni2<sup>+</sup> has not been previously reported.

The results obtained in the present study clearly demonstrate the remarkable capacity of QCS to biosorb Ni2<sup>+</sup> from aqueous solutions containing various types of impurities with different concentrations.

Additionally, the results of this study show that the impurities in the water greatly affect the performance of the biosorption of heavy metals. Furthermore, this study provides valuable information on the effect of ionic strength, the type, and concentration of background electrolytes on the biosorption of Ni2+, which is of grea<sup>t</sup> importance for the application of biosorption technology in the treatment of industrial wastewater contaminated with Ni2+.



*Processes* **2020**, *8*, 1229 **Table 6.** Parameters of the fractional power model for the biosorption of Ni2+ by QCS at 0.2, 2, and 20 mM of background electrolytes.

