## Abstract?

**Abstract**

The kinetics, mechanism, isotherm, and thermodynamics of adsorption of Pb^{2+} onto wood-activated carbon-supported zerovalent iron (WAC-nZVI) nanocomposite was successfully studied. WAC-nZVI was characterized by a combination of spectroscopic and analytical techniques (BET, PZC, FTIR, SEM, and EDX). BET surface area was 101.50 m^{2}/g and BJH Adsorption average pore diameter 116.73 Å. The adsorption of Pb^{2+} studied in batch process depends on various operational parameters ranging from effect of pH to ionic strength. Kinetics data were best described by pseudo-second-order model based on high initial adsorption rate, h_{2} (166.67 mgg^{−1} min^{−1}) and correlation coefficient (*R*^{2} > 0.99). The mechanism was controlled by both external and intraparticle diffusion models confirmed by Bangham and Boyd models. Equilibrium data were fitted to seven isotherm models. The Langmuir monolayer adsorption capacity (77.52 m^{2}/g) surpassed those previously investigated for adsorption of Pb^{2+} onto nanoadsorbents. Validity of kinetics and isotherm models was studied using three statistical models. Post-adsorption characterization by SEM, EDX, and FTIR confirmed the presence of Pb^{2+} on the loaded-WAC-nZVI. Thermodynamic parameters (∆*H*^{o}, ∆*S*^{o}, ∆*G*^{o}) confirmed the feasibility, spontaneity, and randomness of the adsorption process. This study revealed a great potential of novel WAC-nZVI in effective removal of Pb^{2+} from waste water.

## Public Interest Statement

The release of heavy metal ions into the environment via unguided and unguarded anthropogenic activities remains ubiquitous challenge for the past decade. Lead is a hazardous metal well known for environmental contamination and health problems in many parts of the world. Its potential sources are reported in this article. WHO revealed that childhood lead exposure is estimated to contribute to about 600,000 new cases of children developing intellectual disabilities every year and also account for 143,000 deaths per year with the highest burden in developing countries; 4% of the global burden of ischemic heart disease; 5% of the global burden of stroke and there is no known level of lead exposure that is considered safe. This article has currently investigated the solution for water contaminated with lead ions using wood-activated carbon-supported zerovalent iron (WAC-nZVI) nanocomposite via adsorption as a low-cost and efficient technique. The outcome of this was validated.

## 1. Introduction

The release of heavy metal ions into the environment via unguided and unguarded anthropogenic activities remains ubiquitous challenge for the past decade. Lead is a hazardous metal well known for environmental contamination and health problems in many parts of the world. It can be potentially found in sources such as gold-leaded soil, hair dye, batteries, paints, pesticide, canned food, plants grown around industrial areas, cosmetics, tobacco smoke, ammunition (*1*). It is an accumulative toxicant that adversely affects copious body system such as neurologic, hematologic, gastrointestinal, cardiovascular, and renal systems. Those highly vulnerable to this hazardous effect are children and there are recent reports of some outbreaks in some areas in West Africa such as seen in Niger and Zamfara States of Nigeria (*2*, *3*). Report from WHO revealed that childhood lead exposure is estimated to contribute to about 600 000 new cases of children developing intellectual disabilities every year, and also account for 143 000 deaths per year with the highest burden in developing countries; 4% of the global burden of ischemic heart disease; 5% of the global burden of stroke and there is no known level of lead exposure that is considered safe. However, the dose–response analyses conducted by the Joint Food and Agriculture Organization of the United Nations (FAO)/WHO Expert Committee concluded that permissible level of lead in drinking water and air are 10 μg/l and 0.5 μg/m^{3} (*4,5*). Quite a number of conventional technologies such as ion exchange, solvent extraction, electrodialysis, reverse osmosis, ultrafiltration, cementation, chemical precipitation (*6*) have been used, however, adsorption has proven to be efficient, simple, explicit, cost-effective, and readily available technique of immobilization of heavy metals and dyes from the environment.

Several bioadsorbents have been reported for adsorption of Pb^{2+} such as acid-modified rice husk (*6*); citric acid-modified clam shells (*7*), peat moss and peat moss-derived biochar (*8*); activated carbon made from sewage sludge (*9*), kaolin- and graphene-supported nZVI (*10, 11*), carbon-supported nanoscale zerovalent iron particles (*12*); granular activated carbon/zerovalent iron (*13*) but at the advent of nanoscience, researchers have been exploring the use of nanoadorbents due to their high surface area, effectiveness, and rapid adsorption than several bioadsorbents. The current trend in nanoscience research is the impregnation of nanoparticles into low-cost adsorbent in order to increase its efficiency. This is one of the primary focuses of this research. Hence, the quest for efficient adsorbent for uptake of toxic Pb^{2+} propelled the research into the development of nanocomposite by impregnation and bottom-up approach. Activated carbon has been identified as effective adsorbents for pollutants removal. However, its application is still resisted because of some limitations such as availability, quality, and, most especially, its high cost in the developing countries. This has instigated us to explore the use of locally available material (Wood of *Cholophoral Excelsa* which is readily available in South-west Nigeria) for preparation of activated carbon and we further explored the opportunity of improving its adsorption capacity by impregnating it with iron nanoparticle via bottom-up approach by chemical reduction in a single-pot system. The two main approaches used in nanotechnology are “bottom–up” and “top–down.” In the “bottom-up” approach, materials, and devices are built from molecular components which assemble themselves chemically by principles of molecular recognition (*14*). It is a synthesis approach where the precursors or the building blocks are added onto the substrate to form the nanostructure substances.

To the best of our knowledge, there has not been any report on nZVI impregnated on activated carbon from readily available low-cost wood of *Cholophoral Excelsa* abundant in Africa. Based on the literature report and to the best of our understanding, there has never been any report on the material—raw wood dust of *cholophoral excelsa.* Other researchers used commercial activated, however, this present study produced activated carbon from neglected *cholophoral excelsa* and incorporated zerovalent iron nanoparticles into it forming activated carbon iron-coated zerovalent iron nanocomposite**.** Therefore, the objectives of this research are: (i) Bottom-up approach preparation of wood-activated carbon (WAC)-supported nanoscale zerovalent iron (nZVI) and characterization using Brunauer–Emmett–Teller (BET) and Barrett–Joyner–Halenda (BJH); point of zero charge (PZC); Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), energy-dispersive X-ray (EDX), and transmission electron microscope (TEM); (ii) investigation of the effect of adsorption functional parameters—pH, ionic strength, adsorbent dose, contact time, initial concentration, and temperature; (iii) determination of the kinetic and rate-controlling step (mechanism) using eight models—pseudo-first- and -second-order models, Elovich, fractional power, intraparticle diffusion, Spahn and Schlunder Model (external diffusion), Bangham and Boyd models, (iv) analyzing equilibrium data with seven isotherm models—Langmuir, Freundlich, Temkin, Dubinin–Raduskevich (D-R), Halsey, Harkin–Jura, and Jovanovic (v), and determination of randomness, spontaneity, and feasibility of the adsorption process using thermodynamic parameters—change in standard enthalpy (Δ*H*°), entropy (Δ*S*°), and Gibb’s free energy (Δ*G*°).

## 2. Materials and methods

### 2.1 Materials

All the reagents used were of analytical grade mostly purchased from Sigma-Aldrich, USA, namely: sodium borohydride (NaBH_{4}) (for the chemical reduction), ferric chloride (FeCl_{3}), HNO_{3,} and NaOH. Absolute ethanol from BDH, while raw wood dust of *Cholophoral excelsa*, was obtained at sawmill workshop close to Landmark University campus.

### 2.2. Methods and characterization

#### 2.2.1. WAC-nZVI nanocomposite preparation

Preparation of novel WAC-nZVI was carried out using two precursors: (A) nanoscale zerovalent iron, ZVI and (B) wood-activated carbon, WAC. The precursor B was prepared following the previously work by Dada et al. (*15*) and kept in the desiccator for further use. In a distinctive procedure for the preparation of WAC-nZVI, excess borohydride is important for better formation of iron nanoparticle. Therefore, a carefully weighed amount of precursor B was initially introduced into 0.023 M FeCl_{3} and homogenized for 3 h using a magnetic stirrer. Thereafter, 0.123 M NaBH_{4} was introduced to 0.023 M FeCl_{3} in ratio 5:1 under nitrogen-controlled glove box single-pot system giving WAC-nZVI (black) was obtained. The impregnation of wood-activated carbon-supported zerovalent iron nanocomposite (WAC-nZVI) was carried out modifying similar procedure reported in our previous studies (*16–18*) and equation of reaction is as stated in Equation (1):(1) $$WAC+4F{e}^{3+}+3B{H}_{4}^{-}+9{H}_{2}O\to WAC-4Fe\downarrow +3{H}_{2}B{O}_{3}^{-}+12{H}^{+}+6{H}_{2}\uparrow $$(1)

WAC-nZVI was thereafter kept in a desiccator for further characterization and adsorption studies.

#### 2.2.2. Characterization

BET surface area was determined using Micrometritics AutoChem II Chemisorption Analyzer. Point of zero charge (PZC) was determined by modifying the procedure reported by Srivastava et al. (*19*). Morphology and elemental constituents were determined using scanning electron microscopy (SEM) integrated with energy-dispersive X-ray (EDX) using a TESCAN Vega TS 5136LM typically at 20 kV at a working distance of 20 mm with samples coated in a Golden Balzers’ Spluttering device and functional groups were determined by Fourier transform infrared spectroscopy (FTIR) using Schimadzu FTIR model IR 8400S.

#### 2.2.3. Adsorption experiment

##### 2.2.3.1. Batch equilibrium studies

Sorption experiment was done by agitating 100 mg of the WAC-nZVI with 50 cm^{3} of different initial Pb^{2+} concentrations from 10 to 200 ppm in 60 cm^{3} of Teflon bottle intermittently for 3 h. The combination was filtered and the filtrate was immediately analyzed in triplicate for residual Pb^{2+} ions concentrations using atomic absorption spectrophotometer (AAS). The mean value of the residual Pb^{2+} concentration for each set of the experiments was calculated and used. Adsorption operational parameters such as effect of pH, contact time, initial concentration, adsorbent dose, temperature, and ionic strength were investigated following a similar procedure (*18, 20–22*).

### 2.3. Adsorption analysis

#### 2.3.1. Quantity adsorbed and removal efficiency

Quantity of Pb^{2+} adsorbed (*q*_{e}), removal efficiency, and error analysis were calculated using Equations (2)–(6). Adsorption capacities and the removal efficiency were obtained using Equations (2) and (3), respectively (*22, 23*):(2) $${q}_{e}=\frac{({C}_{o}-{C}_{e})V}{W}$$(2) (3) $$\%\phantom{\rule{0.277778em}{0ex}}E=\frac{{C}_{o}-{C}_{e}}{{C}_{o}}\times 100$$(3)

#### 2.3.2. Sum of Square Error (SSE), Chi-square test (*χ*^{2}) and Normalized Standard Deviation (Δ*q*) Statistical Validity

The best fit, suitability, and agreement of kinetic and isotherm models were validated using three statistical models: sum of square error (SSE), chi-square test (*χ*^{2}), and normalized standard deviation (Δ*q*).

The sum of square error (SSE) is mostly used by researchers with the mathematical expression given in Equation (4):(4) $$\text{SSE}=\sum _{i=1}^{n}{\left({q}_{e,\text{cal}}-{q}_{e,exp}\right)}^{2}$$(4)

Better agreement between the experimental quantity adsorbed and the calculated quantity adsorbed can be judged using this tool (*24*).

The chi-square test measures the difference between the experimental and calculated quantities adsorbed (*q*_{e,exp} and *q*_{e,cal}, respectively). Magnitude of the value of chi-square depends on the agreement between the *q*_{e,exp} and the *q*_{e,cal}. If data evaluated from the model are similar to experimental data, *χ*^{2} would be small and if they differ, *χ*^{2} will be large (*25*).(5) $${\mathit{\chi}}^{2}=\sum _{i=1}^{n}\frac{{\left({q}_{e,exp}-{q}_{e,\text{cal}}\right)}^{2}}{{q}_{e,\text{cal}}}$$(5)

The normalized standard deviation Δ*q* (%) was evaluated using Equation (6).(6) $$\mathrm{\Delta}q(\%)=100\frac{\sqrt{\sum _{i=1}^{n}{\left(\frac{{q}_{e,exp}-{q}_{e,\text{cal}}}{{q}_{e,exp}}\right)}^{2}}}{n-1}$$(6)

where *n* is the number of data points and other parameters are the same as earlier defined. Lower value of Δ*q* indicates good fit between experimental and calculated data (*26*).

## 3. Results and discussion

### 3.1. Characterization (BET, BJH, PZC, FTIR, SEM–EDX)

The following physicochemical properties of the WAC-nZVI nanocomposite vis-à-vis surface area, micropore area, BJH adsorption cumulative surface area of pores, pore volume, pore diameter, pore width, average particle size by Brunauer–Emmett–Teller (BET) and Barrett–Joyner–Halenda (BJH). The point of zero charge is of basic importance in surface science. The point of zero charges obtained for WAC-nZVI revealed that adsorption of Pb^{2+} would take place at a pH > pH_{(pzc)} (*19**,**27*). The result presented in Table 1 showed that adsorption of Pb^{2+} was favorable at a pH above PZC (Figure S1).

**Table 1. Physicochemical properties of WAC-nZVI nanocomposites**

The relatively higher values of the external surface area compared to the micropore surface area implies that WAC-nZVI utilized its external surfaces for adsorption than its micropore surfaces (*21*).

Figure 1(a) and (b) depict the FTIR spectra of wood dust-activated carbon-supported iron nanocomposite (WAC-nZVI) before and after adsorption of Pb^{2+}. Stated in Table 2 are important FTIR bands of WAC-nZVI with their possible functional groups assigned before and after Pb^{2+} adsorption. The reduction in vibration band intensities after adsorption is a confirmation of participation of functional group in adsorption process.

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18 July 2017FTIR spectra for (a) WAC-nZVI before adsorption and (b) Pb–WAC-nZVI after adsorption.

**Table 2. Important FTIR bands of WAC-nZVI with their possible functional groups before and after Pb**^{2+} adsorption

^{2+}adsorption

Revealed in Figure 2(a) is the scanning electron microscopy (SEM) image of WAC-nZVI nanocomposite before adsorption. The surface was fibrous, cellulosic fiber flat-like, straight lamina showing the evidence of pores of activated cell wall of plant of *Chlorophora excelsa* and indication of zerovalent iron nanoparticle with surface area of BET 101.5033 m²/g, pore volume 0.056673 cm³/g, pore width 22.3334 Å, pore diameter 116.727 Å. The lamina structural nature of WAC-nZVI enhanced the flow of Pb^{2+} into the pores of WAC-nZVI. These characteristics boosted the performance of WAC-nZVI in the immobilization of Pb^{2+} as supported by the findings in previous work by Dada et al.(*17*) and Anees et al. (*28*). A change in morphology which is attributed by the robustness and swollen of WAC-nZVI after Pb^{2+} adsorption was confirmed by the SEM analysis in Figure 2(b)

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18 July 2017SEM images of (a) WAC-nZVI before adsorption and (b) Pb–WAC-nZVI after adsorption.

In order to further confirm Pb^{2+} adsorbed onto WAC-nZVI, energy-dispersive X-ray (EDX) studies of WAC-nZVI before and after adsorption was carried out. The EDX spectra give the characteristic peaks of the nanoparticles and the information on the surface atomic distribution. EDX spectra of (a) WAC-nZVI before and (b) loaded Pb–WAC-nZVI after adsorption are revealed in Figure 3(a) and (b). The EDX spectrum in Figure 3(a) revealed the intense peaks of the core shell zerovalent iron and other elemental constituents before adsorption which was supported by the FTIR result. Other elements present could be traceable to the additives during the course of the analysis. In most metal adsorption studies, the residual concentration was determined by atomic adsorption spectroscopy (AAS). This could not prove the presence of the metal ions on the adsorbent. However, the presence of Pb^{2+} on WAC-nZVI as seen in the EDX spectrum in Figure 3(b) was an evidence of the adsorption of Pb^{2+} onto WAC-nZVI.

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18 July 2017EDX analysis of (a) WAC-nZVI before adsorption and (b) Pb–WAC-nZVI after adsorption.

### 3.2. Influence of pH, adsorbent dose, and contact time

The pH of the solution in adsorption studies influences both the chemistry of solution and surface charge of the adsorbents (*29, 30*). Investigation of the effect of pH was carried out between the pH ranges 1–8. Pb^{2+} in solution exits as Pb^{2+}, Pb(OH)^{+}, Pb(OH)_{2} in acidic medium causing electrostatic competition between Pb^{2+}, H^{+}, and other cationic species as a result of protonation leading to low removal efficiency and quantity adsorbed as seen in Figure 4. However, as the pH increases tending toward pH 6, increase in quantity of Pb^{2+} adsorbed was evident due to the decrease in electrostatic repulsion, low competition among positive ions, and availability of active sites for adsorption. The optimum percentage of Pb^{2+} removed was attained at pH 6 which was corroborated by the findings of Xu et al. (*31*) and Pirouz et al. (*32*).

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18 July 2017^{2+} adsorbed onto WAC-nZVI.

*; WAC-nZVI dose = 100 mg*; Volume of Pb2+ solution = 50 mL; Stirring speed = 200 rpm; Contact time = 30 min, and Temperature = 25± 2°C.

The interaction between the Pb^{2+} ions and WAC-nZVI was maximized by the investigation of the effect of adsorbent dose on the uptake of Pb^{2+}. The percentage removal efficiency increases with the increase in adsorbent dose because of the increase in number of active sites as revealed in Figure 5. At 10 mg WAC-nZVI, 51.73% Pb^{2+} was adsorbed, while at 100 mg 97.3% was adsorbed until a saturated point was reached when no significant increase in the removal efficiency was attained based on limited number of active sites. This performance confirmed the efficacy of the nanocomposite prepared being a blend of activated carbon (WAC) from neglected material and zerovalent iron nanoparticles (nZVI). However, the quantity adsorbed on WAC-nZVI is a measure of the occupancy capacity of the adsorbent. Obviously, at 10 mg, 93.71 mg Pb^{2+} was attained and this decreased with decrease in the number of active sites. Other factors responsible for this are: interference between binding sites and higher adsorbed dose; insufficiency of Pb^{2+} ions in solution with respect to available binding sites; aggregation arising from high sorbent dose leading to decrease in total surface area of adsorbent and an increase in diffusional path length and unsaturation of the adsorption sites during the adsorption reaction. This finding is supported by the previous work of Gong et al. (*33*).

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18 July 2017^{2+} adsorbed.

The build-up of charges around the adsorbent in a solid–liquid system takes time. Therefore, effect of contact time was investigated as one of the factors affecting the immobilization of Pb^{2+} onto WAC-nZVI. The effect of contact time was studied at contact time of 10–120 min at optimum conditions. Figure 6 showed a rapid increase in contact time at the first 10–30 min into the adsorption process. However, a steep and uninterrupted step was observed between 30 and 60 min, while the graph leveled off for 120 min without a significant change in the quantity adsorbed (18).

^{2+}onto wood activated carbon supported zerovalent iron (WAC-ZVI) nanocomposite

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18 July 2017^{2+} adsorbed onto WAC-nZVI .

### 3.3. Batch kinetic studies and statistical validity

Data from kinetic experiment were subjected to eight kinetic and mechanism models.

#### 3.3.1. Pseudo-first-order (Lagergren’s rate equation)

The Lagergren’s rate equation of pseudo-first order is given in Equation (7) (*34, 35*):(7) $$log({q}_{e}-{q}_{t})=log\phantom{\rule{0.277778em}{0ex}}{q}_{e}-\frac{{k}_{1}t}{2.303}$$(7) (8) $${h}_{1}={k}_{1}{q}_{e}$$(8)

Equation (8) defines *h*_{1} the initial adsorption rate from pseudo-first-order rate equation, the plot of log(*q*_{e} − *q*_{t}) versus *t* gave a linear relationship (Figure 7), where k_{1} and *q*_{e} were determined from the slope and intercept of the linear plot (Figure 7(a))

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18 July 2017(a–d): Linear plots of (a) Pseudo-first-order, (b) Pseudo-second-order, (c) Elovich, (d) Fractional power.

Solid–liquid interaction of WAC-nZVI and Pb^{2+} is suggesting that one Pb^{2+} is adsorbed on the surface of one WAC-nZVI as demonstrated in Equation (9):(9) $$WAC+P{b}_{aq}^{2+}\stackrel{{k}_{2}}{\to}WAC\bullet P{b}_{solid\phantom{\rule{0.277778em}{0ex}}phase}$$(9)

From evaluated parameters presented in Table 3, it is obvious that *q*_{e,exp} = 89.2 mgg^{−1} and *q*_{e,cal} = 5.572 mgg^{−1} coupled with regression coefficient, *R*^{2} < 0.95 and larger values of sum of square error (SSE), chi-square test (*χ*^{2}), and normalized standard deviation (Δ*q*). These results as well as lower value of *h*_{1} = 0.193 mgg^{−1} min^{−1} showed that kinetics of liquid-phase adsorption of Pb^{2+} onto WAC-nZVI did not fit well to pseudo-first order.

**Table 3. Adsorption kinetic models’ parameters for the sorption of Pb**^{2+} onto WAC-nZVI

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#### 3.3.2. Pseudo-second order

This model adopts that one Pb^{2+} is sorbed onto two sorption sites on WAC-nZVI nanocomposites’ surface according to Equation (10):(10) $$2WAC+P{b}_{aq}^{2+}\stackrel{{k}_{2}}{\to}WA{C}_{2}\bullet P{b}_{solid\phantom{\rule{0.277778em}{0ex}}phase}$$(10)

Evidence of chemisorption mechanism is substantiated in the pseudo-second-order model (Equation (11)) (*16, 30, 36*):(11) $$\frac{t}{{q}_{t}}=\frac{1}{{h}_{2}}+\frac{1}{{q}_{e}}t$$(11) (12) $${h}_{2}={k}_{2}{q}_{e}^{2}$$(12)

Defined in Equation (12) is pseudo-second-order initial adsorption rate (mg^{2}/g^{2} min). Linear plot of *t*/*q*_{t} against *t* in Figure 7(b), gave a straight line and evaluated data obtained are presented in Table 3. The linearity of the plot, close and good agreement between the calculated *q*_{e} and *q*_{e}, experimental values (89.2 and 90.90, respectively), higher value of *h*_{2} = 166.67 mg^{2}/g^{2} min, correlation coefficients (*R*^{2} > 0.99), and lower values of the validity models are strong clues of the applicability of pseudo-second-order model. It is suggested that the kinetic of adsorption of Pb^{2+} onto WAC-nZVI was best described by pseudo-second-order model supporting chemisorption process.

#### 3.3.3. Elovich model

Equation (13) described the Elovich model as:(13) $${q}_{t}=\frac{1}{\mathit{\beta}}\ell n\left(\mathit{\alpha}\mathit{\beta}\right)+\frac{1}{\mathit{\beta}}\ell n\left(t\right)$$(13)

The slope of $1\phantom{\rule{-0.166667em}{0ex}}/\phantom{\rule{0.0pt}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\mathit{\beta}$ and intercept $1\phantom{\rule{-0.166667em}{0ex}}/\phantom{\rule{0.0pt}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\mathit{\beta}\ell n(\mathit{\alpha}\mathit{\beta})$ were determined from linear plot of *q*_{t} vs. ln(*t*) (Figure 7(c)). Regression coefficient, *R*^{2} > 0.95 is close to unity, Elovich’s constant, *α* = 1.60 × 10^{+34} g min^{2}/mg defines the rate of reaction, 1/*β* value above unity reflects the number of sites available for adsorption, whereas the value of *1/β* ln (*αβ*) = 86.82 mgg^{−1} indicates the adsorption quantity when ln(*t*) equals to zero (*37*). All these parameters revealed that Elovich model also better described the liquid-phase adsorption (*30*).

#### 3.3.4. Fractional power

Equation (14) portrayed the fractional power model given as (*18*):(14) $$log({q}_{t})=log(k)+vlog(t)$$(14)

where *v* is a positive constant less than unity (*v* = 0.012 min^{−1}) displaying the time dependence of liquid-phase adsorption of Pb^{2+} onto WAC-nZVI. The *k* = 83.9 mgg^{−1} was determined from slope and intercept of a linear plot of log (*q*_{t}) vs. log (*t*) (Figure 7(d)) suggesting the strength of the site for Pb^{2+} immobilization. The lower values of SSE, *χ*^{2,} and Δ*q* evaluated as 0.0842, 0.001, and 0.081, respectively, validated the appropriateness of fractional power in describing the time dependence of adsorption process (*38*).

### 3.4. Adsorption mechanism

The adsorption mechanisms, the rate-controlling steps were determined using intraparticle diffusion, external diffusion, Bangham and Boyd models. Their mathematical expressions are given in Equations (15)–(20) (*17, 39*):

Intraparticle diffusion (Morris and Weber model) (*40*): (15) $${q}_{t}={k}_{id}{t}^{0.5}+C$$(15)

External diffusion (Spahn and Schlünder model): (16) $$ln\left[\frac{{C}_{t}}{{C}_{o}}\right]=-{k}_{ext}\left(\frac{A}{V}\right)t$$(16)

A/V is external adsorption area to the total solution volume, and *t* is sorption time.

Bangham model: (17) $$loglog\left(\frac{{C}_{o}}{{C}_{o}-{q}_{t}m}\right)=log\left(\frac{{k}_{o}m}{2.303V}\right)+\mathit{\alpha}log\left(t\right)$$(17)

where *α* and *K*_{o} are the constants and *t* is the contact time (min).

Boyd model: (18) $$F=1-\left(6\phantom{\rule{-0.166667em}{0ex}}/\phantom{\rule{0.0pt}{0ex}}\phantom{\rule{-0.166667em}{0ex}}{\mathit{\pi}}^{2}\right)exp\left(-{B}_{t}\right)$$(18) (19) $$F=\frac{{q}_{t}}{{q}_{e}}$$(19)

where *q*_{t} is the amount of the Pb^{2+} adsorbed at time t (mg/g) and *q*_{e} is the amount of the Pb^{2+} adsorbed at equilibrium (mg/g), *F* is the fraction of Pb^{2+} adsorbed at time t, and *B*_{t} is the mathematical function of *F*. Substituting Equation (19) in (15), Equation (18) simplifies to:(20) $${B}_{t}=-0.4977-ln(1-F)$$(20)

The calculated *B*_{t} values were plotted against time *t* (min). Depicted in Figure 8(a)–(d) are the linear plots of (a) intraparticle diffusion, (b) external diffusion (Spahn and Schlünder model), (c) Bangham, (d) Boyd adsorption mechanism models for adsorption of Pb^{2+} onto WAC-nZVI. In this study, the intraparticle diffusion constant (*k*_{id}) and the thickness of the surface (*C*) were determined from the slope and intercept of linear plot of *q*_{t} vs. *t*^{0.5}. The intercept (*C* = 19.397) which is the thickness of the surface gives information about the contribution of the surface adsorption in the rate-determining step. The larger the intercept, the greater the contribution of the pore to adsorption (17). The plot (Figure 8(a)) not passing through the origin indicating that intraparticle diffusion is not the only rate-determining step (*26*). However, it is suggested that other step like external diffusion maybe involved in the rate-determining steps. Parameters of Spahn and Schlunder model were evaluated from the linear plot of *ln (C*_{t}*/C*_{o}*)* vs. *t* (Figure 8(b), Table 4)

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18 July 2017^{2+} onto WAC-nZVI.

**Table 4. Adsorption mechanism models for immobilization of Pb**^{2+} onto WAC-nZVI

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More so, Bangham model was applied to confirm the intraparticle diffusion. The pore diffusion mechanism was further supported by double logarithm plot (Bangham model) since plot of $loglog\left(\frac{Co}{Co-{q}_{t}m}\right)$ against $log\left(t\right)$ gave a straight line (Figure 8(c)) with high correlation coefficient, *R*^{2} > 0.95, *the values of α* and k less than unity (Table 4) and Boyd model with *R*^{2} < 0.95. All these values are suggesting that intraparticle diffusion or pore diffusion is one of the rate-determining steps (*41*, *42*)

### 3.5. Equilibrium studies and isotherm models

#### 3.5.1. Initial concentration

The initial Pb^{2+} concentration constitutes a significant driving force allowing the ionic mass transfer between the aqueous and the solid phases (*43*). Effect of initial concentration plays one of the major roles in the uptake of Pb^{2+}. The concentration range of 10–200 mg/L was investigated at optimum conditions. Specifically, the increase in adsorption capacity with an increase in concentration is due to the concentration gradient developed at solid–solution interface. At higher concentration of Pb^{2+}, the active sites of WAC-nZVI were bombarded by more of Pb^{2+} as the process continued until a saturated point was reached. The quantity adsorbed increased with an increase in initial concentration due to the availability of the active sites as revealed in Figure 9. However, the percentage removal efficiency decreased with an increase in concentration because of decrease in the rate of binding of Pb^{2+} to the active sites at the approach of equilibrium.

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18 July 2017^{2+} adsorbed onto WAC-nZVI at various initial Pb^{2+}concentrations.

#### 3.5.2. Adsorption isotherms and statistical validity

In order to understand the interaction between WAC-nZVI and Pb^{2+}, the data obtained from equilibrium adsorption studies were analyzed using seven of two parameters isotherm models: Langmuir, Freundlich, Temkin, Dubinin–Raduskevich (D–R), Halsey, Harkin–Jura, and Jovanovic. Description of the interaction between WAC-nZVI and Pb^{2+}, estimation of the adsorption capacity, information about adsorption mechanisms, surface properties, and affinity of the adsorbent can be equally obtained from the evaluated parameters from these isotherm models. Based on the statistical model errors which are normally and independently distributed, all the isotherm models are subjected to three statistical errors analyses for validity test. Given in Table 5 are the isotherm models equations, their linear and nonlinear forms as seen in Equations (21)–(28) as well as the various parameters plotted. Presented in Figures 10 (a)–(g) are the corresponding linear plots for Langmuir, Freundlich, Temkin, Dubinin–Raduskevich (D–R), Halsey, Harkin–Jura, and Jovanovic isotherm models, respectively. The evaluated parameters of the isotherm models are well presented in Table 6.

**Table 5. Different adsorption isotherm models (***15, 21, 44–46*)

*15, 21, 44–46*)

^{2+}onto wood activated carbon supported zerovalent iron (WAC-ZVI) nanocomposite

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18 July 2017^{2+} onto WAC-nZVI, and (h) Plot of Langmuir dimensionless separation factor for adsorption of Pb^{2+} onto WAC-nZVI.

**Table 6. Isotherm models’ parameters and evaluated values for adsorption of Pb**^{2+} onto WAC-nZVI

^{2+}onto WAC-nZVI

Langmuir isotherm model is a semi-empirical isotherm derived from a proposed kinetic mechanism based on the assumptions that the surface is energetically homogeneous, and there is no interaction between neighboring adsorbed specie (Pb^{2+}), adsorption takes place only at specific localized sites on the surface and the saturation coverage corresponds to complete occupancy of these sites. Given in Table 5 are Langmuir equation and the expression for Langmuir separation factor as seen in Equations (22) and (23), respectively. The parameters *q*_{e} and *C*_{e} are the quantity of metal ions adsorbed (mg/g) and concentration (mg/L) at equilibrium, respectively, q_{max} is the theoretical maximum monolayer sorption capacity (mg/g), and *K*_{L} (L/g) represents the Langmuir isotherm constant. The essential features of the Langmuir isotherm may be expressed in terms of equilibrium parameter, *R*_{L}, which is a dimensionless constant referred to as separation factor.

The equilibrium data were also best described by the Langmuir isotherm model with *R*^{2} value of 0.9723 (Figure 1(a)). The maximum monolayer (*q*_{max}) Pb^{2+} adsorption capacity obtained was 77.07 mg/g**.** The essential features of the Langmuir isotherm may be expressed in terms of dimensionless separation factor, *R*_{L}, given as (*30*, *47*):(23) $${R}_{L}=\frac{1}{1+{K}_{L}{C}_{o}}$$(23)

*R*_{L} value indicates the adsorption nature to either unfavorable or unfavorable. It is unfavorable if *R*_{L} > 1, linear if *R*_{L} = 1, favorable if 0 < *R*_{L} < 1, and irreversible if *R*_{L} = 0 (*15*). The value of *R*_{L} which ranges between 7.44 × 10^{−2} and 3.77 × 10^{−3} (Figure 10(h)) indicated that the immobilization of Pb^{2+} onto WAC-nZVI was favorable. From the comparison of the Langmuir monolayer adsorption capacities presented in Table 7, the WAC-nZVI performed effectively and distinctly than other existing nanoparticles and nanocomposites reported in the literature for the uptake of Pb^{2+}. This performance enlisted WAC-nZVI among novel, effective, and efficient adsorbents for uptake of Pb^{2+}. Based on the values of correlation coefficients (*R*^{2}), the close agreement between *q*_{e,exp} and *q*_{e,cal}, and lower values of sum of square error (SSE), chi-square test (*χ*^{2}), and normalized standard deviation (Δ*q*) statistical validity models presented in Table 6, it is obvious that the equilibrium data were best described by Langmuir and D–R isotherm models and fairly described by Temkin isotherm models (Figure 10(a), (c), and (d), respectively).

**Table 7. Comparison of the previously reported adsorbents used in Pb**^{2+} uptake with the present ones under investigation

^{2+}uptake with the present ones under investigation

Freundlich, Halsey, and Harkin–Jura are mainly describing heterogeneous and multilayer adsorption (*21*, *46*, *56*, *57*). Generally, these isotherm parameters are mainly determined from the slope and intercepts of their linear plots indicated in Table 5. The K_{f} and n_{f} are the Freundlich isotherm constants describing adsorption capacity and intensity, respectively, determined from the intercept and slope of the plot of log *q*_{e} against log *C*_{e} (Figure 10 (b)) . Since the value of 1/*n*_{f} (0.283 in Table 6) lies between 0 and 1 and n_{f} (3.53, Table 6) being less than 10 are indication of a favorable adsorption. Adsorption of Pb^{2+} onto WAC-nZVI is poorly described by Freundlich, Halsey, Harkin–Jura, and Jovanovic (Figure 10 (b), (e), (f), and (g), respectively, and Table 6). Based on *R*^{2} and relatively low SEE, *χ*^{2}, and Δ*q* presented in Table 6, the isotherm models fit the equilibrium data well in the following order: Langmuir > Dubinin–Raduskevich (D–R) > Temkin > Freundlich > Halsey > Jovanovic > Harkin–Jura. However, from the evaluated parameters of D–R isotherm models, the value of E being less than 8 kJ, revealed that electrostatic force played a substantial role in the adsorption process. This was supported by the research finding of Feng et al. (*42*) and Wang et al. (*48*).

### 3.6. Adsorption thermodynamic studies

Temperature is another important parameter in the adsorption studies because some important thermodynamic parameters such as enthalpy change (Δ*H*°), entropy change (Δ*S*°), and Gibbs free energy change (Δ*G*°) could be determined. The temperature investigated ranged from 298 to 338 K. Close observation of Figure 11 revealed that 97.2% of Pb^{2+} was adsorbed with an increase in temperature due to increase in number of active sites and the decrease in the thickness of the boundary layer surrounding the adsorbent, as a result, the mass transfer resistance of Pb^{2+} in the boundary layer decreased (*55*)

^{2+}onto wood activated carbon supported zerovalent iron (WAC-ZVI) nanocomposite

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18 July 2017^{2+} adsorbed onto WAC-nZVI.

The thermodynamic parameters were determined from the van’t Hoff’s equation (58):(29) $$log{K}_{C}=\frac{\mathrm{\Delta}S}{2.303R}-\frac{\mathrm{\Delta}H}{2.303RT}$$(29)

Evaluated parameters of Δ*H*°, Δ*S*°, and Δ*G*° determined from the slope and intercept of linear plot of log *K*_{c} against 1/T (Figure 12) are presented in Table 8.

^{2+}onto wood activated carbon supported zerovalent iron (WAC-ZVI) nanocomposite

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18 July 2017^{2+} onto WAC-nZVI.

**Table 8. Thermodynamic parameters for adsorption of Pb**^{2+} onto WAC-nZVI

^{2+}onto WAC-nZVI

It can therefore be ascertained from Table 8 that the reaction is endothermic because the value of ΔH is positive (Δ*H* = +4.761 kJ mol^{−1}), the standard entropy change ∆*S*^{o} (38.169 J mol^{−1} K^{−1}) indicating the degree of randomness at the solid–liquid interface during the sorption of Pb^{2+} onto WAC-nZVI and the negative values of the standard Gibbs free energy (∆G^{o}) indicate the viability, feasibility, and spontaneity of the adsorption process. This finding is in support with the report of other researchers (*55*).

### 3.7. Salinity/ionic strength

In waste water, salt is present in different concentrations depending on the source and quality of the effluent released into it. The presence of these dissolved salt and co-existing ions could affect the adsorption of Pb^{2+}. Figure 13 depicts the result of effect of ionic strength on adsorption of Pb^{2+} onto WAC-nZVI. It was obvious that the percentage of Pb^{2+} removed reduced from 91.42 to 86.40%. This decrease in the amount of Pb^{2+} uptake was due to electrostatic attraction arising from compressed electrical diffuse double layer. Also, increase in the number of Pb^{2+}, Na^{+}, and other competing ions led to electrostatic competition between Pb^{2+} and Na^{+} on the available adsorption sites which resulted to decrease in percentage of Pb^{2+} removed (*21, 59*).

^{2+}onto wood activated carbon supported zerovalent iron (WAC-ZVI) nanocomposite

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18 July 2017^{2+} adsorbed onto WAC-nZVI.

However, critical survey of the ranges of decrease in percentage did not show a drastic effect on the efficiency of WAC-nZVI in immobilization of Pb^{2+} from the aqueous solution. Hence, WAC-nZVI nanocomposite could find relevance in adsorption of Pb^{2+} from saline and natural water since 86.4% efficiency was obtained.

## 4. Conclusion

The immobilization of Pb^{2+} onto WAC-nZVI vis-à-vis the kinetics, equilibrium, and thermodynamic studies was carried out successfully. The kinetic data were tested with eight kinetic and mechanism models. The kinetics was best described by pseudo-second-order, the adsorption mechanism was dominated by both intraparticle and external diffusions confirmed by Bangham and Boyd models. Of all the seven isotherm models investigated, equilibrium data analyzed fitted best to Langmuir isotherm models indicating that the interaction between Pb^{2+} and WAC-nZVI was predominately chemisorption in nature. This was confirmed by the shift in bands from the FTIR spectra. However, electrostatic force played a substantial role in the adsorption process based on the D–R energy value, E < 8 k J mol^{−1}. Comparative investigation of the monolayer adsorption capacity of WAC-nZVI for Pb^{2+} revealed that WAC-nZVI is a better nanoadsorbent with better performance than those previously reported. The result from the thermodynamic studies showed that immobilization of Pb^{2+} was spontaneous, feasible, and endothermic in nature. Study of effect of ionic strength revealed that WAC-nZVI is a better candidate for industrial wastes in the presence of other competing ions. The immobilization of Pb^{2+} by WAC-nZVI proved that it is an efficient and an effective nanoadsorbent and it is therefore recommended for utilization on large scale for decontamination of water and industrial treatment of effluent.

Physicochemical properties | WAC-nZVI |
---|---|

pH | 7.53 |

PZC | 5.60 |

BET surface area | 101.5033 m²/g |

t-Plot micropore area | 78.6414 m²/g |

t-Plot external surface area | 22.8619 m²/g |

BJH adsorption cumulative surface area of pores between 17.000 and 3,000.000 Å diameter | 8.389 m²/g |

Pore volume | |

Single-point adsorption total pore volume of pores less than 1,094.743 Å diameter at P/Po = 0.981990668 | 0.056673 cm³/g |

t-Plot micropore volume | 0.036247 cm³/g |

BJH Adsorption cumulative volume of pores between 17.000 and 3,000.000 Å diameter | 0.024482 cm³/g |

Pore size | |

Adsorption average pore width (4 V/A by BET) | 22.3334 Å |

BJH Adsorption average pore diameter (4 V/A) | 116.727 Å |

Functional group(s)/peaks | Intensities | ||
---|---|---|---|

Functional group(s) | Vibration bands/peaks (cm^{−1}) | WAC-nZVI before adsorption | Pb(II)-loaded WAC-nZVI after adsorption |

O–H stretching | 3,417.98 | 42.474 | 3 |

H–O–H bending | 1,637.62 | 84.066 | 2.5 |

C=C | 1,340.57–1,309.71 | 53.881 | 0 |

Si–O-Al | 966.37 | 61.453 | 1.5 |

C–O | 860.28 | 67.45 | 1 |

Fe^{0} | 688.61 | 68.624 | 1.02 |

574.81 | 56.232 | 0.5 | |

414.71 | 82.49 | 1.5 |

Pseudo-first-order | WAC-nZVI | Pseudo-second-order | Elovich | Fractional power | |||
---|---|---|---|---|---|---|---|

k_{1} (min^{−1}) | 0.035 | k_{2} (g/mg/min) | 0.020 | α (g.min^{2}/mg) | 1.60 × 10^{+34} | v (min^{−1}) | 0.012 |

h_{1} (mg/g/min) | 0.193 | h_{2} (mg/g/min) | 166.667 | β (g.min/mg) | 0.933 | k_{3} (mg/g) | 83.946 |

R^{2} | 0.932 | R^{2} | 1.000 | R^{2} | 0.953 | R^{2} | 0.954 |

SSE | 6993.642 | SSE | 2.921 | SSE | 0.026 | SSE | 0.0842 |

χ^{2} | 1255.140 | χ^{2} | 0.032 | χ^{2} | 3 × 10^{−4} | χ^{2} | 0.001 |

Δq | 23.438 | Δq | 0.479 | Δq | 0.0448 | Δq | 0.081 |

q_{e,exp} (mg/g) | 89.200 | q_{e,exp} (mg/g) | 89.200 | q_{e,exp} (mg/g) | 89.200 | q_{e,exp} (mg/g) | 89.200 |

q_{e,cal} (mg/g) | 5.572 | q_{e,cal} (mg/g) | 90.909 | q_{e,cal} (mg/g) | 89.040 | q_{e,cal} (mg/g) | 88.909 |

Intraparticle diffusion | WAC-nZVI | External diffusion | Bangham | Boyd | |||
---|---|---|---|---|---|---|---|

k_{ip} (mg/g/min ^{0.5}) | 0.348 | k_{fd} | 0.002 | K_{o} | 0.022 | R^{2} | 0.933 |

C | 85.440 | Α | 0.012 | ||||

R^{2} | 0.987 | R^{2} | 0.967 | R^{2} | 0.954 |

S/N | Isotherms | Nonlinear form | Linear form | Equations | Plots |
---|---|---|---|---|---|

1 | Freundlich | $q{}_{e}=K{}_{f}C{}_{e}^{1\phantom{\rule{-0.166667em}{0ex}}/\phantom{\rule{0.0pt}{0ex}}\phantom{\rule{-0.166667em}{0ex}}{n}_{f}}$ | $logq{}_{e}=log{K}_{f}+1\phantom{\rule{-0.166667em}{0ex}}/\phantom{\rule{0.0pt}{0ex}}\phantom{\rule{-0.166667em}{0ex}}{n}_{f}logC{}_{e}$ | (21) | log q_{e} vs. log C_{e} |

2 | Langmuir | $q{}_{e}={q}_{\text{max}}\frac{K{}_{L}C{}_{e}}{1+K{}_{L}C{}_{e}}$ | $\frac{{C}_{e}}{{q}_{e}}=\frac{1}{{K}_{L}{q}_{\text{max}}}+\frac{C{}_{e}}{q{}_{\text{max}}}$ ${R}_{L}=\frac{1}{1+{K}_{L}{C}_{o}}$ | (22) and (23) | $\frac{{C}_{e}}{{q}_{e}}$ vs. C_{e} |

3 | Temkin | $q{}_{e}=\frac{RT}{{b}_{T}}ln\left({A}_{T}C{}_{e}\right)$ | $q{}_{e}=\frac{RT}{{b}_{T}}ln{A}_{T}+\left(\frac{RT}{{b}_{T}}\right)ln{C}_{e}$ | (24) | q_{e} vs. ln C_{e} |

4 | Dubinin–Radushkevich (D–R) | q_{e} = q_{d} exp ( - A_{DKR}ɛ^{2}) | ln q_{e} = ln q_{d} − A_{DKR}ɛ^{2} $E=-\left[\frac{1}{\sqrt{2A{}_{D-R}}}\right]$ | (25) | ln q_{e} vs. ɛ^{2} |

5 | Halsey | ${q}_{e}=Exp\left(\frac{ln{k}_{H}-lnCe}{{n}_{H}}\right)$ | $\ell n{q}_{e}=\left[\left(\frac{1}{{n}_{H}}\right)\ell nK\right]-\left(\frac{1}{{n}_{H}}\right)\ell n{C}_{e}$ | (26) | ln q_{e} vs. ln C_{e} |

6 | Harkin–Jura | ${q}_{e}={\left(\frac{A}{{B}_{2}-log{C}_{e}}\right)}^{1\phantom{\rule{-1.00006pt}{0ex}}/\phantom{\rule{-1.49994pt}{0ex}}2}$ | $\frac{1}{{q}_{e}^{2}}=\left[\frac{B}{A}\right]-\left[\frac{1}{A}\right]log{C}_{e}$ | (27) | $\frac{1}{{q}_{e}^{2}}$ vs. log C_{e} |

7 | Jovanovic | ${q}_{e}={q}_{\text{max}}\left(1-{exp}^{\left({K}_{j}\phantom{\rule{0.277778em}{0ex}}{C}_{e}\right)}\right)$ | ln q_{e} = ln q_{max} − k_{j}Ce | (28) | ln q_{e} vs. C_{e} |

Langmuir | Values | Freundlich | Values | Temkin | Values | D-R | Values |
---|---|---|---|---|---|---|---|

q_{max} (mgg^{−1}) | 77.519 | k_{f} | 32.885 | b_{T} (J mol ^{−1}) | 277.892 | q_{d} | 82.163 |

K_{L} (Lmg^{−1}) | 1.344 | 1/n_{f} | 0.283 | β (Lg^{−1}) | 8.916 | A_{DKR} | 4 × 10^{−8} |

R_{L} | 7.44 × 10^{−2}–3.77 × 10^{−3} | n_{f} | 3.53 | A_{T} (Lg^{−1}) | 180.925 | E (J/mol) | 3,535.5 |

R^{2} | 0.972 | R^{2} | 0.64 | R^{2} | 0.842 | R^{2} | 0.969 |

SSE | 131.231 | SSE | 259.091 | SSE | 112.375 | SSE | 342.532 |

χ^{2} | 1.748 | χ^{2} | 3.251 | χ^{2} | 1.514 | χ^{2} | 4.204 |

Δq | 4.502 | Δq | 6.326 | Δq | 4.166 | Δq | 7.306 |

Halsey | Values | Harkin–Jura | values | Jovanovic | values | ||

1/n_{H} | −0.283 | A | 133.33 | q_{max} | 18.5061 | ||

n_{H} | −3.53 | B | 1.0933 | K_{j} | −0.0482 | ||

K_{H} | 4.42 × 10^{−6} | 1/A | 0.0075 | ||||

R^{2} | 0.6402 | R^{2} | 0.3417 | R^{2} | 0.45 | ||

SSE | 259.693 | SSE | nd | SSE | 78.7266 | ||

χ^{2} | 3.257 | χ^{2} | nd | χ^{2} | 0.8537 | ||

Δq | 6.333 | Δq | nd | Δq | 2.6616 |

Note: nd = non-determinate.

S/N | Adsorbents | Adsorption capacity (mg/g) | Ref |
---|---|---|---|

1 | Amino-functionalized Fe_{3}O_{4}-SiO_{2} magnetic nanomaterial | 76.6 | (48) |

2 | Copolymer 2-hydroxyethyl methacrylate with monomer methyl methacrylate | 31.5 | (49) |

3 | Silica-supported dithiocarbamate | 70.4 | (50) |

4 | Nanometer TiO_{2} | 22.5 | (51) |

5 | Exfoliated Graphene Nanosheets | 35.5 | (52) |

6 | Modified nanometer SiO_{2} | 6 | (53) |

7 | Amino-functionalized mesoporous | 57.74 | (54) |

Nanomesoporous silica | |||

8 | Magnetic Chitosan/GO | 76.94 | (55) |

9 | WAC-nZVI | 77.5194 | Present study |

T (^{o}C) | T (K) | ΔG (kJ mol^{−1}) | ΔH (kJ mol^{−1}) | ΔS (J mol^{−1} K^{−1}) | K_{c} |
---|---|---|---|---|---|

25 | 298 | −6592 | 4.761 | 38.169 | 14.297 |

35 | 308 | −7009 | 15.434 | ||

45 | 318 | −7397 | 16.401 | ||

55 | 328 | −7769 | 17.262 | ||

65 | 338 | −8115 | 17.943 |

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## Acknowledgment

The serene environment and opportunity given to Dada, Adewumi Oluwasogo by both Landmark University and the University of Ilorin to undertake this doctoral research is highly appreciated. The assistance rendered by Ogunlaja Adeniyi in Rhodes University, South Africa for the SEM/EDX analyses is thankfully acknowledged.