Isotherms, kinetics and thermodynamics of hexavalent

Journal of Environmental Chemical Engineering 6 (2018) 2335–2343

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Journal of Environmental Chemical Engineering journal homepage: www.elsevier.com/locate/jece

Isotherms, kinetics and thermodynamics of hexavalent chromium removal using biochar Bharat Choudharya, Debajyoti Paula,b, a b

T

⁎

Centre for Environmental Science and Engineering, Indian Institute of Technology Kanpur, Kanpur, 208016, UP, India Department of Earth Sciences, Indian Institute of Technology Kanpur, Kanpur, 208016, UP, India

A R T I C LE I N FO

A B S T R A C T

Keywords: Chromium(VI) removal Biochar Isotherms Kinetics Thermodynamics

This study investigates the isotherm and kinetics of aqueous Cr(VI) removal using Eucalyptus globulus bark biochar (EBB) produced by pyrolysis of residual bark biomass at 500 °C. Various experimental parameters such as Cr(VI) initial concentration (range of 1–240 mg/L), reaction time (15–240 min) and temperature (303–323 K) were studied to understand the EBB–mediated Cr(VI) removal using two–parameter and three–parameter isotherms, sorption kinetics, and thermodynamics. Our data suggest that adsorption of Cr(VI) on biochar follow both Langmuir and Temkin isotherms; the estimated maximum removal capacity is 21.3 mg/g. The estimated ΔH° (12.07 kJ/mol) and ΔS° (110 J/mol–K) indicate endothermic and physical nature of sorption, and enhanced randomness at the sorbate–sorbent interface. The negative ΔG° values (−21.19 to −23.39 kJ/mol at 303–323 K) confirm spontaneous sorption dominated by physisorption. Cr(VI) removal kinetic was governed by the pseudo–second order rate with Cr(VI) removal by EBB dominantly controlled by film diffusion. Our results also show that Cr(VI) removal using EBB was unaffected in the presence of high concentration (800–5000 mg/L) of foreign ions compared to the control experiment. Thus, the developed low–cost EBB seems promising for Cr(VI) removal from various industrial wastewater sources.

1. Introduction Discharge of chromium containing effluent from leather tanning, electroplating, and metallurgy industries to the environment is considered to be the major contributor of water pollution globally [1]. Aqueous Cr occurs essentially as Cr(III), which in trace amounts is required for human metabolic activities, whereas trace amounts of Cr(VI) may cause mutagenic and carcinogenic effects [2]. Compared to several conventional precipitation and electrochemical methods used for Cr(VI) remediation [3], which are not only costly but also produce huge amounts of secondary waste, Cr(VI) removal using biomass–derived sorbents is economically viable and generates minimal secondary waste. Biochar is a carbon–enriched porous material generally produced by simple thermal pyrolysis of biomass under inert or oxygen–limited atmosphere. Biochar prepared from various biomasses such as Leersia hexandra Swartz leafs [4], oleaster (Elaeagnus) seed and cherry (Prunus avium) stone [5], Onopordom Heteracanthom weed [6], pineapple–peel [7], Pistacia terebinthus L. seeds [8] have been studied for Cr (VI) removal. Biochar has also been utilized effectively for removal of other heavy metal contaminants [9,10] as well as some organic dyes from contaminated water [11,12]. A recent study concluded that for

⁎

micro–pollutant removal from wastewater, biochar is more environmentally beneficial than the well–known coal based powdered activated carbon; production of biochar involves comparatively lower cost and energy, and use of biochar also lowers the carbon footprints of wastewater treatment facilities [13]. Hence, use of biochar in environmental remediation seems promising for treatment of wastewater. In this regard, understanding the sorption kinetics and thermodynamics of aqueous Cr(VI) on biochar will reveal the biochar potential for Cr removal. Recently, we explored the feasibility and effectiveness of solid phase batch extraction of aqueous Cr(VI) using Eucalyptus bark biochar (EBB) and explained the mechanistic aspect of Cr(VI) removal through a combination of sorption–reduction facilitated by solid biochar surface functional groups and simultaneous aqueous reduction by biochar–derived dissolved organic matter [14]. In this study, we investigated the isotherms, kinetics, and thermodynamic aspects of aqueous Cr(VI) removal using the EBB sorbent to understand the sorption mechanism and optimize the removal process, both of which evaluate the practical applicability of the EBB for Cr(VI) removal. Thus, series of experiments were carried out to evaluate the effects of initial Cr(VI) concentration, reaction time, and temperature in order to understand the modelling

Corresponding author at: Department of Earth Sciences, Indian Institute of Technology Kanpur, Kanpur, 208016, UP, India. E-mail address: [email protected] (D. Paul).

https://doi.org/10.1016/j.jece.2018.03.028 Received 17 November 2017; Received in revised form 12 March 2018; Accepted 13 March 2018 Available online 15 March 2018 2213-3437/ © 2018 Elsevier Ltd. All rights reserved.


B. Choudhary, D. Paul

L, shaking time (15–240 min), and temperature (303–323 K) to evaluate the modelling aspect (isotherms and kinetics) of Cr(VI) removal. Additionally, the influence of foreign ions for e.g., sodium(I), potassium(I), magnesium(II), calcium(II), chromium(III), iron(III), cadmium(II), manganese(II), copper(II), nickel(II), and zinc(II) in their stable forms were evaluated to determine the practical applicability of EBB in the Cr (VI) removal from typical wastewater samples. All chemicals used for experiments were of analytical grade (Merck, India). The experimental batch equilibrium data obtained for EBB-mediated Cr(VI) removal for the studied temperature range (303–323 K) were assessed using various two–parameter and three–parameter isotherms. Further, the experimental data obtained at various initial Cr(VI) concentrations (i.e., 20, 30, and 40 mg/L) were evaluated using commonly utilized kinetic models to determine the rate controlling step of Cr(VI) removal by EBB. Apart from linear regression coefficients (R2), a non–linear regression model with error function like chi–square test and normalized standard deviation were also assessed to identify the suitable isotherm to explain the obtained equilibrium data. The chi–square (χ2) and the normalized standard deviation (Δq) can be expressed as:

aspects (isotherm and kinetics) of biochar–mediated Cr(VI) removal. Further, the two–parameter and three–parameter isotherm assessment were also carried out using the experimental equilibrium data to establish the Cr(VI) removal mechanism. The applicability of biochar in the treatment of various industrial wastewater was evaluated by studying the interference of foreign ions on aqueous Cr(VI) removal. 2. Material and methods 2.1. Biochar and Cr (VI) solution preparation The preparation of Eucalyptus globules plant bark biochar (EBB) is explained in detail in Choudhary et al. [14]. Briefly, the plant bark residue was pre–cleaned with ultrapure water from water purification system (Direct–Q® 3, Millipore Merck), subsequently air–dried and then ground to powder. The pyrolysis of plant bark residue was carried out at 500 °C for 2 h under oxygen–limited atmosphere using a digital muffle furnace, and the EBB produced was cooled and passed through 250 μm mesh size sieve to obtain uniform-sized particles. Hexavalent chromium stock solution of 2000 mg/L was obtained by dissolving accurately weighed potassium dichromate (K2Cr2O7, analytical grade, Merck) in 1% nitric acid solution. For various studies, all analytical grade chemicals and reagents were used.

χ2 =

2.2. Surface characterization of biochar

n

∑i =1

(qe . exp − qe . cal )2 qe . cal

∆q (%) = 100 ×

The biochar samples before and after Cr(VI) removal were characterized for its surface area (SABET), average pore diameter (PD), pore size distribution (PSD), and total pore volume (Vtotal) and micropore volume (Vmicro) using an Autosorb-1C instrument (Quantachrome, USA). The biochar samples were degassed at 200 °C for 24 h to remove any adsorbed gases and moisture before the actual analysis. Further, detailed surface characterization of biochar samples before and after Cr (VI) removal using various analytical techniques such as Fourier transform infrared (FT-IR) spectroscopy, X-ray diffraction (XRD), X-ray photoelectron spectrometry (XPS), field emission scanning electron microscopy, were described in our previous work [14].

∑

(1)

[(qe . exp − qe . cal )/ qe . exp ]2 (2)

n−1

where qe.exp value (amount of solute removed at equilibrium) was obtained from the batch experiment, qe.cal value was estimated from the respective isotherms for corresponding qe.exp value, and n present the number of independent observations in the dataset (n = 12 for this study) of the batch experiment. The best fit of the model to the experimental data was evaluated on the basis of smaller values of χ2 and Δq. 3. Results and discussion 3.1. Surface characterization of biochar

2.3. Cr(VI) removal batch experiments

The adsorption isotherm of N2 at 77 K for the biochar samples before and after Cr(VI) removal were shown in Fig. 1. For both the samples, the nitrogen uptake gradually increased with increasing relative pressure and nearly horizontal to the P/Po axis, which is characteristic of the Type-I isotherm indicating microporous nature of biochar. The specific surface area (SABET), average pore diameter (PD), pore size distribution (PSD), total pore volume (Vtotal) and micropore volume (Vmicro) of the biochar are summarized in Table 1. The SABET and Vtotal of the EBB after Cr(VI) removal increased compared to the raw EBB due to leaching of dissolve organic matter as well as surface oxidation of

Aqueous Cr(VI) removal using EBB under different experimental conditions were performed in batches in glass stopper flasks. A control experiment was also performed adding a fixed sorbent dosage (i.e., 2 g/ L EBB) to a solution containing 50 mL of 20 mg/L Cr(VI) concentration adjusted to pH 2 using 0.5 M HNO3. This solution containing EBB was agitated at 100 rpm for 6 h in a water bath shaker (RSB–12, Remi, India). It was then vacuum–filtered for phase separation and the aqueous filtrate was used to determine Cr(VI) concentration and to estimate the percentage of EBB–mediated Cr(VI) removal. Following the diphenylcarbazide colorimetric method [15], aqueous Cr(VI) concentration was measured by using a pre–calibrated UV–visible spectrophotometer (Lambda–25, Perkin Elmer) at 540 nm wavelength maximum. The UV–visible spectrophotometer was optimized using a 60 mg/L Cr(VI) standard solution prepared dissolving vacuum dried potassium dichromate in 0.005 M sulphuric acid. Results of our previous work [14] showed that near complete aqueous Cr(VI) removal could be achieved at pH 1 and 2, but maximum sorption of Cr on EBB was observed only at pH 2. Therefore, the influence of all other batch experimental parameters on EBB–mediated Cr(VI) removal were carried out at pH 2. Except for the sorbent dosage experiments that were replicated thrice, all other experiments were carried in duplicates for which the results agreed within 4–6%. The accuracy of the experimental data were checked by performing analysis of a 2 mg/L standard Cr(VI) solution using the diphenylcarbazide colorimetric method. The batch experiments were repeated under various conditions, such as sorbent dosage (1–5 g/L), Cr(VI) concentration in the range 1–240 mg/

200 EBB after Cr(VI) removal 150 100 EBB 50 0 0.0

0.2

0.4

0.6

0.8

1.0

Fig. 1. Nitrogen adsorption isotherm at 77 K for the biochar samples before and after Cr (VI) removal.

2336



Table 1 Specific surface area (SABET), average pore diameter (PD), total pore volume (Vtotal), pore size distribution (PSD), micropore volume (Vmicro) and meso- and macro- pore volume (Vmeso+macro) of biochar (EBB) before and after Cr(VI) removal. SABET (m2/ g)

Samples

EBB EBB after Cr(VI) removal

265.0 518.6

PD (Å)

24.97 24.63

Vtotal (cc/ g)

0.165 0.319

Table 2 Two– and three–parameter isotherm variables for Cr(VI) sorption on EBB at different temperatures. Temperature (K)

303

313

323

Experiemntal qe (mg/g)

20.3

24.2

27.6

Langmuir Isotherm Qmax (mg/g) KL (L/mg) R2 χ2 Δq (%)

21.3 0.087 0.996 0.076 6.74

25.4 0.105 0.997 0.038 5.13

28.4 0.117 0.997 0.030 4.59

Freundlich Isotherm KF (mg/g)/(mg/L)n 1/n R2 χ2 Δq (%)

5.95 0.27 0.804 2.07 10.61

6.45 0.30 0.838 3.57 12.94

6.99 0.31 0.840 4.53 13.88

Temkin Isotherm KT (L/g) b (kJ/mol) R2 χ2 Δq (%)

19.09 1.03 0.973 0.064 1.85

13.08 0.82 0.962 0.140 2.50

12.29 0.74 0.982 0.084 1.86

Dubinin–Radushkevich Isotherm KDR (mol2/kJ2) qDR (mg/g) E (kJ/mol) R2 χ2 Δq (%)

0.0195 16.41 5.1 0.896 2.407 11.20

0.0205 17.93 4.9 0.964 7.218 15.68

0.0200 20.15 5.0 0.959 7.928 16.37

Redlich–Peterson Isotherm KRP (L/g) aRP (L/mg)–βRP βRP R2 χ2 Δq (%)

305.2 26.1 0.90 0.977 1.390 3.86

266.6 21.1 0.88 0.983 1.540 4.24

294.9 21.7 0.86 0.983 1.960 3.87

Sips Isotherm Ks (L/mg) as (L/mg) –βS βs R2 χ2 Δq (%)

14.3 0.536 0.813 0.944 3.307 3.31

14.2 0.409 0.831 0.964 3.237 3.38

14.9 0.372 0.839 0.970 3.521 2.62

Tóth Isotherm Qmax (mg/g) KT (L/g) nT R2 χ2 Δq (%)

8.951 30.372 0.898 0.979 1.270 38.83

9.336 24.483 0.872 0.985 1.394 43.79

9.717 25.687 0.861 0.985 1.780 46.00

PSD (cc/g) Vmicro

Vmeso+macro

0.142 0.286

0.023 0.033

biochar by potassium dichromate (pH 2). Further, the PSD data suggest that the biochar samples are highly microporous in nature, with Vmicro being 86–90% of the Vtotal. Further, Choudhury et al. [14] have presented detailed surface characterization of EBB. In summary, a positive zeta potential (ζ = 15.6 mV) of EBB at pH 2 indicated favourable conditions for Cr(VI) sorption; the isoelectric point (pHIEP) of EBB was estimated to be at pH 3.18. FESEM results also revealed highly porous EBB surface that may control intraparticle diffusion of Cr(VI). Further, the FT-IR and high resolution XPS data indicated a dominant role of carboxylic and phenolic surface functional groups in Cr(VI) sorption and reduction respectively, on biochar surface. 3.2. Effect of EBB dosage Sorbent dosage is considered as an essential parameter that controls the degree of solute removal from aqueous media. The effect of EBB dosage over a range of 1–5 g/L for Cr(VI) removal (of 20 mg/L initial concentration) is shown in Fig. 2. As expected, removal of aqueous Cr (VI) at pH 2 increases from 85% to 99% with EBB dosage increment from 1 g/L to 5 g/L. In other words, the Cr(VI) removal increased with an increase dosage of EBB, which is due to high number of available binding sites at higher sorbent dosage. However, the capacity of EBB–mediated Cr(VI) removal was found to decrease from 17 mg/g for 1 g/L dosage to 4 mg/g for 5 g/L dosage (Fig. 2); the removal capacity is a measure of amount of aqueous Cr(VI) removed per unit mass of the sorbent. Thus, 2 g/L of EBB dosage was fixed to study the other experimental parameters that influences the aqueous Cr(VI) removal. 3.3. Two–parameter isotherms for EBB–mediated Cr(VI) removal 3.3.1. Langmuir isotherm This is one of the most commonly studied isotherm model, which at equilibrium condition describes the correlation between the amounts of solute sorbed on sorbent (mg/g) versus the solute concentration in the solution (mg/L). This model assumes that at equilibrium, monolayer

sorption of solute occurs at fixed number of homogeneously distributed sorption sites over the sorbent surface and these sites also have equal affinity for the adsorbate. The non–linear and linear equations describing the Langmuir isotherm are given as follows [16]:

20

100

16 95

qe = 12

Ce 1 Ce = + qe Qmax KL Qmax

90 8 85 Cr(VI) removal capacity 0 0

1

2

3

4

5

(3)

(4)

where Ce (mg/L) is the solute aqueous concentration at equilibrium, qe (mg/g) is the amount of solute sorbed per unit weight of sorbent at equilibrium, Qmax is the maximum amount of solute sorbed per unit weight of sorbent (mg/g) to form a single layer, and KL (L/mg) is the isotherm constant. Note that in our case Qmax includes Cr(VI) removal capacity of EBB resulting from both sorption and reduction process. A linear plot of Ce/qe versus Ce (Eq. (4)) yields a slope and an intercept, which were used to estimate Qmax and KL (Table 2). An increase in the

4

80

Qmax KL Ce 1 + KL Ce

6

Fig. 2. Effect of EBB dosage on the removal of 20 mg/L initial Cr(VI) concentration at pH 2. Error bars show 1σ deviations based on three replicate analyses.

2337



log qe = log KF +

a

25

1 log Ce n

(6) n

where the Freundlich equilibrium constant KF (mg/g)/(mg/L) and 1/n relate to sorption capacity and sorption intensity of the sorbent, respectively. A linear plot between log qe and log Ce (Eq. (6)) gives an intercept and a slope, which were used to estimate the value of KF and 1/n, respectively. The value of 1/n < 1 indicates favourable sorption. At pH 2, the obtained Freundlich constants (KF and 1/n) values for Cr (VI) sorption on to EBB at different temperatures are listed in Table 2. The values of 1/n is in the range of 0.27–0.31, which suggests favourable sorption of Cr(VI) onto EBB. However, poor R2 (0.80–0.84) and higher χ2 and Δq values reveals unsuitability of Freundlich isotherm to explain the sorption equilibrium data. This is also observed in the plot of qe versus Ce (Fig. 3a–c), were the calculated qe values from Freundlich isotherm does not fit the experimental qe values.

20 15

qe_Exp.– 303K qe_Cal.– Langmuir qe_Cal.– Freundlich qe_Cal.– Temkin qe_Cal.– Dubinin–Radushkevich

10 5 0 0 35

50

100 150 Ce (mg/L)

200

b

30

3.3.3. Temkin isotherm According to this model, the heat of sorption of solute in a layer decreases linearly with surface coverage owing to sorbent–solute interactions, where the solute sorption is characterized by a uniform distribution of binding energies [19]. Temkin isotherm can be given in the following forms:

25 20 15

qe_Exp.– 313K qe_Cal.– Langmuir

10

qe_Cal.– Freundlich qe_Cal.– Temkin

5

qe_Cal.– Dubinin–Radushkevich

qe =

RT ln(KT Ce ) b

(7)

qe =

RT RT lnKT + ln Ce b b

(8)

0 0 40

50

100 150 Ce (mg/L)

200

where b (kJ/mol) is a constant associated with heat of sorption, KT (L/ g) is the Temkin isotherm constant, R (0.00813 kJ/mol–K) is the gas constant, and T (K) is temperature. For our data, the intercept and slope obtained from a linear plot of qe versus ln Ce (Eq. (8)) were used to estimate the Temkin isotherm constants KT and b and the obtained results are listed in Table 2. Fig. 3a–c shows the evaluation of experimental and calculated qe values (using Eq. (7)). Note that a value of the constant b < 8 kJ/mol indicates a weak sorbent–sorbate interaction [20]. Choudhary et al., [14] found that after sorption equilibrium, some amount of Cr was released to the solution from the sorbent surface but did not provide a reason for this. This can be explained by the weak sorbent–sorbate interaction as indicated by the b value of ∼1 kJ/mol (Table 2) determined from our data. High R2 and low χ2 and Δq values similar to that obtained for the Langmuir isotherm model suggest that Temkin isotherm is the second best model that may also explain the equilibrium data of Cr(VI) sorption on EBB.

c

35 30 25 20

qe_Exp.– 323K qe_Cal.– Langmuir qe_Cal.– Freundlich qe_Cal.– Temkin qe_Cal.– Dubinin–Radushkevich

15 10 5 0 0

50

100

150

200

Fig. 3. Comparison of experimental (Exp.) and calculated (Cal.) qe values obtained from two–parameter isotherms studied at different temperatures (a) 303 K, (b) 313 K, and (c) 323 K. Vertical bars show upper and lower bounds of data.

3.3.4. Dubinin–Radushkevich isotherm This isotherm assumes that sorption is a function of porous structure of the sorbent [21], and has been mainly used to differentiate between chemical versus physical nature of sorption. The isotherm is expressed in various forms as follows:

calculated Qmax value with an increase in solution temperature suggests an endothermic nature of the sorption process [17]. Langmuir isotherm results obtained for EBB–mediated Cr(VI) removal, studied at various solution temperatures (303–323 K), are also presented in plots of qe versus Ce (Fig. 3a–c). The isotherm plots also reveal that the calculated qe values agree well with the experimental qe values determined using the Langmuir isotherm (Eq. (3)). Further, comparatively much lower χ2 and Δq (except for Temkin isotherm) values (Table 2) and stronger regression coefficient (R2 = 0.99) were observed for the Langmuir isotherm relative to the all other isotherm models.

qe = qDR e−KDR ε

2

(9)

ln qe = ln qDR − KDR ε 2

(10)

1⎞ ε = RT ln ⎛1 + Ce ⎠ ⎝ ⎜

⎟

(11) 2

where qDR (mg/g) and KDR (mol /kJ ) represent the Dubinin–Radushkevich isotherm constants, and ε is the Polanyi potential determined using Eq. (11). The mean energy of sorption process (E) is determined using an equation as follows:

3.3.2. Freundlich isotherm This empirical model assumes that the sorption process on a heterogeneous surface is in the form of multilayers, where sorption sites have varied affinity for the adsorbate. The non–linear and linear forms of the Freundlich isotherm can be presented as [18]:

qe =

KF Ce1/ n

2

E=

1 2KDR

(12)

Using our data in a linear plot of ln qe versus ε (Eq. (10)), qDR and KDR values were estimated from the values of intercept and slope 2

(5)

2338



respectively; these parameters along with the mean free energy (E) are presented in Table 2. The E values indicating chemical and physical sorption typically range from 8 to 16 kJ/mol and < 8 kJ/mol, respectively [22]. The estimated E is in the range 4.9–5.1 kJ/mol (Table 2), suggesting physical nature of Cr(VI) sorption on EBB. The relatively poor R2 values (0.89–0.96) obtained from the linear plot (Eq. (10)) along with high χ2 and Δq values suggest that the Dubinin–Radushkevich isotherm does not explain the equilibrium sorption data. The plot of qe versus Ce shows the comparison of model calculated qe and experimental qe values (Fig. 3a–c).

a

10 5 0

3.4. Three–parameter isotherm for EBB–mediated Cr(VI) removal

0

3.4.1. Redlich–Peterson isotherm This isotherm is a three–parameter empirical model that includes the characteristics of both the Langmuir and Freundlich isotherms, and explains the sorption equilibrium data obtained from a wide–range of solute concentration. Redlich–Peterson isotherm is described by a non–linear equation as follows [23]:

KRP Ce 1 + aRP CeβRP

25

(13)

b qe_Exp.– 313K qe_Cal.– Redlich-Peterson qe_Cal.– Sips qe_Cal.– Toth

10

0 0 35

50

100 150 Ce (mg/L)

200

c

30 25

qe_Exp.– 323K qe_Cal.– Redlich-Peterson qe_Cal.– Sips qe_Cal.– Toth

20 15 10 5 0 0

Ks Ceβs

50

100

150

200

(14)

where as (L/mg)–βS and Ks (L/g) are the Sips isotherm constants, and βS is the Sips isotherm exponent. When βS is close to unity at high sorbate concentrations, then data fit will approximate Langmuir isotherm model. On the other hand, the data may be fitted to Freundlich isotherm model at low sorbate concentrations. Similar to the Redlich–Peterson isotherm, Sips isotherm exponent βS values (Table 2) suggest that our data fit Langmuir isotherm. Fig. 4 shows a better fit between experimental and calculated qe values for the Sips model. However, very high χ2 values (3.2–3.5; Table 2) obtained for the Sips isotherm compared to other three–parameter isotherms suggest its non–applicability to explain the equilibrium data.

Fig. 4. Comparison of experimental (Exp.) and calculated (Cal.) qe values obtained from three–parameter isotherms studied at different temperatures (a) 303 K, (b) 313 K, and (c) 323 K. Vertical bars show upper and lower bounds of data.

(Eq. (3)). The values of Tóth isotherm constant and exponent values estimated in this study are listed in Table 2. The estimated nT is close to unity (Table 2), which suggest that Cr(VI) sorption fit the Langmuir isotherm. Although the R2 (∼0.98) and χ2 values (1.3–1.8) are similar to the Redlich–Peterson values, the experimental qe values differ from the model–calculated qe values resulting in very high Δq values (Table 2; Fig. 4), which suggest this model is unsuitable to explain the equilibrium data. In conclusion, the sorption of Cr(VI) on EBB can be best fitted only by the Redlich–Peterson isotherm.

3.4.3. Tóth isotherm According to this isotherm, quasi–Gaussian energy distribution is asymmetrical in which maximum binding sites have sorption energy less than the mean energy value. It is useful in describing the sorption process for both low and high solute concentrations in a heterogeneous system. Tóth isotherm can be expressed by a non–linear equation as [25]:

qe =

200

5

3.4.2. Sips isotherm This isotherm is also called as Langmuir–Freundlich isotherm and can be expressed as [24]:

1 + aS Ceβs

100 150 Ce (mg/L)

15

where aRP (L/mg)−βRP and KRP (L/g) are the isotherm constants, and βRP is an exponent having values between 0 and 1. At low surface coverage (βRP = 0), Eq. (13) takes the form of Henry’s law equation, whereas at high surface coverage (βRP = 1) the same equation reduces to Langmuir isotherm. In this study, the βRP values are close to 1 (Table 2), which suggest that the EBB–mediated Cr(VI) removal equilibrium data can be approximated to fit the Langmuir isotherm model. Comparatively higher R2 (∼0.98) and lower χ2 values (1.39–1.96) among the tested three–parameter isotherms (Table 2) suggest that the sorption equilibrium data can be best explained by Redlich–Peterson isotherm. A better fit among the experimental qe values and the Redlich–Peterson isotherm calculated qe values is also observed in Fig. 4.

qe =

50

20

e

qe =

qe_Exp.– 303K qe_Cal.– Redlich-Peterson qe_Cal.– Sips qe_Cal.– Toth

15

3.5. Thermodynamics of EBB–mediated Cr(VI) removal Thermodynamics of EBB–mediated Cr(VI) removal were evaluated using the standard state thermodynamic variables −Gibbs free energy change (ΔG°), enthalpy change (ΔH°), and entropy change (ΔS°). All these variables were determined from the following equations:

Qmax KT Ce 1

[1 + (KT Ce ) nT ]nT

(15)

where KT (L/g) and nT are the Tóth isotherm constant and exponent, respectively. At nT = 1, Eq. (15) reduces to the Langmuir isotherm form 2339

ΔG ° = −RT ln KL

(16)

−ΔH ° ⎞ 1 ΔS ° ⎞ +⎛ ln KL = ⎛ ⎝ R ⎠ ⎝ R ⎠T

(17)



Table 4 Pseudo–first order kinetic, second order kinetic and intraparticle difusion parameters of Cr(VI) removal by EBB at different initial concentrations.

8.70 8.65 8.60 8.55 8.50

y = -1.4523x + 13.219 R² = 0.9781

8.45 8.40 8.35 3.1

3.1

3.2

3.2

3.3

3.3

Fig. 5. Van’t Hoff plot of ln KL versus 1/T for Cr(VI) removal by EBB sorbent studied at different temperatures (303, 313, and 323 K). Vertical bars show upper and lower bounds of data.

Table 3 Thermodynamic parameters for Cr(VI) removal on EBB at different temperatures. Temperature (K)

ΔG° (kJ/mol)

ΔH° (kJ/mol)

ΔS° (J/mol–K)

R2

303 313 323

−21.19 −22.39 −23.39

12.07

110

0.978

Cr(VI) Concentration (mg/L)

20

30

40

Experimental qe (mg/g)

9.98

14.2

16

Pseudo–first order model k1 (min−1) qe,cal (mg/g) R2

0.03 3.24 0.989

0.005 2.49 0.975

0.003 2.17 0.967

Pseudo–second order model k2 (g/mg–min) qe,cal (mg/g) R2

0.019 10.20 0.999

0.005 13.80 0.998

0.004 16.40 0.997

Intraparticle diffusion Kid (mg/g–min0.5) C R2

0.044 9.32 0.894

0.197 10.07 0.955

0.384 9.62 0.969

nature is also verified from our earlier results showing an increase in the sorption/removal capacity (Qmax) with increasing temperature (Table 2). Further, the positive ΔS° (110 J/mol–K) value suggests increasing randomness due to Cr(VI) sorption on EBB. The negative ΔG° (avg. ∼ −22 kJ/mol) indicates that sorption of Cr(VI) on EBB is spontaneous. Also, ΔG° in the range 0 to −20 kJ/mol represents physisorption and −80 to −400 kJ/mol represents chemisorption [26]. Therefore, Cr(VI) removal using EBB is primarily controlled by physisorption process.

where KL is a constant from Langmuir isotherm (Note: the unit L/mg was converted to L/mol using the atomic mass of Cr = 51.9961 g/mol), R (0.008314 kJ/mol−K) is the gas constant, and T (K) is solution temperature. A linear van’t Hoff plot (Fig. 5) of ln KL versus 1/T gives slope and intercept to determine the value of ΔH° and ΔS°, respectively. The results obtained are listed in Table 3. If ΔH° < 25 kJ/mol, the sorption is considered as physical, whereas ΔH° > 40 kJ/mol suggest chemical sorption [22]. The positive value of ΔH° (12.07 kJ/mol) indicates endothermic nature of Cr(VI) sorption on EBB. The endothermic

3.6. Kinetics of EBB–mediated Cr(VI) removal Kinetic models are generally studied to understand the sorbent–sorbate interactions, i.e., the rate of solute removal by a sorbent with respect to the equilibration time. The widely studied pseudo–first order and pseudo–second order kinetic rate models were evaluated to predict the EBB–mediated Cr(VI) removal rate under optimized conditions. 30

0.5

b

25 t/qt (min-g/mg)

a

-0.5 -1.5 -2.5

20 ppm 30 ppm 40 ppm

-3.5

20 15 10

0

-4.5 0 16

50

100

150 t (min)

200

250

0

300 6

c

5

14

50

100

150 200 t (min)

d

Bt

10

3 2


8

250


4

12

t


5

1

6

0

0

150 200 (min)

250

Fig. 6. (a) Pseudo–first order kinetic and (b) Pseudo–second order (c) Intraparticle diffusion, and (d) Boyd model kinetic plots for Cr(VI) removal by EBB at different initial concentrations (20, 30, and 40 mg/L). Vertical bars show upper and lower bounds of data.

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dqt = k2 (qe − qt )2 dt

Table 5 Effect of various foreign ions on the removal (in%) of EBB for 40 mg/L initial Cr(VI) concentration compared to the control experiment. Element

Added as

Control Sodium(I) Potassium(I) Calcium(II) Magnesium(II) Chromium(III) Iron(III) Cadmium(II) Manganese(II) Copper(II) Nickel(II) Zinc(II)

– NaCl KCl CaCl2 MgCl2 CrCl3 FeCl3 Cd(NO)3 MnSO4 CuSO4 NiCl2 ZnSO4

Foreign ions added (mg/L)

Cr(VI) added (mg/L)

Ratio [M(n):Cr (VI)]

Removal ± SD (%)

– 5000 5000 800 800 800 800 800 800 800 800 800

40 40 40 40 40 40 40 40 40 40 40 40

– 125 125 20 20 20 20 20 20 20 20 20

78.1 76.5 78.5 77.2 75.9 76.1 74.9 78.1 76.9 78.0 77.5 76.9

(20)

Integration of Eq. (20) using the same boundary conditions stated earlier, we get the linear equation as:

t 1 t = + qt qe k2 qe2 ± ± ± ± ± ± ± ± ± ± ± ±

0.5 0.7 0.9 0.5 0.4 0.5 0.7 0.6 0.9 1.0 0.5 0.7

(21)

where qe (mg/g) is the amount of sorbed solute at equilibrium conditions, qt (mg/g) is the amount of sorbed solute at any time t (min), and k1 (min−1) is the model rate constant. Integrating Eq. (18) using the boundary conditions qt = 0 at t = 0 and qt = qe at t = te results in the following equation:

where k2 (g/mg−min) is the pseudo–second order rate constant. Using the slope and intercept values obtained from a plot of t/qt versus t for the three studied initial Cr(VI) concentrations (Fig. 6b), the values of k2 and qe were calculated (Table 4). Not only the R2 for each of the three cases is > 0.99, but also the calculated qe values are very similar to the obtained experimental qe values (Table 4), which confirms that EBB–mediated Cr(VI) removal was controlled by the pseudo second–order rate kinetics. Further, porous nature of the sorbent facilitates removal of solute via a multi–step process usually controlled by three different mechanisms [29]: (i) solute transport from the aqueous media onto the sorbent surface in the form of film diffusion, (ii) diffusion of solute within the sorbent pore spaces, and (iii) sorption of ions on the interior surface of the sorbent. Thus, to predict the adsorption mechanism of Cr(VI) on EBB and to determine the rate limiting step, experimental kinetic data were evaluated by intraparticle diffusion and film diffusion kinetic models. Weber and Morris introduced a graphical method to ascertain whether intraparticle diffusion (or pore diffusion) is the rate limiting step or to predict if a multi–step mechanism is involved in the removal process [30]. Intraparticle diffusion model explaining pore diffusion kinetics is expressed as:

ln(qe − qt ) = ln qe − k1 t

qt = Kid t 0.5 + C

M = metal ion; n = oxidation number; SD = 1σ standard deviation based on three measurements.

The pseudo–first order rate is given as [27]:

dqt = k1 (qe − qt ) dt

(18)

(19)

From a linear plot of ln(qe − qt) versus t (Fig. 6a), the slope and intercept obtained were used to calculate k1 and qe, respectively. Although, the regression coefficient (R2) for each of the three linear plots obtained for the three different initial Cr(VI) concentrations of 20, 30, and 40 mg/L is > 0.97, the calculated qe values for the three cases are substantially lower than the experimental qe values (Table 4). Therefore, the EBB–mediated Cr(VI) removal is not a first–order reaction. Pseudo–second order rate law is based on the assumption that the rate of solute sorption is directly proportional to the square of the number of vacant binding sites and is given as follows [28]:

(22)

where qt (mg/g) is the amount of Cr (VI) sorbed per unit mass of EBB at time t (min), Kid (mg/g–min0.5) is the intraparticle diffusion model constant, and C is a constant. In the above linear Eq. (22), the intercept C is related to the boundary layer thickness. Further, Weber and Morris [30] assumed that if intraparticle diffusion is the only rate limiting step, then C = 0, i.e., the straight line in a linear plot of qt versus t0.5 (Fig. 6c) will pass through the origin. The shape of the intraparticle diffusion plots (Fig. 6c) shows multi–linearity (two stages) indicating that as per the model assumption intraparticle diffusion is not the only rate limiting step. Further, the first steeper segment is representative of surface

Table 6 A comparison of maximum sorption capacity (Qmax) for Cr(VI) removal using various modified and unmodified sorbents of different origin under specific experimental conditions. Adsorbent

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Eucalyptus bark biochar (EBB) Wheat straw biochar Wheat wicker biochar Oak wood biochar Oak bark biochar Sugar beet tailing biochar Ficus carica bark Tartaric acid modified wheat bran Formaldehyde treated eucalyptus bark Treated fertilizer industry waste Iron loaded bamboo charcoal Iron–cobalt loaded bamboo charcoal Nano magnetite coated corn cob activated carbon Uncoated corn cob activated carbon Polyaniline coated chitin Fe3O4 onto alginate biopolymer crosslinked with Ce3+ ions Dolomite Mesoporous magnetite (Fe3O4) nanospheres Modified graphene

Qmax (mg/g)

21.3 28.1 28.1 4.1 7.4 123.0 19.7 16.2 45.0 15.2 29.4 44.4 57.4 56.4 24.6 14.3 8.4 7.3 21.6

NA: not available.

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Experimental conditions

References

pH

Eq. time (h)

Temp. (K)

Sorbent dosage (g/L)

2.0 2.0

6 24

303 298

2 4

This study [36]

2.0

48

308

10

[17]

2.0 3.0 2.2 2.0 2.0 5.0

24 3.5 3.33 3 1.17 8

298 303 296 305 303 298

2 5 1.5 g/20 mL 5 4 2

[37] [22] [38] [39] [40] [41]

2.0

24

300

5

[42]

4.2 5.0 2.0 4.0 2.0

1 1.67 96 72 0.67

303 NA 303 308 293

2 2 1 2 8

[43] [44] [45] [46] [26]



along with their respective optimized experimental conditions. The removal capacity of 21.3 mg/g Cr(VI) for the low–cost EBB prepared in this study is higher than several other types of sorbents studied by others.

sorption (film diffusion) by which Cr(VI) diffuse through the solution onto the EBB surface. The second less–steeper segment represents gradual sorption approaching equilibrium, suggesting intraparticle (pore) diffusion to be the rate limiting step. Essentially, the less–steeper linear segment in the linear plot relates to the rate–limiting step [31]. Similar multi–linearity in intraparticle diffusion plots for Cr(VI) sorption on modified chitosan resin has also been reported [29]. Another study on aqueous Cr(VI) and Pd(II) removal by biomass also reported a two stage linearity in the intraparticle diffusion plot [32,33]. The slope and intercept obtained from the less–steeper second linear segment in Fig. 6c were used to estimate Kid and C, respectively (Table 4). The calculated Kid values suggest that intraparticle diffusion rate increased from 0.044 to 0.384 mg/g–min0.5 with a corresponding increase in the initial Cr(VI) concentration from 20 to 40 mg/L (Table 4). This suggests higher Cr(VI) concentration leads to a higher concentration gradient, and faster diffusion and sorption. Boyd film diffusion model determines if the film diffusion resistance is the rate limiting step, which is expressed as follows [34]:

4. Conclusions

where the fraction of Cr(VI) sorbed on EBB at any time t is given by F = qt/qe; qe and qt (mg/g) represent the amount of Cr(VI) sorbed on EBB surface at equilibrium and at any time t (min), respectively. Bt is a mathematical function of F. According to Reichenberg [35], Eq. (23) can be expressed as follows:

An ecofriendly and low–cost biochar developed from Eucalyptus plant bark (EBB) was investigated for Cr(VI) removal from aqueous media on the basis of sorption isotherms, kinetics, and thermodynamics using optimized batch experimental conditions. The equilibrium isotherm data suggest that Cr(VI) sorption on EBB is best explained by both Langmuir and Temkin isotherms. The maximum sorption capacity estimated from Langmuir isotherm is ∼21 mg/g at 303 K. Our experimental kinetic data of EBB–mediated Cr(VI) removal best fit the pseudo–second order kinetic model. Further, the sorption kinetics (Weber and Morris, and Boyd rate–limiting kinetics models) suggests that the intraparticle diffusion was not the rate limiting step for Cr(VI) sorption on EBB and that sorption was primarily controlled by film diffusion. The negative ΔG° of sorption process confirms the spontaneous nature of Cr(VI) sorption, whereas positive ΔH° and ΔS° values indicate endothermic and physical nature of sorption and increasing randomness at the interface of Cr(VI)–EBB, respectively. Our results also suggest that the developed biochar has tremendous potential for selective Cr (VI) removal from various wastewater samples without any toxic secondary waste generation.

For F > 0.85, Bt = −0.4977 − ln(1 − F )

Acknowledgments

∞ 6 1 ⎛ ⎞ e (−n2Bt ) F = 1 − ⎛ 2⎞ ∑ ⎝ π ⎠ n = 1 ⎝ n2 ⎠

(23)

(24) 2

⎛ For F < 0.85, Bt = ⎜ π − ⎝

π 2F ⎞ ⎞ π−⎛ ⎟ ⎝ 3 ⎠⎠ ⎜

DP acknowledges funding received from the Ministry of Environment and Forest (MOEF), India (Grant #19/45-2010–RE) to carry out this research. Authors deeply thank the editor Prof. Dr. Eder C. Lima and five anonymous reviewers for insightful comments and suggestions that significantly improved clarity of this manuscript.

⎟

(25)

This model suggests that if experimental data in a plot of Bt versus t exhibit a linear relationship with an intercept at zero, then sorption is driven by intraparticle diffusion, which is also the rate limiting step. Whereas, if the plot is either non–linear or linear with an intercept, then film diffusion process controls sorption. The experimental data plots of Bt versus t show linear relationships with non-zero intercepts (Fig. 6d), which strongly suggest that the EBB–mediated Cr(VI) removal was primarily governed by film diffusion process.

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3.7. Effect of foreign ions on Cr(VI) removal One of our objectives was to evaluate the interference of foreign ions on EBB–mediated Cr(VI) removal by comparing data with that of the control experiment (pH 2, 50 mL of 40 mg/L Cr(VI), EBB = 2 g/L, agitation = 6 h at 100 rpm). Known concentrations of various metal ions such as sodium(I), potassium(I), magnesium(II), calcium(II), chromium(III), iron(III), cadmium(II), manganese(II), copper(II), nickel (II), and zinc(II) in its stable form were added to a 40 mg/L Cr(VI) solution to prepare different binary mixtures, which were used to study EBB–mediated Cr(VI) removal in the presence of these ions. Results in terms of percent of Cr(VI) removal is presented in Table 5. A negligible change (within 3%) in Cr(VI) removal using EBB was found compared to the control experiment. Thus, we conclude that the presence of studied foreign ions shows no significant change in the EBB–mediated Cr(VI) removal and hence EBB can be effectively utilized for the remedial treatment of environmental wastewater by removing Cr(VI) in the presence of higher concentrations of other metal ions. 3.8. Performance of EBB for Cr(VI) removal The Cr(VI) removal performance of our developed EBB was compared with the sorption/removal capacities of several other reported biochar, organic/inorganic treated biomass, and inorganic sorbents. Table 6 present the Cr(VI) removal/sorption potential of listed sorbents 2342



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