Removal from Aqueous Solution Using Pistia

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Chem Sci Trans., 2013, 2(1), 85-104 DOI:10.7598/cst2013.318

Chemical Science Transactions ISSN/E-ISSN: 2278-3458/2278-3318 RESEARCH ARTICLE

Equilibrium, Kinetic and Thermodynamic Study on Chromium(VI) Removal from Aqueous Solution Using Pistia Stratiotes Biomass BISWAJIT DAS, NABA KUMAR MONDAL*, PALAS ROY and SOUMYA CHATTARAJ Department of Environmental Science, The University of Burdwan, West Bengal, India [email protected]

Received 18 July 2012 / Accepted 16 August 2012

Abstract: A basic investigation on the adsorption Cr(VI) ions from aqueous solution by Pistia stratiotes biomass was investigated under batch mode. The influence of solution pH, sorbent dose, initial chromium(VI) concentration, contact time, stirring rate and temperature on the removal process were investigated. A biosorbent dosage of 5 g L-1 showed maximum metal uptake capacity (q e) of 7.24 mg g-1 for an initial metal ion concentration of 10 ppm. Sorption equilibrium time was observed in 15 min. The equilibrium adsorption data were analyzed by the Freundlich, Langmuir, Dubinin-Radushkevich and Temkin adsorption isotherm models. The kinetics of chromium(VI) ion was discussed by pseudo-first-order, pseudo-second-order and intra-particle diffusion models. It was shown that the adsorption of chromium(VI) ions could be described by the pseudo-second order kinetic model. Thermodynamic parameters such as Gibbs free energy (Go ), the enthalpy (Ho ) and the entropy change of sorption (So) have also been evaluated and it has been found that the adsorption process was spontaneous, feasible and endothermic in nature. Desorption experiments with 2 M NaOH inferred the reusability of the adsorbent. The results indicated that Pistia stratiotes biomass can be used as an effective and low-cost adsorbent to remove Cr(VI) ions from aqueous solutions. Keywords: Adsorption, Biomass, Desorption, Chromium(VI) ion

Introduction Nowadays pollution due to heavy metal contaminants from aqueous solutions is one of the most important environmental concerns due to their high toxicity and impact on human health. Cr(VI) is known to be one of the heavy metal and is widely used in many industries including electroplating, leather tanning, dye, cement and photography industries. The effluents from these industries usually contain considerable amount of chromium, which ultimately spreads into the environment through soils and water streams and finally accumulates along the food chain which causes human health hazards. The hexavalent form


Chem Sci Trans., 2013, 2(1), 85-104

of chromium has been considered more hazardous to public health due to its mutagenic and carcinogenic properties1-2. The recommended limit of Cr(VI) in waste water is only 0.05 mg/L3. But the industrial and mining effluents contain much higher concentrations compared to the permissible limit. Therefore, the concentrations of Cr(VI) must be reduced to levels that satisfy environmental regulations for various bodies of water. The conventional methods for removing heavy metal ions from water and wastewater include chemical precipitation, ion exchange, electrochemical deposition, solvent extraction, membrane filtration and adsorption. Among these, adsorption is effective and economical4. Many heavy metal adsorption studies have focused on the application of activated carbons5-6. However, it is quite expensive with relatively high operating costs. Hence there is a growing demand to find low cost and efficient adsorbents to remove heavy metals from aqueous solution. A wide variety of materials have been used as adsorbents for the removal of Cr(VI) and a number of adsorption studies have been reported using adsorbents like soya cake7, rubber tyres and saw dust8, activated sludge9, fly ash10, cow dung carbon11, rice bran12, hazelnut shell13, rice husk based activated carbon14 etc. In this present study, P. stratiotes biomass was investigated as a potential and low cost adsorbent for the removal of Cr(VI) ions from aqueous solutions. The objective of the present work was to investigate and explore the possibility of utilizing P. stratiotes biomass powder as a sorbent for removing Cr(VI) ions from aqueous solutions. The effect of various experimental parameters such as adsorbent dose, initial Cr(VI) concentration, contact time, stirring rate, temperature and pH were investigated. Adsorption kinetics, isotherms and thermodynamic parameters were also evaluated and reported.

Experimental All the reagents used for the current investigation were of GR grade from E. Merck Ltd., India. Stock solution (100 mg/L) of Cr(VI) was prepared by dissolving K2Cr2O7 in double distilled water. The solution was further diluted to the required concentrations before use. Before mixing the adsorbent, the pH of each Cr(VI) solution was adjusted to the required value by 0.1 M NaOH or 0.1 M HCl solution.

Adsorbent collection and preparation P. stratiotes, a floating macrophyte was collected from the surrounding area of University of Burdwan, West Bengal, India. The macrophyte was washed several times with distilled water and then it was initially sun-dried for 7 days followed by drying in hot air oven at 343±1 K for 2 days. The dried material was crushed and sieved to give a fraction of 250 mesh screen. The material was washed thoroughly with deionised water to remove all impurities that might be present in the material and then stored in sterile, closed glass bottles and used as an adsorbent.

Adsorbent characterization Adsorbent characterization was performed by means of spectroscopic and quantitative analysis. The surface area of the adsorbent was determined by Quantachrome surface area analyzer (model- NOVA 2200C). The pH of aqueous slurry was determined by soaking 1g of biomass in 50 mL distilled water, stirred for 24 h and filtered and the final pH was measured15. The physico-chemical characteristics of the adsorbent were determined using standard procedures16. The concentrations of sodium and potassium were determined by Flame Photometer (Model No. Systronics 126). The equilibrium Cr(VI) concentration was determined by using 1,5-diphenylcarbazide as the complexing agent and a UV-VIS

Chem Sci Trans., 2013, 2(1), 85-104


spectrophotometer (Systronics, Vis double beem Spectro 1203) at a λmax of 540 nm. For stirring purpose magnetic stirrer (TARSONS, Spinot digital model MC02, CAT No. 6040, S. No. 173) was used. The pH of zero-point charge or pHZPC was determined based on the previous method17. The Fourier transform infrared (FTIR) spectra of the adsorbent was recorded with Fourier transform infrared spectrophotometer (PERKIN-ELMER, FTIR, Model-RX1 Spectrometer, USA) in the range of 400-4000 cm-1. In addition, scanning electron microscopy (SEM) analysis was carried out using a scanning electron microscope (HITACHI, S-530, Scanning Electron Microscope and ELKO Engineering, B.U. BURDWAN) at 15 kV to study the surface morphology of the adsorbent.

Batch Adsorption procedure Batch adsorption studies were carried out in 250 mL glass-stoppered Erlenmeyer flasks with 50 mL of the working Cr(VI) ion solution of different concentrations ranging from 10 to 25 mg/L. A weighed amount (0.25 g) of adsorbent was added to the solution. The flasks were agitated at a constant speed of 600 rpm for 25 minute in a magnetic stirrer at 313±1 K. The influence of pH (2.0–8.0), initial Cr(VI) concentration (10, 15, 20, 25 mgL-1), contact time (1, 3, 5, 10, 15 and 25 min), adsorbent dose (0.05, 0.1, 0.15, 0.2, 0.25 and 0.3 g/50 mL) were evaluated during the present study. Samples were collected from the flasks at predetermined time intervals for analyzing the residual Cr(VI) concentration in the solution. The amount of Cr(VI) ions adsorbed in milligram per gram was determined by using the following mass balance equation: qe =

(Ci − Ce )V m


Where Ci and Ce are Cr(VI) concentrations (mg/L) before and after adsorption, respectively, V is the volume of adsorbate in liter and m is the weight of the adsorbent in grams. The percentage of removal of Cr(VI) ions was calculated from the following equation: Removal (%) =

(Ci − Ce ) x100 Ci


Desorption experiments For the desorption study, 2.0 g of P. stratiotes boimass was first treated with 50 mL of 10 mg/L of Cr(VI) ions solution for 1 h. After adsorption experiment adsorbent was collected by filtration and washed with distilled water for three times to remove excess Cr(VI) ions. Then the exhausted adsorbent was contacted with 50 mL of different concentrations of NaOH (0.5, 1, 1.5 and 2 M). The mixture was stirred at 800 rpm for 90 min, filtered and analyzed. The percentage of desorption (Dp) of Cr(VI) ions was calculated from the following equation: m  (3) D p =  r  x 100  mo  Where mr is the amount of Cr(VI) ions desorbed (mg) and mo is the amount of Cr(VI) ions adsorbed (mg).

Results and Discussion Characterization of adsorbent The adsorbent was found to be stable in water, dilute acids and bases. The adsorbent behaves as neutral at pH zero charge. Adsorption of cation is favored at pH > pHzpc, while the adsorption of anion is favored at pH< pHzpc17. The point of zero charge is 5.07 (Figure 1). The physicochemical properties of adsorbent are summarized in Table 1.


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0.6 0.4


0.2 0.0 -0.2 -0.4 -0.6 -0.8 2



5 pHi




Figure 1. pH of zero point charge of adsorbent (Experimental conditions: adsorbent dose: 1.5 g in 100 mL, Temperature: 313 K) Table 1. Physicochemical characteristics of adsorbent Analysis pHslurry pHzpc Specific gravity Moisture content, % Bulk density, g cm-3 Particle density, g cm-3 Conductivity, µS/cm Surface area, m2/g Na+, mg L-1 K+, mg L-1

Value 6.5 5.07 0.253 0.115 0.217 0.385 43.63 27.95 108 570

The FTIR spectrum of P. stratiotes biomass before Cr(VI) adsorption is shown in Figure 2. The FTIR spectra of biomass showed peaks at 3423, 2920, 2850, 1630, 1579, 1422, 1321, 1253, 777 and 618 cm-1 which may be assigned to OH group, -CH3, -CH2 group, amide, carboxylate, C-N stretch of aromatic primary amine, C-N stretch of aromatic secondary amine, C-Cl stretch and C-Br stretch, respectively18. The intensity of the peaks for chromium-loaded biomass was either minimized or shifted slightly (Figure 3). For instance, the wavenumber at 3423 cm-1 shifted to 3411 cm-1, indicating interaction between hydroxyl group and chromium ions. The participation of carboxylate group for chromium adsorption was confirmed by the shifted wavenumber from 1579 to 1563 cm-1. The peak at 1253 cm-1 representing C-N stretching of aromatic primary amine also shifted to 1229 cm-1 after chromium adsorption. Therefore it can be concluded that the functional groups which can bind Cr(VI) ions are of the type –OH, -COO- and –C-N.

Chem Sci Trans., 2013, 2(1), 85-104





Figure 2. FTIR of biomass before adsorption




Figure 3. FTIR of biomass after adsorption SEM analysis is another useful tool for the analysis of the surface morphology of an adsorbent. The SEM micrographs of biomass surface before and after chromium(VI) ions adsorption are shown in Figures 4 and 5 respectively. The porous and irregular surface structure of the adsorbent can be clearly observed in the SEM image shown in Fig. 4. As can be observed from Figure 5 there is a clear demarcation in the surface morphology of biomass after treatment.


Chem Sci Trans., 2013, 2(1), 85-104

Figure 4. SEM image of biomass before adsorption

Figure 5. SEM image of biomass after adsorption

Effect of initial Cr(VI) ion concentration




4 e

Rem oval((%) %) Removal qqee((mg/g) mg/g)








Concentration, C t timg/L(



qe, mg/g

Removal, %

The rate of adsorption is a function of the initial concentration of the adsorbate, which makes it an important factor to be considered for effective adsorption. The effect of different initial Cr(VI) ion concentration on adsorption of Cr(VI) ion onto P. stratiotes biomass is presented in Figure 6. The percentage removal of Cr(VI) ion decreased with increasing of the initial Cr(VI) ions concentration. This can be explained by the fact that all adsorbents have a limited number of active sites and at a certain concentration the active sites become saturated19. However, the adsorption capacity at equilibrium increased with increase in initial Cr(VI) ion concentration. It is possible that the initial concentration of the metal ions provides the necessary driving force to overcome the mass transfer resistance of Cr(VI) ion between the aqueous and the solid phase20. The increase in the initial Cr(VI) ions concentration also enhances the interaction between the Cr(VI) ions in the aqueous phase and the biomass surface. This also resulted in higher uptake of Cr(VI) for the given amount of biomass. Similar results were obtained in the adsorption of Cr(VI) ions by natural plant material21.





Figure 6. Effect of initial concentration on Cr(VI) adsorption (Experimental conditions: adsorbent dose: 0.25 g/ 50 mL, agitation speed: 200 rpm, pH: 2.0, Temperature: 313 K, Contact time: 15 min)

Chem Sci Trans., 2013, 2(1), 85-104


Effect of pH The pH of the solution is one of the most critical parameters in the adsorption process, which affects surface charge of the adsorbent material and the degree of ionization and specification of adsorbate22. The effect of pH on the removal efficiency of Cr(VI) ion was studied at different pH values ranging from 2.0 to 8.0, the results are given in Figure 7. It was observed that a sharp decrease in the Cr(VI) ion removal occurred when the pH value of the solutions changed from 2.0 to 8.0. The maximum adsorption of Cr(VI) ions are obtained at pH 2.0. So pH 2.0 was selected as optimum pH for Cr(VI) ion adsorption onto P. stratiotes biomass. From the stability diagram23, it was evident that the most prevalent form of Cr(VI) in aqueous solution was acid chromate (HCrO4-), chromate (CrO42-), dichromate (Cr2O72-) and other oxyanions of Cr. Dominant form of Cr(VI) at initial pH of 2 is acid chromate24 (HCrO4-). Increase in pH facilitate the conversion of HCrO4- to other forms, CrO42- and Cr2O72-. The decrease in Cr(VI) ion removal efficiency at higher pH might be due to the competition between OH- and chromate ions (CrO42-), where the former being the dominant species wins the race. The pH at zero point charge (pzc) was found to be 5.07. This is in agreement with our experimental observations showing a very low removal at pH>5.07. Again the FTIR spectral analysis indicates the presence of –OH functional group onto biomass surface. This –OH group is protonated at lower pH and thereby facilitate the approach of HCrO4- ions to the surface of the adsorbent which results in higher uptake of metal. With decrease in acidity of the solution, the functional group on the adsorbent surface become de-protonated resulting in an increase in the negative charge density on the adsorbent surface as a result there is weakening of electrostatic force between adsorbate and adsorbent which ultimately led to the lowering of sorption capacity. 3.0 100

Removal Removal (%)(%) qq e (mg/g) (mg/g) e



70 1.5

qe, mg/g

Removal, %



60 50




30 0.0 2





Figure 7. Effect of pH on Cr(VI) adsorption (Experimental conditions: Initial Cr(VI) concentration: 10 mg/L, adsorbent dose: 0.25 g/ 50 mL, agitation speed: 200 rpm, Temperature: 313 K, Contact time: 15 min)

Effect of adsorbent dose In this study, six different adsorbent dosages were selected ranging from 0.05 to 0.3 g while the Cr(VI) concentration was fixed at 10 mg/L. The results are presented in Figure 8. It was


Chem Sci Trans., 2013, 2(1), 85-104

observed that percentage of Cr(VI) ion removal increased with increase in adsorbent dose. Such a trend is mostly attributed to an increase in the sorptive surface area and the availability of more active binding sites on the surface of the adsorbent25. However, the equilibrium adsorption capacity showed an opposite trend. As the adsorbent dosage was increased from 0.05 to 0.3 g, the adsorption capacity reduced to 2.43 and 1.658 mg g -1, respectively. This may be due to the decrease in total adsorption surface area available to Cr(VI) ion resulting from overlapping or aggregation of adsorption sites26-27. Thus with increasing adsorbent mass, the amount of Cr(VI) ion adsorbed onto unit mass of adsorbent gets reduced, thus causing a decrease in qe value with increasing adsorbent mass concentration. Furthermore maximum Cr(VI) ion removal (99.48%) was recorded by 0.25 g P. stratiotes biomass and further increase in adsorbent dose did not significantly change the adsorption yield. This is due to the non-availability of active sites on the adsorbent and establishment of equilibrium between the Cr(VI) ion on the adsorbent and in the solution. 110


100 2.4 90 2.2

70 2.0 60

Rem oval((%) %) Removal qqee((mg/g) mg/g)

50 40

qe, mg/g

Removal, %




30 1.4

20 0.05






Adsorbent dose, g

Figure 8. Effect of adsorbent dose on Cr(VI) adsorption (Experimental conditions: Initial Cr(VI) concentration: 10 mg/L, agitation speed: 200 rpm, pH:2.0, Temperature: 313 K, Contact time: 15 min)

Effect of contact time The uptake of Cr(VI) ion as a function of contact time is shown in Figure 9. As illustrated in Figure 9, adsorption of Cr(VI) ion increased with rise in contact time upto 15 min. Further increase in contact time did not increase the Cr(VI) adsorption process. The equilibrium was nearly reached after 15 min for four different initial Cr(VI) ion concentrations. Hence, in the present work, 15 min was chosen as the equilibrium time. The fast adsorption rate at the initial stage may be explained by an increased availability in the number of active binding sites on the adsorbent surface. The sorption rapidly occurs and normally controlled by the diffusion process from the bulk to the surface. In the later stage the sorption is likely an attachment-controlled process due to less available sorption sites. Similar findings for Cr(VI) adsorption onto other adsorbents have been reported by other investigators28-29.

Chem Sci Trans., 2013, 2(1), 85-104



Removal, %



10mg/L 15mg/L 20mg/L 25mg/L



75 0






Time, min

Figure 9. Effect of contact time on Cr(VI) adsorption (experimental conditions: adsorbent dose: 0.25g/50 mL, agitation speed: 200 rpm, pH: 2.0, Temperature: 313 K)

Effect of shaking rate The effect of shaking rate on Cr(VI) adsorption is shown in Figure 10 and it appears that shaking rate has pronounced effect on the amount of Cr(VI) adsorbed. As the shaking rate increased from 50 to 200 rpm, the adsorption capacity increased from 1.69 to 1.9896 mg g-1. However beyond 200 rpm, the adsorption capacity remained constant and the shaking rate of 200 rpm was selected in subsequent analysis. The increase in adsorption capacity at a higher shaking rate could be explained in terms of the reduction of boundary layer thickness around the adsorbent particles15. Therefore, with increasing shaking rate the concentrations of Cr(VI) ions near the adsorbent surface would be increased. A higher shaking rate also encouraged a better mass transfer of Cr(VI) ions from bulk solution to the surface of the adsorbent and shortened the adsorption equilibrium time. 100







Rem oval((%) %) Removal qe((mg/g) q mg/g) e

90 88

qe, mg/g

Removal, %

1.90 94

1.80 1.75



84 0


200 300 Stirring rate, rpm


1.65 500

Figure 10. Effect of shaking rate on Cr(VI) adsorption (Experimental conditions: Initial Cr(VI) concentration: 10 mg/L, adsorbent dose: 0.25g/50 mL, pH: 2.0, Contact time: 15 min, Temperature: 313 K)


Chem Sci Trans., 2013, 2(1), 85-104

Effect of temperature Temperature has pronounced effect on the process of adsorption. The percentage of Cr(VI) adsorption was studied as a function of temperature in the range 298-313 K. The results obtained are shown in Figure 11. The results showed that adsorption of metal ion by the biomass increased with increasing temperature, which is typical for the biosorption of most metal ions from their solution30-31. 100 90












30 296

qe, mg/g

Removal, %


Removal Rem oval((%)%) qe((mg/g) q m g/g) e

0.6 298









Temperature, K

Figure 11. Effect of temperature on Cr(VI) adsorption (Experimental conditions: Initial Cr(VI) concentration: 10 mg/L, adsorbent dose: 0.25 g/50 mL, pH: 2.0, Contact time: 15 min, shaking rate: 200 rpm)

Adsorption isotherms An adsorption isotherm represents the equilibrium relationship between the adsorbate concentration in the liquid phase and that on the adsorbents surface at a given condition. A number of isotherms have been developed to describe equilibrium relationships. In the present study, Langmuir, Freundlich, Temkin, Dubinin-Radushkevich (D-R) models were used to describe the equilibrium data. The results are shown in Table 2 and the modeled isotherms are plotted in Figure 12. Table 2. Adsorption isotherm constants for adsorption of Cr(VI) onto biomass Adsorption Parameters R2 χ2 SSE SAE isotherms Langmuir qmax, mg/g 7.24 0.936 0.206 1.042 1.618 isotherm KL, L/mg 8.117 Freundlich -1 1/n KF, mg/g, (L mg ) 5.854 0.799 0.2993 0.9866 1.8144 isotherm n 2.8 Temkin isotherm B, mg/g 1.202 0.882 0.1791 0.5549 1.2734 A 141.88 D-R isotherm qm, mg/g 6.719 0.957 0.1313 0.487 1.2414 β, mol2kJ-2 0.018 E, kJ mol-1 5.27

Chem Sci Trans., 2013, 2(1), 85-104


6.0 5.5

qe, mg/g

5.0 4.5 4.0

Experimental Langmuir Freundlich Temkin D-R

3.5 3.0 2.5 2.0 0.0






C, mg/L

Figure 12. Comparison between the measured and modelled isotherm profiles for the adsorption of Cr(VI) ions by P. stratiotes biomass (Experimental conditions: adsorbent dose: 0.25 g/50 mL, agitation speed: 200 rpm, pH: 2.0, contact time: 15 min, temperature: 313 K)

The Langmuir isotherm model The Langmuir isotherm model32 was used to describe observed sorption phenomena and suggests that uptake occurs on a homogeneous surface by monolayer sorption without interaction between adsorbed molecules. The linear form of the equation can be written as:

1 1 1 = + qe q q max K L C e q max


Where Ce is the equilibrium concentration of Cr(VI) (mg/L), qeq is the amount of metal adsorbed per specific amount of adsorbent (mg/g), qmax is the maximum adsorption capacity (mg/g) and kL is an equilibrium constant (L/mg) related to energy of adsorption which quantitatively reflects the affinity between the adsorbent and adsorbate. Where, qmax and kL can be determined from the linear plot of 1/qeq vs. 1/Ce. The shape of the Langmuir isotherm can be used to predict whether a sorption system is favorable or unfavorable in a batch adsorption process. The essential features of the isotherm can be expressed in terms of a dimensionless constant separation factor (RL) that can be defined by the following relationship33. RL=

1 1 + K L Ci


Where, Ci is the initial concentration (mg/L) and kL is the Langmuir equilibrium constant (L/mg). The value of separation factor RL provides important information about the nature of adsorption. The value of RL indicated the type of Langmuir isotherm to be irreversible (RL=0), favourable (0 0, sorption system is favorable34. The evaluated constants are given in Table 2.


Chem Sci Trans., 2013, 2(1), 85-104

The Freundlich isotherm model The Freundlich isotherm is applicable to non-ideal adsorption on heterogeneous surfaces and the linear form of the isotherm can be represented as35:

log q eq = log K F +

1 log C e n


Where, KF is the Freundlich constant related to sorption capacity (mg/g) (L/g)1/n and n is related to the adsorption intensity of the adsorbent. Where, KF and 1/n can be determined from the linear plot of log qeq versus log Ce. The evaluated constants are given in Table 2.

The Temkin isotherm model Temkin isotherm takes into account the interactions between adsorbents and metal ions to be adsorbed and is based on the assumption that the free energy of sorption is a function of the surface coverage34. The linear form of the Temkin isotherm is represented as: (7) qe = B ln A + B ln Ce Where Ce is the equilibrium concentration of the adsorbate in mg/L, qe is the amount of adsorbate adsorbed at equilibrium (mg/g), RT/bT = B where T is the temperature (K) and R is the ideal gas constant (8.314 J mol-1 K-1) and A and bT are constants. A plot of qe versus lnCe enables the determination of constants A and B. The constant B is related to the heat of adsorption and A is the equilibrium binding constant (L/min) corresponding to the maximum binding energy. The values of A and B are given in Table 2.

The Dubinin-Radushkevich isotherm model The Dubinin-Radushkevich model36 was chosen to estimate the heterogeneity of the surface energies. The linear form of D-R isotherm equation is represented as: (8) ln q e = ln q m − βε 2 Where

ε = RT ln(1 +

1 ) Ce


Where qm is the theoretical saturation capacity (mol/g), β is a constant related to the mean free energy of adsorption per mole of the adsorbate (mol2/J2) and ε is the polanyi potential, Ce is the equilibrium concentration of adsorbate in solution (mol/L), R (J mol-1 K-1) is the gas constant and T(K) is the absolute temperature. The D-R constants qm and β were calculated from the linear plots of lnqe versus ε2 and are given in Table 2. The constant β gives an idea about the mean free energy E (kJ/mol) of adsorption per molecule of the adsorbate when it is transferred to the surface of the solid from infinity in the solution and can be calculated from the relationship37; E=

1 2β


If the magnitude of E is between 8 and 16 kJ mol-1, the sorption process is supposed to proceed via chemisorption, while for values of E < 8 kJ mol-1, the sorption process is of physical nature37.

Error analysis Due to the inherent bias resulting from linearization, three different error functions of nonlinear regression basin [sum of the square of the errors (SSE), sum of the absolute errors (SAE)

Chem Sci Trans., 2013, 2(1), 85-104


and chi-square (χ2)] were employed in this study to find out the best-fit isotherm model to the experimental equilibrium data. SSE is given as: n


∑ (q i =1

e , estm

− qe ,exp )i2


Here, qe,estm and qe,exp are, respectively, the estimated and the experimental value of the equilibrium adsorbate solid concentration in the solid phase (mg/g) and n is the number of the data point. SAE is given as: n


∑q i =1

e , estm

− qe,exp

(12) i

Chi-square (χ2) is given as:

 (qe,exp − qe,estm ) 2    ∑ q i =1   i e ,e stm  n

χ2 =


The respective values are given in the Table 2. As shown in Table 2, the DubininRadishkevich (D-R) adsorption isotherm model yielded best fit to the experimental equilibrium adsorption data than the Langmuir, Freundlich and Temkin isotherm models for Cr(VI) sorption according to the values of R2, χ2, SSE and SAE. It was also seen from Table 2 that the Langmuir maximum adsorption capacity (qmax) is 7.24 mg/g and the equilibrium constant KL is 8.117 L/mg. The separation factor (RL) values are 0.012,0.0081, 0.0061 and 0.0049 while initial Cr(VI) concentrations are 10, 15, 20 and 25 mg/L, respectively. All the RL values were found to be less than one and greater than zero indicating the favorable sorption of Cr(VI) onto biomass. The Freundlich constant KF indicates the sorption capacity of the sorbent and the value of KF is 6.859 mg/g. Furthermore, the value of ‘n’ at equilibrium was 2.8. The value of n between 1 and 10 represents a favorable adsorption38. From D-R isotherm the value of the adsorption energy was found to be 5.27 kJ/mol. The estimated value of E for the present study was found in the range expected for physical adsorption (Table 2). Thus the sorption of Cr(VI) on the surface of biomass was physical in nature. The effectiveness of P. stratiotes biomass as an adsorbent for Cr(VI) adsorption was also compared with other reported adsorbents. The maximum adsorption capacity obtained in this study is comparable with other adsorbents as shown in Table 3. Table 3. A comparisons of maximum adsorption capacities for Cr(VI) ions by different adsorbents Adsorbents Sugar cane bagasse Sugar beet pulp Soya cake Formaldehyde modified saw dust Red mud Dust coal Iron(III) hydroxide P. stratiotes biomass

qmax, mg/g 13.4 17.2 0.288 3.60 1.6 4.4 0.5 7.24

References [39] [39] [40] [41] [42] [43] [44] This study


Chem Sci Trans., 2013, 2(1), 85-104

Adsorption kinetics modeling In order to analyze the rate of adsorption and possible adsorption mechanism of Cr(VI) onto biomass, the Lagergren first order45, pseudo-second-order46 and Intraparticle diffusion47 kinetic models were applied to adsorption data.

The pseudo-first-order kinetic model The Lagergren first order rate equation is represented as:

log(qe − qt ) = log qe −

k1t 2.303


Log (qe-qt)

Where qe and qt are the amounts of Cr(VI) adsorbed (mg/g) at equilibrium and at time t, respectively and k1 is the Lagergren rate constant of first order adsorption (min-1). Values of qe and k1 at different initial concentrations were calculated from the slope and intercept of the plots of log (qe –qt) versus t (Figure 13). The respective values are given in the Table 4.

Time min

Figure 13. Pseudo first-order kinetic plots for adsorption of Cr(VI) onto biomass (Experimental conditions: adsorbent dose: 0.25 g/ 50 mL, agitation speed: 200 rpm, pH: 2.0, Temperature: 313 K) Table 4. Kinetic parameters for adsorption of Cr(VI) onto P. stratiotes biomass Kinetic model



Intraparticle diffusion

parameters qe,exp, mg/g k1, min-1 qe,cal, mg/g R2 k2, g/mg-1 min-1

Concentration of Cr(VI) solution 10 mg/L 15 mg/L 20 mg/L 1.9896 2.985 3.984 0.172 0.161 0.142 0.402 1.032 1.047 0.891 0.982 0.986 1.24 0.393 0.383

25 mg/L 4.90 0.089 0.954 0.995 0.3047

qe,cal, mg/g R2 Kd, mg/g.min1/2

2.024 0.999 0.099

3.086 0.999 0.241

4.084 0.999 0.249

5.020 0.999 0.252

I R2

1.566 0.805

1.934 0.896

2.883 0.915

3.776 0.935

Chem Sci Trans., 2013, 2(1), 85-104


The pseudo-second-order kinetic model The pseudo-second- order kinetic model which is based on the assumption that chemisorption is the rate-determining step can be expressed as:

1 t t = + 2 qt k 2 q e q e



Where k2 is the rate constant of second order adsorption (g/mg/min). Values of k2 and qe were calculated from the plots of t/qt versus t (Figure 14). The respective constant values are given in Table 4.

Time min

Figure 14. Pseudo second- order kinetic plots for adsorption of Cr(VI) onto biomass (Experimental conditions: adsorbent dose: 0.25 g/ 50 mL, agitation speed: 200 rpm, pH:2.0, Temperature: 313 K)

The intraparticle diffusion model The kinetic results were analyzed by the Weber and Morris intraparticle diffusion model to elucidate the diffusion mechanism. The model is expressed as: (16) q t = Kd t1/ 2 + I Where I is the intercept and Kd is the intra-particle diffusion rate constant. The intercept of the plot reflects the boundary layer effect. Larger the intercept, greater is the contribution of the surface sorption in the rate controlling step. Figure 15 presents intra-particle plot for Cr(VI) sorption onto biomass. The calculated diffusion coefficient Kd values are listed in Table 4. The kd value was higher at the higher concentrations. Intraparticle diffusion is the sole rate-limiting step if the regression of qt versus t1/2 is linear and passes through the origin. In fact, the linear plots at each concentration did not pass through the origin. This deviation from the origin is due to the difference in the rate of mass transfer in the initial and final stages of the sorption. This indicated the existence of some boundary layer effect and further showed that intraparticle diffusion was not the only rate-limiting step. It is clear from the Table 4 that the pseudo- second-order kinetic model showed excellent linearity with high correlation coefficient (R2>0.99) at all the studied concentrations in comparison to the other kinetic models. In addition the calculated qe values also agree with the experimental data in the case of pseudo-second-order kinetic model. It is also evident from Table 4 that the values of the rate constant k2 decrease with increasing initial Cr(VI) concentrations. This is due to the lower competition for the surface active sites at lower concentration but at higher concentration the competition for the surface active sites will be high and consequently lower sorption rates are obtained.

Chem Sci Trans., 2013, 2(1), 85-104

qt , mg/g


t 1/2

Figure 15. Intraparticle diffusion model for adsorption of Cr(VI) onto biomass (Experimental conditions: adsorbent dose: 0.25 g/ 50 mL, agitation speed: 200 rpm, pH: 2.0, Temperature: 313 K)

Thermodynamic treatment of the sorption process In order to study the feasibility of the adsorption process, the thermodynamic parameters such as free energy, enthalpy and entropy changes can be estimated from the following equations48:

KC =

C Ae Ce


∆G 0 = − RT ln K C log K C =


∆S ∆H − 2.303R 2.303RT 0



Where Ce is the equilibrium concentration in solution in mg/L and CAe is the equilibrium concentration on the sorbent in mg/L and Kc is the equilibrium constant. The Gibbs free energy (∆Go) for the adsorption of Cr(VI) onto biomass at all temperatures was obtained from Eq. 18 and are presented in Table 5. The values of ∆Ho and ∆So were calculated from the slope and intercept of the plot logKc against 1/T (Figure not shown) and are also listed in Table 5. Table 5. Thermodynamic parameters for adsorption of Cr(VI) onto biomass Temperature, K

∆Go, kJ/mol

298 303 308 313

-0.1434 -0.1798 -0.4923 -13.671

∆Ho, kJ/mol

∆So, kJ/mol

Ea, kJ/mol




S*, J K mole-1 1.10x10-38

In order to support that physical adsorption is the predominant mechanism, the values of activation energy (Ea) and sticking probability (S*) were calculated from the experimental data. They were calculated using modified Arrhenius type equation related to surface coverage (θ) as follows49:

Chem Sci Trans., 2013, 2(1), 85-104


C 


θ = 1 − e  C S * = (1 − θ ) e


− Ea RT


The sticking probability, S*, is a function of the adsorbate/adsorbent system under consideration but must satisfy the condition 0 < S*< 1 and is dependent on the temperature of the system. The values of Ea and S* can be calculated from slope and intercept of the plot of ln(1-θ) versus 1/T respectively (Figure not shown) and are listed in Table 5. From Table 5 it is clear that the reaction is spontaneous in nature as Go values are negative at all the temperature studied. Again positive Ho value confirms that the sorption is endothermic in nature. The positive value of So reflects the affinity of the adsorbents for the Cr(VI) ions. The values of Ea was found to be 217.59 kJ mol-1 for the adsorption of Cr(VI) onto biomass. The positive value of Ea indicates the endothermic nature of the adsorption process which are in accordance with the positive values of ∆Ho. The result as shown in Table 5 indicate that the probability of the Cr(VI) ions to stick on surface of biomass is very high as S*

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