Desalination 249 (2009) 914–921
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Desalination j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d e s a l
Study of the adsorption of phenol by two soils based on kinetic and isotherm modeling analyses B. Subramanyam ⁎, Ashutosh Das School of Civil Engineering, SASTRA University, Thanjavur-613402, Tamil Nadu, India
a r t i c l e
i n f o
Article history: Received 20 September 2008 Accepted 26 May 2009 Available online 12 October 2009 Keywords: Adsorption Phenol removal Soils Kinetics Isotherms
a b s t r a c t Various natural adsorbents, which have been in used for removal of pollutants, in general, and phenol, in particular, are mostly directed towards improving the adsorption capacity of the adsorbents by various pretreatments (chemical, thermal or biological), which necessarily lead to increase in the cost as well as in the level of difﬁculties in regeneration/disposal of the adsorbent. The present studies, on the other hand, are aimed towards evaluating the feasibility of using two common soils as potential low-cost adsorbents for the removal of phenol from its aqueous solution, in their natural forms (i.e., without any pretreatment). Accordingly, experiments were carried out (in batch mode) for optimization of the adsorption parameters (such as pH, contact time, equilibrium time and adsorbent dosage), for varying initial phenol concentrations. The results showed that the maximum phenol adsorption capacity was found at pH ~6, under a constant temperature of 30 ± 2 °C (at 6-hour equilibrium period). Several kinetic models (viz. Lagergren ﬁrst-order, pseudo-second-order, Elovich and intra-particle diffusion) as well as isotherm models (Langmuir, Freundlich, Redlich and Peterson and Sip) were applied to the experimental data. The pseudo-secondorder model was found to be the most suitable model describing the adsorption of phenol by two soils (which indicated this adsorption as a chemisorption process). On analysis of equilibrium isotherms for the adsorption of phenol by two soils, Redlich–Peterson and Sip isotherms were found to be the best representative for phenol-sorption on two selected, soil adsorbents. © 2009 Elsevier B.V. All rights reserved.
1. Introduction The sources of phenols in natural water bodies can be mostly traced to the natural decay processes or releases of the efﬂuents from coking plants, coal distillery plants, the pulp and paper industries and so forth . Although, phenol (collectively with its derivatives, viz. nitro-phenol, chloro-phenol, ortho-phenols) has been used in the synthesis of several organic compounds, such as paints, lubricants, plastic, pharmaceuticals, herbicides and resins , yet it is considered as a major toxic pollutant as well, even at a concentration of as low as 0.1 ppm [3,4]. The most common methods used for removal of phenol from industrial efﬂuents include stripping, solvent extraction, oxidation (using O3, H2O2, and ClO2), ion exchange, biodegradation and adsorption methods [5–7]. Out of all these treatment methods, adsorption has been known to be one of the most-widely used treatment methods for removal of phenol from industrial efﬂuents, by virtue of its cost-effectiveness as well as efﬁciency. Activate carbon is being used as one of the most effective adsorbents for dephenolation, because of its possession of high
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surface area per unit weight and, thus, high adsorption capacity for phenolic compounds. Yet, in view of the high cost and tedious procedures for the preparation and regeneration of activated carbons, there have also been constant attempts by the researchers to use low cost, naturally occurring adsorbents as a substitute to remove phenol, in speciﬁc, and organic and inorganic contaminants, in general, from wastewaters. Due to their ultra-ﬁne size range and, thus, high surface area, natural soils are being explored as potential adsorbents for the removal of phenol [8–15]. The various soils used for adsorption include primary clay minerals (viz. bentonite, montmorillonite, kaolonite and smectite) as well as rocks and ores (viz. zeolites, peat and pumice [2,16–25]. Sameer AlAsheh et al., in his studies, had investigated different types of activated bentonite (subject to both thermal and chemical activation) as potential adsorbents for removal of phenol from solution, which (due to activation) itself gets converted into cationic surfactant bentonite (CTAB/Al) thus adsorbing highest uptake of phenol . Feryal Akal, in his studies, has investigated pumice (treated with cationic surfactants like HDTMA and BDTDA), for removal of phenol and 4-chlorophenols. The treated pumice was found to have good adsorption capability . Froehner et al., in their studies, used natural bentonite and vermiculite (before treatment and after treatment with hexadecyltriumethylammonium) as adsorbents for removing phenol. The treated bentonite and vermiculite show good adsorption capacity than that of untreated ones
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. In fact, natural adsorbents, silicate minerals, carbonate minerals and metal oxides (such as, SiO2, Fe2O3 and Al2O3) are usually found in natural soils as admixtures in varying proportions, thus, possibly responsible for contributing to the adsorption potential to the original soil . Therefore, the determination of the exact type of mechanism for phenol adsorption by complex adsorbents like natural soil adsorbents is often almost impossible to decipher . Since, mineral constituents of clay are yet to be understood adequately, and, it shows wide spatial compositional variation, the ﬁndings at one place may not be applicable to another place. In this context, the utilization of existing resource in its original form (with its unique physico-chemical characteristics) may often be more preferred to the study of processed clay— at least, economically . In fact, all the clay minerals studied, cited in preceding paragraphs, were all modiﬁed/pretreated before adsorption. The present work is focussed on evaluating the adsorption capacity of the locally available soils (i.e., two predominant clay types of southern India), without any modiﬁcation, to evaluate their virgin adsorption potentials. Accordingly, the objective of the present study is to evaluate the effectiveness of two locally available soils [namely, Kalathur (Kr) and Adhanur (Ar)] for adsorption of phenol from aqueous solution.
2.2. Adsorbate Phenol (C6H5OH) of analytical reagent (AR) grade (supplied by Ranbaxi Laboratories Ltd., India), was used for the preparation of synthetic adsorbate of various initial sorbate concentrations (Co) in the range of 20–100 mg/l. The required quantity of phenol was accurately weighed and dissolved in distilled water and make up to 1 l. Fresh stock solution was prepared everyday and stored in a brown color glass bottle (to prevent photo-oxidation). 2.3. Analysis of phenol The concentration of phenol was determined by spectrophotometric analysis using 4-aminoantipyrine method (at a wavelength of 500 nm) . The equilibrium concentrations were determined using an Elico UV/Vis spectrophotometer (characteristic peak at 270 nm). The calibration plot of absorbance versus concentration for phenol showed a linear variation up to 40 mg/l concentration. The samples were diluted with distilled water up to 40 mg/l. The pH of the aqueous solution of phenol was found to vary from 7.08 to 7.43 for the phenol concentration ranging between 20 and 100 mg/l. 2.4. Adsorption studies (batch studies)
2. Materials and methods 2.1. Selection and characterization of the adsorbent samples The two soil (namely Kr and Ar) samples (0–50 cm) were collected from Thanjavur districts, Tamil Nadu (India), located at a distance of 1000 m away from industries (so as to minimize pollution-loading on the soil samples). Soil samples, thus collected, were dried for 2 h, at 100 °C in an electric oven, followed by crushing (24 h, in a ball mill) and sieving (100–635 SIEVE NO ASTM E11-87), to obtain the particles having an average diameter of 0.05 mm. Each sample, thus obtained, was dried, desiccated and preserved for subsequent analysis and experiments in air-tight containers. The physical and chemical analyses of the soils were carried out to estimate their basic characteristics . Kr soil series was found to be light brownish gray to very dark grayish brown, with surface horizon was within 25 cm and the subsurface horizon was double the thickness of surface horizon (both horizons were dominant in montmorillonite, more than 40%), whereas Ar series of soils were dark brown to very dark yellowish brown with sandy clay loam in texture and a sand belt at the bottom each of the horizons. Both the horizons were near neutral in pH. The samples were collected at a depth of 50 cm from the surface. The characteristics of the adsorbents are presented in Table 1.
Table 1 The chemical composition of Ar and Kr soils.
To study the effect of various parameters (namely, pH, adsorbent dosage, initial concentration and contact time), batch experiments were conducted at room temperature (30 ± 2 °C). For each experiment, 100 ml of phenol solution of known concentration, at varying amounts of adsorbents were taken in conical ﬂasks (250 ml) and agitated occasionally. The samples were equilibrated for 24 h, withdrawn at appropriate time and were ﬁltered through Whatman ﬁlter paper (No. 42) and analyzed for phenol concentration. The amount of phenol adsorbed by the adsorbent was calculated from the differences between the phenol concentration at initial time and after appropriate time using the following equation: Q =V
ðC0 −Ce Þ : M
Where C0 is the initial sorbate concentration (mg/l), Ce is the ﬁnal concentration in the solution (mg/l), V is the solution volume (l) and M is the mass of adsorbent (g). 2.5. Optimization of pH The adsorption of phenol by two soils (Ar soil and Kr soil) was studied at various pH ranges (2–12). The pH of the solution was adjusted using HCl and NaOH solution of 0.1 M at room temperature 30 ± 2 °C and the studies were carried out for 6 h (optimized equilibrium time) with initial concentration of the phenol solution as 100 mg/l (optimized concentration). 2.6. Optimization of adsorbent dosage for kinetics and isotherm studies
Ar soil (%)
Kr soil (%)
SiO2 Al2O3 CaO Fe2O3 MgO TiO2 Na2O Loss on ignition Cation exchange capacity (meq/100 mg) Speciﬁc gravity (g/cm3) Surface area (m2/g) Porosity Organic matter
46.1 23.2 0.8 16.1 2.3 0.1 2.5 8.9 30–35 2.03 10.8 0.28 11.21
54.5 22.3 0.7 10.8 2.2 0.1 1.9 7.5 33–38 2.11 11.9 0.33 11.98
For the optimum dosage of adsorbent per unit mass of adsorbate, phenol solution was added to different dosages of adsorbents till the equilibrium was attained. The kinetics of analyzing adsorptive uptake determined adsorption of phenol from aqueous solution at different intervals. Various kinetic models (namely, pseudo-ﬁrstorder, pseudo-second-order, the Elovich equation and intra-particle diffusion) were used to study the kinetics of adsorption of phenol by two soils. The adsorption isotherm studies were carried out to compare the adsorption capacity and intensity of the adsorbents. Two parameter models and three parameter models (using Langmuir, Freundlich and Redlich–Peterson and Sip isotherms, respectively)
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were used to describe the equilibrium adsorption of phenol in the present study. 2.7. Error analysis To evaluate the validity of kinetic and isotherm models to represent the experimental data, different error functions of nonlinear regressions have been used by a number of researchers in the ﬁeld [28–30]. However, in the present study, for calculation of error function of non-linear regression, MATLAB (v07) was used, using Marquardt method (also called the Levenberg–Marquardt method). Here, the method of linear descent was used in early iterations and then gradually switched to the Gauss–Newton approach. 3. Results and discussion 3.1. Effect of pH The most critical parameter affecting the adsorption process in the removal of phenol by the natural soil is reported to be the pH of the adsorption medium . As discussed in preceding paragraphs, the adsorption of phenol by Ar soil and Kr soil was studied at various pH values of the phenol–soil solutions (100 ml, 100 mg/l) and the effect of pH on the adsorption of phenol by two soils has been presented in Fig. 1. It is evident (from Fig. 1) that the removal of phenol by both the soils seemed to show a minor variation in the pH range of 2 to 6. However, when pH was made to exceed 6, there was a distinct decline in adsorption of phenol from the solution. This phenomenon of reduction in adsorption with increase on pH may be explained in the following paragraphs. For initial pH below 6.0, a signiﬁcantly high electrostatic attraction exists between the positively charged surfaces of the adsorbent and phenolate ion (C6H5O–). In fact, at lower pH, the adsorbent surface of the soil seemed to have more cations sites, with high concentration of unionized species of halogenated organic compounds , which may be expected to favour chemisorptions of phenolate ions. On the contrary, an increase in pH may lead to a decrease in percentage of the unionized species (i.e., halogenated organic compounds) due to limited surface area of the adsorbent. The hindrance in increase of the ionized species (or phenolate ions), may be calculated as follows, using the ionic fraction of phenolate ions (φions) : φions =
1 ⌊1 + 10ðpKa−pHÞ ⌋
where (pKa for phenol = 9.95). Thus, change in pH has been found to affect the adsorptive process through dissociation of functional groups on the adsorbents surface. This may lead to a shift in the kinetics of the reaction and subsequently, the equilibrium characteristics of adsorption process .
In fact, since the major sources of the surface — charge in soils include both inorganic and organic components, therefore, in addition to the charges by the organic compounds (mostly, halogenated organic compounds, as discussed in preceding paragraphs), the charges by the inorganic compounds in soils are mostly reported to be contributed by the silicate clay minerals (which carry a permanent charge) and non-crystalline materials (namely, metal oxides and hydrous oxides, such as iron, aluminum, manganese and titanium, reported to carry variable charges in the soils) . Since all the metal oxides are amphoteric, they have zero potential charge (PZC). The PZC values of various oxides present in soils were presented in Table 2. Phenol, being a weak acid (pKa = 9.95), was found to have adsorbed to lesser extent at higher pH values due to repulsive forces prevailing at higher pH values. The presence of oxides of iron, aluminum, manganese silicon and calcium on the adsorbents in when these adsorbents contact with the solution formation of charges seemed to follow the following equations: þ
M−OH þ H →M−OH2 þ
M–OH þ OH →M−O þ H2 O
where M stands for: iron, aluminum, manganese, titanium and silicon. Thus, the optimum pH for removal of phenol by both soils was found as pH 2.0, but the experiments were conducted at pH 6.0, because the natural pH of both the soils (Ar and Kr) was between 6.15 and 5.88 respectively. So, the rest of the experiments (like kinetic and isotherm) were conducted at pH 6.0. Besides, signiﬁcantly high electrostatic repulsion was observed between the adsorbent and adsorbate (phenolate ion) at higher pH, this indicates that chemisorptions might be involved in the removal of phenol by both soils. Similar behavior has been reported by Srivastava et al. (in their studies on phenol adsorption by ﬂy ash) . A similar mechanism could be expected of the adsorbents in the present study due to their possessing high silica-content (compatible to ﬂy ash) in both the samples, as well. The adsorption of phenol was expectedly reported to show decreases as pH increases in the soils. 3.2. Effect of adsorbent dosage The effect of adsorbent dosage on the uptake of phenol by two soils (namely Ar and Kr) was studied at different doses (50–1600 mg/100 ml) for the concentration of 100 mg/l and the results were shown in Fig. 2. The removal of phenol was found to increase with an increase in adsorbent dosage. The removal of phenol remained almost constant at adsorbent dosage higher than 10 g/l for Kr soil and larger than 14 g/l for Ar soil. 3.3. Effect of initial concentration of phenol and contact time on adsorption by two soils (namely Kr and Ar) The effect of initial concentration of phenol adsorption on Kr soil, as a function of time, is shown in Fig. 3. The plot shows an increase adsorption of phenol per unit weight with increasing initial concentration. The results also reveal the uptake of phenol at initial
Table 2 Point Zero Charge (PZC) of minerals.
Fig. 1. Effect of pH on the removal of phenol, at 30 = 2 °C; te = 6 h; C0 = 100 mg/l; dosage of Ar soil (14 mg/l) and Kr soil (10 g/l).
Fe3O4 SiO2 Al2O3 MgO TiO2 MnO2
6.5 2 7.5–9.5 12.4 4.5 4
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were calculated from the intercept and slope of the plots of t/q versus t. The results of k2 and correlation coefﬁcients (r2) were shown in Table 3. The correlation coefﬁcients of the second-order kinetic model were greater than the ﬁrst-order kinetic model. 3.4.3. The Elovich equation The Elovich is one of the useful models, it can be expressed as  dqt = α expðβqt Þ: dt Fig. 2. Effect of adsorbent dosage on the removal of phenol, at 30 ± 2 °C; te = 6 h; C0 = 100 mg/l; dosage of Ar soil (14 mg/l) and Kr soil (10 g/l).
stages of the contact time to be somewhat fast, with reduction in uptake rate being closer to equilibrium time (after 6 h). Based on the result, the contact time was ﬁxed as 360 min for two soils (namely Kr and Ar).
Adsorption kinetic is important from the point of view to control the process efﬁciency. Various kinetic models have been used by various researchers, where the pseudo-ﬁrst-order [34,35] and pseudo-second-order models were studied . 3.4.1. Pseudo-ﬁrst-order model The pseudo-ﬁrst-order rate equation of Lagergren is generally described by the following equation: ð5Þ
Where kt is the pseudo-ﬁrst-order rate constant. After integration, by applying the conditions, qt = 0 at t = 0 and at t = t, qt = qt, Eq. (2) becomes logðqe qt Þ = log qe
kt t: 2303
Where qe is the amount of phenol adsorbed at equilibrium in mg/g. Value of kt was calculated from the plots of log (qe − qt) versus t for different concentrations of phenol. The results of k1 and correlation coefﬁcients were shown Table 3. 3.4.2. Pseudo-second-order model The pseudo-ﬁrst-order kinetic model is expressed as follows: t 1 t = + : q qe k2 q2e
Where, α is the initial adsorption rate (mg g− 1 min− 1) and β is the desorption constant (g mg− 1). To simply the Elovich equation, assumed αβt ≫ t and by applying boundary conditions qt = 0 at t = 0 and qt =qt at t =t Eq. (5) becomes: qt =
1 1 lnðt + t0 Þ ln t0 : β β
Where t0 = 1/(αβ). If t is much larger than t0, Eq. (6) can be simpliﬁed as:
3.4. Adsorption kinetic study
dqt = kt ðqe qt Þ: dt
Where k2 is the second-order rate constant (g/mg min), by plotting of t/q versus t is a linear relationship. Values of k2 and qe
Fig. 3. Effect of initial concentration of phenol adsorption on Kr soil; at 30 ± 2 °C; te = 6 h; C0 = 100 mg/l.
1 1 lnðαβÞ + lnðtÞ: β β
A plot between qt versus ln(t) yields a linear relationship with a slope of (1/β) and an intercept of (1/β) ln(αβ). The term 1/β indicates the number of sites available for adsorption. The values of α, β and correlation coefﬁcients were shown in Table 3. 3.4.4. Intra-particle diffusion model Adsorption kinetic data was further used to determine whether the intra-particle diffusion is rate limiting and also to ﬁnd the diffusion rate constant, ki (mg/g min0.5). Weber and Morris  intraparticle diffusion model is characterized by the relationship between speciﬁc adsorption and the square root of time, according to the following equation: ki = qt = 0:5 : t
A plot between qt versus t0.5 for Kr soil is shown in Fig. 4. If data exhibits multi-linear plots, then two or more steps inﬂuence the sorption process. The external resistance to mass transfer surrounding the particle is considered to be signiﬁcant only in the early stage of adsorption, whereas the second linear portion dominated the gradual adsorption stage with intra-particle diffusion . Indeed, the plots were found to be of general type, i.e. at the ﬁrst stage and at the second stage. The initial or ﬁrst stage may also be attributed to the boundary layer diffusion effect, while the second stage may be due to intra-particle diffusion effects. In the present study, the adsorption rate constant (ki), at phenol concentration of 100 mg/l for Ar soil was found to be 0.469 and that for Kr soil was 0.598 (with r2 values of 0.996 and 0.923). Therefore, the slope of this linear portion may be deﬁned as a rate parameter (ki) and characteristic of the adsorption rate in the region, where intra-particle diffusion has been reported to be the rate-limiting factor . 3.4.5. Kinetic results interpretation In the adsorption process prediction of the rate-limiting step is an important factor. Kinetic studies help to identify the adsorption process and to predict the required economical design of wastewater treatment mechanism. For a solid–liquid adsorption, the solute transfer in adsorption process can be either external mass transfer (boundary layer diffusion) for nonporous medium or intra-particle diffusion for porous medium or both mechanisms . The results were shown in Table 3, the correlation coefﬁcients for pseudo-ﬁrst-order and pseudo-second-order models, obtained at all
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Table 3 The adsorption kinetic rate model rate constants for the Ar soil and Kr soil (temp 30 ± 2 °C at pH ~6). Adsorbent
Initial concentration (mg/l)
20 40 60 80 100 20 40 60 80 100
1.0714 2.4286 3.5714 5.1429 6.7143 1.9000 3.7000 5.5000 7.7000 9.5000
0.0046 0.0046 0.0092 0.0069 0.0115 0.0092 0.0115 0.0046 0.0069 0.0092
0.985 0.983 0.991 0.993 0.990 0.994 0.997 0.995 0.996 0.994
0.897 2.028 2.877 4.909 6.427 1.698 3.491 5.012 7.178 8.872
0.012 0.004 0.005 0.001 0.002 0.0056 0.0024 0.0012 0.0011 0.0009
0.0178 0.0300 0.0779 0.0454 0.1228 0.0293 0.0571 0.0567 0.0995 0.1315
initial phenol concentrations were nearly equal, but for pseudo-ﬁrstorder, Qcal and Qexp values showed striking differences. Therefore, based on kinetic reaction, the adsorption was found to favour pseudosecond-order reaction. Thus, based on these results, the pseudosecond-order kinetic model was found to be the rate-limiting step. The Elovich kinetic model was also used to explain the present adsorption phenomena for both the soils (namely Ar and Kr soils). The values of the two constants (α and β) of this Elovich equation, were obtained from the slope and intercept of a plot of qt versus ln(t), which have the good linearity (r2 values varies from 0.931 to 0.984), and has been interpreted to understand the initial rate of the process as well as the nature of sites involved in the adsorption process. This can be explained by two assumptions, the ﬁrst explanation postulates a variation in the release of energies during chemisorption in proportion to the extent of coverage and the second explanation assumes the variation in activation energies required for chemisorptions corresponding to the heterogeneity in the nature of the active sites . As observable from the data (Table 3), the values of α and β showed a general trend of variation (increase in case of α and decrease in case of β) with increase in initial phenol concentration, in case of both the soils studied. Based on the values of α and β, thus obtained and applied in Eq. (7), all concentrations for both the soils, t ≫ t0 (with ‘t0’-values varying between 5.51 and 1.65 min), thereby justify the ﬁrst assumption of the occurrence of chemisorptions. Nevertheless, when the trend of variation of t0 was studied in relation to variation in initial phenol concentrations, it was observed that Kr soil shows a distinct increasing trend, whereas in Ar soil, there is no speciﬁc trend. Therefore, although both the soils seem to undergo chemisorptions, yet the release of energy (or rate of coverage) seem to increase with an increase in initial phenol concentration for Kr soil only. Secondly, as noted before with increasing the initial phenol
0.988 0.971 0.996 0.981 0.998 0.997 0.998 0.978 0.992 0.997
1.229 2.833 4.032 7.353 7.937 2.278 4.854 6.944 9.709 12.048
4.065 1.715 0.421 0.447 0.196 0.933 0.488 0.353 0.233 0.196
0.045 0.071 1.984 1.483 3.096 2.994 3.080 3.048 3.024 3.096
0.982 0.956 0.984 0.931 0.963 0.963 0.964 0.955 0.971 0.963
concentration (from 20 to 100 mg/l), the β-values showed a general trend of reduction (4.065 to 0.196 g/mg for Ar soil, from 0.933 to 0.196 g/mg for Kr soil). Thus, 1/β (which is apparently indicative of the number of sites available for adsorption, as per the second assumption) showed a distinct increase in both the soils with increase in concentration, again reinforcing the occurrence of chemisorptions in both the soils-adsorbate systems. 3.5. Adsorption isotherm study Various adsorption isotherm equations have been used to study the nature of adsorption, with the basic idea of optimizing the design of an adsorption process. The most commonly used isotherms are Langmuir and Freundlich isotherms. The Langmuir isotherm equation  follows Henry's law at low concentrations and is valid for homogeneous surfaces. However, for heterogeneous surfaces, Freundlich isotherm equation  is suitable (over restricted ranges of concentrations). Besides, the Redlich–Peterson equation  is also widely used as a compromise between Langmuir and Freundlich isotherms and is mostly used to represent solute adsorption data on heterogeneous surfaces. Sip model  equation follows Freundlich isotherm at lower solute concentration and follows Langmuir isotherm at higher solute concentration. In present study, adsorption of phenol was evaluated and compared with popular two and three parameter single-solute isotherm models. The two parameter models (Langmuir and Freundlich isotherms) were linearized and hence the isotherm parameters were estimated using least-square method. For three parameter models (Redlich–Peterson and Sip isotherms), MATLAB (v07) was used to determine the unknown parameters (namely, KRP, αRP, β, KS and α), correlation coefﬁcient and the percentage deviation, using the values obtained in laboratory study on phenol adsorption on the two soils selected. The percent deviation was calculated as follows:
Percent deviation =
qe;exp qe;calc × 100: qe;calc
The equation for bi-parametric Langmuir's isotherm equation can be expressed as follows:
Fig. 4. Plots of intra-particle diffusion kinetic model for Kr soil; at 30 ± 2 °C; te = 6 h; C0 = 100 mg/l.
qm bCe : 1 + bCe
Where qe is the amount of solute adsorbed per unit weight of adsorbent at equilibrium (mg/g), Ce is the equilibrium concentration of the solute in the bulk solution (mg/l), qm is the maximum adsorption capacity (mg/g) and b is the constant related to the free energy of adsorption (l/mg).
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The Freundlich equation is an empirical model that considers heterogeneous adsorptive energies on the adsorbent surface and the equation expressed as follows: 1=n
qe ¼ KF Ce
Where KF is a constant, indicating the relative adsorption capacity of the adsorbent ((mg1 − (1/n) L1/n)/g)) and n is a constant, representing the intensity of adsorption. The Redlich–Peterson equation is expressed as follows: qe =
KRP Ce : ⌊1 + ðαRP Ce Þβ ⌋
Where KRP (l/g) and αRP (l/mg)β are Redlich–Peterson isotherm constants and β is the exponent which lies between 1 and 0. Sip isotherm model equation is expressed as follows: β ðKS Ce Þ qe = : ½1 + ðαS Ce Þβ
Where KS (l/g) and αs (l/mg)β are the Sips isotherm constants and β is the exponent which lies between 1 and 0. 3.6. Isotherm results interpretation It is necessary to ﬁnd a suitable model for better understanding of the mechanism and to assess the adsorption characteristics and magnitude based on the suitable model obeyed by the two soils (namely, Ar and Kr). For this purpose, Langmuir, Freundlich, Redlich–Peterson and Sip isotherm models were considered and compared against experimental data for the goodness of ﬁt. Figs. 5 (comparison of Langmuir and Freundlich isotherms) and 6 (comparison of Redlich– Peterson and Sip isotherms) represent the comparison of experimental and calculated amount of phenol adsorbed on the soil samples. The ﬁtness/suitability of the models was evaluated based on the study of correlation coefﬁcient, absolute sum of squares and standard deviation of residuals (sy. x). For Ar soil, all the models discussed in preceding paragraphs were found to represent the experimental data well. Langmuir isotherm model was found to ﬁt the data reasonably, with a correlation coefﬁcient of 0.998, absolute sum of squares 1.157 and standard deviation of residuals 0.3243. Freundlich isotherm model was found to be in good agreement between the experimental and observed data, with a correlation coefﬁcient of 0.983. The absolute
Fig. 6. Comparison of Redlich–Peterson and Sip isotherm models for phenol adsorption on Ar soil with experimental results (temp 30 ± 2 °C at pH ~6).
sum of square value is 10.05, it indicates a slight divergence with the experimental data. Both the three-parametric models (Redlich– Peterson and Sip isotherms) were found to ﬁt the experimental data and seemed to show remarkably similar degree of ﬁtness with regard to the plots as well as parameters. The ﬁtted parameter values for all the isotherms used are shown in Tables 4 and 5. Figs. 7 and 8 show comparison of Langmuir and Freundlich isotherms and comparison of Redlich–Peterson and Sip isotherms, respectively, for Kr soil. Langmuir isotherm model could reasonably ﬁt the data, with a correlation coefﬁcient of 0.995, absolute sum of squares 4.801 and standard deviation of residuals 0.8282. Freundlich isotherm model was found to be in good agreement between the experimental and observed data, with a correlation coefﬁcient of 0.976. The absolute sum of square value is 24.16, it indicates a high divergence from the experimental data. In case of three parameter isotherm models, the correlation coefﬁcient, absolute sum of squares and standard deviation of residuals (sy.x) of these two model (Redlich–Peterson and Sip isotherms) results, again a remarkable similarity (with regard to plots as well as parameters) were observed to be similar to that in case of Ar soil. The values of the parameters for all the isotherms used are shown in Table 4.
Table 4 Two parameter isotherm model parameters for two soils at 30 ± 2 °C. Isotherms
Langmuir best ﬁt values b qm Std. Error b qm r2 Absolute sum of squares Standard deviation of residuals (sy.x)
Fig. 5. Comparison of Langmuir and Freundlich isotherm models for phenol adsorption on Ar soil with experimental results (temp 30 ± 2 °C at pH ~6).
Freundlich best ﬁt values KF n Std. Error KF n r2 Absolute sum of squares Standard deviation of residuals (sy.x)
Adsorbent Ar soil
0.001194 0.5134 0.998 1.157 0.3243
0.002753 1.384 0.9952 4.801 0.8282
0.2492 0.08892 0.983 10.05 0.9559
0.7663 0.09842 0.976 24.16 1.858
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Table 5 Three parameter isotherm model parameters for two soils at 30 ± 2 °C. Isotherms
Redlich–Peterson best ﬁt values KRP αRP β Std. Error KRP αRP β r2 Absolute sum of squares Standard deviation of residuals (sy.x) Sip best ﬁt values KS β α Std. Error KS β α r2 Absolute sum of squares Standard deviation of residuals (sy.x)
Adsorbent Ar soil
1.287 0.05 0.8679
2.276 0.04652 0.9717
0.05259 0.009485 0.06091 0.9985 0.8751 0.2958
0.2048 0.01959 0.1617 0.9953 4.782 0.8928
1.547 0.9044 0.02785
2.921 0.9165 0.03635
0.1622 0.03692 0.003202 0.9988 0.6949 0.2636
0.8888 0.08919 0.00855 0.9958 4.199 0.8365
Fig. 8. Comparison of Redlich–Peterson and Sip isotherm models for phenol adsorption on Kr soil with experimental results (temp 30 ± 2 °C at pH ~6).
3.7. Validation of adsorption isotherm models Since for both the soils, all the four isotherm models studied, such as the Langmuir, Freundlich, Redlich–Peterson and Sip showed high r2 values (more than 0.9). It indicates the possibility of simultaneous validity of multiple isotherm models and corresponding axioms. It was also observed that the distribution of the average percent deviation was reduced from more than 1.5% to less than 0.3% from two parameter models to three parameter models (Fig. 9). On comparison of all the three ﬁtness parameters (namely, the correlation coefﬁcient, absolute sum of squares and standard deviation of residuals), both the three parameter models seemed to be most suitable for understanding the adsorption mechanisms of both the soils studied. Hence, the best ﬁtting order of the isotherm models for both the soil is determined to be Sip (=Redlich–Peterson)>Langmuir>Freundlich. 4. Conclusions In the present study, adsorption batch studies onto two soils (namely Kr and Ar) using phenol as adsorbate were carried out. The studies
Fig. 9. Plots of percent deviation for Kr soil.
indicate Kr soil as a more effective adsorbent for removal of phenol from aqueous solution, in comparison to Ar soil. Both the adsorbents showed higher percent of phenol removal for low initial concentration of phenol in the solution. Based on the kinetic modeling (pseudo-second-order model and Elovich model) the adsorption phenomenon seemed to be a chemisorption process. Similarly, based on diffusion study, it seemed that the rate-limiting step might be chemisorptions in the ﬁrst stage and followed by an intra-particle diffusion phenomenon in the later stages. Although all the four adsorption isotherm models (namely, the Langmuir, Freundlich, Sip and Redlich–Peterson) were obeyed fairly well by both the soils, yet the best models explaining the adsorption were found to be the Sip and Redlich–Peterson isotherm models. Both the soils were found to be potential adsorbent even in their raw (untreated form), best being, and Kr soil. References
Fig. 7. Comparison of Langmuir and Freundlich isotherm models for phenol adsorption on Kr soil with experimental results (temp 30 ± 2 °C at pH ~6).
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