Single and Multicomponent Equilibrium Studies for the Adsorption of

9646

Langmuir 2004, 20, 9646-9656

Single and Multicomponent Equilibrium Studies for the Adsorption of Acidic Dyes on Carbon from Effluents Keith K. H. Choy, John F. Porter, and Gordon McKay* Department of Chemical Engineering, Hong Kong University of Science and Technology, Clear Water Bay Road, Kowloon, Hong Kong SAR, China Received March 17, 2004. In Final Form: July 5, 2004 The ability of activated carbon to adsorb three acidic dyes, namely, Acid Blue 80 (AB80), Acid Red 114 (AR114), and Acid Yellow (AY117), from wastewater has been studied at 20 °C. The three single-component systems and the three binary equilibrium systems have been measured experimentally. The three singlecomponent isotherms were analyzed using the Langmuir, Freundlich, Redlich-Peterson, and Sips equations. The Redlich-Peterson equation gave the lowest errors using the sum of the squares of the errors closely followed by the Sips and Langmuir equations; the Freundlich fits were significantly worse. The three bisolute experimental equilibrium sets of data were analyzed by incorporating the previous four singlecomponent isotherm equations into the ideal adsorbed solution theory (IAST). The solution methods for each of the four isotherm equations are presented in the paper, and the predicted results for the three bisolute systems, using the four isotherm equations, are compared. For the three bisolute systems (AB80 + AR114, AB80 + AY117, and AR114 + AY117), the Redlich-Peterson isotherm gives the best correlation with the experimental isotherm data.

1. Introduction It is projected that 10-20% of dyes (active substances) in the textile sector will be lost in residual liquors through incomplete exhaustion and washing operations. The rate of loss is approximated to be 1-2% and 10% for pigments and paper and leather dyes, respectively. Effluent treatment processes for dyes are currently able to get rid of about half of the dyes lost in residual liquors. Therefore, ∼400 tonnes daily1 find their way into the environment, primarily dissolved or suspended in water. Adsorption is a physiochemical wastewater treatment process, which is gaining prominence as a means of producing high quality effluents, which are low in concentrations of dissolved organics. Dissolved molecules are attracted to the surface of the adsorbent by physical/ chemical forces. The important characteristics of an adsorbent must be expressed in terms of both adsorptive characteristics and physical properties. The requirement of adequate adsorptive capacity restricts the choice of adsorbents for practical separation processes to microporous adsorbents with pore diameters ranging from a few angstroms to a few tens of angstroms. This includes both the traditional microporous adsorbents such as activated carbon and the more recently developed crystalline alumino silicates or zeolites. Activated carbon is the most popular used adsorbent in wastewater treatment,2 and it is widely used for the removal of color.3 Several equilibrium studies on the adsorption of dyes using activated carbon and its derivatives have been carried out.4-9 Activated carbon has also been applied in the kinetic study of the adsorption of basic and acidic dyes.10-13 In studies of adsorption systems, success has been achieved in describing the adsorption behavior by several equilibrium isotherm models. In 1906, Freundlich sug* To whom correspondence should be addressed. Phone: (852)2358-8412. Fax: (852)2358-0054. E-mail: [email protected]. (1) Reisch, M. S. Chem. Eng. News 1996, 74 (3), 10. (2) Allen, S. J.; Brown, P.; McKay, G.; Flynn, O. J. Chem. Technol. Biotechnol. 1992, 54, 271. (3) Allen, S. J.; Whitten, L.; McKay, G. Dev. Chem. Eng. Miner. Process. 1998, 6 (5), 231.

gested a model to describe the adsorption properties of heterogeneous systems.14 A few years later, in 1918, Langmuir suggested a theory to describe monolayer adsorption on homogeneous surfaces.15 Another popular isotherm was proposed by Redlich and Peterson.16 This isotherm is quite similar to the Langmuir isotherm, but it has a power factor in the equation. Sips combined the Langmuir and Freundlich equations and proposed a Langmuir-Freundlich/Sips equation.17 Although considerable information is available on single-component adsorption, most industries discharge effluents that contain several components. Experimental results on binary mixtures have been reported by Kolthoff and van der Groot,18 Amiot,19 and El-Dib et al.;20 these authors presented the isotherms for the adsorption for hydrocarbon mixtures onto activated carbon. In 1931, a model for competitive adsorption based on the Langmuir equation was first developed by Markham17 to describe adsorption equilibrium in multicomponent systems and is based on the same assumptions as the Langmuir equation for single adsorbates.15 (4) McKay, G. Chem. Eng. J. 1983, 27, 187. (5) McKay, G.; Al-Duri, B. Chem. Eng. Sci. 1988, 43 (5), 1133. (6) Lin, C. C.; Liu, H. S. Ind. Eng. Chem. Res. 2000, 39, 161. (7) Gupta, G. S.; Prasad, G.; Singh, V. N. Water Res. 1990, 24, 25. (8) Walker, G. M.; Weatherly, L. R. Trans. Inst. Chem. Eng. 2000, 78 (B), 219. (9) Choy, K. K. H.; Porter, J. F.; McKay, G. J. Chem. Eng. Data. 2000, 45, 575. (10) Spahn, H.; Schlu¨nder, E. U. Chem. Eng. Sci. 1975, 30, 529. (11) Ko, D. C. K.; Tsang, D. H. K.; Porter, J. F.; McKay, G. Langmuir 2003, 19, 722. (12) Zhou, M. L.; Martin, G. Environ. Technol. 1995, 16, 827. (13) Chen, B.; Hui, C. W.; McKay, G. Langmuir 2001, 17, 740. (14) Freundlich, H. Z. Phys. Chem. 1906, 57, 385. (15) Langmuir, I. J. Am. Chem. Soc. 1918, 40, 1361. (16) Redlich, O.; Peterson, D. L. J. Phys. Chem. 1959, 63, 1024. (17) Do, D. D. Adsorption Analysis: Equilibrium and Kinetics, 1st ed.; Imperial College Press: London, 1988. (18) Kolthoff, I. M.; Van der Groot, E. Recl. Trav. Chim. Pays-Bas 1929, 48, 265. (19) Amiot, M. R. C. R. Acad. Sci. 1934, 199. (20) El-Dib, M. A.; Aly, U. A. Proc. First Conf. Mech. Power Eng. Giza, Egypt 1977, 85.

10.1021/la040048g CCC: $27.50 © 2004 American Chemical Society Published on Web 09/22/2004

Adsorption of Acidic Dyes on Carbon from Effluents

Jain and Snoeyink21 and Srivasta and Tyagi22 have investigated competitive adsorption on activated carbon from aqueous bisolute solutions of organic adsorbates and have developed a model that adequately predicts adsorption equilibria in such systems. According to Jain and Snoeyink, adsorption without competition can be incorporated into the Langmuir theory for a binary adsorbate system. Al-Duri and McKay23 reported the extended empirical Freundlich isotherm of Fritz and Schlu¨nder24 with a modification that greatly reduced the amount of experimentation and mathematics required for their system involving binary dyes and activated carbon. Al-Duri and McKay23 used this modified extended Freundlich isotherm for binary dye mixtures on peat. Sheindorf et al.25 used a Freundlich type multicomponent isotherm and examined the effect of an increase in the number of organic solutes in solution on the competitive adsorption of organic compounds. Other relevant studies include those of Jossens et al.26 who reported a three-parameter adsorption isotherm and Fritz et al.2727 who studied the competitive adsorption of two dissolved organics. Thermodynamic studies on multicomponent equilibrium adsorption by Hill28 and Young and Crowell29 formed the basis of a model by Myers and Prausnitz30 and Radke and Prausnitz.31 The ideal adsorbed solution theory (IAST),30 which required only single-component equilibrium data to predict multisolute sorption, was extended to ideal liquid solute systems31 and further developed to incorporate activity coefficients32,33 and nonideal mixtures.34,35 Due to the assumption of an ideal adsorbed phase, at high concentrations and high sorbent loadings, nonideal behavior was anticipated in the adsorbed phase;31 however, it has been successfully applied to estimate competitive isotherms even at moderate to high concentrations.36 O’Brien and Myers37 developed an algorithm, called FASTIAS, for calculating multicomponent gas adsorption equilibria, and Moon and Tien38 extended this IAST application to Langmuir systems. Because certain theoretical equations, such as the Freundlich and DubininRadushkevich isotherms, predict an infinite value for Henry’s constant, some authors have said that these isotherms are unsuitable for the calculation of the spreading pressure and other thermodynamic properties.39 Despite this, both equations are still used.40,41 (21) Jain, J. S.; Snoeyink, V. L. J.sWater Pollut. Control Fed. 1973, 45, 2463. (22) Srivastava, S. K.; Tyagi, R. Water Res. 1995, 29, 483. (23) Al Duri, B.; McKay, G. Chem. Eng. Sci. 1991, 46, 193. (24) Fritz, W.; Schlu¨nder, E. U. Chem. Eng. Sci. 1974, 29, 1279. (25) Sheindorf, C.; Rebhun, M.; Sheintuch, M. Water Res. 1982, 16, 357. (26) Jossens, L.; Prausnitz, J. M.; Fritz, W.; Schlu¨nder, E. U.; Myers, A. L. Chem. Eng. Sci. 1978, 33, 1097. (27) Fritz, W.; Schlu¨nder, E. U. Chem. Eng. Sci. 1981, 36, 721. (28) Hill, T. L. J. Phys. Chem. 1949, 17, 520. (29) Young, D. M.; Crowell, A. D. Physical Adsorption of Gases; Butterworths: London, 1962. (30) Myers, A. L.; Prausnitz, J. M. AIChE J. 1965, 11, 121. (31) Radke, C. J.; Prausnitz, J. M. AIChE J. 1972, 18 (4). (32) Minka, C.; Myers, A. L. AIChE J. 1973, 19, 453. (33) Myers, A. L. AIChE J. 1983, 29 (4), 691. (34) Talu, O.; Zwiebel, I. AIChE J. 1986, 32 (8), 1263. (35) Lee, C. S.; Belfort, G. Ind. Eng. Chem. Res. 1988, 27, 951. (36) Seidel-Morgensern, A.; Guiochon, G. Chem. Eng. Sci. 1993, 48 (15), 2787. (37) O’Brien, J. A.; Myers, A. L. Ind. Eng. Chem. Process Des. Dev. 1985, 24 (4), 1181. (38) Moon, H.; Tien, C. Ind. Eng. Chem. Res. 1987, 26 (10), 2042. (39) Talu, O.; Myers, A. L. AIChE J. 1988, 34 (11), 1887. (40) McGinley, P. M.; Katz, L. E.; Weber, W. J. Environ. Sci. Technol. 1993, 27 (8), 1524. (41) Richter, E.; Schutz, W.; Myers, A. L. Chem. Eng. Sci. 1989, 44 (8), 1609.

Langmuir, Vol. 20, No. 22, 2004 9647 Table 1. Physical Properties of Activated Carbon Filtrasorb F400 total surface (N2 BET method) (m2 g-1) bed density, backwashed and drained (kg m-3) particle density (g cm-3) particle voidage fraction

1150 425 × 103 1.30 0.38

Most of the published applications of the IAST to date relate to the gas-phase sorption of hydrocarbons, primarily alkanes and volatile organic compounds (VOCs),42-44 and the sorption of priority pollutants (VOCs, aromatics, and phenolics) from water26,27,45-47 on activated carbon. Other studies using the IAST have examined the sorption of herbicides48,49 and synthetic organic contaminants.50 Almost all the previous studies, focusing on the IAST, have incorporated isotherm equations based on the “bestfit” single-component isotherm model in determining the spreading pressure. In the present paper, four isotherms have been tested in the IAST, namely, the Langmuir, Freundlich, RedlichPeterson, and Sips isotherms. The models have been applied to three binary adsorption systems of acidic dyes on activated carbon. 2. Experimental Materials and Procedures Adsorbent. The adsorbent used in this study was a granular activated carbon (GAC) of type F400; it was supplied by Chemviron Carbon Ltd. This carbon was described by the supplier as a generally effective water treatment activated carbon. Activated Carbon Filtrasorb 400 was crushed by using a hammer mill and washed with distilled water to remove fines. It was dried at 110 °C in an oven for 24 h and then sieved into several discrete particle size ranges, namely, 200-355, 355-500, 500710, and 710-1000 µm. The 500-710 µm size range of activated carbon was used for all the experiments in this study. The carbon particles were asssumed to be spheres having a diameter given by the arithmetic mean value between respective mesh sizes (the average particle dameter, dp, was 605 µm). The particles appeared irregularly shaped under a microscope but approximated more closely to spheres than to cylinders or parallel pipes for the size ranges under investigation. Table 1 gives the physical properties of Activated Carbon Filtrasorb F400. Adsorbates. Three dyes, namely, Acid Blue 80 (AB80), Acid Red 114 (AR114), and Acid Yellow 117 (AY117), were used in this study. The dyestuffs were used as the commercial salts. Acid Blue 80 and Acid Yellow 117 were supplied by Ciba Speciality Chemicals, and Acid Red 114 was supplied by Sigma-Aldrich Chemical Co. Some information regarding the three acidic dyes, which were used to measure and prepare standard concentration dye solutions, is listed in Table 2. The data include the color index number, molecular mass, dye content, and wavelength at which the maximum absorption of light occurs, λmax. The structures of the three acidic dyes are shown in Figure 1. The equilibrium isotherms were determined by contacting a constant mass of carbon with a range of dye concentration solutions. A series of fixed volumes (0.050 dm3) of solutions with predetermined initial dye concentrations were prepared and brought into contact with predetermined masses (0.05 g) of Activated Carbon Filtrasorb F400 (dp ) 500-710 µm). Therefore, (42) Costa, E.; Sotelo, J. L.; Calleja, G.; Marron, C. AIChE J. 1981, 27, 5. (43) Li, J. M.; Talu, O. Chem. Eng. Sci. 1994, 49 (2), 189. (44) Hu, X. J.; Do, D. D. Chem. Eng. J. 1995, 41 (6), 1585. (45) Thacker, W. E.; Crittenden, J. C.; Snoeyink, V. L. J.sWater Pollut. Control Fed. 1984, 56 (3), 243. (46) Ceresi, J. E., Jr.; Tien, C. Sep. Technol. 1991, I, 273. (47) Smith, E. H. Water Res. 1991, 25 (2), 125. (48) Xing, B. S.; Pignatello, J. J.; Giliotti, B. Environ. Sci. Technol. 1996, 30 (8), 2432. (49) Kilduff, J. E.; Wigton, A. Environ. Sci. Technol. 1999, 33 (2), 250. (50) Knappe, D. R. U.; Matsui, Y.; Snoeyink, V. L.; Roche, P.; Prados, M. J.; Bourbigot, M. M. Environ. Sci. Technol. 1998, 32 (11), 1694.

9648

Langmuir, Vol. 20, No. 22, 2004

Choy et al.

Figure 1. Dye structures of Acid Red 114, Acid Blue 80, and Acid Yellow 117. Table 2. Information Regarding the Acidic Dyes names of the dyes

color index number molecular mass (g) dye content (%) λmax (nm) Dmol (cm2 s-1)

Acid Blue 80

Acid Red 114

Acid Yellow 117

61 585 676 60 626 4.674 × 10-6

23 635 830 45 522 3.893 × 10-6

24 820 848 60 438 3.754 × 10-6

a constant M/V ratio was used throughout the process. The jars were sealed and agitated in the shaker bath (200 revolutions/ min shaking rate) for 21 days at a constant temperature of 20 ( 0.5 °C until equilibrium was reached.10 For the multicomponent systems, all solutions were prepared with solutions of equal mass concentrations. The samples were analyzed using a Varian Cary IE spectrophotometer to determine the equilibrium concentration.

3. Theory of Equilibrium Adsorption Modeling The measurement and analysis of single- and multicomponent adsorption isotherms were performed in this research. A single-component system comprises one solute (adsorbate) and one solid phase (adsorbent), and a single curve can be drawn of the solute concentration in the solid phase, qe, as a function of the solute concentration in the fluid phase, Ce, at one specific temperature; this is called an isotherm. To optimize the design of a sorption system to remove acidic dyes from wastewaters, it is important to establish the most appropriate correlation to describe the equilibrium curves. The results of equilibrium adsorption measurements can be expressed and correlated

in the form of adsorption isotherm equations. The equilibrium modeling of the isotherm studies was divided into two parts: single-component and multicomponent equilibrium studies. Single-Component Isotherm Studies. In this study, four isotherms were used to correlate the adsorption of acidic dyes onto activated carbon, namely, the Langmuir, Freundlich, Redlich-Peterson, and Sips isotherms.

Langmuir Isotherm qe )

KLCe 1 + aLCe

(1)

Freundlich Isotherm qe ) aFCebF

(2)

Redlich-Peterson Isotherm qe )

KRCe 1 + aRCeβ

(3)

Sips Isotherm qe )

KSCe1/bS 1 + aSCe1/bS

(4)

Multicomponent Isotherm Studies. Multicomponent equilibrium studies have passed through many


Langmuir, Vol. 20, No. 22, 2004 9649

stages of development since the beginning of the last century when none of the multicomponent equilibrium studies dealt with competitive adsorption and only a few were concerned with the selectivity of adsorption processes. Ideal Adsorbed SolutionTheory (IAST). The IAST is a multicomponent adsorption model; it provides a thermodynamically consistent and practical method for predicting binary sorption isotherms using singlecomponent isotherm data alone.30 The original paper presented an analysis for gas-phase systems, and this was subsequently extended to adsorption from aqueous solutions.31 The IAST started with the following assumptions: (1) All components in a mixture behave as ideal adsorbed solutes according to Raoult’s law. Therefore, the equilibrium fluid-phase concentration of each component in the multicomponent system should be proportional to its adsorbed-phase mole or mass fraction. (2) The chemical potentials in both the adsorbed and fluid phases should be equal for each component; therefore, the spreading pressure should be constant for all components in a given mixture. To be able to use the IAST to predict multicomponent adsorption equilibria based on single-component data alone, it is necessary to determine values for two variablessthe solid-phase mole fractions and the spreading pressuressimultaneously. The solution method presented below incorporates four different isotherm equations; they are the Langmuir, Freundlich, RedlichPeterson, and Sips equations. From the mass balance for each nonvolatile component i, the sum of the material in the solid phase and the liquid phase at equilibrium must be equal to its initial solutionphase concentration; that is,

C0,i ) Ce,i +

M q V e,i

Hence, transforming each of the terms in eq 8 into those based on single-component data gives the following for one component of a multicomponent system:

[ (∑ ) ] 0 Ce,i

C′0,i )

j)1

0 qe,j

si

(9)

(∑ ) n

sj

j)1

0 qe,j

-1

Rearranging eqs 1 and 8 allows the following to be substituted into eq 9 to obtain the equivalent purecomponent fluid and adsorbed-phase concentrations at the specified spreading pressure: 0 0 /KL,i )) - 1 exp(ψ(aL,i

0 Ce,i )

0 ) qe,i

(10)

0 aL,i

0 KL,i 0 0 [1 - exp(-ψ(aL,i /KL,i ))] 0 aL,i

(11)

completing the development of the first equation set. The Freundlich Isotherm in the IAST. A second equation set can be derived based on the Freundlich isotherm. Again, the spreading pressure can be evaluated, but this time, using the form of the integral proposed by Kidnay and Myers:52

ψ)

πA ) RT

∫0C

e

qe d ln Ce(qe) dqe ) d ln qe bF

(12)

Substituting the following into eq 9 using eqs 2 and 12, 0 ) ψbF,j qe,j

0 Ce,j )

(6) ψ)

The IAST dictates that the spreading pressure should be constant for each component in a given system:

ψ1 ) ψ2 ) ... ) ψn

(7)

Analytical Solution Method for the IAST. The Langmuir Isotherm in the IAST. Using the Langmuir isotherm as a basis, the spreading pressure, ψ, can be evaluated by

q

V

-1

(13)

( ) 0 qe,j aF,j

1/bF,j

(14)

The Sips Isotherm in the IAST. By applying the Sips isotherm, the spreading pressure, ψ, can be evaluated:53

si ) 1 ∑ i)1

K

∫0C Cee dCe ) aLL ln(1 + aLCe) e

sj

0 si and qe,i ) siqT ) si Ce,i ) Ce,i

(5)

n

πA ) RT

n

since

where M is the mass of the adsorbent and V is the volume of the solution. From the overall mass balance, the sum of the mole or mass fractions in each phase must be exactly equal to unity; that is, for the solid phase,

ψ)

+

M

(8)

This form of the integral is proposed by McKay and AlDuri.51 (51) McKay, G.; Al-Duri, B. Chem. Eng. Sci. 1988, 43 (5), 1133.

πA ) RT

∫0C

e

KS qe dCe ) ln(1 + aSCebS) (15) Ce bSaS

Similarly, rearranging eqs 4 and 15 allows the following to be substituted into eq 9 to obtain the equivalent purecomponent fluid and adsorbed-phase concentrations at the specified spreading pressure: 0 ) Ce,i

0 qe,i

(

)

0 0 0 exp((ψaS,i bS,i )/KS,i )-1 0 aS,i

1/bS,i

0 KS,i 0 0 0 ) 0 [1 - exp(-ψ(aS,i bS,i )/KS,i )]17 aS,i

(16)

(17)

For all the three equation sets, an appropriate convergence scheme (e.g., Newton-Raphson or secant) can then be (52) Kidnay, A. J.; Myers, A. L. AIChE J. 1966, 12, 981. (53) Ko, D. C. K.; Cheung, C. W.; Choy, K. H. H.; Porter, J. F.; McKay, G. Chemosphere 2004, 273.

9650


Choy et al.

used to identify the values of ψ and s1 by minimizing the SSE between the experimental liquid-phase solute concentrations and those predicted by the IAST model. n

SSE )

(Ce,cal - Ce,exp)2i ∑ i)1

(18)

Numerical Solution Method for the IAST. The Redlich-Peterson Isotherm in the IAST. A novel computer numerical IAST method was developed in this paper in order to apply the Redlich-Peterson isotherm (eq 3) in the IAST model; it is necessary because an analytical solution is not available for the spreading pressure (eq 19) when incorporating the Redlich-Peterson equation. To calculate the spreading pressure, a numerical computer integration method is used to solve eq 19.

ψ)

πA ) RT

∫0C

e

qe dCe ) Ce

∫0C

KRCe

e

Ce(1 + aRCeβ) KR

dCe )

∫1 + a C β dCe R

(19)

e

By applying a numerical integration program, the values of the spreading pressure, ψ, can be obtained with different Ce values. In a binary system, with species 1 and 2, the spreading pressures of components 1 and 2 are shown in eqs 20 and 21.

ψ1 )

∫0

ψ2 )

∫0

K0R,1

C0e,1

β10

(1 + a0R,1Ce ) K0R,2

C0e,2

β20

(1 + a0R,2Ce )

dCe

(20)

dCe

(21)

s1 s2 1 ) + 0 qT q0 qe,2 e,1

(22)

For a given (guess values) pair of qe,1 and qe,2, the values of s1, s2, and qT can be calculated.

qT ) qe,1 + qe,2

(23)

s1 )

qe,1 qT

(24)

s2 )

qe,2 qT

(25)

By applying the Redlich-Peterson equation in eq 22, it gives eq 26.

1 ) qT

s1 0 KR,1C0e,1

+ 0

1 1 + a0R,1 C0β e,1

s2 K0R,2

(26)

C0e,2 0

2 1 + a0R,2 C0β e,2

Another numerical program was built up to solve eq 26, which calculates the C0e,2 value from a given C0e,1 value. By providing an initial guess value, the C0e,1 value of the corresponding qe,1, the value of C0e,2 can be calculated by the program. Then, using a numerical integration program

on eqs 20 and 21, the values of ψ1 and ψ2 can be obtained from the values of C0e,1 and C0e,2. Since the IAST dictates that the spreading pressure should be constant for each component in a given system, for a binary system: ψ1 ) ψ2, the program will optimize the C0e,1 value until the spreading pressures of components 1 and 2 are equal. Hence, the values of Ce,1 and Ce,2 can be calculated from C0e,1 and C0e,2 by eqs 27 and 28.

Ce,1 ) C0e,1s1

(27)

Ce,2 ) C0e,2s2

(28)

A computational algorithm of the Redlich-Peterson IAST numerical solution method is shown in Figure 2. Similarly, an appropriate convergence scheme can then be used to identify the values of qe,1, qe,2, Ce,1, and Ce,2 by minimizing the error between the experimental initial liquid-phase solute concentrations and those predicted by the IAST model using eq 18. This IAST numerical method, incorporating the Redlich-Peterson isotherm in the IAST model, can be applied to all other isotherm equations, such as the Langmuir, Freundlich, and Sips equations. The multicomponent equilibrium adsorption data can be derived using only single-component isotherm parameters and system parameters (M and V). 4. Results and Discussion Single-Component Isotherm Studies. The purpose of investigating adsorption isotherms is, first, to measure the adsorption capacity of the adsorbent particle and, second, to ascertain the solid-liquid equilibrium distribution of the solute. The comparisons of all the studies are interpreted in terms of molar units, since the singlecomponent data have been used to predict the multicomponent equilibria by the IAST. First, the monolayer saturation capacities of three acidic dyes have been estimated by the Langmuir equation. Figure 3 shows that AB80 has an adsorption saturation capacity of 0.2536 mmol g-1, while that of AY117 is 0.2191 mmol g-1. AB80 and AY117 appear to have similar adsorption capacities, whereas activated carbon has a much lower affinity for AR114, with a saturation capacity of 0.1250 mmol g-1. The differences between the adsorption capacities of the three acidic dyes may be due to the different adsorption mechanisms, ionic charges, electron affinities, or molecular volumes. Mechanism of Adsorption. Acidic dye adsorption is mostly due to physical adsorption, and thus, the structure of the acidic dye is the main factor affecting the adsorption capacity. All three acidic dyes contain two sulfonic acid groups (see Figure 1), which ionize in water to form the anionic colored component RSO3- and a Na+ cation. The two sodium sulfonic groups in AB80 and AY117 exist on two separate benzene rings; the structures of these two acidic dyes are symmetric. Since the two sodium sulfonic groups in AR114 are on one benzene ring, the adsorption affinity may suffer Coulombic repulsion due to the closeness of the two sulfonic groups. The higher values in adsorption capacities for AB80 and AY117 suggest that this is the case. The adsorption capacity of AB80 on activated carbon is greater than that of AY117, and this may due to the fact that the molecular volumes of the two acidic dyes are different. The molecular volumes of AB80 and AY117 are 321.80 and 463.80 cm3 mol-1, respectively.54 (54) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases & Liquids; McGraw-Hill: New York, 1987.


Langmuir, Vol. 20, No. 22, 2004 9651

Figure 2. Computational algorithm for the Redlich-Peterson IAST numerical solution method.

experimental and theoretical data of the equilibrium solidphase concentration, qe, using the sum of the squares of the error (SSE) function. p

SSE )

Figure 3. Langmuir isotherm plots for three acidic dyes on activated carbon.

Since the molecular volume of AB80 is much smaller than that of AY117, the molecular mobility of AB80 in solution and in the adsorbent is faster and therefore responsible for the higher adsorption capacity of AB80. Analysis of the Isotherm Data. In this work, the optimum isotherm parameters in four isotherm equations were found by minimizing the difference between the

(qe,cal - qe,exp)2i ∑ i)1

(29)

Four different isotherm equations, namely, the Langmuir, Freundlich, Redlich-Peterson, and Sips equations, were tested for the equilibrium adsorption of three acidic dyes (AB80, AR114, and AY117) on activated carbon, and the data were compared with each other. Table 3 shows the results of different isotherm parameters and SSE values for the Langmuir, Freundlich, Redlich-Peterson, and Sips equations. Figures 4-6 show a comparison of the experimental points with the theoretical Langmuir, Freundlich, Redlich-Peterson, and Sips isotherm equations obtained using the best-fit analysis. From the figures, only the Freundlich equation does not fit well for the three acidic dye/carbon systems; the other three isotherms are able to adequately correlate the equilibrium behaviors, and all three acidic dyes show little or no significant difference between the Langmuir, Redlich-Peterson, and Sips isotherms. It is difficult to confirm which equation provides the best correlation of the data from these figures. Therefore, the SSE values of each equation can be used to compare the fitting of the experimental data. It was found that the Redlich-Peterson sorption isotherm gives the lowest SSE values for all three acidic dye systems compared to the other three isotherm equations (see Table 3).

9652


Choy et al.

Figure 4. Comparison of theoretical isotherm curves with experimental results for Acid Blue 80 on activated carbon.

Figure 5. Comparison of theoretical isotherm curves with experimental results for Acid Red 114 on activated carbon.

Table 3. Sorption Isotherm (Langmuir, Freundlich, Sips, and Redlich-Peterson) Parameters and SSE Values for AB80, AR114, and AY117 in Single-Component Systems AB80

AR114

AY117

14.904 119.24 0.1250 1.348

40.072 182.86 0.2191 2.894

Freundlich Isotherm aF [(dm3)bF (mmol)1-bF g-1] 0.4526 0.2379 bF 0.2878 0.2903 SSE value (10-4) 35.363 4.805

0.4488 0.2829 21.839

Sips Isotherm KS [(dm3)bS (mmol)1-bS g-1] 19.23 aS (dm3 mmol-1)bS 74.34 bS 0.9438 SSE value (10-4) 1.346

5.014 36.55 0.7969 0.8710

14.96 63.76 0.8279 1.482

Redlich-Peterson Isotherm KR (dm3 g-1) 28.319 20.705 aR (dm3 mmol-1)β 103.57 131.21 β 0.9646 0.8986 SSE value (10-4) 1.088 0.538

55.402 200.26 0.9097 1.191

KL (dm3 g-1) aL (dm3 mmol-1) qm (mmol g-1) SSE value (10-4)

Langmuir Isotherm 25.683 101.26 0.2536 1.524

Although the Langmuir and Sips equations do not give the lowest SSE values in the correlation, they still give very low SSE values, close to the SSE values from the Redlich-Peterson equation, for all three acidic dye systems. The Langmuir and Sips equations still show an excellent fit with the acidic dye experimental data for the sorption of divalent acidic dyes onto activated carbon. The major benefit for using the Langmuir and Sips equations to describe the acidic dye/carbon adsorption system is that they can produce an analytical solution for the spreading pressure of the IAST model, while the Redlich-Peterson equation cannot. Incorporating the Langmuir or Sips isotherm in the IAST can simplify the model calculation; a “lumped” numerical method must be adopted when applying the Redlich-Peterson isotherm in the IAST model. A detailed methodology of the IAST solution was presented in the theory section, and a more detailed discussion of the effect of the isotherm type on the IAST will be presented in the multicomponent isotherm section.

Figure 6. Comparison of theoretical isotherm curves with experimental results for Acid Yellow 117 on activated carbon.

Multicomponent Isotherm Studies. Three bisolute equilibrium isotherms have been determined for the sorption of Acid Blue 80 (AB80), Acid Red 114 (AR114), and Acid Yellow 117 (AY117) onto activated carbon. This present study is based on the application of several common single-component isotherms with the IAST to predict the multicomponent experimental isotherm data. Ideal Adsorbed Solution Theory (IAST). The isotherm data for the binary systems are predicted from the single-component dye sorption data alone. Since the IAST is incorporated with the single-component isotherm equation to predict multicomponent systems, a detailed analysis has been carried out to investigate the influence of different single-component isotherm equations on the results of IAS model simulations. The Langmuir, Freundlich, Redlich-Peterson, and Sips equations were used to predict the binary-component equilibria. Figures 7 and 8 show the comparison between the experimental data and the predictions based on the IAST model with different isotherm equations for the AB80 + AR114 binary-component system. Visually, the IAST-


Figure 7. IAST model analysis of Acid Blue 80 in the AB80 + AR114 binary system.

Langmuir, Vol. 20, No. 22, 2004 9653

Figure 9. IAST model analysis of Acid Red 114 in the AY117 + AR114 binary system. Table 4. IAST Model Evaluation Using the SSE Function SSE values (10-4) calculated from different IAST models

IAST-F IAST-L IAST-S IAST-RP

Figure 8. IAST model analysis of Acid Red 114 in the AB80 + AR114 binary system.

Freundlich (IAST-F) model provides the worst fit for both acidic dye systems. For the AR114 dye, the correlation between the predicted data and the experimental data is poor; the IAST-F model overpredicts the equilibrium concentration, Ce, of the AR114 dye. For the AB80 dye, although there is some similarity between the shape of the predicted binary isotherm and the experimental data, the model significantly underpredicts the equilibrium concentration of the AB80 dye; the model only produces a good fit to the experimental data for the AB80 dye in the low equilibrium solute concentration region, suggesting a much greater affinity than that of the AB80 dye for the surface sites. The considerable and increasing discrepancy between the model predictions and the experimental measurements indicates that the IAST-F model is not suitable for modeling this binary system beyond Ce values of 0.003 mmol dm-3. In terms of predicting the general shapes of the other two isotherms, the IAST-Langmuir (IAST-L) model affords a significant improvement over the IAST-F model pairing. For the AR114 dye, the IAST-L model produces an

AB80 + AR114

AB80 + AY117

AR114 + AY117

AB80

AR114

AB80

AY117

AR114

AY117

7.650 10.59 6.618 5.150

8.646 68.24 10.17 4.315

0.322 0.467 0.041 0.037

0.179 1.002 0.179 0.058

1.597 23.62 1.771 0.906

19.48 20.23 18.92 17.06

extremely good fit to the experimental data for AR114 in equilibrium solute concentrations of up to 0.02 mmol dm-3. However, the error at higher sorption capacities is again both significant and increasing; the IAST-L model overpredicts the equilibrium concentration of the AR114 dye at the high solid-phase concentration region, and the sorption capacity of the AR114 dye is underpredicted in the IAST model. Again, the equilibrium concentration of the AB80 dye is underpredicted by the IAST-L model, although not by as much as the IAST-F model. The IAST-Sips (IAST-S) and IAST-Redlich-Peterson (IAST-RP) models produce very similar results to those of the IAST-L model in both acidic dyes. The comparison of the SSE values of three acidic dyes in three binarycomponent systems is shown in Table 4. The IAST-RP results are marginally closer to the experimental data than the IAST-L and IAST-S results for the AB80 and AR114 dyes in the AB80 + AR114 binary system. The comparison between the experimental data and the predictions based on the IAST model with different isotherm equations for the AY117 + AR114 binarycomponent system is shown in Figures 9 and 10. Visually, the results in the AY117 + AR114 binary system are very similar in shape to those in the AB80 + AR114 system; the AY117 dye substitutes for the role of the AB80 dye in the binary-component system. Similarly, the equilibrium concentration of the AR114 dye is overpredicted by the IAST-F model. The IAST models with the other three isotherms, the Langmuir, Sips, and Redlich-Peterson isotherms, also produce a good fit for the AR114 dye to the experimental data at equilibrium solute concentrations up to 0.027 mmol dm-3, and then, the models start to underpredict the equilibrium concentration at high sorption capacities where the error at higher solid-phase concentrations is

9654


Figure 10. IAST model analysis of Acid Yellow 117 in the AY117 + AR114 binary system.

Figure 11. IAST model analysis of Acid Blue 80 in the AB80 + AY117 binary system.

again both significant and increasing. From Table 4, incorporating the Redlich-Peterson equation in the IAST model still gives the lowest SSE values compared with those of the other isotherm equations. It means the IASTRP model predicts the best binary results in the AR114 + AY117 binary system. Comparing Figures 7 and 10, it can be seen that the sorption behaviors of the AY117 and AB80 dyes are very similar in the binary-component system when mixed with the AR114 dye. The IAST models may provide a good prediction in the AB80 + AY117 binary dye mixture if two dyes have similar sorption behaviors, as they have little adsorbate-adsorbate interaction between each other. The results of the AB80 + AY117 binary system are shown in Figures 11 and 12; the IAST-RP, IAST-L, and IAST-S models produce a good fit to the experimental data for both acidic dye systems. There is a small deviation between the predicted data and the experimental data at the higher solid-phase concentrations, but the error is very small. Although the prediction by the IAST-F model is worse than those of the other three IAST models, it still gives

Choy et al.

Figure 12. IAST model analysis of Acid Yellow 117 in the AB80 + AY117 binary system.

a close fit between the predicted dye concentrations and the experimental data compared with the other two binary dye systems. It implies that the AB80 + AY117 dye mixture is much closer to an ideal solution; the adsorbentadsorbate interaction in this binary system is limited. For both dyes, the results for the IAST-RP set are marginally closer to the experimental data than those of the IAST-L and IAST-S sets. The SSE values of the AB80 + AY117 system with different isotherm equations are shown in Table 4. Table 4 presents the IAST model prediction with experimental data using the SSE function for all three binary dye systems. From examining the error analysis, it is apparent that, irrespective of the method used to calculate this error, the IAST-RP model predicts the bestfit data and the lowest SSE in all three binar-component dye systems; this is consistent with the results in the single-component system. Quality of Binary Isotherm Correlations. The discrepancies in the quality of the binary equilibrium isotherms between the theoretical IAST prediction and the experimental results are probably due to the differences in the nonideal behaviors of the binary dye mixtures. This can be interpreted from the single and binary isotherm data. The IAST is based on the ideal adsorbed solute theory, which implies that the solutes in binary or mulitcomponent mixtures behave independently of each other, without competition, interaction, or displacement effects. This type of behavior is well classified by the assumptions implicit in the Langmuir equilibrium behavior.55 To test this behavior, the extended Langmuir isotherm can be used to compare the three binary systems. The equation is

qe,i )

0 Ce,i KL,i

1+

∑

(30)

0 aL,i Ce,i

The predictions for the AB80 + AY117, AB80 + AR114, and AR114 + AY117 mixtures by the extended Langmuir (55) Butler, J. A. V.; Ockrent, C. J. Phys. Chem. 1930, 34, 2841.


Figure 13. Extended Langmuir analysis of Acid Blue 80 and Acid Yellow 117 in the AB80 + AY117 binary system.

Langmuir, Vol. 20, No. 22, 2004 9655

Figure 15. Extended Langmuir analysis of Acid Red 114 and Acid Yellow 117 in the AR114 + AY117 binary system.

Figure 16. Dimensionless concentration isotherms as a function of the separation factor.

Figure 14. Extended Langmuir analysis of Acid Blue 80 and Acid Red 114 in the AB80 + AR114 binary system. Table 5. Extended Langmuir Model Evaluation for Three Binary Systems Using the SSE Function SSE values (10-4) AB80 + AR114 AB80 + AY117 AR114 + AY117 AB80 extended 13.92 Langmuir model

AR114

AB80

AY117

AR114

AY117

3.54

2.577

0.816

17.147

236.2

model are shown in Figures 13-15. The SSE values for the three binary systems are shown in Table 5 and indicate that the binary AB80 + AY117 system is the only system with any reasonable degree of correlation. Early work by Markham and Benton56 stated that the extended Langmuir isotherm could only be applied to solutes with similar adsorption characteristics, particu(56) Markham, E. D.; Benton I. J. Am. Chem. Soc. 1931, 53, 497.

larly affinities and equilibrium saturation capacities. This certainly applies to the present three binary systems. However, for the IAST binary predictions in Figures 7-12 and for the SSE values in Table 4, the AB80 + AY117 results are very good; in the AB80 + AR114 system, AR114 is good but AB80 is barely satisfactory; in the AY117 + AR114 system, AR114 is good but AY117 is poor. If we consider the possible deviation from ideal reversible equilibrium behavior or equal surface affinity for the adsorbent of one dye species over another, one option is to assess the relative irreversibility/reversibility characteristics of the single-component systems by comparing the solutes using the dimensionless separation factors (McKay, 1982) obtained by plotting the dimensionless solid-phase concentration, q ()qe/qmax), versus C ) Ce/ Ce,max). The plots for the three dyes are shown in Figure 16. The dimensionless separation factors (R values) are 0.022, 0.020, and 0.035 for AB80, AY117, and AR114, respectively. The separation factors of AB80 and AY117 are almost the same. Low R values provide an indicator toward strong irreversibility, thus minimizing and impeding the potential for equilibrium exchange sorption between solute molecules or ions. The very low R values indicate that all three dyes exhibit a high degree of

9656


irreversibility. However, lower separation factors are observed for AB80 and AY117 compared with AR114, thus suggesting why these two dyes are less amenable to reversible equilibrium adsorption than AR114. The better IAST fit for the AB80 + AY117 data is probably due to the lower but similar R factors of the single-component dye systems. Both of these dyes have a similar competitive affinity for the adsorption sites and similar affinities to adsorb/desorb at the sites. In both binary systems where a poor fit is observed, AR114 is a common factor. AR114 is different from the other two dyes due to its two negatively charged sodium sulfonic groups being very close to each other, as shown in Figure 1, possibly resulting in Coulombic repulsion or sterically hindered competition for the adsorption sites at the carbon particle surface. This difference in site affinity of AR114 from the other two dyes is sufficient to create nonideal solute adsorption in the binary systems containing AR114. Although other isotherms were used besides the Langmuir, Sips, Freundlich, and Redlich-Peterson isotherms, all having exponents in their expressions, these isotherms are used to better describe heterogeneous effects of the adsorbent particle surface and not interaction, competition, and exchange displacement. Consequently, although the Sips and Redlich-Peterson isotherms improved the binary system fits, it was not a significant improvement. 5. Conclusion In summary, multicomponent isotherm prediction using the IAST depends on the quality of the fit of singlecomponent parameters. It is assumed that the best-fit single-component isotherms and parameter set would produce the best-fit IAST model. The assumption is supported by the SSE values presented in Tables 3 and 4; the Redlich-Peterson isotherm has the highest correlation factors in the single-component system when compared with the Langmuir, Freundlich, and Sips isotherms. Therefore, the IAST-RP model provides the best prediction to the binary data in comparison with the IAST-F, IAST-L, and IAST-S models. The assessment of the difference in irreversibility of the dye carbon systems offers a qualitative explanation of the poorer fits in the AB80 + AR114 and AY117 + AR114 systems. Moreover, without a more detailed investigation into interaction or extending the analysis to incorporate activity coefficients or possibly separation factors, the IAST model provides

Choy et al.

a better prediction at lower solute concentrations and solidphase concentrations, since the mixture solution behavior is much closer to the ideal solution. Nomenclature aL ) Langmuir isotherm constant, dm3 mmol-1 aF ) Freundlich isotherm constant, (dm3)bF(mmol)1-bF g-1 aS ) Sips isotherm constant, (dm3 mmol-1)bS aR ) Redlich-Peterson isotherm constant, (dm3 mmol-1)β bF ) Freundlich isotherm constant, dimensionless bS ) Sips isotherm constant, dimensionless C ) liquid-phase concentration, mmol dm-3 C0 ) initial liquid-phase concentration, mmol dm-3 Ce ) equilibrium liquid-phase concentration, mmol dm-3 dp ) diameter of sorbent, cm Dmol ) molecular diffusion coefficient, cm2 s-1 KL ) Langmuir isotherm constant, dm3 g-1 KS ) Sips isotherm constant, (dm3)bS(mmol)1-bS g-1 KR ) Redlich-Peterson isotherm constant, dm3 g-1 M ) weight of adsorbent, g qe ) equilibrium solid-phase concentration, mmol g-1 qT ) total equilibrium solid-phase concentration, mmol

g-1 qm ) monolayer capacity of Langmuir equation, mmol g-1 s ) mole fraction of sorbate in the adsorbed phase, dimensionless SSE ) sum of the squares of the error, dimensionless V ) liquid-phase volume, dm3 Greek Letters

β ) Redlich-Peterson isotherm constant, dimensionless ψ ) spreading pressure, dimenionless λmax ) maximum absorption wavelength, nm Superscripts 0 ) single component Subscripts cal ) value predicted/calculated by model exp ) experiment i ) ith component in a multisolute system j ) jth component in a multisolute system

Acknowledgment. One of the authors, K.K.H. Choy, is grateful to DAG and RGC, Hong Kong SAR, for the provision of financial support during this research program. LA040048G

Single and Multicomponent Equilibrium Studies for the Adsorption of

Recommend Documents