Ind. Eng. Chem. Res. 2003, 42, 1093-1097
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The Double Selectivity Model for the Description of Ion-Exchange Equilibria in Zeolites† Francesco Pepe,*,‡ Domenico Caputo,§ and Carmine Colella§ DICMA (Dipartimento di Ingegneria Chimica, Mineraria e delle Tecnologie Ambientali), Alma Mater Studiorum Universita` di Bologna, V.le Risorgimento 2, 40136 Bologna, Italy, and DIMP (Dipartimento di Ingegneria dei Materiali e della Produzione), Universita` di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli, Italy
A thermodynamic model has been proposed for the description of cation-exchange equilibria on zeolites. The model is based on the hypothesis that zeolites can be modeled as composed by two different groups of cation sites available for ion-exchange reactions, each characterized by its own selectivity toward any given exchange reaction, and each having ideal behavior concerning the zeolite-cation interaction. The model has been tested by comparing its previsions with equilibrium experimental data, relative to uni-divalent and uni-univalent exchange reactions on clinoptilolite. In general, the comparison between model and experimental results was satisfactory, and in the majority of the cases, the model was capable of reproducing the experimental data obtained at different total normalities in solution. A reasonable agreement was also found between the equilibrium constants predicted by the model and those evaluated on the basis of the experimental data. Introduction Zeolites are crystalline, hydrated aluminosilicates of alkaline and alkaline earth metals, with a porous structure, characterized by cavities and interconnected channels. Due to their chemical and structural characteristics, these materials are suitable for ion exchange and for selective adsorption processes.1 Furthermore, natural zeolites are readily available in many areas of the world at relatively low costs and have been successfully used for ion-exchange applications such as removal of ammonium and heavy metals from wastewaters, treatment of low-level radioactive wastes, and remediation of sites contaminated with fission products.2 The evaluation of the ion-exchange properties of a zeolite is based on the collection of equilibrium data relative to the particular exchange reaction. On the basis of these data, the main thermodynamic parameters, such as the equilibrium constant K and the excess of Gibbs free energy ∆G°, can then be calculated using a suitable model. The use of a reliable model for the exchange process is particularly important when one needs to predict either the ion-exchange behavior of the zeolite for varying compositions of the aqueous phase or the equilibrium behavior of multicomponent systems based on experimental data relative to binary systems. Many works have dealt with modeling the equilibria of the ion-exchange reactions in zeolites. Recently, Pabalan and Bertetti1 presented state of the art relative to the thermodynamics of ion-exchange processes on chabasite, phillipsite, clinoptilolite, and many other * Corresponding author. Present address: Dipartimento di Ingegneria, Universita` del Sannio, C.so Garibaldi 107, 82100 Benevento, Italy. Tel: +39-0824-305872. Fax: +39-0824305841. E-mail:
[email protected]. † An earlier version of this paper was presented at “Chemical Reactor Engineering VIII: Novel Reactor Engineering for the New Millenium”, June 24-29, 2001, Barga, Italy. ‡ Alma Mater Studiorum Universita ` di Bologna. § Universita ` di Napoli Federico II.
natural zeolites. Following an approach that can be traced back to the early works of Vanselow3 and Gaines and Thomas,4 they considered both phases as solutions, which are in general characterized by nonideal behavior. In particular, they proposed describing such nonidealities by means of the Pitzer model5 concerning the aqueous phase and the Margules equation concerning the solid phase. The description of the exchanger as a solid solution with nonideal behavior has often been used when dealing with ion-exchange processes on polymeric resins. This approach was proposed by Boyd et al.,6 who showed that if solid-phase activity coefficients are neglected when describing the solution equilibria, thermodynamically inconsistent results can be obtained. Later, Freeman7 suggested describing the nonideal behavior of the solid solution by incorporating the techniques developed for the evaluation of liquid-phase fugacity coefficients when dealing with vapor-liquid equilibria. Smith and Woodburn,8 Shallcross et al.,9 Allen et al.,10 and Ioannidis et al.11 suggested in particular using the Wilson equation12 to describe the solid-phase nonideality. On the other hand, Barrer and co-workers12-15 (also see Maes and Cremers16) suggested focusing the attention on the fact that different classes of sites are present in the zeolitic structure and are available for the exchange reactions. As shown by Barrer and Klinowski,17 models of this kind are very flexible and are capable of describing almost any kind of exchange isotherm. A model based on this approach was recently proposed by Melis et al.18,19 to describe the thermodynamics of ion exchange on polymeric resins. According to their model, a distribution of classes of sites exists in the resins, where each class has ideal behavior, and is characterized by its own exchange selectivity toward the cations involved in the reactions. Therefore, the mass action law can be used to describe the zeolite-solution equilibrium, with the overall behavior depending on the
10.1021/ie020512h CCC: $25.00 © 2003 American Chemical Society Published on Web 02/01/2003
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relative amount of the different sites available. The authors showed that this model is particularly well suited for the prevision of multicomponent equilibrium conditions from binary data since it requires a smaller amount of binary data than the “solid solution” models.18 Furthermore, Melis et al.19 showed that the model can be applied to the description of the dynamics of multicomponent exchange processes. A similar approach has been more recently followed by Bricio et al.20 for describing exchange equilibria involving different cations (H+, Na+, K+, Ca2+, Mg2+, and NH4+) on styrenedivinylbenzene resins. The aim of the present work is to propose a model for the description of equilibrium conditions in cationicexchange processes involving zeolites. The model, derived from the one proposed by Melis et al.,18,19 is based on the hypothesis that two different types of sites are present in the zeolite. Assuming that the zeolite-cation interactions are ideal, for any given exchange reaction, the behavior of each type of cation site is characterized by only one equilibrium constant. The model describes the overall behavior of the zeolite by combining the results relative to the two types of sites and by taking into account the relative amount of each type of sites. Furthermore, the reliability and the flexibility of the model proposed will be discussed by comparing its previsions with a large set of experimental data previously published.21,22 Thermodynamic Model The cation exchange between a solution containing AzA+ cations and a zeolite containing BzB+ cations can be described by means of the following reaction:
zBAzA+ + zABLzB a zABzB+ + zBALzA
(1)
in which L is a portion of zeolite framework holding unit negative charge21 and zA and zB are the valences of the two cations. If, for example, the Ca2+/Na+ exchange is considered, reaction 1 reduces to the following: 2+
+
+ 2NaL a 2Na + CaL2
zBAzA+ + zAB(L2)zB a zABzB+ + zBA(L2)zA
K2(A,B) (4)
where Li (i ) 1, 2) represents the portion of “type i” cation sites holding unit negative charge and K1(A,B) and K2(A,B) are the equilibrium constants for the AzA+/BzB+ exchange reactions on cation sites “1” and “2”, respectively. The equilibrium equations corresponding to the two reactions (3) and (4) are the following:
[BzB+]zA[A(Li)zA]zB γzBA
Ki(A,B) )
i ) 1,2
[AzA+]zB[B(Li)zB]zA γzAB
(5)
in which γA and γB are the activity coefficients for the cations AzA+ and BzB+. Since the total number of equivalents, both in solution and in the solid, is constant during the exchange process, it is useful to express the concentrations that appear in eq 5 as equivalent fractions, rather than moles. Therefore, the two molar concentrations [AzA+] and [BzB+] can be expressed as follows:
[AzA+] )
NEA(s)
[BzB+] )
zA
NEB(s) zB
)
N(1 - EA(s)) zB
(6)
where N is the total normality in solution and EA(s) and EB(s) are the equivalent fractions of AzA+ and BzB+ cations in the solution phase. Similarly, in the solid phase, considering that two different groups of sites are taken into account, it is possible to write:
[A(Li)zA] )
qiEA(zi) zA
[B(Li)zB] )
qiEB(zi) zB
)
qi(1 - EA(zi)) zB
i ) 1,2 (7)
and considering the total number of cation sites,
EA(z) ) p1EA(z1) + p2EA(z2)
EB(z) ) p1EB(z1) + p2EB(z2)
(2)
(8)
The main hypothesis of the model proposed here is that two different groups of sites are present in the zeolite, arbitrarily labeled as “type 1” and “type 2”. However, since in general more than two groups of cation sites are actually available for exchange reactions, it is important to recognize that these two groups are actually to be intended as “pseudo-groups”, lumping different “real” groups of sites. Sites “1” and “2” are assumed to represent two fractions, p1 and p2, of the overall cation-exchange capacity Q. Therefore, the exchange capacity attributable to site “1” is equal to q1 ) p1Q and that attributable to site “2” is equal to q2 ) p2Q, with p1 + p2 ) 1. Furthermore, it is assumed that each site undergoes the exchange reactions independently of the other and that the deviations from ideality in the zeolite-cation interactions are negligible so that no activity coefficient is required to describe the behavior of the solid phase. Following these hypotheses, for the exchange process AzA+/BzB+ mentioned above, the following two reactions are to be considered rather than eq 1:
In these two equations EA(zi) and EB(zi) are the fractions of Li cation sites exchanged with AzA+ and BzB+ cations respectively (i ) 1,2), whereas EA(z) and EB(z) are the corresponding fractions evaluated with reference to the overall number of sites, and therefore to the total cationexchange capacity Q. Once eqs 6 and 7 are substituted into the equilibrium equation (5), the following expressions are obtained in which cation AzA+ has arbitrarily been taken as a reference:
Ca
z BA
zA+
+ zAB(L1)zB a zAB
zB+
+ zBA(L1)zA
K1(A,B) (3)
()
N Ki(A,B) ) (Γ) qi
zA-zB(1
- EA(s))zA(EA(zi))zB
(EA(s))zB(1 - EA(zi))zA
i ) 1,2 (9)
Here, Γ is the following combination of activity coefficients γA and γB:
Γ ) (γB)zA/(γA)zB
(10)
which, once N and EA(s) are assigned, can be computed by means of a “standard” thermodynamic model, such as the Pitzer model.5
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Equations 5-10 show that once a set of experimental data relative to a binary exchange isotherm is available in the form of couples of equivalent fractions in solution and in the zeolite phase (EA(s)/EA(z)), the model parameters can be evaluated. Following the approach of Rodriguez and co-workers,23,24 the parameters to be evaluated were considered to be the two thermodynamic constants K1(A,B) and K2(A,B), plus the fraction p1 of “type 1” sites. It is important to observe that the value of p1 does not depend on the couple AzA+/BzB+, but rather is characteristic of the zeolite under consideration. Results and Discussion With the aim of verifying the reliability of the model, a comparison with data taken from the literature was carried out. In particular, the data presented by Pabalan21 and Pabalan and Bertetti22 were considered. These authors studied the thermodynamics of a number of binary cationic-exchange reactions (namely, Ca2+/ Na+, K+/Na+, Sr2+/Na+, Ca2+/K+, and Sr2+/K+) on clinoptilolite. They carried out a large number of experiments on the equilibrium conditions between the zeolite and aqueous solution by varying the solution composition and using either Cl- or NO3- as counterions. They pointed out that the processes considered could in all cases be considered as “true” ion-exchange reactions (i.e., with a negligible influence of other phenomena such as adsorption). They found that the cationexchange capacity of the zeolite used was Q ) 2.04 equiv/kg. Furthermore, they presented the ion-exchange isotherms relative to T ) 25 °C and total normalities N ) 0.005, 0.05, and 0.5 equiv/L for the couples Ca2+/Na+, K+/Na+, and Sr2+/Na+, and those relative to T ) 25 °C and total normality N ) 0.05 equiv/L for the couples Ca2+/K+ and Sr2+/K+. The estimation of the most likely values for the characteristic parameters of the model (namely, the fraction of “type 1” sites, p1, and the five couples of equilibrium constants, K1 and K2) was performed by means of a nonlinear regression. Only the data relative to N ) 0.05 equiv/L and to solutions in which Cl- was present as a counterion were taken into account. The objective function (U) was chosen to be the sum of the absolute deviations between calculated and experimental equivalent fractions in the zeolite,
U)
m
∑ i)1
|
|
exp (EI(z))i - (EI(z) )i exp (EI(z) )i
(11)
in which m is the total number of experimental points. The Pitzer model5 was used to calculate the activity coefficients, and therefore Γ. Except for the uniunivalent system Na+/K+ (for which Γ was very close to 1, regardless of the value of x), in general, values of Γ ranging between 1.4 and 1.6 were obtained. This indicates that the solution has remarkably nonideal behavior and that the use of a thermodynamic model to properly take into account this nonideality is fully justified. The regression indicated that the minimum value of U was obtained for p1 ) 0.30. The corresponding values for the five couples (K1, K2) at p1 ) 0.30 are reported in Table 1. The corresponding predicted isotherms, together with the experimental values obtained by Pabalan21 and Pabalan and Bertetti,22 are reported
Figure 1. Ca2+/Na+ exchange isotherms on clinoptilolite at T ) 25 °C with different total normalities. Table 1. Values of the Equilibrium Constants at T ) 25 °C (p1 ) 0.30) K1 Ca2+/Na+ Ca2+/K+ K+/Na+ Sr2+/Na+ Sr2+/K+
K2
8.46 × 10-3 1.15 1.52 × 10-2 3.63 × 10-5 1.99 65.3 3.38 × 10-3 3.30 -2 6.32 × 10 5.89 × 10-4
Kave ) (K1)p1(K2)p2
Kexp
0.263 2.22 × 10-4 22.9 0.419 2.39 × 10-3
0.205 3.03 × 10-4 24.3 0.338 3.12 × 10-3
in Figures 1-4 in which the equivalent fractions of cations entering the zeolite phase are plotted versus the equivalent fractions of the same cations in the solution phase. Figures 1-4 show that, in general, a good agreement exists between model and experimental results and that this agreement is kept even when the total normality is varied by a factor of 10. Since cations having rather different characteristics for what concerns size and hydration were taken into account, it appears possible to conclude that, at least in the conditions considered here, the lumping procedure, which allowed the two groups of sites “type 1” and “type 2” to be individuated, is acceptable. In particular, for the systems Ca2+/Na+ and Sr2+/Na+ (Figures 1 and 2, respectively), the couples (K1, K2) found at N ) 0.05 equiv/L led to average absolute deviations of 8.2% and 3.6%, respectively. The quality of the fit slightly decreased when K1 and K2 were used to predict the curves relative to N ) 0.5 equiv/L (average absolute deviations of 12.1% and 8.8%, respectively) and, at least for the system Ca2+/Na+, to N ) 0.005 equiv/L (average absolute deviation of 12.4%). On the other hand, for the system Sr2+/Na+ at N ) 0.005 equiv/L (top curve of Figure 2), a worst situation was encountered, with an average absolute deviation of 20.2%, probably due to some nonideal behavior in the solid phase. For the systems Ca2+/K+ and Sr2+/K+ (Figure 3), for which data were only available at N ) 0.05 equiv/L, it was possible to individuate two couples (K1, K2) leading to average absolute deviations of 8.7% and 9.6%. Eventually, a better fit was obtained for the K+/Na+ exchange
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Figure 2. Sr2+/Na+ exchange isotherms on clinoptilolite at T ) 25 °C with different total normalities.
Figure 4. K+/Na+ exchange isotherm on clinoptilolite at T ) 25 °C with different total normalities.
the following expression to the experimental values of EA(z) vs EA(s):4
ln(Kexp) )
∫01ln(Kv) dEA(z)
(12)
where KV is the Vanselow selectivity coefficient, which is, in turn, given by the following expression:
KV )
[BzB+]zA[A(L)zA]zB γBzA [AzA+]zB[B(L)zB]zA γAzB zA zB N zA-zB(1 - EA(s)) (EA(z)) (13) Q (E )zB(1 - E )zA
()
)Γ
Figure 3. Ca2+/K+ and Sr2+/K+ exchange isotherms on clinoptilolite at T ) 25 °C and total normality of 0.05 equiv/L.
(Figure 4), for which data were available at N ) 0.005, 0.05, and 0.5 equiv/L. For what concerns this system, it is important to observe that, in practice, the total solution normality plays no role. Indeed, for zA ) zB, N vanishes from eq 9; furthermore, it turned out that the value of the combination of activity coefficients Γ was very close to 1 not only regardless of the value of x, as indicated above, but also regardless of the value of N. Therefore, a single curve was capable of describing all the available experimental data, and the corresponding average absolute deviation was 5.4%. A further comparison between model and experimental results is reported in Table 1. There, for the five exchange reactions taken into account, the values of Kave, defined as the weighted average between K1 and K2 [Kave ) (K1)p1(K2)p2], are reported together with the experimental values of the equilibrium constants at 25 °C, Kexp. The values of Kexp were obtained by applying
A(s)
A(z)
Table 1 shows that there is a good agreement between Kave and Kexp. Once again, the fact that the equilibrium constants provided by the model are reasonably close to the values obtained from the experimental values can be considered as proof of the model reliability. Another check of the validity of the thermodynamic constants obtained can be made by applying to such constants the so-called “triangle rule”: according to this rule, if all the possible binary exchanges involving a given triplet of cations AzA+/BzB+/CzC+ are taken into account, it must be:
R ) [K(A,B)]zC[K(B,C)]zA[K(C,A)]zB ) 1
(14)
In the situation considered here, the data relative to two such triplets are available, namely, Ca2+/Na+/K+ and Sr2+/Na+/K+. For the first one, considering the Kave’s, R ) 2.28 is obtained, against a value of 1.15 obtained considering the Kexp’s. Similarly, for the triplet Sr2+/Na+/K+, the Kave’s give R ) 0.334, against a value of 0.183 obtained considering the Kexp’s. The fact that, in both cases, the value of a is reasonably close to 1 can be taken as a further indication of the reliability of the results obtained. Conclusions A thermodynamic model has been proposed, aimed at describing cation-exchange equilibria on natural
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zeolites. The model is based on the hypothesis that zeolites can be modeled as composed by two different groups of sites available for cationic-exchange reactions, each characterized by its own selectivity and each having ideal behavior concerning the zeolite-cation interaction. The model has been compared with some experimental data available in the literature21,22 relative to ion-exchange reactions on clinoptilolite, and concerning the couples Na+/Ca2+, K+/Na+, Sr2+/Na+, Ca2+/K+, and Sr2+/K+. The comparison showed that the model is capable of providing data in good agreement with the experimental results. Furthermore, the model allowed the evaluation of the equilibrium constants for the five exchange reactions. Also, for such constants, the comparison with their experimental values, obtained by means of the equation proposed by Gaines and Thomas,4 was rather satisfactory. List of Symbols EI(s) ) equivalent fraction of cation I in solution EI(z) ) equivalent fraction of cation I in the zeolite K ) equilibrium constant m ) number of experimental points N ) total normality in solution, equiv/L pi ) fraction of sites of type i Q, q ) cation-exchange capacity, equiv/kg U ) objective function zI ) valence of cation I Greek Symbols R ) combination of equilibrium constants defined in eq 14 Γ ) combination of activity coefficients defined in eq 10 γI ) activity coefficient of cation I Subscripts 1, 2 ) relative to sites of “type 1” and of “type 2” ave ) averaged value exp ) experimental value
Literature Cited (1) Pabalan, R. T.; Bertetti, F. P. Cation exchange properties of natural zeolites. In Natural Zeolites: Occurrence, Properties, Applications; Bish, D. L., Ming, D. W., Eds.); Reviews in Mineralogy and Geochemistry; Mineralogical Society of America: Washington, D.C., 2001; Vol. 43, p 453. (2) Colella, C. Environmental applications of natural zeolitic materials based on their ion exchange properties. In Natural Microporous Materials in the Environmental Technology; Misaelides, P., Macasek, F., Pinnavaia, T. J., Colella, C., Eds.; NATO Sciences Series, Series E: Applied Sciences 362; Kluwer: Dordrecht, The Netherlands, 1999; p 207. (3) Vanselow, A. P. Equilibria of the base-exchange reactions of bentonites, permutites soil colloides and zeolites. Soil Sci. 1932, 33, 95. (4) Gaines, G. L., Jr.; Thomas, H. C. Adsorption studies on clay minerals. II: a formulation of the thermodynamics of exchange adsorption. J. Chem. Phys. 1953, 21, 714. (5) Pitzer, K. S. Ion interaction approach: theory and data correlation. In Activity Coefficients in Electrolyte Solutions; Pitzer, K. S., Ed.; CRC Press: Boca Raton, FL, 1991; p 75.
(6) Boyd, G. E.; Schubert, J.; Adamson, A. W. The exchange adsorption of ions from aqueous solutions by organic zeolites. I: ion exchange equilibria. J. Am. Chem. Soc. 1947, 69, 2818. (7) Freeman, J. Thermodynamics of binary ion exchange systems. Chem. Phys. 1961, 35, 189. (8) Smith, R. P.; Woodburn, E. T. Prediction of multicomponent ion exchange equilibria for the ternary system SO42--NO3--Clfrom data on binary systems. AIChE J. 1978, 24, 577. (9) Shallcross, C. D.; Hermann, C. C.; McCoy, J. B. An improved model for the prediction of multicomponent ion exchange equilibria. Chem. Eng. Sci. 1988, 43, 279. (10) Allen, R. M.; Addison, P. A.; Dechapunya, A. H. The characterization of binary and ternary ion exchange equilibria. Chem. Eng. J. 1989, 40, 151. (11) Ioannidis, S.; Anderko, A.; Sanders, S. J. Internally consistent representation of binary ion exchange equilibria. Chem. Eng. Sci. 2000, 55, 2687. (12) Wilson, G. M. Vapor-Liquid Equilibrium XI. A New Expression for the Expansion for the Excess Energy of Mixing. J. Am. Chem. Soc. 1964, 86, 127. (13) Barrer, R. M.; Meier, W. M. Exchange equilibria in a synthetic crystalline exchanger. Trans. Faraday Soc. 1959, 55, 130. (14) Barrer, R. M.; Munday, B. M. Cation exchange in the synthetic zeolite K-F. J. Chem. Soc. (A) 1971, 2914. (15) Barrer, R. M.; Klinowski, J.; Sherry, H. S. Zeolite exchangers. Thermodynamic treatment when not all ions are exchangeable. J. Chem. Soc., Faraday Trans. 2 1973, 69, 1669. (16) Barrer, R. M.; Klinowski, J. Cation exchangers with several groups of sites. J. Chem. Soc., Faraday Trans. 1 1979, 75, 247. (17) Maes, A.; Cremers, A. Site group interaction effects in zeolite-Y. Part 2: Na-Ag selectivity in different site groups. J. Chem. Soc., Faraday Trans. 1 1978, 75, 136. (18) Barrer, R. M.; Klinowski, J. Ion exchange involving several groups of homogeneous sites. J. Chem. Soc., Faraday Trans. 1 1972, 68, 73. (19) Melis, S.; Cao, G.; Morbidelli. M. A new model for the simulation of ion exchange equilibria. Ind. Eng. Chem. Res. 1995, 34, 3916. (20) Melis, S.; Markos, J.; Cao, G.; Morbidelli, M. Ion-exchange equilibria of amino acids on a strong acid resin. Ind. Eng. Chem. Res. 1996, 35, 1912. (21) Bricio, O. J.; Coca, J.; Sastre, H. Modeling equilibrium isotherms for styrene-divinylbenzene ion-exchange resins. Chem. Eng. Sci. 1998, 53, 1465. (22) Pabalan, R. T. Thermodynamics of ion exchange between clinoptilolite and aqueous solutions of Na+/K+ and Na+/Ca2+. Geochim. Cosmochim. Acta 1994, 58, 4573. (23) Pabalan, R. T.; Bertetti, F. P. Experimental and modeling study of ion exchange between aqueous solutions and the zeolite mineral clinoptilolite. J. Sol. Chem. 1999, 28, 367. (24) Valverde, J. L.; De Lucas, A.; Rodriguez, J. F. Comparison between heterogeneous and homogeneous mass action models in the prediction of ternary ion exchange equilibria. Ind. Eng. Chem. Res. 1999, 38, 251. (25) De Luca, A.; Valverde, J. L.; Romero, M. C.; Gomez, J.; Rodriguez, J. F. The ion exchange equilibria of Na+/K+ in nonaqueous and mixed solvents on a strong acid cation exchanger. Chem. Eng. Sci. 2002, 57, 1943.
Received for review July 12, 2002 Revised manuscript received December 9, 2002 Accepted December 20, 2002 IE020512H
