Langmuir 2007, 23, 1227-1233
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Cesium Uptake from Aqueous Solutions by Bentonite: A Comparison of Multicomponent Sorption with Ion-Exchange Models Z. Klika,*,† L. Kraus,† and D. Vopa´lka‡ Department of Analytical Chemistry and Material Testing, VSˇ B-Technical UniVersity OstraVa, 17 listopadu 15, 708 33 OstraVa-Poruba, Czech Republic, and Department of Nuclear Chemistry, Czech Technical UniVersity in Prague, Beˇ hoVa´ 7, 115 19 Prague 1, Czech Republic ReceiVed July 18, 2006. In Final Form: October 23, 2006 The removal of cesium from concentrated aqueous solutions into Ca/Mg-bentonite for a wide range of bentoniteto-water (m/V) ratios was studied experimentally and theoretically. Using the batch technique, the equilibrium of Cs uptake was measured. The nonlinear character of cesium sorption substantially influenced by the m/V ratio was observed. The experimental data were evaluated using the multicomponent Langmuir isotherm and an ion-exchange model based on the ion-exchange reaction between Cs+ and M2+ (Ca2+/Mg2+) initially sorbed on bentonite. Constants k1,Cs ) 0.521 mmol‚g-1, k2,Cs ) 968 L‚mol-1, and k2,M ) 592 L‚mol-1 were obtained for Cs uptake described by multicomponent Langmuir isotherm. For the ion-exchange model, the thermodynamic equilibrium constant K ) 75.5 mL‚g-1 with a standard deviation of sK ) 17.4 mL‚g-1 was determined. Using the t test, the calculated data of multicomponent Langmuir and ion-exchange isotherms were fit to experimental data, and the best agreement was obtained for the ion-exchange model. The results show that Cs uptake by bentonite could be substantially decreased in systems with a high bentonite-to-water (m/V) ratio as a consequence of the presence of desorbed divalent cations in the liquid phase.
Introduction Smectite minerals, usually present in bentonites, sediments and/or soils, sorb cesium and many other metal cations present in aqueous solution very well. The metal cations are very easily ion exchanged with hydrated cations Na+, K+, Ca2+, and Mg2+ present in the interlayer of the smectites. A number of studies have focused on the retention of radioactive Cs nuclides (137Cs and 135Cs) using smectites1-3 and/or bentonite.4-7 The results from the batch method are mostly used for the construction of equilibrium isotherms (Cs retained by the solid phase in relation to the equilibrium concentration of Cs in aqueous solution). Cesium removal from aqueous solutions by montmorillonite or bentonite is usually interpreted as a sorption process; therefore, Langmuir, Freundlich, and Dubinin-Radushkevitch isotherms are used.6,8 The fit of the adsorption isotherm of solutes onto solid surfaces in solution systems is not often favorable; therefore, some improvements have been suggested. For example, for the sorption of Cs and Sr on bentonite, Liang et al.9 proposed a modified two-stage Freundlich sorption model. The sorption model (qCs ) KicCs1/ni, where qCs is the adsorbed equilibrium amount of Cs and cCs is the equilibrium concentration of Cs in * Corresponding author. E-mail:
[email protected]. Phone: +42059699-1548. Fax: +420-59699-1665. † VS ˇ B-Technical University Ostrava. ‡ Czech Technical University in Prague. (1) Atun, G.; Bilgin, B.; Mardinli, A. J. Radioanal. Nucl. Chem. 1996, 211, 435-442. (2) Staunton, S.; Roubaud, M. Clays Clay Miner. 1997, 45, 251-260. (3) Kozaki, T.; Sato, H.; Sato, S.; Ohashi, H. Eng. Geol. 1999, 54, 223-230. (4) Miyahara, B.; Ashida, T.; Kohara, Y.; Yusa, Y.; Sasaki, N. Radiochim. Acta 1991, 52/53, 293-297. (5) Oscarson, D. W.; Hume, H. B.; King, F. Clays Clay Miner. 1994, 42, 731-736. (6) Khan, S. A.; Riaz-ur-Rehman, R.; Khan, M. A. Waste Manage. 1994, 14, 629-642. (7) Tsai, S.-Ch.; Quyang, S.; Hsu, Ch-N. Appl. Radiat. Isot. 2001, 54, 209215. (8) Abusafa, A.; Yu¨cel, H. Sep. Purif. Technol. 2002, 28, 103-116. (9) Liang, T. J.; Hsu Ch-N.; Liou, D.-Ch. Appl. Radiat. Isot. 1993, 44, 12051208.
aqueous solution) was linear (nL ≈ 1) in the lower cesium concentration range (i ) L), whereas for a higher concentration (i ) H) a nonlinear Freundlich isotherm was more appropriate (nH ≈ 3.5). The significant difference between nL and nH values led Liang et al.9 to put forth the diffuse double-layer theory. Fitting parameters KL and KH differ as well, so that the linear isotherm (qCs versus log cCs) for solute concentrations below 1 mequiv‚mL-1 gradually assumes a parabolic shape at higher solute concentration. Recently, Sohn and Kim10 also modified the Langmuir isotherm into the shape qCs ) k1k2cCsn/(1 + k2cCsn) in which cCsn is the concentration-dependent factor. Kirkner and Reeves11 developed a relationship for a special case of sorptionscompetitive adsorption. The derived equation is the familiar multicomponent Langmuir isotherm.31 Reeves and Kirkner12 then used this equation (see below) for the description of the three-component sample problem. Cation removal from aqueous solutions by layer silicates is typically represented by a cation-exchange reaction.13-14 Equilibrium constants (K) for cation-exchange reactions on Nabentonites were determined by many authors. For example, Gast15 studied ion exchange with K+, Rb+, and Cs+ ions and determined equilibrium constants (K) of these reactions to be 2.81, 8.51, and 38.4, respectively. Kunishi and Heald16 determined the equilibrium constant to be 2512 for the ion exchange with Rb+ ions; Eliason17 and Lewis and Thomas18 determined the equilibrium constants for the ion-exchange reaction between Na-montmorillonite and Cs+ ions to be 1445 and 2188, respectively. Recently, Liu et al.19 modified the previously developed two-site ion(10) Sohn, S.; Kim, D. Chemosphere 2005, 58, 115-123. (11) Kirkner, D. J.; Reeves, H. Water Resour. Res. 1988, 24, 1719-1729. (12) Reeves, H.; Kirkner, D. J. Water Resour. Res. 1988, 24, 1730-1739. (13) Eberl, D. D. Clays Clay Miner. 1980, 28, 161-172. (14) Cornell, R. M. J. Radioanal. Nucl. Chem. 1993, 171, 483-500. (15) Gast, R. G. Soil Sci. Soc. Am. Proc. 1969, 33, 37-41. (16) Kunishi, H. M.; Heald, W. R. Soil Sci. Soc. Am. Proc. 1968, 32, 201-204. (17) Eliason, J. R. Am. Miner. 1966, 51, 324-325. (18) Lewis, R. J.; Thomas, H. C. J. Phys. Chem. 1963, 67, 1781-1783. (19) Liu, Ch.; Zachara, J. M.; Smith. S. C. J. Contam. Hydrol. 2004, 68, 217-238.
10.1021/la062080b CCC: $37.00 © 2007 American Chemical Society Published on Web 12/13/2006
1228 Langmuir, Vol. 23, No. 3, 2007
Klika et al. Table 1. Chemical Composition of Ca/Mg-Bentonite (B)
SiO2
TiO2
Al2O3
Fe2O3
FeO
CaO
MgO
Na2O
K2O
P2O5
CO2
H2O
43.86
2.47
14.05
11.64
0.16
5.94
2.34
0.21
1.10
0.66
3.90
13.29
exchange model20 to include water activity changes in the exchanger (pristine sediment) phase. They showed that their “water activity-corrected” model yielded an improved prediction of the Cs distribution between pristine sediment and the Cscontaining aqueous solution. Even the removal of Cs from aqueous solution by bentonite is based on the ion-exchange principle, and the equilibrium isotherm data are often fit using sorption isotherms. For the study of Cs uptake from aqueous solution by bentonite or by soils, various sorbent-to-water (m/V) ratios and Cs concentration range have been used. For example, Hsu et al.,21 Hsu and Chang,22 Liang et al.,23 and Song et al.24 used an m/V ratio ranging from 20 to 33 g‚L-1, whereas Atun et al.1 and Atun and Kilislioglu25 performed their studies at bentonite-to-water (m/V) ratios of about 2-4 g‚L-1. The concentrations of Cs in water solutions used by the same authors usually varied from 10-8 to 10-1 mol‚L-1. Except for Khan,26 who studied the influence of the m/V ratio ranging from 5 to 100 g‚L-1 in order of effective Cs removal from water solutions, there are no other data concerning the influence of the m/V ratio on equilibrium adsorption. In natural systems,14,27 the m/V ratio is very high. In this article, equilibrium isotherms for Cs removal from concentrated aqueous solution into Ca/Mg-bentonite are presented. Experimental data determined for a wide scale of bentonite-to-water m/V ratios were fit using semiempirical Langmuir, multicomponent Langmuir, and ion-exchange equilibrium models, and the fits were compared. Experimental Materials and Methods. A CsCl solution containing 5.000 g‚Cs‚L-1 was prepared by the dissolution of CsCl (extra pure fy Merck, Germany) in deionized water. As a sorbent, Ca/Mg-bentonite from Obrnice in the Czech Republic was used. The minerals present in bentonite were identified by X-ray diffraction and optical microscopy. From the chemical analysis (Table 1) and the crystal chemical formulas of identified minerals, the modal composition was quantitatively calculated using the chemical quantitative phase analysis (CQPA) program.28 Accordingly, the bentonite sample contains montmorillonite (46 wt %), quartz (15 wt %), illite-muscovite (19 wt %), calcite (7 wt %), goethite (8.6 wt %), anatase (2.6 wt %), and apatite (1.5 wt %). The cation-exchange capacity (CEC) of the bentonite is 0.500 mequiv‚g-1. It was measured using the modified method for CEC determination.29 Most of the grain sizes of the bentonite used (98.0%) vary from 1 to 90 µm with arithmetic and geometric mean diameters of 20.1 and 13.2 µm, respectively. The chemical analysis of bentonite was performed by X-ray fluorescence (XEPOS, Spectro), and the concentrations of Cs, Na, K, Ca, and Mg in aqueous solutions after (20) Zachara, M.; Smith, S. C.; Liu, Ch.; McKinley, J. P.; Serne, R. J.; Gassman, P. L. Geochim. Cosmochim. Acta 2002, 66, 193-211. (21) Hsu, Ch-N.; Liu, D.-Ch.; Chuang, Ch.-L. Appl. Radiat. Isot. 1994, 45, 981-985. (22) Hsu, Ch-N.; Chang, K-P. Appl. Radiat. Isot. 1994, 45, 433-437. (23) Liang, T. J.; Hsu, Ch-N.; Liou, D.-Ch. Appl. Radiat. Isot. 1993, 44, 12051208. (24) Song, K.-Ch.; Lee, H. K.; Moon, H.; Lee, K. J. Sep. Purif. Technol. 1997, 12, 215-227. (25) Atun, G.; Kilislioglu, A. J. Radioanal. Nucl. Chem. 2003, 258, 605-611. (26) Khan, S. A. J. Radioanal. Nucl. Chem. 2003, 258, 3-6. (27) Flury, M.; Cziga´ny, S.; Chen, G.; Harsch, J. B. J. Contam. Hydrol. 2004, 71, 111-126. (28) Klika, Z.; Weiss, Z.; Chmielova´, M. Proceedings of 10th Conference on Clay Mineralogy and Petrology, Universita Karolina Prague, Czech Republic, 1986, pp 11-18. (29) Ma, Ch.; Eggleton, R. A. Clays Clay Miner. 1999, 47, 174-180.
contact with bentonite dissolution of the sample were determined by atomic absorption spectrometry (AAS Unicam 969). X-ray patterns of solid samples were recorded by a X-ray powder diffractometer (INEL X with PCD, Ge monochromator and Cu KR1 radiation). Batch Experiments. The ratio between the amount of bentonite (m) and volume of Cs solution (V) used for the determination of equilibrium isotherms in the stirred reactor varied from 2.5 to 70.0 g‚L-1. For the isotherm determined at m/V ) 2.5 g‚L-1, 0.500 g of bentonite and 0.200 L of Cs solution of were used, whereas for the other isotherms for m/V ratios of 10.0 g‚L-1 and higher the amount of bentonite varied from 0.500 to 3.500 g. For these isotherms, the volume of Cs solution (V) was always 0.050 L. Initial concentrations of Cs in solutions ranged from 0.55 to 40 mmol‚Cs‚L-1. The suspensions were shaken at ambient temperature for 24 h and then centrifuged for 30 min at 5000 rpm. The experiments show that equilibrium is practically reached after 2 min. The supernatant was filtrated using a Pragopor 5 (0.6 µm) microfilter and acidified by the addition of conc. HNO3 (1.0 mL‚L-1), and Cs was determined by atomic absorption spectroscopy. In six experiments, besides Cs, the concentrations of Na, K, Ca, and Mg were also determined in the filtrate.
Results and Discussion Experimental Data. The equilibrium data for the removal of Cs from water onto Ca/Mg bentonite obtained from batch experiments are plotted in Figure 1. The data represent a broad range of the solid/liquid ratio (m/V) and exhibit nonlinearity in Cs uptake by bentonite (qCs) for the equilibrium concentration of Cs in the liquid phase (cCs). At a given Cs equilibrium concentration, Cs uptake increases with decreasing m/V ratio. For these data, the distribution coefficients Kd were also calculated. It was found that distribution coefficients Kd decrease with increasing equilibrium concentration cCs as well as with increasing m/V ratio. (See plot qCs/cCs ) Kd in Figure 1.) A decrease in the distribution coefficient with increasing dry density of the adsorbent (directly dependent on the m/V ratio) was observed by Kozaki et al.3 and Miyahara et al.4 It is in agreement with reported by Benesˇ et al.,30 who also observed a decrease in Kd with increasing m/V in their radionuclide transport study in surface streams. None of them discussed the whole equilibrium isotherms. Langmuir Isotherms. For experimental data qCs and cCs related to each isotherm characterized by the appropriate mass-to-volume ratio (m/V), coefficients k1 and k2 of the Langmuir isotherm (eq 1) were fit.
qCs )
k1k2cCs 1 + k2cCs
(1)
In eq 1, qCs is the adsorbed amount of Cs in Ca/Mg-bentonite (mmol‚g-1); cCs is the equilibrium concentration of the solute (mol‚L-1); k1 represents the maximum sorbate uptake (mmol‚g-1); and k2 is the coefficient relating to the affinity between the solute and sorbent (L‚mol-1). Obtained coefficients k1 and k2 are given in Table 2. Calculated coefficient k1 varies from 0.507 to 0.530 mmol‚g-1 with mean k1 ) 0.521 mmol‚g-1 and standard deviation sK ) 0.008 mmol‚g-1. This value corresponds well to the abovereported value of CEC determined by an independent method (0.500 mmol‚g-1). In contrast to the k1 value, calculated coefficient (30) Benesˇ, P.; C ˇ ernı´k, M.; Ramos, P. L. J. Radioanal. Nucl. Chem. 1992, 159, 201-218.
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Figure 1. Experimental data and calculated isotherms for each m/V Langmuir isotherm for the removal of Cs from aqueous solution onto Ca/Mg bentonite. qCs, adsorbed amount of Cs (mmol‚g-1) and cCs, equilibrium concentration of Cs in aqueous solution (mol‚L-1). Solid/liquid m/V ratios of isotherms 1-6: 1, 2.5 g‚L-1; 2, 10.0 g‚L-1; 3, 18.0 g‚L-1; 4, 30.0 g‚L-1; 5, 50.0 g‚L-1; and 6, 70.0 g‚L-1. Table 2. Parameters k1 and k2 of Langmuir Isotherms Evaluated from Related m/V Data from eq 1 curve no. 1 2 3 4 5 6
m/V
(g‚L-1
)
k1 (mmol‚g )
k2 (L‚mol-1)
0.526 0.524 0.514 0.507 0.527 0.530
905 367 319 256 171 142
2.5 10.0 18.0 30.0 50.0 70.0
-1
k2 varies significantly with the m/V ratio. The best fit between k2 and m/V data (correlation coefficient r ) 0.995) was found for the regression function given by eq 2, and it is shown in Figure 2. Isotherms 1-6 plotted in Figure 1 are well described by eq 1 using k1 ) 0.521 mmol‚g-1 and k2 that varies with m/V according to eq 2.
k2 ) 1489
m -0.555 V
()
(2)
From the set of experiments relating to one isotherm, one experiment was selected, and except for the amount of Cs adsorbed from aqueous solution, the concentrations of released cations E (Na+, K+, Mg2+, and Ca2+) from bentonite into aqueous solution were also determined. The selected experiments are characterized by m/V, cCs, and qCs data given in Table 3. Moreover, the parallel experiments (blanks) were performed in order to determine the concentration of released cations (Na+, K+, Mg2+, and Ca2+) by leaching with deionized water. The concentrations of Na+, K+, Mg2+, and Ca2+ (cE) given in Table 3 were evaluated using the correction on a blank performed with deionized water. In order for the adsorbed concentration of Cs to be compared with the corresponding desorbed concentration of E elements (Na, K, Mg, and Ca), the total concentrations of desorbed E elements cE,tot (g‚equiv‚g-1) were recalculated on desorbed qE,tot using the equation qE,tot ) cE,tot(V/m). The difference between adsorbed qCs and desorbed qE,tot is relatively small (Table 3), so the ion(31) Butt, J. B. Reaction Kinetics and Reactor Design; Prentice-Hall: Englewood Cliffs, NJ, 1980; p 431. (32) Volesky, B. Sorption and Biosorption; BV Sorbex, Inc.: Montreal, 2003; p 316.
exchange process can be assumed. The Mg2+/Ca2+/K+/Na+ ratio is about 10:5:1:1, so in aqueous solution Mg2+ and Ca2+ ions prevail over Na+ and K+ ions. The divalent ions represent about 90% of all desorbed ions; therefore, we conclude that the adsorption/desorption operates between the Cs+ ion in aqueous solution and divalent cation M2+ bonded in Ca/Mg-bentonite. In Table 3, the experimental concentration of element M (cM,exptl) was calculated from the equation cM,exptl ) 0.5cE,tot. Supposing that ion exchange between M2+ and Cs+ ions begins with the initial values of cM and cCs equal to zero, the number of M2+ cations (mmol) released from bentonite into aqueous solution equals one-half of the number of adsorbed Cs+ ions (mmol).
1 cM,calcdV ) qCsm 2
(3)
where m is mass of the adsorbent (g), V is the volume of aqueous solution (mL), and cM,calcd is the calculated equilibrium concentration of divalent ion M in volume V (mol‚L-1). The regression function cM,calcd ) 1.0088cM,exptl - 0.0002 with correlation coefficient r ) 0.999 shows very good agreement between the experimental and calculated cM data over the whole m/V range (Table 3). It enables us to calculate concentrations cM from eq 3 for all experimental data in which the concentrations of Na, K, Mg, and Ca were not determined analytically. In our experiments (Figure 1), the equilibrium concentration cCs varies from 0 to 0.028 mol‚L-1 for all m/V ratios, whereas the variation of the cM concentration is considerably dependent on the m/V ratio. For example, for m/V ) 2.5 g‚L-1 the concentration cM varies from 0 to about 0.00051 mol‚L-1, whereas for m/V ) 70 g‚L-1 it ranges from 0 to more than 0.01287 mol‚L-1. Such a dramatic increase in the M2+ cation concentration in aqueous solution influences the equilibrium. It means that for higher m/V ratios it is necessary to approach the equilibrium between bentonite and CsCl aqueous solution as a multicomponent system (i.e., the desorbed cations must be taken into consideration). For the evaluation of all experimental data, the multicomponent Langmuir and ion-exchange models were selected.
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(mmol‚g-1) is the adsorbed equilibrium amount of Cs+ in Ca/Mg-bentonite, k1,Cs (mmol‚g-1) is the maximum Cs uptake (mmol‚g-1), and k2,Cs and k2,M (L‚mol-1) are coefficients relating to the affinity between the sorbent and Cs solute and between the sorbent and M solute, respectively. For M2+ ions, no equation similar to eq 6 can be written because 2+ M ions are desorbed from Ca/Mg-bentonite and the maximum M uptake qM ) k1,M relates to cM ) 0 mol‚L-1. This is in contrast to the nature of eq 4. For the adsorption of Cs+ ions in the presence of desorbed M2+ ions in aqueous solution, we can use only eqs 6 and 3. Equation 6 can be rewritten in the form
qCs + qCsk2,McM ) k2,Cs(k1,CscCs - qCscCs)
(7)
After a simple modification of eq 7, we obtain Figure 2. Relationship between coefficient k2 and the m/V ratio.
Multicomponent Langmuir Model. For competitive adsorption, the multicomponent Langmuir isotherm (eq 4) is usually the choice11,31,32
qA )
k1k2,AcA 1+
∑E
(4) k2,EcE
where index A relates to the calculated adsorbed species A and index E relates to all species (including A) present in aqueous solution. For other symbols, see eq 1. The validity of the surface complexation reaction (eq 5) and a fixed number of adsorption sites on solid X is usually assumed.11
X + E T EX
(5)
where X is the chemical formula of the solid (site) and EX is the chemical formula of the sorbed form of the Eth element. For Cs sorption on Ca/Mg-bentonite, eq 4 can be rewritten as
qCs )
k1,Csk2,CscCs 1 + k2,CscCs + k2,McM
(6)
where cCs and cM (mol‚L-1) are equilibrium concentrations of Cs+ and M2+ ions in aqueous solution, respectively; qCs
Figure 3. Regression plots of 1/cM versus (k1,CscCs - qCscCs)/(qCscM).
(
)
k1,CscCs - qCscCs 1 ) k2,Cs - k2,M cM qCscM
(8)
The regression plot 1/cM versus A ) (k1,CscCs - qCscCs)/(qCscM) for all m/V data is shown by the solid line in Figure 3. Using the set of 71 experimental values cCs, qCs, and m/V, plus k1,Cs ) 0.521 mmol‚g-1 (Table 2 and cM, calculated from eq 3), constants k2,Cs and k2,M were obtained from eq 8 using the leastsquares method. The coefficients calculated for all data are k2,Cs ) 968 L‚mol-1 and k2,M ) 593 L‚mol-1. Moreover, the regression plots 1/cM versus A were also evaluated for each of the six isotherms. The calculated coefficient k2,Cs increases regularly from 103 to 861 L‚mol-1 with decreasing m/V ratio from 70 to 2.5 g‚L-1, respectively. Also, the evaluated k2,M for individual isotherms differs. In Figure 3, three regression plots for m/V ) 2.5, 10, and 50 g‚L-1 are denoted by dotted lines. Using coefficients evaluated for all data, the qCs isotherms were calculated from eq 6, and they are compared to experimental data in Figure 4. The relatively bad fitting shown in Figure 4 is a consequence of the inability of the multicomponent Langmuir isotherm to describe all of the experimental data obtained over a wide bentonite-to-water ratio (m/V) interval. Ion-Exchange Model. As illustrated in Table 3, the ion exchange operates practically only between divalent Ca2+ and Mg2+ cations present in montmorillonite and the Cs+ present in aqueous solution. There is very good agreement between the
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Figure 4. Experimental data and isotherms calculated by the multicomponent Langmuir isotherm for removing Cs from aqueous solution onto Ca/Mg bentonite. Solid/liquid m/V ratios of isotherms 1-6: 1, 2.5 g‚L-1; 2, 10.0 g‚L-1; 3, 18.0 g‚L-1; 4, 30.0 g‚L-1; 5, 50.0 g‚L-1; and 6, 70.0 g‚L-1. Table 3. Cs Adsorbed and Mg, Ca, Na, and K Desorbed cation E desorbed m/V (g‚L-1)
103cCs (mol‚L-1)
Cs adsorb. qCs (g‚equiv‚g-1)
Mg2+
Ca2+
2.5 10.0 18.0 30.0 50.0 70.0
1.84 2.62 4.94 10.24 7.02 15.51
0.288 0.252 0.298 0.348 0.273 0.369
0.45 1.40 3.08 6.05 8.12 14.90
0.25 0.93 1.82 3.39 4.04 7.53
cE (g‚eq‚L ) Na+ K+ 0.08 0.23 0.40 0.65 1.01 1.54
sum of all of the ion-exchangeable cations (Na+, K+, Mg2+, and Ca2+) and ion-exchanged Cs for all m/V ratios. The ion-exchange equation between Cs+ and M2+ is
MX2 + 2Cs+ T M2+ + 2CsX
(9)
where M2+ is a divalent cation (Ca2+ and/or Mg2+) and Xrepresents negatively charged exchange sites on the montmorillonite surface. The montmorillonite, the major clay mineral present in bentonite,33 is responsible for cation sorption because of the negative charge arising from the partial substitution of divalent magnesium for trivalent aluminum in the octahedral sheet of montmorillonite.34 The thermodynamic equilibrium constant K (mL‚g-1) for the ion-exchange reaction (eq 9) then follows from the mass action law
K)
cM‚qCs2 γCs ‚ cCs2‚qM γM2
-1
103
0.08 0.28 0.48 0.83 1.15 1.76
cE,tot
qE,tot (g‚equiv‚g-1)
103cM,exptl1) (mol‚L-1)
10cM,calcd2) (mol‚L-1)
0.86 2.84 5.78 10.92 14.32 25.73
0.344 0.283 0.321 0.364 0.286 0.368
0.43 1.42 2.89 5.46 7.16 12.87
0.36 1.26 2.68 5.22 6.83 12.92
exchange reaction, eq 11 can be derived:
qCs + 2qM ) qmax ) CEC
(11)
At the beginning of the ion-exchange reaction, qCs ) 0 mmol‚g-1, qM ) CEC/2 ) 0.250 mmol‚g-1, and the initial concentration of M is cM,0 ) 0 mol‚L-1. The concentration of divalent cation M2+ released from bentonite can be calculated from eq 3. Using eqs 3 and 11, the relationship for the determination of the thermodynamic equilibrium constant (eq 10) corresponding to the ion-exchange equation (eq 9) can be formulated as follows:
m γM V ‚ 2 K) 2 cCs (CEC - qCs) γCs qCs3
(12)
Activity coefficients γCs and γM were calculated using eq 13
(10)
where cCs and cM are equilibrium concentrations of Cs+ and of divalent cation M2+ in aqueous solution, respectively; qCs and qM are adsorbed equilibrium amounts of Cs+ and bivalent cation M2+ (mmol‚g-1) in bentonite, respectively; γCs and γM are the activity coefficients of Cs+ and M2+ ions in aqueous solution, respectively. The maximum sorbate uptake qCs,max is equivalent to CEC, so it equals 0.500 mequiv‚g-1. From the mass balance of the ion-
-log γi )
0.51zi2xI 1 + xI
- 0.3I
(13)
and the ionic strength of the equilibrium solution that contains ions M2+, Cs+, and Cl- was calculated using eq 14
1 I ) (cCs 12 + cM 22 + cCl 12) 2
(14)
where cCl is the concentration of Cl- dissociated from CsCl solution. Assuming the initial concentrations of Cs (cCs,0 ) 0.0376
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Figure 5. Experimental data and calculated isotherms corresponding to the ion-exchange model for removing Cs from aqueous solution onto Ca/Mg bentonite. Solid/liquid m/V ratio of isotherms 1-6: 1, 2.5 g‚L-1; 2, 10.0 g‚L-1; 3, 18.0 g‚L-1; 4, 30.0 g‚L-1; 5, 50.0 g‚L-1; and 6, 70.0 g‚L-1.
Figure 6. Calculated (qCs,calcd) versus experimental (qCs,exptl) Cs uptake on Ca/Mg bentonite. (A) Multicomponent Langmuir isotherm and (B) ion-exchange model. The dotted line illustrates the identity between qCs,calcd and qCs,exptl.
mol‚L-1) and M2+ (cM,0 ) 0 mol‚L-1) in the liquid phase, the concentration of divalent ions released from bentonite equals of the concentration of Cs ions (mmol) exchanged:
1 cMV ) (cCs,0 - cCs)V 2
(15)
The Cl- ions are not sorbed on bentonite; therefore, their concentration equals the initial concentration of Cs (cCl ) cCs,0). Taking into account eq 14, the identity of cCl with cCs,0, and the equation for the calculation of cM (eq 15), the ionic strength of an aqueous solution can be formulated as follows:
1 3 I ) cCs,0 - cCs 2 2
(16)
For each of the 71 sets of experimental data (qCs, m/V, cCs, and cCs,0), the thermodynamic equilibrium constant (K) was calculated from eq 12 using eqs 16 and 13 for the evaluation of the ionic strength (I) and activity coefficients γCs and/or γM. The arithmetic mean and standard deviation of the thermodynamic equilibrium constant were calculated, and then using Grubb’s test for the 5% level of significance (R), the four values of the equilibrium constant were eliminated as outsiders. The newly calculated mean
thermodynamic equilibrium constant K ) 75.5 mL‚g-1 with a standard deviation of sK ) 17.4 mL‚g-1 was then obtained from 71 sets of experimental data. From the experimental data (m/V, CEC, cCs, and cCs,0) and the calculated thermodynamic equilibrium constant (K), the equilibrium amounts of Cs+ (qCs) were calculated from modified eq 12 using Cardan formulas. The experimental data and calculated isotherms from eq 12 are plotted in Figure 5. Comparison of Models. The fit between experimental and calculated data for both models (multicomponent Langmuir isotherm and ion-exchange models) was evaluated using the t test for pair values from program QC-EXPERT35
t)
|dh|x(n - 1) sd
(17)
where |dh| is the absolute value of mean difference dh, defined as n dh ) (1/n)∑i)1 di, and di is given as di ) qCs,calcd,i - qCs,exptl,i for (33) Ochs, M.; Lothenbach, B.; Yui, M. Mater. Res. Soc. Symp. Proc. 1998, 506, 765-772. (34) Hemingway, B. S.; Sposito, G. The EnVironmental Chemistry of Aluminum; CRC Press: Boca Raton, FL, 1989; Chapter 3, p 5585. (35) Meloun, M.; Militky´, J. Statistical Analyses of Experimental Data; Academia: Praha, Czech Republic, 2004; p 953, in Czech.
Cs Uptake from Aqueous Solutions by Bentonite
Langmuir, Vol. 23, No. 3, 2007 1233
the ith compared pair of qCs calculated and experimental. The standard deviation sd of the di values is then defined as
sd )
x
1
n
(di - dh)2 ∑ n i)1
(18)
The interval of credibility of the (qCs,calcd - qCs,exptl) difference can be determined from the following inequality
sd sd e qCs,calcd - qCs,exptl e dh + tcrit (dh - tcrit) xn - 1 xn - 1 (19) where tcrit is tabulated critical Student’s t-test value for a selected level of significance R and degree of freedom ν (ν ) n - 1). The dh ) 9.25 × 10-3 and sd ) 3.76 × 10-2 values for the multicomponent Langmuir model and dh ) 2.66 × 10-3 and sd ) 1.60 × 10-2 for the ion-exchange model were calculated. For the multicomponent Langmuir model, the interval of credibility of (qCs,calcd - qCs,exptl) is between 0.00020 and 0.01829, which does not support the idea of the equivalence of qCs,calcd and qCs,exptl with 95% probability. The calculated interval of credibility of (qCs,calcd - qCs,exptl) is between -0.00122 and 0.00652 and satisfies the requirement that dh ) 0 is inside the interval of credibility; therefore, the equivalence of qCs,cal from the ion-exchange model and qCs,exp can be reported with 95% probability. Probably the best illustration of the agreement between calculated and experimental qCs values can be obtained from the regression plot for the multicomponent Langmuir isotherm (Figure 6A) and for the ion-exchange model (Figure 6B). The regression equation qCs,calcd ) 1.0065qCs,exptl - 0.0026 (correlation coefficient r ) 0.989) for the ion-exchange model offers a better fit with experimental data (Figure 6B) than the regression equation qCs,calcd ) 0.790qCs,exptl + 0.073 (correlation
coefficient r ) 0.9580) for the multicomponent Langmuir model (Figure 6A). In further experiments on the modeling of dynamic sorption performed on laboratory columns filled with a mixture of bentonite and sand, the calculated thermodynamic equilibrium constant K ) 75.5 mL‚g-1 for Cs uptake from aqueous solution by Ca/ Mg-bentonite was for m/V ≈ 630 g‚L-1, and very good results were obtained.36 The application of the equilibrium model based on the ion exchange of cesium with a divalent cation initially sorbed on bentonite in this type of experiment can clarify the migration of cations in the backfill of the final disposal of spent nuclear fuel and their diffusion in the compacted bentonite.
Conclusions The removal of Cs from concentrated aqueous solution by Ca/Mg-bentonite was experimentally studied over a wide range of mass-to-liquid ratio m/V. It was shown that at higher m/V ratios the equilibrium between a single solute (Cs) and a sorbent (Ca/Mg-bentonite) is significantly influenced by Ca2+ and Mg2+ cations moving into CsCl solution from the sorbent. This results in a significant decrease of the distribution coefficient Kd with increasing m/V ratio; therefore, the simple Langmuir isotherm does not express the experimental data well enough. The experimental results of batch sorption experiments were further fitted using multicomponent Langmuir and ion-exchange equilibrium models. The formulation of both of these models was rigorously derived. The ion-exchange model seems to be more convenient, mainly because of its capability to be used simply for conditions not described by batch experiments. The possible application of the developed equilibrium ion-exchange model for conditions close to those in the backfill of the final disposal of spent nuclear fuel and/or in the layer of compacted bentonite will be addressed in the future. Acknowledgment. We acknowledge support from the Ministry of Education of the Czech Republic, project nos. MSM 6198910016 and MSM 6840770020. We also acknowledge the help of A. Svacˇinova´ with laboratory experiments. LA062080B (36) Kraus, L.; Vopa´lka, D.; Klika, Z. Czech. J. Phys., in press.
