Binary and Ternary Cation Exchange on Strong Acid Cation Exchange

Langmuir 1999, 15, 6875-6883

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Binary and Ternary Cation Exchange on Strong Acid Cation Exchange Resin Involving Na, Mg, and Zn in Single and Binary Backgrounds of Chloride, Perchlorate, and Sulfate In H. Rhee† and David A. Dzombak* Carnegie Mellon University, Department of Civil and Environmental Engineering, and Colloids, Polymers and Surfaces Program, Pittsburgh, Pennsylvania 15213 Received January 9, 1997. In Final Form: May 18, 1999 A systematic study with the negatively charged cation-exchange resin Amberlite 200 was performed to investigate the influence of anion type on cation exchange. A comprehensive data set was obtained for binary and ternary cation exchanges involving Na, Mg, and Zn on a strongly acidic, sulfonate cationexchange resin in electrolyte systems with the single anions chloride, perchlorate, and sulfate, and with 1:1 mixtures of them at two total cation concentrations of 0.05 and 0.2 N. The binary and ternary cation exchange data exhibited internal consistency in that Mg and Zn were selected over Na to a comparable degree. The binary and ternary cation exchange data also indicated clearly an effect of anion type, with reduction in selectivity of Mg and Zn relative to Na in the presence of more strongly complexing anions such as sulfate. The effects of anions in cation exchange may be ascribed in part to their association with cations in solution, as demonstrated by application of conventional mass action models for ion exchange with consideration of solution-phase speciation. The ability of mass action models including solution speciation to predict binary and ternary cation exchange in different anion backgrounds based on model parameters extracted only from data obtained in chloride background was also tested. The GainesThomas model provided the best predictions of binary and ternary cation exchange on the sulfonate resin for the different anionic media and ionic strengths. Mass action models can account at least approximately for the effect of anion type on cation exchange if solution speciation and activity correction are properly considered.

1. Introduction Ion exchange is a process in which ions held by electrostatic or shorter-range forces to charged sites on the surface of a solid in contact with aqueous solution are exchanged for ions of similar charge in the solution. The process is not well understood due to nonuniformity of charge distribution within many exchanger materials and the complexity of the physical and chemical processes involved, including electrostatic attraction/repulsion and specific adsorption. The preference of charged solids for one counterion over another ion of the same charge is known as selectivity. Cation selectivity by negatively charged solids is of great interest in soil science, geochemistry, and water treatment. It is determined by the exchanger properties, the solution conditions, and the nature of the electrolyte ions. Binary and ternary cation exchange experiments, primarily with soils, have shown that ion exchangers can exhibit very strong selectivity for certain cations and that electrolyte anions affect cation selectivity.1,2 Reasons for the latter phenomenon are difficult to elucidate with data obtained from soils and from a limited range of solution conditions. Cations have been observed to exhibit stronger adsorptive affinity on ion exchangers in electrolyte solutions containing certain anions. The preference for Cd relative to Ca on zeolite increased in the order of nitrate > mixture * To whom correspondence should be addressed. † Current address: Soon Chon Hyang University, Department of Environmental Engineering, Asan-Si, Chungnam 336-600, Korea. (1) Fletcher, P.; Townsend, R. P. J. Chem. Soc., Faraday Trans. 1 1985, 81, 1731. (2) Sposito, G.; Holtzclaw, K. M.; Charlet, L.; Jouany, C.; Page, A. L. Soil Sci. Soc. Am. J. 1983, 47, 51.

of nitrate/chloride > chloride.1 Mg and Ca showed higher selectivity over Na on Wyoming bentonite in electrolytes containing chloride, compared to perchlorate,2 though some have argued that the data demonstrate no statistically significant difference.3 In other work, the selectivity of Cu2+ over H+ on Dowex resin has been observed to be greater in nitrate compared to chloride anion background.4 Most studies of binary and multicomponent cation exchange have been performed under simple experimental conditions, usually with a single anion in the background electrolyte.5 Cation exchange involving more than three cations has been studied in single anion electrolytes such as chloride or perchlorate at one ionic strength by a few researchers.5 No systematic attempts have been made to study competitive interactions in multi-cation systems involving more than two anions. Conventional mass action models are usually applied to describe binary cation exchange in single anion electrolyte media under a limited range of conditions. The primary objective of this study was to assess the effects of electrolyte anions on cation exchange through development of a comprehensive set of data for a strongly acidic cation-exchange resin and binary and ternary cation exchanges involving Na, Mg, and Zn electrolyte systems with the single anions chloride, perchlorate, and sulfate, and 1:1 mixtures of two of these for total cation concentrations of 0.05 and 0.2 N. These data were used to investigate (i) the influence of the anionic composition of (3) Suarez, D. L.; Zahow, M. F. Soil Sci. Soc. Am. J. 1989, 53, 52. (4) Bonner, O. D.; Livingston, F. L. J. Phys. Chem. 1956, 60, 530. (5) (a) DeLucas, A.; Zarca, J.; Canizares, P. Sep. Sci. Technol. 1992, 27, 823. (b) Sengupta, M.; Paul, T. B. React. Polym. 1985, 3, 217. (c) Bichkova, V. A.; Soldatov, V. S. React. Polym. 1985, 3, 207. (d) Soldatov, V. S.; Bichkova, V. A. Sep. Sci. Technol. 1980, 15, 89.

10.1021/la970031g CCC: $15.00 © 1999 American Chemical Society Published on Web 07/23/1999

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Figure 1. Two-dimensional view of structure of sulfonate styrene-divinylbenzene macroreticular resin.

aqueous solutions in cation exchange and the dependence of cation adsorption capacity on the type of anion in the electrolyte, (ii) the degree to which cation selectivity can be explained by the solution complexation ability of the competing cations, and (iii) the extent to which cations display the same selectivity in binary and ternary systems. Conventional ion exchange mass action models were employed for quantitative data evaluation with consideration of solution-phase speciation. The approach used was novel because ion exchange reactions usually are formulated with free ions as the exchanging species under the assumption that the free species dominates the solution-phase speciation of the exchanging element. 2. Experimental Materials and Methods 2.1. Selection of Electrolyte Ions and Exchanger. Electrolyte ions relevant to natural aquatic systems and meeting specific criteria were selected for study. The criteria for selection were that the ions be (i) high, intermediate, and low in tendency to form solution complexes with each other, to investigate the possibility of adsorption of a complex, (ii) mono- and divalent, for examination of cations of different charge, (iii) not mutually precipitating across the range of concentrations examined to avoid additional complexity, and (iv) not able to decompose the exchanger through a redox reaction. Na, Mg, and Zn were selected along with chloride, perchlorate, and sulfate. The criteria for selection of the solid exchanger were that it have fixed negative charge and well-known surface properties: cation exchange capacity, surface area, charge density, and acidbase characteristics. To avoid the need for large concentrations of the exchanger in suspension in order to observe large differences in electrolyte concentration in the solution phase, an exchanger with a relatively high charge density was desired. It was also desired that the exchanger exhibit minimal structural change such as breakdown and osmotic swelling/shrinking during ion exchange. The strongly acidic sulfonate-group cationexchange resin Amberlite 200 (Rohm and Haas Co.) was chosen for the exchanger. 2.2. Characterization of Strongly Acidic Cation Exchange Resin. Amberlite 200 macroreticular cation-exchange resin (sodium form) particles are spherical and consist of a matrix of styrene with 20% (by weight) divinylbenzene as the crosslinking agent into which sulfonate groups have been incorporated (Figure 1). The sulfonate groups are separated by at least four carbon-carbon bonds (about 0.6 nm) on each aliphatic chain, allowing ample space for cations to be adsorbed independently.8 The hydrocarbon skeleton is stable with respect to temperature change, strong acid and base, and oxidizing agents, but the resin must be kept permanently moist to avoid physical stress due to repeated drying and rewetting. Properties of the Amberlite 200 resin are presented in Table 1. Cation Exchange Capacity. The cation exchange capacity for the Amberlite 200 resin was measured as 4.6 mequiv/g (dry weight basis) by acid-base titration with H-form resin. The resin was

Rhee and Dzombak conditioned with 4% HCl and placed in a 0.1 N NaOH containing 1 M NaCl. The amount of H+ liberated to the supernatant liquid was measured by back-titrating with 0.1 N HCl and using a glass pH electrode. Additional details and an example calculation are provided in Rhee.9 Acid-Base Characteristics. H-form resin samples were placed in 0.01, 0.05, and 0.1 N HCl and then titrated with 0.088 N NaOH solutions which were prepared with 0.01, 0.05, and 0.1 N NaCl, respectively. It was found that the shapes of the base titration curves were exactly the same at the three ionic strengths, which confirmed the absence of pH-dependent, variable charge on the resin surface. Surface Area. The specific surface area of the dried resin was measured as 40 m2/g by the BET-N2 gas adsorption method. The measurement was performed with the Na-form resin, with outgassing of the resin: (i) at room temperature for 2 h and 50 °C for 2 h and (ii) at room temperature for 3 h and then 100 °C for 1 h. The same result was obtained in both cases, though some thermal breakdown of resin particles was observed at 100 °C. Surface Charge Density. The surface charge density was estimated as 11 C/m2. This was calculated by dividing the cation exchange capacity obtained by titration of the H-form resin by the surface area measured by BET-N2 adsorption with the proper unit conversion. 2.3. Preparation of Electrolyte Stock Solutions and Resin. Electrolyte Stock Solutions. Electrolyte stock solutions of 0.2 and 0.05 N were prepared with the following nine salts of analytical grade using deionized water: NaCl, NaClO4, Na2SO4, MgCl2, Mg(ClO4)2, MgSO4, ZnCl2, Zn(ClO4)2, ZnSO4. All salts were obtained from Fisher Scientific except for perchlorate salts which were obtained from Aldrich Chemical. The deionized water had resistivity greater than 17 MΩ‚cm and was obtained from a U.S. Filter ion exchange system. Resin Conditioning. The required amount of Na-form resin as supplied was first washed with deionized water and then placed in glass chromatography columns (30 × 300 mm, Fisher Scientific Co.) for conditioning. Washing was done by mixing resin with the deionized water and then discharging the supernatant until the supernatant was visibly clear. Resin conditioning was performed by flowing electrolyte solutions of NaCl and MgCl2 at 1 N downward through the columns. Conversion to Na-form was done by passing 10 bed volumes of NaCl solution. To get the resin in Mg-form for Mg-Zn binary exchange experiments, the MgCl2 solution was flowed through the column and the effluent was sampled for measurement of the concentration of Na with flame atomic absorption spectroscopy. The addition of the electrolyte solution was continued until Na was not detectable at 0.04 mg/L. The resin saturated with the replacement electrolyte was washed with deionized water to remove any non-counterion electrolytes remaining in the resin until Cl- in the eluent was not detected with ion chromatography. This procedure yielded the conditioned resins of Na- and Mg-form used for the cation exchange experiments. 2.4. Reversibility and Equilibration Time of Cation Exchange. Exchange equilibrium between Na and Mg on the Amberlite 200 resin in the perchlorate background electrolyte was studied with 0.05 equiv/L Na-form resin in 0.05 N Mg(ClO4)2 and 0.05 equiv/L Mg-form resins in 0.05 N NaClO4. Four replicates of these suspensions were prepared in 160 mL polyethylene containers which were placed in a tube rotator (Scientific Equipment Products Co.) for mild agitation. The concentrations of Na and Mg in solution phase samples were measured at 4-h intervals by flame atomic absorption spectroscopy to identify the time required to achieve equilibrium cation concentrations. The same experiments were conducted with (6) (a) Elprince, A. M.; Babcock, K. L. Soil Sci. 1975, 120, 332. (b) Elprince, A. M.; Vanselow, A. P.: Sposito, G. Soil Sci. Soc. Am. J. 1980, 44, 964. (c) Fletcher, P.; Holtzclaw, K. M.; Jouany, C.; Sposito, G.; LeVesque, C. S. Soil Sci. Soc. Am. J. 1983, 48, 1022. (d) Sposito, G.; LeVesque, C. S. Soil Sci. Soc. Am. J. 1985, 49, 1153. (e) Sposito, G.; LeVesque, C. S.; Hesterberg, D. Soil Sci. Soc. Am. J. 1986, 50, 905. (f) Thellier, C.; Sposito, G. Soil Sci. Soc. Am. J. 1988, 52, 979. (7) Parrish, J. R. J. Appl. Chem. 1965, 15, 280. (8) Rhee, I. H.; Dzombak, D. A. Langmuir 1998, 14, 935. (9) Rhee, I. H. Ph.D. Thesis, Carnegie Mellon University, Pittsburgh, PA, 1996.

Effects of Electrolyte Anions on Cation Exchange

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Table 1. Physical and Chemical Propertiesa of Amberlite 200 Cation Exchange Resin ionic form as shipped physical form mean particle diameter wet bead density bead porosityb bead matrix densityc moisture contentd

Na spherical bead 750 ( 100 µm 1.24 ( 0.02 g/mL bead 0.24 mL pore/mL bead 1.32 g/mL matrix 45%

max operating temp functional group cation exchange capacitye specific surface area f surface charge densityg reversible swelling (Na f H) pH range

300 °F sulfonate 4.6 mequiv/g dry 40 m2/g dry 11 C/m2 3-5% 0-14

a Data provided by Rohm and Haas Co. except where indicated otherwise. b Bead porosity measured by Parrish.7 c Calculated from wet bead density and bead porosity. d Measured by weight difference after 12 h of oven drying at 110 °C. e Measured in this study by acid-base titration. f Measured in this study by BET-N2 method, with outgassing for 2 h at 50 °C. g Calculated from cation exchange capacity and surface area.

chloride electrolytes. In all cases, the exchange equilibrium was obtained in less than 4 h and all concentrations of Na and Mg were identical, which indicated that cation exchange was fast, reversible, and reproducible.9 Twelve-hour reaction periods were subsequently used in all experiments to provide ample time for equilibration. 2.5. Exchange Experiment Methods. Surface excess and deficit were determined by monitoring ion loss or gain in the solution phase. The amount of cations associated with the exchanger phase cannot be measured directly via solid-phase separation and extraction of adsorbed ions, as the isolation of the solids cannot be achieved without disturbance of the ionic distribution in the vicinity of the exchanger phase. Binary and ternary cation exchanges were studied for different electrolyte anion compositions at two total cation concentrations (TCC). Small-volume batch experiments for binary and ternary cation exchanges were performed with combinations of Na, Mg, and Zn in the single anion background of chloride (Cl-), perchlorate (ClO4-), and sulfate (SO42-) at TCC ) 0.05 and 0.2 N, and with 1:1 mixtures of Cl-/ClO4-, ClO4-/SO42-, and SO42-/ Cl- at TCC ) 0.05 N. The resin concentration was maintained at 0.01 equiv/L for TCC ) 0.05 N and at 0.04 equiv/L for TCC ) 0.2 N. In each experiment, a predetermined amount of conditioned resin was added to a 160 mL polyethylene bottle in which combinations of electrolyte stock solutions at 0.05 or 0.2 N were placed to obtain the desired composition of cations and anions. The resin weight on a dry basis was about 0.11 and 0.44 g for the corresponding resin concentrations of 0.01 and 0.04 equiv/L. The ratio of the two cations in solution was adjusted to give 10 equivalent fractions ranging from 0.05 to 0.9 for binary cation exchange. For the ternary cation exchange experiments, the concentrations of Na and a divalent cation were varied over nine equivalent fractions at a constant total concentration of another divalent cation in the suspension, i.e., Na-Mg exchange with constant Zn and Na-Zn exchange with constant Mg. After the test suspensions were prepared, they were placed on a rotator and allowed to equilibrate for 12 h. After this reaction period, solid and liquid were separated by gravity settling. Supernatant samples were then taken and analyzed by atomic absorption spectroscopy for cations and by ion chromatography for anions. 2.6. Chemical Analyses. Flame atomic absorption spectroscopy (model 908PBMT, GBC Scientific Equipment Ltd.) was used for analysis of cations. It was found that proper matrix correction was extremely important for accurate analyses. In calibration tests with the various electrolyte solutions, absorbances for Na, Mg, and Zn varied for the different electrolyte backgrounds in the order of sulfate < chloride < perchlorate and this effect was greater for the divalent cations. To remove the different effects of the various electrolytes, the analysis of Na was conducted with the addition of 0.05 M KCl, while Mg and Zn were measured in the presence of 0.02 M EDTA and 0.05 M KCl. With these additions, consistent calibration curves were obtained for the three cations at concentrations ranging from 0.0005 to 0.005 N across the electrolyte compositions of interest. Anion concentrations were analyzed by ion chromatography after dilution with deionized water. However, the analytical error was 5-10%, due to the large dilutions necessary, which was too large to detect small differences in the anion composition in the test solutions. Thus the results were not meaningful to report for this study.

pH measurement was made by a glass electrode and was negligibly affected by the electrolyte compositions of the test solutions. The pH range in the experiments performed was 4.76.0. 2.7. Data Reduction. The equivalent fractions of each cation in the resin and aqueous solution phases were calculated on the basis of the total equivalents of cations adsorbed in the resin phase and dissolved in the solution phase. This is the conventional approach for calculation of surface- and solution-phase equivalent fractions in ion exchange data analysis. It should be recognized, however, that a divalent cation in solution may be complexed and exist as a species that does not act as 2 equiv/mol. The conventional definitions of the solid- and solution-phase equivalent fractions thus are not completely correct. Nevertheless, the conventional concept of 2 equiv/mol for a divalent cation was used in reducing the data for consistency with previous studies on cation exchange.

3. Mass Action Models Various conventional mass action models for cation exchange were applied in fitting the data. Table 2 summarizes the most common mass action models for binary cation exchange, using as an example the exchange of Na+ and Mg2+ on an ion exchanger that possesses discrete sites of -1 charge. The stoichiometric coefficients for Na-Mg exchange are the same for the Kerr, Vanselow, and Gaines-Thomas models, while those in the Gapon and Langmuir-type models differ. In these models, the solid-phase activities are represented by molarity, mole fraction, and equivalent fraction; ideal behavior of cations adsorbed in the solid is assumed, and there is no consideration of activity coefficients for the adsorbed species. 3.1. Formation Constants of Complexes involving Na+, Mg2+, and Zn2+ with Cl-, ClO4-, SO42-. Complexation among electrolyte components was considered in modeling the systems studied. Table 3 shows the formation constants for complexes of Na+, Mg2+, and Zn2+ with Cl-, ClO4-, and SO42-.10 The stability constants for perchlorate complexes were obtained by linear free energy relationships in which the formation constants for metal perchlorate complexes were determined by trends in those for chloride, fluoride, and sulfate.9 The ratio of the concentrations of free ions to total ions dissolved in solution decreases for ions of high charge and for increased concentration. When chloride salts of Na, Mg, and Zn at 0.05 N are dissolved in aqueous solution, the corresponding portions of their free ions are 99.0, 88.1, and 90.4% as determined by calculations with MINEQL+.11 Their percentages are reduced to 96.4, 72.2, and 74.0% in 0.2 N chloride salts. In the 0.05 and 0.2 N sulfate salts of Na, Mg, and Zn, the percentages of free ions are 99.8, (10) Smith, R. M.; Martell, A. E. NIST Critical Stability Constants of Metal Complexes Database; NIST Standard Reference Data: Gaithersburg, MD, 1993. (11) Schecher, W. D.; McAvoy, D. C. MINEQL+ Version 3.0. Environmental Research Software, Inc.: Hallowell, ME, 1994.

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Table 2. Mass Action Models for Cation Exchange between Na and Mg overall exchange equations

half reactionsa

models

Mg2+ + 2P- ) MgP2; kMgP2

Kerr

Mg2+ + 2NaP )

Na+ + P- ) NaP; kNaP

Mg2+ + 2NaP )

Na+ + P- ) NaP; kNaP Gaines-Thomas

Na+ Langmuir-type

Gapon

MgP2 + 2Na+; kV

Mg2+ + 2P- ) MgP2; kMgP2 +

P-

Mg2+ + 2NaP )

) NaP; kNaP

MgP2 +

Mg2+ + P2- ) MgP; kMgP ({P2-} ) {P-}/2) Na+ + P- ) NaP; kNaP 0.5Mg2+ + P- ) Mg0.5P; kMg0.5P

2Na+;

kGT

Mg2+ + NaP ) MgP + Na+; kL

kk )

kv )

([MgP2] ) [Mg0.5P]/2)

Mg0.5P +

Na+ + P- ) NaP; kNaP

kG

{Na } qMg

kL )

kG )

mol/L

{Mg2+}qNa2 {Na+}2XMgP2 {Mg }XNaP 2+

kGT )

0.5Mg2+ + NaP ) Na+;

resin concn

+ 2

MgP2 + 2Na+; kk

Mg2+ + 2P- ) MgP2; kMgP2

Vanselow

mass law equationsb

mole fraction

2

{Na+}2EMgP2 {Mg }ENaP 2+

equivalent fraction

2

{Na+}[MgP]

mol/L

{Mg }[NaP] 2+

{Na+}EMg0.5P

equivalent fraction

{Mg } ENaP 2+ 0.5

a P represents a site with a unit negative charge. b { } and [ ] represent the activity and molar concentration. qMg ) adsorbed Mg concentration ) kMgP2{Mg2+}{P-}2. qNa ) adsorbed Na concentration ) kNaP{Na+}{P-}. X and E represent the mole and equivalent fractions for the adsorbed species. kK, kV, kGT, kG, and kL denote the selectivity coefficients for Kerr, Vanselow, Gaines-Thomas, Gapon, and Langmuir-type cation exchange equations.

Table 3. Formation Constants for Major Solution Complexes Involving Na+, Mg2+, and Zn2+ and Cl-, ClO4-, and SO42log Ka Na+ Mg2+ Zn2+

b

Cl-

ClO4- b

-0.5[NaCl0]

-0.7[NaClO4 0.4[Mg(ClO4)+] 0.25[Zn(ClO4)+]

0.6[MgCl+] 0.46[ZnCl+]

SO420]

-0.72[NaSO4-] 2.23[MgSO40] 2.34[ZnSO40] 3.28[Zn(SO4)22-]

a Values from Smith and Martell10 unless otherwise indicated. Estimated from the stability constants for NO3-, Cl-, and SO42-.9

60.6, and 54.6% and 99.6, 44.9, and 42.8%. The Davies equation is employed for solution-phase activity corrections in MINEQL+. 3.2. Implementation of Models. The mass action models for ion exchange were implemented by assembling the relevant solution phase and ion exchange mass action equations, mole balance equations, and electroneutrality equations and solving then simultaneously with a spreadsheet program. The simplicity of the equilibrium problems involved made this approach convenient. The models could readily be implemented in general chemical equilibrium programs. Parameter values for the mass action models were determined by fitting selected binary cation exchange data using an iterative trial approach and the equilibrium program discussed above. The specific parameters and data sets for which optimization was performed are described in subsequent sections. Optimal parameter values were those corresponding to the minimum sum of squares of residuals (SSR) between calculated and observed solid-phase equivalent fractions for an exchanging ion. Mass action modeling was performed as follows: A. Determination of Selectivity Coefficient 1. Fix kNaP ) 1. 2. Establish two half reactions for Na and Mg (see Table 2). 3. Set up the mole balance equation for total charge sites (CEC) PT )[NaP]+[MgP2])kNaP{Na+}{P-}+kMgP2{Mg2+}{P-}2 4. Solve {P-} for an arbitrary value for kMgP2

5. Calculate [NaP] and [MgP2] and sum up the squares of residuals between calculated and observed values for [MgP2] with respect to every experimental point. 6. Repeat step 5 to obtain the optimized kMgP2 as defined by the least-squares sum of residuals. B. Calculation of the Chemical Equilibrium 1. Follow steps 1 to 5 in part A to calculate [NaP] and [MgP2] for the Kerr model. 2. Perform the relevant calculation for mole or equivalent fractions in the Vanselow and Gaines-Thomas models, and reconstruct the mole balance equation for the Gapon and Langmuir-type equations. (For ternary cation exchange, the mass action equation for the Zn half reaction needs to be included in the mole balance equation.) 4. Results and Discussion 4.1. Cation Exchange Isotherms. Equilibrium ion exchange data are commonly presented in plots of solidphase concentration versus solution-phase concentration for one of the exchanging ions. Exchange isotherms show the preference of an exchanger for one ion over another and are customarily constructed with the experimental data converted to equivalent fraction for both cations adsorbed in resin and dissolved in solution. Figures 2-4 show the binary cation exchange data for combinations of Na, Mg, and Zn in single anion media and in 1:1 mixtures of two anions of chloride, perchlorate, and sulfate at the total cation concentrations (TCC) of 0.05 and 0.2 N. The ternary cation exchange data for the three cations and the same range of solution conditions as in the binary system are exhibited in Figures 5 and 6. Tabulations of the experimental data are available in ref 9. 4.2. Total Amount of Cations Adsorbed on Resin. The total cation equivalents adsorbed on the strongly acidic cation-exchange resin in the binary and ternary cation exchange experiments were close to the cation exchange capacity of the resin (4.6 mequiv/g dry resin) at TCC ) 0.02 and 0.05 N but slightly larger (1.5 to 2.0%) than the cation exchange capacity of the resin at TCC ) 0.2 N. The cation adsorption capacity (CAC) can exceed the cation exchange capacity (CEC) at high ionic strengths12,1 as illustrated in Figure 7. (12) Meares, P.; Thain, J. F. J. Phys. Chem. 1968, 72, 2789.


Figure 2. Data for binary cation exchanges between Na and Mg in the single anion media of chloride, perchlorate, and sulfate at TCC ) 0.05 and 0.2 N, and in 1:1 binary anion mixtures at TCC ) 0.05 N. The curves represent the theoretical nonpreference isotherm for uni-bivalent cation exchange in monovalent anion media (Cl-, ClO4-).

At higher electrolyte concentrations, the cation adsorption capacity for a negatively charged surface depends on the nature and concentration of the electrolyte, as these affect anion adsorption.13 The anion surface deficit near a negatively charged surface increases with ionic strength (see Figure 7), but total adsorbed anion concentration and cation-anion solution complexation also increase. Increased anion adsorption and cation-anion solution complexation can affect total cation adsorption, resulting in CAC exceeding CEC at higher ionic strength. Anions can affect cation adsorption through complexation and anion partitioning to the resin phase by electrostatic, physical, or chemical action. The anion may be attached to the solid as a neutral complex (e.g., MgSO40) or through the long-range electrostatic attraction or shortrange adsorption as a positive complex (e.g., MgCl+, MgClO4+). Thus, solution complexation of cations can have a significant influence in cation exchange. 4.3. Na-Mg Exchange. Figure 2 shows data for binary cation exchanges between Na and Mg in the chloride, perchlorate, and sulfate electrolyte solutions at TCC ) 0.05 and 0.2 N and in the 1:1 mixture of those anions at TCC ) 0.05 N. Also shown are the theoretical nonpreference exchange isotherms, which are based solely on consideration of electrostatic exchange, calculated for univalent-bivalent cation exchange in monovalent anion (Cl-, ClO4-) electrolyte media.14 The preference of the resin for Mg over Na, evident only at TCC ) 0.2 N and low EMg (Figure 2c), was greater in the chloride and perchlorate (13) (a) Helmy, A. K. Soil Sci. 1963, 95, 204. (b) Helmy, A. K. J. Soil Sci. 1963, 14, 217. (c) Van den Hul, H. J.; Lyklema, J. J. Colloid Interface Sci. 1967, 23, 500. (14) Sposito, G. The Thermodynamics of Soil Solutions; Oxford University Press: New York, 1981; pp 136-139.

Langmuir, Vol. 15, No. 20, 1999 6879

Figure 3. Data for binary cation exchanges between Na and Zn in the single anion media of chloride, perchlorate, and sulfate at TCC ) 0.05 and 0.2 N and in 1:1 binary anion mixtures at TCC ) 0.05 N. The curves represent the theoretical nonpreference isotherm for uni-bivalent cation exchange in monovalent anion media (Cl-, ClO4-).

anion media than in the sulfate anion medium. In the sulfate electrolyte, Na was slightly preferred over Mg at high EMg values (parts a and c of Figures 2). The reduced affinity for Mg in the sulfate background arises in part from the formation of the MgSO40 complex in solution, which makes less Mg2+ available to adsorb on the resin. The calculated percentage of MgSO40 complex in solution compared to the total dissolved Mg is diminished with increasing equivalent fraction of Mg in solution (40-36% at TCC ) 0.05 N), which is greater than the reduction in MgCl+ complex in the chloride background (8.1-7.7% at TCC ) 0.05 N) as Mg equivalent fraction increases. 4.4. Na-Zn Exchange. The exchange isotherms for Na-Zn exchange in Figure 3 are similar to those in Figure 2. The extent of Zn adsorption on the resin was greater in the monovalent anion background and at the lower ionic strength (Figure 3a,c). The effect of the anion type in Na-Zn exchange was greater at the lower adsorbed concentrations of Zn (Figure 3a-c). However, the type of anion and the influence of sulfate at TCC ) 0.2 N had a greater effect on Na-Zn exchange than on Na-Mg exchange (compare Figure 3a,c with Figure 2a,c). As in the case of Na-Mg exchange, the reduction of resin affinity for Zn in the sulfate medium can be explained in part by the formation of the ZnSO40 complex in solution. The calculated ratio of Zn complexes to the total dissolved Zn in solution varies from 6.6 to 6.7% in the chloride media and from 51 to 44% in the sulfate media at TCC ) 0.05 N (Figure 3a) as the equivalent fraction of Zn in solution increases. The fraction of Zn solution complexes in NaZn exchanges is greater in the sulfate medium than that of Mg complexes in Na-Mg exchanges, such that Zn selectivity would be expected to be decreased more than

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Figure 4. Data for binary cation exchanges between Mg and Zn in the single anion media of chloride, perchlorate, and sulfate at TCC ) 0.05 and 0.2 N and in 1:1 binary anion mixtures at TCC ) 0.05 N. Dashed line is the nonpreference isotherm for bi-bivalent cation exchange.

Mg selectivity, and this was indeed observed (compare Figures 2c and 3c). 4.5. Mg-Zn Exchange. Figure 4 shows that the results for the Mg-Zn exchange experiments exhibit little selectivity difference between Mg and Zn under the various solution conditions studied. This lack of selectivity was consistent with the heterovalent binary cation exchange data for the Na-Mg and Na-Zn systems, in that the resin selectivity was very similar for Mg and Zn relative to Na as may be seen by comparing Figures 2 and 3. The slight selectivity for Zn relative to Mg in Figure 4 is also consistent with the Na-Mg and Na-Zn exchange data. The ability of Zn to outcompete Mg for the surface despite its greater degree of complexation in solution attests to its greater tendency to interact specifically with resin surface sites. 4.6. Na-Mg-Zn Exchange. Figures 5 and 6 present data for ternary cation exchanges in the single anion background electrolytes of chloride, perchlorate, and sulfate at the two total cation concentrations (TCC) of 0.05 and 0.2 N and in the binary anion media consisting of 1:1 mixtures of those anions at TCC ) 0.05 N. The experiments were performed at a constant amount of Mg (Figure 5) and at constant Zn (Figure 6) in suspension. As in the binary exchange experiments, the selectivity of the divalent cations was reduced in the presence of sulfate and at the higher ionic strength. The anion effect in reducing divalent cation selectivity at the lower surface coverage was marked in the sulfate anion background. Also as in the binary exchange experiments, Mg and Zn exhibited comparable affinities for the resin surface, as evidenced in the comparable exchange isotherms for Mg and Zn in Figures 5 and 6.

Rhee and Dzombak

Figure 5. Data for ternary cation exchanges involving Na, Mg, and Zn in the single anion media of chloride, perchlorate, and sulfate at TCC ) 0.05 and 0.2 N, and 1:1 binary anion mixtures at TCC ) 0.05 N with constant total amount of Mg. The upper and lower solid curves represent the equivalent fractions of Zn and Mg in resin, while the dotted line shows the equivalent fractions of Na in resin.

5. Mass Action Modeling Mass action modeling was performed by first fitting the binary cation exchange data for the chloride media at TCC ) 0.05 N and then applying the models to predict the other binary cation exchanges and the ternary cation exchanges at TCC ) 0.05 and 0.2 N. The exchange isotherms for the experimental data were fitted and predicted with consideration of solution-phase speciation and solid-phase activity. In the mass action model, the customary activity terms for solid-phase activity in the Kerr, Vanselow, Gaines-Thomas, Gapon, and Langmuirtype equations were used with calculation of solutionphase speciation and use of the Davies equation. 5.1. Exchange Isotherm in Terms of the Concentration of Free Ions. All experimental data were adjusted for solution-phase speciation by calculating speciation with MINEQL+ 11 using the total dissolved element concentrations measured by atomic absorption spectroscopy. The experimental exchange isotherms subsequently were plotted on an equivalent basis of total cation concentration in resin versus free cation concentration in solution; the results are presented in Figure 8. (Note that the exchange isotherms in all previous figures are presented with the total dissolved element concentration used to calculate the cation equivalent fraction.) By taking into account solution-phase speciation in preparing the exchange isotherms plots, the selectivity difference related to the different anionic media tended to be reduced, compared to conventional exchange isotherms. When speciation is not considered and the total


Figure 6. Data for ternary cation exchanges involving Na, Mg, and Zn in the single anion media of chloride, perchlorate, and sulfate at TCC ) 0.05 and 0.2 N and in 1:1 binary anion mixtures at TCC ) 0.05 N with constant total amount of Zn. The upper and lower solid curves represent the equivalent fractions of Mg and Zn in resin, while the dotted line shows the equivalent fractions of Na in resin.

dissolved element concentration is assumed to be free ions, the selectivity is higher and lower in mono- and divalent anionic media, respectively (compare the 0.2 N data in Figure 8a,b with the same data plotted in Figures 2c and 3c). While the anion effect is reduced with consideration of speciation, an influence of anion type in cation exchange is still present as is evident in Figure 8. 5.2. Determination of Selectivity Coefficients. The conditional selectivity coefficients for the Kerr, Vanselow, Gaines-Thomas, Gapon, and Langmuir-type equations were extracted from the binary cation exchange data for Na-Mg and Na-Zn in chloride background at TCC ) 0.05 N. The selectivity coefficients were considered for half reactions of the charged site with Na, Mg, and Zn (kNa, kMg, and kZn) as presented in Table 2 and discussed by Dzombak and Hudson.15 kNa was set to 1 as a matter of convention. kMg and kZn were optimized to yield the best fits to the corresponding Na-Mg and Na-Zn exchange data through the least-squares method. The sum of squares of residuals associated with the optimum fits and all predictions are presented in ref 9. (As optimum parameter values were determined by manual adjustment followed by calculation of sum of squares of residuals, standard errors in the parameter values could not be calculated.) The resulting values for the corresponding kMg and kZn were 2.30 and 3.03 for the Gaines-Thomas model and 1.62 and 2.10 for the Gapon model, the two (15) Dzombak, D. A.; Hudson, R. J. M. In Aquatic Chemistry: Interfacial and Interspecies Processes; Huang, C. P., C. R. O’Melia, Morgan, J. J., Eds.; Wiley: New York, 1995; Chapter 4.

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Figure 7. Schematic plots of (a) electrolyte ion concentrations versus distance from the negatively charged surface with an electrolyte solution predicted by Gouy-Chapman theory and (b) surface excess and deficit concentrations predicted by GouyChapman theory (GCT) for a negatively charged surface, and typical observed cation adsorption capacity as a function of cation solution concentration of an electrolyte.

mass action models on which focus was placed. The selectivity coefficients cited for Na, Mg, and Zn were used to predict cation exchange for all the other binary and ternary cation exchange systems studied. 5.3. Predictions of Binary Cation Exchanges. Predictions of Na-Mg and Mg-Zn exchanges in the different anion backgrounds made with the GainesThomas and Gapon models are presented in Figures 9 and 10. The Gaines-Thomas model showed fair and good agreement with the experimental data for Na-Mg exchanges and Mg-Zn exchanges, respectively (Figure 9). It underpredicted adsorption of the divalent cation for the Na-Mg exchanges regardless of the type of background anion at TCC ) 0.2 N. Only slightly different isotherm lines were predicted for the Mg-Zn exchanges in different types of anionic media consistent with the data. The Gapon model provided accurate predictions for Na-Mg exchanges but poor fits for the Mg-Zn exchanges. The predicted Gapon isotherms (Figure 10) were in good agreement with the observed Na-Zn exchanges at TCC ) 0.2 N, but predictions deviated significantly from the data for Mg-Zn exchange. These results demonstrate that while consideration of solution speciation can aid prediction of ion exchange phenomena with conventional ion exchange models, there are basic limitations in using mass action modeling to predict ion exchange across a range of TCC with only one set of selectivity coefficients. The other mass action models generally yielded lower quality predictions, and the results are not presented (see Rhee9). In the Kerr model, where molarity is chosen for activity of the adsorbed species, the calculated divalent cation concentration in heterovalent cation exchange was much higher than the experimental data at TCC ) 0.2 N.

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Figure 8. Plots of equivalent fraction adsorbed cations versus equivalent fraction of free dissolved cations for binary cation exchanges involving Na, Mg, and Zn in different anion media at TCC ) 0.05 and 0.2 N. Free cation concentrations were calculated with MINEQL+. The curves represent the theoretical nonpreference isotherm for uni-bivalent cation exchanges (solid lines at TCC ) 0.05 N, dotted lines at TCC ) 0.2 N) and the dotted line represents for bi-bivalent cation exchange in monovalent anion media (Cl-, ClO4-).

The use of mole and equivalent fractions in the Vanselow and Gaines-Thomas equations caused the predictions for the corresponding divalent cation isotherm curves to be shifted downward at TCC ) 0.2 N. The Langmuir-type equation yielded lower and higher predictions for the exchangeable divalent cation at lower and higher surface coverages of the cation, respectively. This equation may not account for the initial higher selectivity of a divalent cation in heterovalent cation exchange. All the mass action models except the Gapon model yielded the same exchange isotherms for Mg-Zn exchanges. 5.4. Predictions of Ternary Cation Exchanges. Figure 11 shows predictions made with the GainesThomas model of the ternary cation exchanges in the chloride and sulfate media at TCC ) 0.05 and 0.2 N, in which the total amount of Zn present in the resin suspension (TOTZn) was constant at 0.005 and 0.02 N, respectively. The Gaines-Thomas model predicted the exchanger composition well for the Na-Mg-Zn exchanges in the chloride media at TCC ) 0.05 and 0.2 N (Figure 11a) but poorly for ternary cation exchange in the sulfate media as shown Figure 11b. There was good agreement between the calculated and measured values for the exchange isotherm at TCC ) 0.05 N, but at TCC ) 0.2 N, higher and lower adsorptions of Na and Mg were predicted, respectively. Gapon model predictions for the same ternary exchange data as Figure 11 were in poor agreement with the experimental data, even at TCC ) 0.05 N from which the selectivity coefficients were extracted using binary data.

Rhee and Dzombak

Figure 9. Gaines-Thomas mass action modeling for binary cation exchanges in different anion media at total cation concentrations of 0.05 N (s) and 0.2 N (- - -) with solutionphase speciation and the Davies equation for solution-phase activity correction. Note: The abscissa is the equivalent fraction of dissolved cations.

The quality of the fits (presented in Rhee9) can be explained by the poor fitting that was achieved for the binary cation exchanges, as shown in Figure 10c. Thus, the Gapon model, though known to be useful for bi-monovalent cation exchange modeling,6d,14 does not seem to be acceptable as a cation exchange model in multicomponent systems in which several divalent cations are present in the suspension. The Kerr, Vanselow, and Langmuir-type models also did not yield accurate fits for ternary cation exchanges.9 The Vanselow model predictions were even worse when Na-Zn exchanges took place in the presence of Mg. However, the Kerr model showed fair predictions of the measured values at TCC ) 0.05 N. The inaccuracies in prediction of cation exchange on the sulfonate resin for the mass action models, including the Gaines-Thomas model, may relate to incomplete consideration of microscale processes involved in ion exchange, especially specific adsorption. Limited predictive accuracy was also observed in applying available thermodynamic models for ion exchange to the same data set.9 The predictive performance of a more mechanistic ion exchange model with the data set is examined in a related paper.8 6. Summary and Conclusions The type of background electrolyte anion was shown to affect cation exchange on a strong acid cation-exchange resin in several ways, by increasing the total cation adsorption above the measured cation exchange capacity and by reducing the selectivity of certain cations through solution complexation. Regardless of the type of back-


Figure 10. Gapon mass action modeling for binary cation exchanges in different anion media at total cation concentrations of 0.05 N (s) and 0.2 N (- - -) with solution-phase speciation and the Davies equation for solution-phase activity correction. Note: The abscissa is the equivalent fraction of dissolved cations.

ground anion, the total adsorbed amount of cations was increased slightly (1.5-2%) above the cation exchange capacity at total cation concentrations of 0.2 N. The increased divalent cation saturation of the resin was likely due to anion adsorption, probably by adsorption of cationanion complexes.8 The influence of background anion in cation selectivity was observed in uni-bivalent binary cation exchange between Na-Mg and Na-Zn, but the anion effect was weak in homovalent binary cation exchange between MgZn. Mg and Zn were adsorbed selectively by the resin relative to Na to a comparable degree. The affinity of the resin for the divalent cations was not much different in the backgrounds of chloride and perchlorate. However, the affinity of the resin for Mg and Zn was lower in the sulfate background, reflecting greater solution complexation of the cations than in the monovalent anion background. The presence of sulfate in the electrolytes with two-anion mixtures also diminished the selectivity for the divalent cations. Data for the ternary cation exchange of Na, Mg, and Zn were consistent with the binary cation exchange data. Mg and Zn again exhibited similar affinity for the resin surface, with slightly greater adsorption for Zn, and sulfate served to reduce cation adsorption.

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Figure 11. Gaines-Thomas mass action modeling for ternary cation exchanges at constant TOTZn (0.0066 N at TCC ) 0.05 N; 0.019 N at TCC ) 0.2 N) in different anion media at total cation concentrations of 0.05 N (thin lines) and 0.2 N (thick lines) with solution-phase speciation and the Davies equation for solution-phase activity correction. Note: The abscissa is the equivalent fraction of dissolved cations.

Several conventional mass action models were fitted to binary cation exchange data in chloride media and used to predict binary and ternary cation exchange for the other systems studied. The Gaines-Thomas model was best able to predict binary and ternary cation exchange on the sulfonate resin in the different anionic media and different ionic strengths. The predictions of the Gapon model were poor for ternary cation exchange involving two divalent cations. The results indicate that mass action models can account at least approximately for the effect of anion type on cation exchange with proper consideration of solution speciation and activity correction. Inaccuracies in prediction of cation exchange on the sulfonate resin for the mass action models may relate to incomplete consideration of microscale processes involved in ion exchange, especially specific adsorption. Acknowledgment. This work was supported by a Korea Electric Power Corporation Fellowship to In Rhee and by the National Science Foundation through a Presidential Young Investigator Award (Grant No. BCS9157086) to David Dzombak. LA970031G

Binary and Ternary Cation Exchange on Strong Acid Cation Exchange

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