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Ind. Eng. Chem. Res. 2001, 40, 714-720
Equilibrium Modeling of Combined Ion-Exchange and Molecular Adsorption Phenomena Socrates Ioannidis*,† and Andrzej Anderko OLI Systems, Inc., 108 American Road, Morris Plains, New Jersey 07950
A thermodynamic framework is presented for modeling combined ion-exchange and molecular adsorption phenomena at a solid-liquid interface. The analysis of the uptake of both ionic and molecular species by the solid surface is based on the concept of exchange reactions. The adsorption model is coupled with a previously developed comprehensive thermodynamic speciation model for the aqueous phase. A parameter regression procedure is developed that decouples the determination of equilibrium constants from the evaluation of activity coefficients for the adsorbed phase. The model is applied to analyze the behavior of an aqueous aniline system in contact with a clay material saturated with calcium. In this system, an ion-exchange reaction between anilinium and calcium ions takes place simultaneously with the adsorption of neutral aniline molecules. The combined adsorption and speciation model is also used for analyzing the coupling of solid solubility and ion exchange in a system that contains a phosphate rock and a clinoptilolite mineral loaded with a mixture of potassium and ammonium ions. For all investigated systems, good agreement with experimental data is obtained. Introduction Solid-liquid adsorption processes involving the use of ion-exchange resins or activated carbon are routinely applied in chemical process industries for the separation of species from liquid streams.1,2 Knowledge of adsorption phenomena at the solid-liquid interface is also crucial for understanding the fate and transport of environmental contaminants, which commonly come into contact with surfaces that provide sites with which ions and molecules interact.3,4 For a comprehensive representation of such phenomena, it is necessary to account for ion-exchange and molecular adsorption, as well as chemical equilibria and speciation in the bulk aqueous phase. In recent studies,5,6 internally consistent models have been developed for ion exchange and molecular adsorption. These models were coupled with a previously developed computational framework for predicting the properties of bulk aqueous systems.7 A unified thermodynamic framework for ion- and molecular-exchange phenomena makes it possible to analyze solid-liquid interfacial equilibria on surfaces that provide sites for both phenomena. In this work, we perform such an analysis for an aqueous aniline system, which involves the molecular adsorption of aniline with a simultaneous ion-exchange of its dissociated form on a clay silicate loaded with calcium.8 Speciation in the adsorbed phase will be studied in parallel with the speciation in the bulk phase. Further, we analyze the coupling of the solubility of a phosphate rock with ionexchange phenomena on a clinoptilolite zeolite.3 Data Reduction Scheme for Ion- and Molecular-Exchange Reactions Customarily, ion-exchange systems are analyzed in terms of equilibrium constants. Nonideality in the solid and liquid phases is taken into account using activity * Corresponding author. E-mail:
[email protected]. Tel: (973) 377-7600. Fax: (973) 377-7616. † Presently at Hyman Beck & Company, Inc., 100 Campus Drive, Florham Park, NJ 07932.
coefficients. Recently, a data reduction framework has been developed for the representation of ion-exchange systems.5 This framework decouples, in a thermodynamically consistent way, the determination of the equilibrium constant from that of the activity coefficients. Sample applications showed that this data reduction scheme is also suitable for verifying the consistency of experimental data reported at various concentrations. This verification is accomplished by analyzing selectivity coefficient plots. Whereas the exchange reaction concept is customarily used for ion-exchange systems, molecular adsorption has traditionally been modeled using single-component and multicomponent adsorption isotherms. Furthermore, single-component adsorption isotherms can be utilized for multicomponent equilibria using a thermodynamic framework, such as the ideal adsorption solution theory.9 However, the treatment of molecular adsorption within the context of multicomponent phase equilibria can be greatly facilitated by introducing the concept of exchange reactions for molecular adsorption and by using only binary parameters and pure-component saturation capacities.10 Also, this approach introduces the Gibbs-Duhem consistency equation for the adsorbed solid species.11 Along these lines, the ionexchange data reduction scheme can also be applied to molecular adsorption.6 We consider here a system that comprises a bulk and an adsorbed phase. The bulk phase is an aqueous liquid that contains both ions and molecules. The solid medium is considered to provide sites with fixed charges for ion exchange, as well as sites with porosity on which molecular adsorption takes place. Some sites, such as those on mineral oxides, may have variable surface charges and be protonated and deprotonated based on the prevailing bulk-phase pH and ionic strength conditions. Such reactions, along with specific electrolyte adsorption on this type of site, are treated with surface complexation models.12,13 For a system including an adsorbed and a bulk phase that contain both ions and molecules, we can write the equilibrium condition for a species i as14
10.1021/ie000554a CCC: $20.00 © 2001 American Chemical Society Published on Web 12/15/2000
Ind. Eng. Chem. Res., Vol. 40, No. 2, 2001 715
∆µoi + RT ln
asi ali
+ vsi π + ziF∆φ ) 0
(1)
In eq 1, ai is the activity of component i; v is its molar volume; and the superscripts s and l denote the adsorbed and bulk phases, respectively. ∆µoi is the differol ence of the standard potentials (µos i - µi ) between the two phases; F is Faraday’s constant; zi is the charge of species i; and π and ∆φ are the osmotic pressure and electrochemical potential difference in the interface, respectively. At a given equilibrium point, the osmotic pressure and the electrical potential difference are system properties (i.e., they apply to all species in the system). For the calculation of the osmotic pressure, we can use any neutral molecule and set the ∆φ term equal to zero. For example, in aqueous systems, we can choose water as the neutral species and write14
(
π)-
∆µow vsw
)
s RT aw + s ln l vw aw
(2)
where aw is the activity of water. In dilute aqueous ionexchange systems, the water fraction of the exchange medium, and hence the osmotic pressure, can be considered constant for the whole isotherm.14 Therefore, a simple measurement of the water retention by the exchange medium is sufficient for the determination of the adsorbed water activity. By combining eqs 1 and 2, the electrical potential difference can be estimated as
(
)
vsi ∆µoi - ∆µow s vw asi alw RT ∆φ ) ln l s ziF ziF ai aw
( )( )
vis/vws
(3)
We see from eq 3 that the electrical potential difference at the solid-liquid interface varies along an isotherm. By rewriting eq 3 with respect to a species j and substituting it along with eq 2 into eq 1, we get
zj∆µoi - zi∆µoj +
[
∆µow + RT ln
( )](
)
asw
zivsj - zjvsi
alw
vsw
+ RT ln
( )( ) asi ali
zi
alj
asj
zj
)0 (4)
Equation 4 corresponds to an exchange reaction between the species i and j
zj i l + zi j s ) zj i s + zi j l
(5)
Assuming that the partial molar volumes are constant and that a constant osmotic pressure (i.e., a constant solvent adsorbed fraction) is maintained along an isotherm, a pair selectivity equation can be formed by calculating the differences of the left-hand side of eq 4 between two equilibrium points Q1 and Q2 on the exchange isotherm,5 i.e.
ln
(γsj )zi(Q1) (γsj )zi(Q2)
+ ln
(γsi )zj(Q2) (γsi )zj(Q1)
Q1 ) ) [ln Kc]Q 2
ln Kc(Q1) - ln Kc(Q2) (6)
In eq 6, Kc denotes the Vanselow selectivity coefficient and γ is the activity coefficient. For a multicomponent mixture, the charges in eq 6 are replaced by stoichiometric coefficients that are constant for each species in the complete set of exchange reactions. Another way to derive eq 4 is to multiply eq 1, as written for species i, by zj and to multiply the same equation written for species j by zi. Then, by subtracting these two equations, we get
zj∆µoi - zi∆µoj - (zivsj - zjvsi )π + RT ln
( )( ) asi ali
zj
alj
asj
zj
)0 (7)
When eq 2 is substituted into eq 7, eq 4 results. Equation 7 is valid along an isotherm for ion-exchange systems for which constant molar volumes in the adsorbed phase and constant osmotic pressure are assumed. In contrast to ion exchange, the ∆φ term in eq 1 drops out for molecular adsorption, and the osmotic pressure variation along an isotherm can be significant for molecules of different sizes. In many cases, it is fair to assume a constant-thickness layer. This is the case for aqueous systems of sparingly soluble organics for which the solid exchange medium has a much lower capacity for the organic species compared to the capacity for water. When the molecular exchange of a species i with a species j is considered, eq 6 is still valid.6 We can verify this by substituting eq 2, as written for species j, into eq 1 with the zi value set equal to unity and the zj value set equal to the ratio of the molar capacities of species i to species j. It should be noted that the molar volume ratio can be translated into the molar capacity ratio using Gurvitsch’s rule.10 For example, when water is species i, eq 6 becomes
ln
(γsj )(Q1) (γsj )(Q2)
+ ln
[ ] (γsi )(Q2)
(γsi )(Q1)
r Q1 ) [ln Kc]Q ) 2
ln Kc (Q1) - ln Kc(Q2) (8)
where r becomes the ratio of the saturation capacities of the solid for water and the species j. Equation 8 corresponds to the following molecular-exchange reaction:
rH2Ol + j s S rH2Os + j l
(9)
In contrast to ion-exchange systems, the stoichiometry of eq 9 is not observed on a molecular level. Therefore, fractional stoichiometry is used to represent an average molar stoichiometry that is consistent with the equilibrium partitioning between the two phases. The data reduction scheme in molecular adsorption systems commonly involves reduced surface excess plots, whereas the data reduction in ion-exchange systems involves uptake plots.6 In principle, simultaneous data reduction for ion exchange and molecular adsorption requires the use of the prevailing osmotic pressure at each equilibrium point. However, the analysis can be simplified by assuming that the zivsj - zjvsi term in eq 4 is close to zero. This assumption will be employed for the applications presented here. In summary, eq 6 is used in our data reduction scheme for all species pairs involved in either molecular or ion-
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Table 1. List of Adjustable Parameters, Their Interpretations, and Methods of Determination parameter
interpretation
determination
mass balance parameters: single-component saturation capacities (mi), ion exchange capacity (NT)
traditionally used in classical adsorption models
activity coefficient parameters (Wilson parameters Λij) equilibrium constant Kij
measure nonideal interactions in the adsorbed phase assigned to each exchange reaction
exchange reactions. The activity coefficients in the adsorbed phase are calculated from the Wilson model,15 i.e.
ln γsk ) -ln(
∑j
xsj Λkj) +
∑i
( )
xsi 1 -
Λik
∑j
xsj Λij
(10)
where Λik and Λki are the two Wilson parameters for the binary pair i-k. The Wilson parameters comprise effects of both lateral and vertical interactions. Such activity coefficients are characterized as global surface activity coefficients. The two types of interactions in the adsorbed phase could be decoupled with the introduction of surface heterogeneity parameters within a model that preserves the current model structure.16 However, for the determination of the surface heterogeneity parameter, comprehensive experimental adsorption studies would be required for a range of model systems. Consistent determination of the parameters from data for natural systems, where several processes occur simultaneously, would become a more difficult task because of the coupling of the model parameters. Having determined the Wilson parameters, the equilibrium constant is calculated at each equilibrium point Q, i.e.
ln K ) ln Kc(Q) + ln(γsi )zj - ln(γsj )zi
(11)
Equation 11 implies that the resulting equilibrium constant is invariant to compositional changes in the adsorbed phase.5,6 It is noteworthy that eq 11 does not depend on the normality of the aqueous system. Hence, for ion-exchange systems, the plot of the selectivity coefficient with respect to the aqueous mole fraction should be invariant with respect to the aqueous normality (Vanselow plots).5 Deviations from eq 11 are more pronounced in the limits of the concentration range, mainly because of an inherently larger experimental uncertainty.17 In molecular adsorption systems, the validity of eq 11 is based on the selection of the right stoichiometric coefficient r. This stoichiometric coefficient is computed as the ratio of the molar-adsorption capacities, which can be experimentally determined. When these capacities are not reported, they have to be estimated using, for example, Gurvitsch’s rule.10 In addition to the consistency test of the invariance of the equilibrium constant with respect to the liquid composition, the proposed framework employs the triangular rule as an additional consistency test. The triangular rule test is a mathematical statement of the linear dependence of the N(N - 1)/2 equilibrium constants in an N-species system. Only N - 1 equilibrium constants are required to uniquely determine the system of reactions considered for solving the mass balance in the mixture.
The saturation capacities are ideally determined from adsorption of a pure vapor phase. If such data are not available, then they are obtained graphically from surface excess graphs.22 The ion-exchange capacities are reported for each material. Determined from selectivity plots based on data reduction schemes.5,6 Derived from the model based on a decoupling scheme.5,6
Having determined the thermodynamic parameters, the set of equilibrium constants is numerically solved by assuming a monolayer for the adsorbed-phase mass balance, i.e.
nsi
N
l)
∑ i)1 m
(12)
i
In eq 12, mi denotes the capacity of the solid medium for species i and nsi is the concentration of species i in the adsorbed phase (mmol/g). For ion-exchange systems, eq 12 becomes N
NT )
nsi ∑ i)1
(13)
because the solid has the same capacity (mequiv/g) for all species. This capacity is denoted by NT and is assumed to be constant along an isotherm. In general, eq 12 can be modified if multiple layers are formed. In Table 1, we summarize the adjustable parameters used by the model outlined in this section. It should be noted that the equilibrium constant is an outcome of the decoupling process, as illustrated above. The parameters that are directly regressed from the mixture selectivity data are those of the activity coefficient model. Aniline-Water Sorption on a Calcium-Montmorillonite Clay In this section, a case study of aniline adsorption on a clay material8 is presented. Aniline is a molecule that raises environmental concerns because it could appear as an intermediate during the degradation of pesticides and in the manufacture of products such as rubber. The adsorption of aniline from solution on clays is strongly pH-dependent because of the formation of anilinium ions at low pH. The pKa value for aniline at 25 °C is 4.601.18 The speciation of aniline in aqueous solutions, as calculated with the OLI software,7 is shown in Figure 1. This system is difficult to model using the traditional approach based on the use of adsorption isotherms. Even when a satisfactory equation is found to represent the isotherm, a variable set of parameters must be devised depending on the pH range.8 This is due to the simultaneous occurrence of ion exchange and molecular adsorption. Clearly, all exchange phenomena have to be incorporated in the model in order to obtain a satisfactory representation of experimental data over a wide range of conditions. In the model proposed here, the exchange phenomena at the solid-liquid interface are represented by two equilibrium constants. These constants represent the ion-exchange reaction between the anilinium and calcium ions and the molecular-
Ind. Eng. Chem. Res., Vol. 40, No. 2, 2001 717
Figure 1. Speciation of aniline in the aqueous phase.
Figure 2. Equilibrium constant for the molecular-exchange reaction in the system aniline-water.
exchange reaction between the water and the aniline molecules, i.e.
2anilinium+ l + Ca - montmorillonites2 ) 2anilinium - montmorillonites + Ca2+ l (14) anilinel + 3H2O - montmorillonites ) aniline - montmorillonites3 + 3H2O (15) The ion-exchange capacity of the solid surface is reported as 0.920 mequiv/g,8 while the capacity of the solid for aniline is set to 0.438 mmol/g, equal to the maximum capacity reported at pH 7. The capacity of the solid for water is estimated as 1.292 mmol/g by applying Gurvitsch’s rule. These values give the stoichiometry reported in eq 15, which denotes the exchange by the solid medium of 1 mol of aniline with approximately 3 mol of water. From the experimental protocol, we deduce that about 2.2 g of solid/L were used in the experiments. The uptake plots are reported for pH 4.6 and pH 7 at 20 °C. By assuming that the aniline dissociation constant remains the same at 20 °C, we note from Figure 1 that aniline in the bulk phase is mostly in the molecular form. Hence, by using the surface excess data reported at pH 7, we can calculate the thermodynamic parameters for the molecular-exchange reaction between aniline and water without interference from the ionexchange reaction. The data reduction scheme gives the values of the Wilson parameters as being equal to 0.148 and 0.165 for the aniline-water and water-aniline pairs, respectively. The equilibrium constant (ln K) is 7.02 as an average value obtained from Figure 2. For these calculations, the aqueous activity coefficient of aniline was set equal to its infinite dilution value, while that of water was set equal to unity. After the molecularexchange parameters had been determined, the ionexchange parameters were determined using the data for the pH 4.6 isotherm. It should be noted that molecular exchange has to be taken into account for the determination of the ion-exchange parameters, and therefore, an iterative numerical procedure has to be applied. The equilibrium constant of reaction 14 is determined as 1.263 in log units, while the Wilson
Figure 3. Adsorption isotherms of aniline on calcium-montmorillonite clay at two pH values.
coefficients for the calcium-anilinium and aniliniumcalcium pairs are obtained as 0.376 and 0.074, respectively. Our results for both isotherms are shown in Figure 3. The model parameters are determined based on the assumption that the two equilibrium constants (molecular- and ion-exchange) are invariant with respect to the bulk composition and pH variations. Although the adsorbed phase contains both ions and molecules, the parameter identification can be simplified by separately considering surface excess and uptake plot data. To keep the number of model parameters low, we have set the ion-molecule Wilson parameters to unity. In Figure 4, we plot the adsorbed phase speciation for an initial aniline input of 0.0088 mol in a system containing 2.2 g of clay/L. This corresponds to the fourth experimental point, counting from the last point reported on the pH 4.6 isotherm. Figure 4 reveals that the speciation in the adsorbed phase is different from that in the bulk phase. The neutral point for the adsorbed phase is at pH 5 rather than pH 4.6.
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Ind. Eng. Chem. Res., Vol. 40, No. 2, 2001 Table 2. Comparison of Experimental Adsorbed-Phase Concentrationsa with Model Calculations (Exp/Model) clinoptilolite/ phosphate rock mass ratio
K
Ca
P
pH
1:1 2:1 3:1 5:1 10:1 20:1
1.86/2.75 1.38/1.85 1.14/1.51 1.01/1.22 0.82/0.98 0.70/0.85
0.014/0.014 0.009/0.008 0.008/0.006 0.006/0.005 0.004/0.003 0.002/0.003
0.015/0.020 0.030/0.035 0.044/0.046 0.069/0.062 0.094/0.078 0.116/0.085
8.2/6.2 8.6/6.2 8.7/6.2 8.9/6.2 9.0/6.3 9.0/6.3
a
Figure 4. Adsorbed-phase speciation as a function of pH for the aniline + calcium-montmorillonite clay aqueous system at a total aniline input of 0.0088 mol in a system with 2.2 g of clay/L.
Solubility and Ion Exchange In this section, we study the coupling between ion exchange on a clinoptilolite mineral and the dissolution of a phosphate rock from North Carolina (NC)3. For the solubilization reaction of the phosphate rock, we assume an idealized empirical form
Ca9.5Na0.3Mg0.1(PO4)5(CO3)1.1F4 + 10H+ T 9.5Ca2+ + 0.3Na+ + 0.1Mg2+ + 1.1CO32- + 5H2PO4- + 4F- (16) The empirical formula for the NC phosphate rock is3 Ca9.57Na0.31Mg0.12(PO4)4.87(CO3)1.13F4.25. Equation 16 is further used for the analysis of experimental data. The experimental protocol involves an aqueous system containing a clinoptilolite mineral, which was loaded with various ratios of potassium to ammonium ions, along with a phosphate rock.3 The release of calcium ions from the phosphate matrix induces ion-exchange reactions on the clinoptilolite matrix between the calcium and potassium and calcium and ammonium ions. The study of this system is important for understanding the controlled release of ammonium for uptake by plants.3 Also, we consider here ion-exchange reactions of the above ions with sodium, which is included in the rock’s formula. At the same time, we assume that the effect of magnesium ions is minimal because of their low concentration in the phosphate matrix. For example, the ion-exchange reactions of Ca2+ with the ions K+, NH4+, and Na+ are represented in the database as follows
Ca - clinoptilolite2 + 2K+ ) 2K clinoptilolite + Ca2+ (17a) Ca - clinoptilolite2 + 2Na+ ) 2Na clinoptilolite + Ca2+ (17b) Ca - clinoptilolite2 + 2NH4+ ) 2NH4 clinoptilolite + Ca2+ (17c)
Concentrations are in millimoles per liter.
The stability constant log(Ksp) of eq 16 has been set equal to -18. For comparison, a stability constant of -20.56 is reported19 for a similar mineral with the formula Ca9.54Na0.33Mg0.13(PO4)4.8(CO3)1.2F2.48. The dissolution reaction of the phosphate rock leads to the formation of two new solids in the system, i.e., Ca10(PO4)6F2 and CaF27. With the stability constant set equal to -18, total dissolution is obtained. Considering one of the experimental protocols,3 in which a constant mass of clinoptilolite (25 g) is added to water (10 mL) in a series of repeated experiments with a variable mass of the phosphate rock, the partial dissolution of the rock results in an invariance of ion concentrations in the sequence of experiments. A constant clinoptilolite/aqueous-phase mass ratio of 40:1 was kept for a series of six experiments. The clinoptilolite/phosphate rock mass ratios were varied from 1:1 to 20:1 by changing the mass of the phosphate rock in the solution. To reproduce the reported data, we have regressed the solubility constants of Ca10(PO4)6F2 and CaF2 using the aqueous concentrations of the K+ and Ca2+ ions and the total phosphorus concentration in the aqueous systems. The HPO4- and H2PO42- ions are the two major phosphorus species in the aqueous solutions. The obtained log Ksp parameters were -6.265 and -12.374 for the Ca10(PO4)6F2 and CaF2 solids, respectively. For comparison, experimental values reported in the literature18 for Ca10(PO4)6F2 range between -1.10 and -3.57. Also, a value of -11.2 can be calculated for the solid CaF2 from its standard thermodynamic properties.20 A comparison between the calculations and experimental data is shown in Table 2. A certain discrepancy in the pH calculations is shown in Table 2. The calculated values would be closer to the reported ones3 if CO2 were allowed to enter the aqueous solution (i.e., in a system open to the atmosphere). For cases in which only clinoptilolite or clinoptilolite and phosphate rock were in the aqueous solution, the reported pH values were about 7, 7.5, and 8. It is noteworthy that a lower number of fluorine atoms in the empirical formula of the phosphate rock (eq 16) would increase the final pH of the solution but at the expense of worse predictions of the concentrations of other ions. The thermodynamic parameters, i.e., the equilibrium constant and Wilson parameters for the ion-exchange reaction between the K+ and Ca2+ ions, were obtained from a previous work.5 In the same study, the thermodynamic parameters for the Ca2+-Na+ and K+-Na+ systems are also reported. The thermodynamic parameters for the K+-NH4+, Na+-NH4+, and Ca2+-NH4+ exchange reactions on clinoptilolite are obtained by reducing the available uptake data.21 The analysis of these three ammonium systems can also be used to verify the internal consistency of the parameters by
Ind. Eng. Chem. Res., Vol. 40, No. 2, 2001 719 Table 3. Parameters for Ion-Exchange Systems on Clinoptilolite (1-2)
Λ12
Λ21
ln K
K+-Na+ Ca2+-Na+ Ca2+-K+ NH4+-Na+ NH4+-K+ NH4+-Ca2+
2.415 1.792 0.164 1.731 2.405 1.475
1.235 3.123 6.054 0.717 1.398 7.793
3.198 -1.772 -8.537 1.694 -1.691 5.055
Figure 6. Concentrations of aqueous species versus the initial charge of K+ on clinoptilolite in a system with NC phosphate rock.
Figure 5. Uptake plots for the three systems NH4+-K+, NH4+Na+, and NH4+-Ca2+ on clinoptilolite.
applying the triangular rule. The triangular rule can be applied in three ternary systems formed from the six binaries. These ternary systems are Na+-NH4+-K+, Na+-NH4+-Ca2+, and Ca2+-NH4+-K+. The uptake curves for the three ammonium systems21 include reverse and forward exchange points and reveal a maximum exchange capacity for ammonium. By considering only a small fraction of other exchangeable ions on the matrix, we have assumed a maximum ammonium fraction on the matrix equal to 0.65, 0.62, and 0.60 for the Na+-NH4+, Ca2+-NH4+, and K+-NH4+ systems, respectively. With these values, the reported equivalent fractions were normalized. The normalization procedure ensures that the parameter values are independent of the exchange capacity of clinoptilolite. The thermodynamic parameter values for all six ionexchange systems are shown in Table 3. An exchange capacity of 2.04 mequiv/g has been assumed for clinoptilolite.16 This value is reasonably close to those reported3 for clinoptilolite saturated with K+ and NH4+. To examine the compliance of the parameters reported in Table 3 with the triangular rule, we calculate Na+ K+ K+ Ca2+ Na+ the quotients (KNH +) (KNa+)/(KNH +), (KNH +) (KCa2+)/ 4 4 4 + 2+ + + Na Ca K K 2 2 (KNH +) , and (KNH +) (KCa2+)/(KNH +) . For the first quo4 4 4 tient, we compute a value of about 1.00, whereas for the other two quotients, a value of about 0.90 is obtained. Our calculations for the uptake plots for the three ammonium systems are shown in Figure 5. In Figure 5, the equivalent mole fraction of ammonium in the adsorbed phase is plotted versus the equivalent mole fraction in the bulk phase. The model parameters were further applied to predict aqueous ion concentrations and solid equivalent fractions in a series of experiments in which the ratio of
Figure 7. Adsorbed-phase composition on clinoptilolite versus the initial loading of K+ in a system with NC phosphate rock.
K+/NH4+ in the clinoptilolite loadings was fixed. A 5:1 mass ratio of clinoptilolite to phosphate rock and a 40:1 clinoptilolite to water mass ratio were used. Our predictions for the aqueous concentrations of the NH4+, K+, and Ca2+ ions and total P are shown in Figure 6, along with the experimental data. Our predictions for the NH4+ ions are close to the experimental data. However, this is less true for the K+ predictions because the fully K+ loaded clinoptilolite shows higher aqueous K+ concentrations than those in the 5:1 row of Table 2. The total aqueous P concentration is somewhat underpredicted. Low Ca2+ concentration values are obtained from both the simulation and experiment. For this series of the K+-NH4+ experiments, the solid-phase equivalent concentrations at the equilibrium points are also reported.3 We compare our predictions with experimental data for four K+/NH4+ initial loading ratios in Figure 7. As shown in Figure 7, the phosphate rock has similar K+ and NH4+ equivalent mole fractions. Our predictions are in close agreement with experimental data. The remaining adsorbed ions are Na+ and Ca2+.
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Conclusions
Literature Cited
The model presented in this work quantitatively reproduces exchange reactions on a solid surface that provides sites for both ion-exchange and molecular adsorption. As shown in a number of examples, the accuracy of adsorption calculations depends on the accuracy of aqueous speciation. Thus, a combination of the adsorption model with a thermodynamic speciation model for the bulk phase is indispensable. The data reduction scheme for multicomponent systems that exhibit both ion-exchange and molecular adsorption phenomena can be easily implemented within the framework of a numerical package for multiphase equilibrium computations. The parameters can be regressed either by analyzing data in separate ranges where either molecular adsorption or ion exchange predominate (as in the case of aniline adsorption) or by simultaneously regressing data from various isotherms. Additionally, the procedure facilitates testing the consistency of the overall model by analyzing binary systems that constitute a ternary system.
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Acknowledgment This work was supported by the Gas Research Institute under Contract 5094-250-2863 and by the Center for Nuclear Waste Regulatory Analyses, Southwest Research Institute. Discussions with Drs. Roberto T. Pabalan and Rajat Gosh are gratefully acknowledged. Notation a ) activity E ) equivalent mole fraction F ) Faraday’s constant K ) equilibrium constant Kc ) selectivity coefficient m ) adsorption saturation capacity n ) number of moles N ) number of species NT ) ion-exchange capacity (mequiv/g) Q ) point on the isotherm surface R ) universal gas constant r ) molar capacity ratio T ) temperature v ) molar volume x ) mole fraction z ) ionic charge Greek Symbols γ ) activity coefficient ∆ ) difference Λ ) Wilson parameter µ ) chemical potential π ) osmotic pressure φ ) electrochemical potential Subscripts i, j, k ) species w ) water Superscripts l ) equilibrium bulk phase o ) standard state s ) equilibrium adsorbed phase
Received for review June 5, 2000 Revised manuscript received October 17, 2000 Accepted October 20, 2000 IE000554A
