I n d . Eng. Chem. Res. 1993,32, 125-132
Literature Cited Boyd, G. E.; Soldano, B. A. Self Diffusion of Cations in and through Sulfonated Polystyrene Cation Exchange Polymers. J . Am. Chem. SOC.1964, 75,6091-6099. Carta, G.; Bauer, J. S. Analytic Solution for Chromatography with Nonuniform Sorbent Particles. AIChE J . 1990,36, 147-150. Carta, G.; Saunders, M. S.; Mawengkang, F. Studies on the Diffusion of Amino Acids in Ion Exchange Resins. In Fundamentals of Adsorption; Mersmann, A. B., Scholl, S. E., Eds.; AIChE: New York, 1991; pp 181-190. Cowan, G. H.; Gosling, I. S.; Sweetenham, W. P. Modeling for Scaleup and Optimization of Packed-Bed Columna in Adsorption and Chromatography. In Separations for Biotechnology; Verrall, M. S., Hudson, M. J., Eds.; Ellis Horwood: Chicheater, U.K., 1987; pp 152-175. DeCarli, J. P., 11; Carta, G.; Byers, C. H. Displacement Separations by Continuous Annular Chromatography. AZChE J . 1990, 36, 1220-1228.
Dye, S. R.; DeCarli, J. P., 11; Carta, G. Equilibrium Sorption of Amino Acids by a Cation Exchange Resin. Znd. Eng. Chem. Res. 1990,29,849-857.
Gregor, H. P. Gibbs-Donnan Equilibria in Ion Exchange Resin Systems. J. Am. Chem. SOC.1951, 73,642-650. Hamilton, P. B.; Bogue, D. C.; Anderson, R. A. Ion Exchange Chromatography of Amino Acids. Analysis of Diffusion (Mass Transfer) Mechanisms. Anal. Chem. 1960,32, 1782-1792. Helfferich, F. Zon Exchange; McGraw-Hill: New York, 1962; pp
12s
Helfferich, F.; Plesset, M. S. Ion Exchange Kinetics. A Nonlinear Diffusion Problem. J . Chem. Phys. 1958,28,41&424. Jones, I. L. Ion Exchange Equilibrium and Transport of Amino Acids in a New Class of Cation Resins: Dowex Monoephere EP. Masters Thesis, University of Virginia, Charlottesville, VA, 1991. Kataoka, T.; Yoshida, H. Estimating Equation of Resin Phase Self-Diffusivity. J . Chem. Eng. Jpn. 1976, 9, 74-75. Kataoka, T.; Yoahida, H.; Yamada, T. Liquid Phase Mass Transfer in Ion Exchange Based on the Hydraulic Radius Model. J . Chem. Eng. Jpn. 1973,6, 172-177. Kataoka, T.; Yoehida, H.; Sanada, H. Estimation of the Resin Phase Diffusivity in Isotopic Exchange. J . Chem. Eng. Jpn. 1974, 7 , 105-109.
Patell, S.; Turner, J. C. R. The Kinetics of Ion Exchange Using Porous Exchangers. J . Sep. Process Technol. 1979, 1 , 31-39. Reid, R. C.; Prausnitz, J. M.; Polig, B. E. The Properties of Cases and Liquids; McGraw-Hilk New York, 1987. Saunders, M. S.; Vierow, J. B.; Carta, G. Uptake of Phenylalanine and Tyrosine by a Strong-Acid Cation Exchanger. AIChE J . 1989, 35, 53-68.
Yoehida, H.; Kataoka, T. Intraparticle Maee Transfer in Bidisperaed Porous Ion Exchanger. Part I1 Mutual Ion Exchange. Can. J . Chem. Eng. 1985,63, 430-435.
Received for review June 25, 1992 Revised manuscript received October 15, 1992 Accepted October 27,1992
250-309.
Cation Exchange with Reverse Micelles Seyed N.Ashrafizadeh, Martin E. Weber, and Juan H. Vera* Department of Chemical Engineering, McGill University, Montreal, Quebec, Canada H3A 2A7
Experimental and modeling studies on the extraction of K+and Mg2+from an aqueous phase to an organic phase using a dinonylnaphthalenesulfonic acid (HD)reverse-micellar system were conducted at 25 O C . Systems containing two cations (binaries) and three cations (ternary) were investigated. Experiments for the binary systems were conducted with constant and variable total normality of cations. The system exhibited behavior similar to that of conventional ion-exchange resins. The selectivity was in the order Mg2+ > H+> K+.The distribution coefficient for Mg2+ and K+and the molar ratio of water to surfactant in the micellar phase were independent of surfactant concentration. The solubility of HD in the aqueous phase was low. The results of the equilibrium partition experiments were correlated using a thermodynamic model. Interaction parameters determined from binary system experimental data were used to predict the ternary system partition behavior with good agreement.
Introduction A reverse-micellar phase can act as a liquid ion-exchange system. The reverse micelles, which contain the ion-exchange sites, are analogues of solid ion-exchange-resin beads. These liquid ion exchangers are prepared by dissolving compounds with ionogenic groups in organic solvents which are immiscible with water. As discussed by Kunin (1973),solutions of dinonylnaphthalenesulfonicacid (HD) in nonpolar organic liquids serve as analwes of solid cross-linked strong acid cation exchangers. The sulfonic acid molecules are present in the organic phase as reverse micelles and as a layer at the interface between the organic and aqueous phases (Van Dalen and Wijikstra, 1978). The hydrogen ion of the sulfonic acid can be replaced by other cations; thus the reverse micellar phase acta as a liquid cation exchanger. In this work, the equilibrium between an aqueous phase containing different electrolytes and an organic phase containing HD reverse micelles at 25 "C was studied. The T o whom correspondence should be addressed.
experiments were carried out to determine the equilbrium compositions of the cations (H+, K+,Mg2+)and the surfactant (HD) in the aqueous and organic phases, and the amount of water uptake of the reverse-micellar phase for systems containing either two or three cations. The cation exchange for the systems containing three cations was predicted using a thermodynamic model based on the activity coefficient of cations in both phases. The parameters obtained from the three binary systems were used to calculate these activity coefficients in the ternary system.
Thermodynamic Modeling Although the effect of the presence of ions on the behavior of reverse-micellax systems has been considered by several authors, there is no model for the prediction of the selectivity of cation extraction. Adamson (1961)used the osmotic pressure to treat reverse-micellar systems. He proposed that the assumption of phase equilibrium requires that the mean activity of the salt be equal in both micellar and bulk aqueous phases. He expressed the higher total ionic concentration in the
Q888-5885/93/2632-Q125$Q4.oO/Q0 1993 American Chemical Society
126 Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993
micelle units, as compared to the external aqueous phase, in the form of an osmotic pressure difference. On the basis of such a model, he derived equations governing the distribution of electrolyte and water between the micelles and the external aqueous phase. Leodidis and Hatton (1989) presented a phenomenological model for the selective solubilization of cations in the reverse micelles of Aerosol OT (AOT) surfactant. Their primary goal was to model the large differences in water uptake by AOT microemulsions for the different cations. They used the modified Poisson-Boltzmann theory by making the assumption that the activity corrections for the ions can be expressed as a linear combination of a series of different interaction terms, while neglecting the ion-ion terms. Their model distinguished the different cations via their charge, hydrated size, and electrostatic free energy of hydration. Recently Vijiyalakshmi et al. (1990) and Vijiyalakshmi and Gulari (1991) proposed a model which assumed that the adsorption of counterions onto the surfactant surface of the reverse micelle is described by the Stern double layer model. Their model is simpler than the Leodidis-Hatton model, but it cannot distinguish between different ions with the same charge. Earlier studies (Little and Singleteny, 1964; Van Dalen et al., 1974) showed that a small number of HD surfactant molecules participate in each reverse micelle, about 7-15. These small reverse micelles have a low molar ratio of water to HD, W,, in the micellar phase. Experiments carried in this work also showed a low molar ratio of water to HD in the organic phase (W, I10). Thus, considering that for a given HD concentration the value of W,varies with the third power of the micellar diameter, we conclude that the HD reverse micelles formed in this work are also very small. Since one of the basic assumptions of treatments using the electrical double layer is that charged surfaces are parallel planes, the use of such treatments for small micelles does not seem to be justified. In this work, the extraction of cations using the HD reverse-micellar system is modeled with a modification of the thermodynamic approach previously used by Smith and Woodburn (1978) for ion exchange with resins. The first step in the development of a model to predict multicomponent systems is to attempt the prediction of ternary equilibria using binary data only. Binary equilibrium data are reproduced by adjusting parameters in the model, and these parameters are then used to estimate the activity coefficients of the ions in the ternary system. Following Shallcross et al. (1988) and Allen and Addison (1990), the ion exchange is represented by a reversible reaction of the form, z,RZJMJ+ zJM:l+
z,R,,M,
+ z,MIZ~+
(1)
where the ion M, replaces ion MJ in the reverse micelle R, and z, is the charge number of ion M,. The thermodynamic equilibrium constant F,for this reaction is
where Ci is the molar concentration of species i in the aqueous phase, Yi is the equivalent fraction of species i in the micellar phase, yi is the activity coefficient of species i in the aqueous phase, and T~is the activity coefficient of species i in the micellar phase. The three equilibrium constants must satisfy the so-called triangular relation (Bajpai et al., 1973), namely, (Kj)zk(Ki)z(K!)z~ =1 (3)
In this work three cations were employed, H+, K+, and Mg2+,and a single anion, C1-. To evaluate the activity coefficients of the ions in the aqueous phase, Allen et al. (1989) used the extended DebyeHuckel relation with the parameters given by Robinson and Stokes (1959) and Klotz (1964), while Shallcross et al. (1988) used the Pitzer method. We use an extension of the method proposed by Haghtalab and Vera (1992) which considers the effect of mixed ions to calculate the mean ionic activity Coefficients of electrolytes in multieledrolyte solutions. The equations for the activity coefficients of two 1:l electrolytes (HCl and KC1) have the form m2 In Y + ~= In yoal - -[[In Toil - In ~ ' ~ 2 1 (4) 21 ml In y+2= In y0+2- z [ l n yoi2 - ln y o k l l (5) For a 1:l and a 2:l binary system in water with HC1 or KCl as electrolyte 1 and MgClz as electrolyte 2, the expressions for the activity coefficients take the form m2
In yil = In yoi1 - -[2 I In y+2= In
In yoAtl- lnyoi2]
(6)
ml
- -[[In yoi2 - 2 In yO+ll
(7) 21 According to the method of Haghtalab and Vera (1992), for the ternary-cation system the mean ionic activity coefficients of the electrolytes 1 and 2 of the 1:l type and electrolyte 3 of the 2:l type are given by m2 In yil = In yoil - -[In yoil - In yoi2] 21 m3
~
m1 In yiz = In yoaz- -[In 21
[ ln 2y0+i- In
- In
Yok3I
(8)
-
where yo+l is the mean ionic activity coefficient of electrolyte 1 in a solution of pure electrolyte in water and ml is the molality of the electrolyte 1 in the aqueous phase. The ionic strength of the aqueous phase, I , is given by 1p I = -Xmizi2 (11) 2i=1
where mi is the molality of ion i and P is the number of ionic species in the aqueous phase. We use the equation proposed by Bromley (1973) for calculating the activity coefficients of the pure electrolyte in water:
where A is the Debye-Huckel constant (A = 0.5108 mol-lI2 kg1I2)and I3 is the Bromley parameter (BHa = 0.1433, BKCl = 0.0240, BMgClt = 0.1129 kg/mol). Both A and B are functions of temperature. The values used here are at 25 OC.
In this work, the activity coefficients of the ions are calculated from the activity coefficients of the electrolytes
Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 127 assuming that the contributions of the cation and anion partition in the form suggested by the Debye-Huckel model (Lewis and Randall, 19611, i.e., In yi =
zi2 Iz+z-l
-In y*
where yi is the activity coefficient of ion i in the aqueous solution and y* is the mean ionic activity coefficient of the electrolyte containing ion i in the same solution. Thus for the cations, In y+ =
z+* In y+
Iz+z-l
The reverse micelles were assumed to contain only surfactant, water, and cations, i.e., no Cl-. Following Smith and Woodburn (1978) and Allen and Addison (1990), the Wilson equation was used to estimate the activity coefficients of ions in the micellar phase:
Although the triangular relation, eq 3, between the equilibrium constants is a thermodynamic requirement, previous studies of ion exchange have not used it in the fitting of binaries or in the prediction of ternaries. In fact, only two equilibrium constants are required to calculate the ternary equilibrium values. If this relation is not imposed, the prediction of the ternary system depends upon the pair of equilibrium constants chosen as independent variables. On the other hand, previous workers (Brinkman et al., 1974; Allen et al., 1989) have imposed constraints on the Wilson parameters. Brinkman et al. (1974) used the relation proposed by Hala (1972): A&A;
=A~A~AL
Allen et al. (1989) used a reciprocal relation between the Wilson parameters: ~ 1 i 1. =~ 1i
where L is the number of cations in the system and A+ and, A) are the Wilson interaction parameters (At = 1 and A{
sf).
The above equations were used to fit the experimental data for the three binary systems and to predict the ternrvy system as described below. The equilibrium constant, K+,and the two Wilson parameters were obtained by fitting the binary data. In each case the equilibrium micellar equivalent fractions, Y j ,were calculated from
A Neldel-Mead Simplex algorithm (Woods, 1985) was used to minimize the average absolute deviation between the experimental and fitted Y j values.
cE IYYP -
Fb
=
1=1
E
q
(23)
The results obtained in this work using some of these approaches are discussed in a subsequent section.
j=1
#
(22)
i
(17)
where E is the number of experimental points. Equation 17 was chosen as objective function for the minimization in agreement with the argument presented by Allen et al. (1989). The estimated parameters are functions of the normality of the ions. Once the parameters for all three binary systems have been obtained, the prediction of the ternary system is made using the following equations:
Experimental Methods and Procedures Ion-exchange experiments were performed by contacting 15 mL of an aqueous solution of KC1, MgCl,, and HC1 with 15 mL of an organic solution, predominantly heptane, containing the surfactant. Dinonylnaphthalenesulfonic acid (HD) dissolved in kerosene at a concentration of approximately 50% was obtained from Pfaltz & Bauer and used without purification. The concentration of HD in this solution was measured by potentiometric titration (Danesi et al., 1973). Heptane was added to this solution to obtain the desired HD concentrations. The experiments were carried out in 50-mL test tubes with gasket-tightened caps. The tubes were placed on a vibrating shaker at 200 rpm and agitated for 60 min in a constant-temperature room at 25 "C. The samples were then centrifuged at 8OOO rpm for 20 min at 25 "C to achieve phase separation. The samples were left to settle at 25 "C for 24 h before the phases were analyzed. Pasteur pipets were used to collect samples from each of the phases. The amounb of surfactant in the organic and aqueous phases were determined by UV spectroscopy on a Bomem-Michelson 100 spectrophotometer at 285 nm. The water content of the reverse-micellar phase, in weight percent, was determined by Karl Fischer titration using a Metrohm-Brinkmann Model 701/1 KF Titrator. In a few cases, the results were checked against IR measurements. In addition, some samples were prepared by injecting a known amount of water into the organic phase. In all cases the Karl Fischer readings were accurate to *2%.
(19)
An iterative technique was required to find the reverse micellar phase composition (Yi, Yj, Yk) for a given aqueous solution composition (Ci, Cj, Ck). The calculated ternary compositions were compared with measured ternary equilibrium data. The quality of the prediction was measured by a value, F,,calculated with the following equation:
The cations were K+, Mg2+,and H+. When two cations are present, the system is referred to as binary; when three cations are present, a ternary. The concentrations of K+ and Mgn+in the aqueous phase were determined by atomic absorption spectroscopy on a Thermo Jane11 Ash Model 757 Spectrophotometer. Since this method measurea small concentrations, the samples were diluted with water by a factor of several hundreds or, in the concentrated cases, several thousands. The concentration of H+ in the aqueous phase was measured with a Fisher Scientific pH meter with a precision of f0.01 in the pH scale. Most samples were diluted by a factor of 50 in order to be in the most sensitive part of the pH range (pH between 2.5 and 4.0).
128 Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993
The concentrations of cations in the reverse-micellar phase were obtained by mass balance assuming that no Clenters the micelles and that the organic solvent and water are immiscible. The calculation takes into account the amount of water which moves from the original aqueous phase to the reverse-micellar water pools. A sample calculation is described in detail elsewhere (Ashrdizadeh, 1992). Two types of experiments were conducted. In experiments of the first type, which were used to test the model, the normality of the ions was constant. Aqueous phases containing a combination of cations having a common anion (Cl-) with constant normality were contacted with equal volumes of an organic phase with a fixed concentration of HD surfactant. For example, in extracting Mg2+ with the HD organic phase, the initial concentration of the Mg2+was varied between 0 and 1 N, while the total normality of the aqueous phase was maintained at 1 N by adding HC1. Since the concentration of the surfactant in the organic phase was constant, the total normality of the system was constant. Reverse micelles containing only K+ or Mg2+(Le., KD or MgD2reverse micelles) were prepared following the procedure described in the Appendix. Experiments were conducted with KD and MgD2 reversemicellar phases following the same procedure used for the HD reverse-micellar phase. Experiments for the three binaries, K+/H+,Mg2+/H+,and Mg2+/K+,as well as the ternary, K+/H+/Mg2+,were conducted. In experiments of the second type, organic phases with fixed concentrations of HD (0.1,0.2, or 0.3 M) were contacted with equal volumes of a series of aqueous solutions with different concentrationsof K+ or Mg2+.In these binary experiments the normality of the aqueous phase varied. The experimental results are reported in terms of the parameters defined below. The molar ratio of water to surfactant in the organic phase at equilibrium, W,, is given by aP0 w,= 18.02C0,
where CY is the weight fraction of water in the organic phase measured by Karl Fischer titration, po (g/L) is the density of the organic phase, and C , (mol/L) is the concentration of surfactant in the organic phase. The equivalent ionic fractions for cation i in the aqueous phase, X i , and in the organic phase, Yi, are defined by (25) (26) The sum of the cation fractions in each phase is unity. A distribution coefficient Ki is defined for species i as the ratio of the molarity of i in the reverse micelles to the molarity of i in the bulk aqueous phase: Ki = Ci/Ci (27) It is important to note that a high value of Ki for ion i in a binary system does not necessarily imply a high selectivity for that particular ion. The selectivity is related to the ratio of Ki/Kj and is better seen from plots of Yi vs X i for binary systems. Experimental Results a. Systems with Constant Normality. Since ion exchange occurs with electroneutrality, the equilibrium curves are plotted at constant normality. In this format,
1 OI
>x
f
0.8
0
r
n
.-c
U
0.6 L
0
.-c c 0 .-t
0.4
L 0 c c
c
.-3: 0.2 0-
w
0
1 0
-
. - .
0.2
0.4
. - . -
0.6
0.8
1
Equivalent f r a c t i o n in aqueous phose, Xug++ Figure 1. Equilibrium curves for the Mg2+/K+binary with three different constant normalities. The dash and dash-dot curves correspond to the fit using procedures A and B from Table I.
the variables are X i , the equivalent fraction of cation i in the aqueous phase, and Yi,the equivalent fraction of cation i in the organic phase. Neglecting the small amounts of anion C1- which exist in the reverse micelles at equilibrium and the small amount of surfactant which transfers to the aqueous phase, the normalities of the aqueous and organic phases at equilibrium are the same as the normalities at preparation. Experiments for the binary system Mg2+/K+were carried out at a constant normality of 0.1 for the organic phase while the normality of the aqueous phase was either 0.1, 0.2, or 0.5. The results, which are presented in Figure 1, show that a different Yi vs X i curve was obtained for each normality. This behavior is similar to that of an ion exchanger. At low XM8+the reverse micelles were selective for Mg2+. With increasing normality the equilibrium curve shifted downward indicating a lower selectivity for Mg2+ as the normality of the aqueous phase increased. Experiments for the binary systems, Mg2+/H+and K+/H+,were carried out at constant normalities of 0.1 and 0.2 for the organic and aqueous phases, respectively. The equilibrium curves for these binaries are shown in Figures 2 and 3. The curves denoted procedure A and procedure B in Figures 1-3 are discussed in the next section. The order of selectivity at 0.2 N aqueous phase is Mg2+> H+ > K+. The equilibrium data for the ternary system, Mg2+/ K+/H+,are presented in Table 111. For all experiments the normalities of the organic and aqueous phases were 0.1 and 0.2, respectively. The first three columns give equivalent fractions in the aqueous phase while columns 4-9 give equivalent fractions in the reverse micelles. Columns 4,6, and 8 contain the experimental values of Yi; the remaining columns labeled “pred” are discussed later. Each of the data points for these experiments at constant normality of ions is an average value of three replicate samples. Since the organic-phase composition is determined by mass balance closure from aqueous-phase measurements, the magnitude of relative error in the organic-phase compositions depnda on the normality of both phases. The error is larger for the systems with higher normality of ions in the aqueous phase. From the three replicates for each binary and ternary point, sample variances were obtained and a pooled standard deviation was
Ind. Eng. Chem. Res., Vol. 32,No. 1, 1993 129 1 a 4 2.
d
+
0.8
y
r
.-
0 c
U
C
2
F 0.6
100
U
0 0-
200
0
P
c
C
a
C
c
-E I-
50
n c
t 0.4
a
I
U
G c
c
.E 0.2
g
C
20
U
E
P'
0
c
Y
+
10
is
0
0
0.2
0.4
0.6
0.8 Equivalent fraction in aqueous phase, Xu,++
1
Figure 2. Equilibrium curves for the Mg2+/H+binary with constant normality. The curves correspond to the fit using procedures A and B from Table I.
2
'
0
1
I
I
0.4
0.6
0.8
Concrntrotlon of K T In aqurour phase, M
Figure 4. Distribution coefficient of surfactant and cation K+ vs equilibrium concentration of K+ in the aqueous phase for three surfactant concentrations (K+/H+ binary).
+
*= f
8
0.2
0.8
r
0
.-
U
+o)
0.6
I
0
c
e
200
e
0
0.4
r
c
5
c
P)
.P
,':n U
.C
.-t0
500
+
C
c
0.2
c
0
.-
w
:.-.ec
e e
0 0
0,2
0;4
0.6
0.8
1
Equivalent fraction in aqueous phase, X H +
Figure 3. Equilibrium curves for the K+/H+ binary with constant normality. The curves correspond to the fit using procedures A and B from Table I.
calculated. Following Skoog and West (1976),using this value the 95% confidence interval for Yi was calculated as f0.014. b. Systems with Variable Normality. In these experimenta, the concentration of HD surfactant was fixed a t three values, 0.1, 0.2,and 0.3 M. The surfactant distribution between the two phases, the water content of the organic phase, and the distribution of ions were determined. Figures 4 and 5 show the distribution coefficient of the surfactant, C,/C,, and of the cations K+ and Mg2+ as functions of the concentration of cation in the aqueous phase for three surfactant concentrations. Figure 4 is for the K+/H+ binary while Figure 5 is for the Mg2+/H+binary. The HD concentration in the aqueous phase was small, and it decreased with increasing salt concentration. The HD partitioned strongly to the organic phase with
20
10
3
P L
5
c
s 7
-
0
.
0.2
-
.
-
Concentration o f Mg
.
0.6
0.4
++
-
I
0.8
in aqueous phase, M
Figure 5. Distribution coefficient of surfactant and cation M2' vs equilibrium concentration of Mg2+in the aqueous phase for three surfactant concentrations (MgZ+/H+binary).
distribution coefficients between 100 and 500. For the same overall HD normality, the concentration of HD in the aqueous phase was lower in the Mg2+/H+system that in the K+/H+ system. The distribution coefficient of the ions was large for small concentrations of K+ and Mg2+. The value of K i was only weakly dependent on the surfactant concentration. The molar ratio of water to surfactant in the organic phase, W,,is plotted against the salt concentration in the
130 Ind. Eng. Chem. Res., Vol. 32, No. 1,1993 12
Table I. Results of Ternary Predictions with Different Procedures for Fitting the Binaries binary restriction imposed param procedure eq 3 eq 22 eq 23 obtained Ft 9 0.046 no no A no B no Yes 6 0.051 no 8 0.064 no no C Yes no 8 0.091 D" yes no E yes Yes 5 0.112 no 7 0.138 yes no F yes
. 0
c U
"The difference between procedures C and D is discussed in the text.
I
aqueous phase for H+, K+, and Mg2+in Figure 6. The largest values of W, were obtained when the system contained only one cation, H+.The water uptake decreased with increasing salt concentration similar to the behavior of other reverse-micellar systems (Leodidis and Hatton, 1989). Over the range of concentrations tested, W , was independent of HD concentration.
Comparison of Modeling and Experiment There are three ways of comparing the experimental results with theory. Two of them assume the composition in one phase is known and predict the composition in the other phase. These are the equivalent of typical dew or bubble point calculations. The third possibility is to calculate the composition of both (the aqueous and the organic) phases at equilibrium given an overall composition. The latter case is the equivalent of a flash calculation. We performed calculations for the most frequently encountered situation, i.e., where the composition of the aqueous phase is known. Parameters were obtained by fitting the binary systems ( Yigiven Xi) by six procedures and then used to predict ternary ion-exchange equilibria. A summary of the results is given in Table I. Procedure A fitted the three binary systems without any constraint, thus yielding nine parameters. Procedure B applied the reciprocal relation, eq 23, to each binary system to give six parameters. Procedures C through F imposed eq 3. In procedure C the three binary systems were fitted simultaneously while satisfying eq 3. In procedure D the two binary systems containing the most selected cation, Mg2+,were fitted without constraint and the third binary (H+/K+)was fitted using the equilibrium constant calculated by applying eq 3. Procedures C and D required eight parameters. In procedure E eqs 3 and 23 were imposed to give five parameters while procedure F imposed eqs 3 and 22 to give seven parameters. The results of fitting the binary systems using procedures A and B are shown in Figures 1-3. On the scale of the figures, the fitted curves following procedures A and C are indistinguishable. Procedure C is the soundest from the thermodynamic point of view since it used all available thermodynamic relationships. Although procedure B produces a poorer fit, it uses less adjustable parameters. Procedure D used the same binary parameters as procedure A for the two Mgz+ binaries, and thus it gave the same fit for them. The fit of the third binary (H+/K+),however, deteriorated badly. The binary fits using procedures E and
1
O B
4
I
,
3 0
0.2
0.6
0.4
0.8
Conc. of cation in aqueous phase, M Figure 6. Water to surfactant ratio as a function of equilibrium concentration of cations in the aqueous phase for three surfactant concentrations (the curves correspond to the MgZ+/H+binary, the K+/H+ binary, and the situation when only H+ is present).
F were all worse than those obtained with procedure D. Table I1 gives the binary parameters for procedures A and C and an indication of the quality of the fit, as defined by eq 17. The parameters reported for procedures A and C are far from meeting the reciprocal relation, eq 23, imposed on procedure B. On the other hand, as shown in Figures 1-3, the fit obtained with procedure B is not appreciably worse than the fit obtained with procedure A or C. This fact indicates that the two Wilson parameters are highly correlated with each other. Table I shows the results of the ternary predictions using the six procedures. The quality of the prediction is indicated by the value of Ftas defined by eq 21. The results presented in Table I seem to confirm the finding of Bajpai et al. (1973) and of Allen and Addison (1990) for ion-exchange systems. The beat prediction of the ternary system is obtained with the binary parameters of procedure A. The prediction of procedure C, although poorer than that of procedure A, is the best of the four procedures (C through F) which imposed eq 3. The ternary predictions with procedure A are compared with measured data in the columns labeled =prednin Table 111. The predictions are good although it is clear that the model underpredicts the concentration of H+ in the reverse micelles.
Conclusion The counterion of an anionic surfactant in the reversemicellar phase was partially substituted with cations from the aqueous phase. The selectivity was greater for Mg2+ than for K+ and H+. This phenomenon can be used to
Table 11. Equilibrium Constants, Wilson Parameters, and Quality of Fit for the Three Binaries procedure A procedure C 1
2
K:
a:
A::
K+
H'
0.8940 2.4504 23.491
8.8413 1.7367 1.3900
1.3858 6.1287 0.2259
MgZ+
H+
Mg2+
K+
1
Fb
0.028 0.015 0.025
K:: 0.5018 5.1000 20.2500
a:
A:
Fb
10.8534 3.4111 3.0728
2.9798 7.8259 1.7213
0.035 0.017 0.025
Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 131 Table 111. Experimental Data and Values Predicted Using Procedure A"
Yh@+
Wexp)
YK+
YH+
Mg2+
K+
H+
e=P
pred
exP
pred
exP
pred
0.09 0.21 0.31 0.38 0.52 0.60
0.69 0.54 0.45 0.37 0.20 0.12
0.22 0.25 0.24 0.25 0.28 0.28
0.24 0.31 0.42 0.45 0.52 0.57
0.32 0.40 0.44 0.48 0.55 0.59
0.19 0.16 0.11 0.09 0.05 0.02
0.24 0.18 0.15 0.13 0.08 0.05
0.57 0.41 0.47 0.46 0.43 0.41
0.44 0.42 0.41 0.39 0.37 0.36
'F, = 0.046.
separate ions with different charge numbers. For ions with the same charge, K+ and H+, the extent of exchange is governed by other ionic parameters. Complete substitution of one counterion by another was possible only after several contacts of the reverse-micellar phase with fresh aqueous phases containing high concentrations of the desired cations. The partition coefficients for the K+/Mg2+binary system were lower for higher normalities of the cations. Moreover, the same equilibrium curve was obtained using either a KD reversemicellar phase in contact with a MgC1, solution or a MgDz micellar phase in contact with a KC1 solution. This behavior is similar to that of conventional ion-exchange resins. The distribution coefficient for an organic phase containing HD reverse micelles was high for both K+ and Mg2+ at low electrolyte concentrations. The surfactant concentration had little effect on the distribution coefficient. The concentration of surfactant in the aqueous phase varied with both electrolyte and surfactant concentrations in the system, but the surfactant concentration in the aqueous phase was always less than 2 mM. Higher electrolyte concentrations decreased the concentration of surfactant in the aqueous phase. The water uptake of the system was low, with W, varying between 4 and 10 for a wide range of electrolyte concentrations (0-1 M). The value of W, decreased with electrolyte concentration, but it was independent of surfactant concentration. Observed W, values followed the trend
W,(H+) > Wo(Mg2+)> Wo(K+) The chemical potential of the ions in the water pool is expected to be affected by changes in the size of the reverse micelles due to changes in the water to surfactant ratio and the concentrations of ions. The results presented in Figure 6, however, suggest that changes in the sizes of the reverse micelles are small and their effect is expected to be absorbed by the adjustable parameters of the Wilson equation. In fact, the Wilson equation satisfactorily fit the experimental binary data in the reverse-micellar phase. Although not presented here, calculations were also carried out using the method followed by Allen and Addison (1990) to calculate the activity coefficient of the ions in the aqueous phase. The extension of the method of Haghtalab and Vera (1992) used in this work improved the results of the ternary predictions with respect to the method used by Allen and Addison (1990). The accuracy of the prediction of the ternary system was better when the equilibrium constants for the two binaries with the most selective cation for reverse-micellar phase were used. The use of the triangular relation, eq 3, did not improve the prediction of the few ternary points available. Although the limited test performed here does not give a final answer, the results obtained tend to confirm the findings of Bajpai et al. (1973) and of Allen and Addison (1990). These authors concluded that the best ternary predictions
are obtained with parameters from an unconstrained fit of the binary systems and the use of the equilibrium constants of the two binary systems containing the most selected ion.
Acknowledgment This work was supported by the Natural Sciences and Research Council of Canada.
Nomenclature A = Debye-Huckel constant, mol-'/* kg1/2 B = Bromley adjustable parameter C = concentration of cations in aqueous phase, mol/L C, = molarity of cation i in aqueous phase, mol/L C, = molarity of cation i in reverse-micellar water pools, mol/L C, = concentration of surfactant in aqueous phase, mol/L C,, = concentration of surfactant in organic phase, mol/L E = number of experimental data points Fb = binary goodness of fit Ft = ternary goodness of fit Z = ionic strength, mol/kg K i = distribution coefficient of species i E,= thermodynamicequilibriumconstant for species i moving from aqueousto reverse-micellar phase and speciesj moving from reverse-micellar to aqueous phase L = number of cations in the system m = molality of ions in aqueous phase, mol/kg of solvent M,= cation i in the system N = normality of ions in the system P = total number of ions in the system R = surfactant molecule without counterion H+ W,= molar ratio of water to surfactant in organic phase X,= equivalent fraction in the aqueous phase Yi= equivalent fraction in the organic phase z = valence number of ions (positive or negative integer) Greek Letters CY = weight fraction of water in the organic phase y = activity coefficient of ions in aqueous phase 9 = activity coefficient of ions in reverse micellar phase yt = mean ionic activity coefficient A{ = Wilson parameter p, = density of the organic phase, g/L Subscripts f = mean ionic i, j , k = ions i, j , and k 1 = electrolyte Superscripts exp = experimental value fit = fitted value pred = predicted value O = function in pure electrolyte/water mixture
Appendix: Preparation of KD and MgDz Reverse Micelles In order to conduct the experiments with reverse micelles containing only K+ (KD reverse micelles), it was
132 Ind. Eng. Chem. Res., Vol. 32,No. 1,1993
necessary to substitute K+ for the surfactant counterion H+ in the reverse-micellar phase. To make KD reverse micelles, the organic HD phase was contacted with a concentrated aqueous solution of 2 M KC1 at a volume ratio of 1. The same procedure as described for extraction experiments was used to contact the phases. At equilibrium both phases were collected and the organic phase was contacted three times with another fresh aqueous phase. To ensure complete removal of the cation H+ from the micellar phase, the organic phase was contacted with an aqueous phase containing KC1 and a small amount of KOH with a pH of about 10. It was assumed that any remaining trace amounts of H+ ion reacted with OH- ion producing water. After each contact, the pH of the equilibrium aqueous phase was measured. The total amounts of the H+ion measured at equilibrium were within 1%of the initial amount of H+ ion in the original phase. Moreover, after contacting this new micellar phase with an electrolyte solution, MgC12solution, the concentration of H+ in the aqueous phase at equilibrium did not increase more than 0.2 mM, which confiied the nearly complete substitution of H+ by K+. The same procedure was used to prepare reverse micelles containing only Mg2+(MgD2reverse micelles). Contacting the original HD micellar phase with the concentrated MgC12solution for four times replaced more than 99% of H+ counterion with Mg2+.
Literature Cited Adamson, A. W. A Model for Micellar Emulsions. J. Colloid Interface Sci. 1961,29,261-267. Allen, R. M.; Addison, P. A. Ion Exchange Equilibria for Ternary Systems from Binary Exchange Data. Chem. Eng. J. 1990,44, 113-118. Allen, R. M.; Addison, P. A.; Dechapunya, A. H. The Characterization of Binary and Ternary Ion Exchange Equilibria. Chem. Eng. J. 1989,40,151-158. Ashrafiideh, S.N. Cation Exchange with Reverse-Micelles. M.Eng. Thesis, McGill University, Montreal, Quebec, 1992. Bajpai, R. K.; Gupta, A. K.; Rao, M. G. Binary and Ternary IonExchange Equilibria. Sodium-Manganese-Dowex 50W-X8 and Cesium-Manganese-Strontium-Dowex 5OW-X8 Systems. J.Phys. Chem. 1973,77,1288-1294. Brinkman, N. D.; Tao, L. C.; Weber, J. H. The Calculation of the Parameters for the Wilson Equation for a Ternary System. Ind. Eng. Chem. Fundam. 1974,13,156-157. Bromley, L. A. Thermodynamic Properties of Strong Electrolytes in Aqueous Solutions. AIChE J. 1973,19,313-320.
Danesi, P. R.; Chiarizia, R.; Scibona, G. A Simple Purification Method for the Liquid Cation Exchanger Dinonylnaphthalene Sulfonic Acid. J. Inorg. Nucl. Chem. 1973,35, 3926-3928. Haghtalab, A.; Vera, J. H. An Empirical Mixing Rule for Estimating Mean Ionic Activity Coefficients in Multielectrolyte Solutions from Binary Data Only. Can. J. Chem. Eng. 1992,70,574-579. Hala, E. Liquid-Vapor Equilibrium. LII. On Boundary Conditions Between Constants of Wilson and NRTL Equations in Three and More-Component Systems. Collect. Czech. Chem. Commun. 1972,37,2817-2819. Klotz, I. M. Chemical Thermodynamics: Basic Theory and Methods, revised ed.; W. A. Benjamin: New York, 1964;p 416. Kunin, R. Ion Exchange and Solvent Extraction: Marcel Dekker: New York, 1973;pp 155-180. Leodidis, E. B.; Hatton, T. A. Specific Ion Effects in Electrical Double Layer; Selective Solubilization of Cations in Aerosol-OT Reversed Micelles. Ind. Eng. Chem. Res. 1989,223,741-753. Lewis, G. N.; Randall, M. Thermodynamics, 2nd ed., revised by Pitzer, K. S., Brewer, L.; McGraw-Hill New York, 1961;pp 337, 338. Little, R. C.; Singleterry, C. R. Solubility of Alkali Dinonylnaphthalene Sulfonates in Different Solvents. J. Phys. Chem. 1964,68,3453-3465. Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd ed.; Butterworths: London, England, 1959;pp 236, 246,468. Shallcross, D. C.; Hermann, C. C.; McCoy, B. J. An Improved Model for the Prediction of Multicomponent Ion Exchange Equilibria. Chem. Eng. Sci. 1988,43,279-288. Skoog, D. A,; West, D. M. Fundamentals of Analytical Chemistry, 3rd ed.; Holt, Rinehart and Winston: New York, 1976;pp 58-66. Smith, R. P.; Woodburn, E. T. Prediction of Multicomponent Ion Exchange Equilibria for the Ternary System SOq--NO,Cl- from Data of Binary Systems. AZChE J. 1978,24,577-587. Van Dalen, A.; Wijkstra, J. Liquid-Liquid Extraction of Complexed Metal Ions by Inclusion in Dinonyl Naphthalene Sulphonic Acid Micelles. J. Inorg. N u l . Chem. 1978,40,875-881. Van Dalen, A.; Gerritsma, K. W.; Wijkstra, J. Determination of the Aggregation Number of Dinonyl Naphthalene Sulfonic Acid by Metal Ion Extraction. J. Colloid Interface Sci. 1974,48,122-127. Vijayalakshmi, C. S.; Gulari, G. An Improved Model for the Extraction of Multivalent Metals in Winsor I1 Microemulsion Systems. Sep. Sci. Technol. 1991,26,291-299. Vijayalakshmi, C. S.; Annapragada, A. V.; Gulari, E. Equilibrium Extraction and Concentration of Multivalent Metal Ion Solutions by Using Winaor I1 Microemulsions. Sep. Sci. Technol. 1990,25, 711-727. Woods, D. J. Nelder-Mead Simplex Algorithm; Report 85-5,Department of Sciences, Rice University, Houston, Texas, 1985. Receiued for review May 18, 1992 Revised manuscript receiued September 14, 1992 Accepted October 4, 1992
