Ind. Eng. Chem. Fundam. 1989, 22, 31 1-317
for the three temperatures are plotted in Figures 2 and 6 for the experiments without vehicle oil and in Figure 4 for the experiments with vehicle oil. The excellent agreement between the kinetic parameters derived from the nonisothermal method at two heating rates and the conventional method is more clearly illustrated in Figure 8. Conclusions The data presented clearly show that the nonisothermal method of kinetic analysis developed by Kubo et al. (1966) can be applied to studies of coal liquefaction, thereby providing a rapid and convenient means of obtaining empirical expressions to describe the rate of conversion of coal. The liquefaction of coal has previously been considered to be a first-order reaction with respect to coal (Weller et al., 1951a,b; Falkum and Glem, 1952; Ishii et al., 1965). However, the results presented in this paper show the liquefaction of Wandoan coal to be most suitably described by second-order kinetics over the entire range of reaction conditions studied. Therefore, when coal is regarded as a single reactant, the coal liquefaction process may be represented as
coal
k
31I
product
where the reaction product is a general term which includes gas, water, oil, and asphaltenes. Acknowledgment The authors wish to thank M. Shibaoka, J. F. Stephens, and I. W. Smith for their continuing interest and encouragement. Registry No. Fe20s, 1309-37-1; S, 7704-34-9. Literature Cited Falkum. E.; Glem, R. A. Fuel 1052, 31, 133. Ishil, T.; Maekawa, Y.; Takeya, G. Kagaku Kogaku 1065, 2 9 , 988. Kubo, T.; Shirasakl, S.; Keto, M. J . Chem. Soc. Jpn., Ind. Chem. Sect. 1966, 69, 357. Okutanl, T.; Yokoyama. S.; Yoshkle, R.; Ishll, T. Ind. Eng. Chem. Rod. Res. h v . 1070, 18, 387. Weller, S.; Pellpetz, M. G.; Friedman, S. Ind. Eng. Chem. 1951a, 43. 1572. Welter, S.; Pellpetz, M. G.; Friedman, S. Ind. Eng. Chem. 1951b, 43, 1575. Yokoyama, S.; Ueda, S.; Maekawa, Y.; Shlbaoka, M. Am. Chem. Soc., Div. FuelChem., Prepr. 1970, 2 4 , 289.
Received for review April 26,1982 Revised manuscript received March 3, 1983 Accepted April 18,1983
Binary and Ternary Ion-Exchange Equilibria with a Perfluorosulfonic Acid Membrane Marcia J. Manning' and Stephen S. Melsheimer Department of Chemical Engineering, Clemson Unlverslty, Clemson, South Carolina 2963 1
Binary and ternary ion-exchange equilibrium data were obtained for the Du Font Nafion 120 perfiuorosuifonic acid membrane for several exchange systems. The total concentration of the external solution and the ionic content of the membrane were varied. The resulting binary selectivity coefficients indicated that potassium is the most preferred of the counterions studied. The sequence of increasing preference is H+ < Na+ < Ca2+< K+. The binary selectivities proved to be only moderately dependent upon the total concentration and ionic ratio of the external solution. Ternary equilibrium data were taken for combinations of the metal ions with hydrogen. It was found that binary selecthrtty data could be successfully used to predict the temary h x c h a n g e equilibria. Exchanger phase composition in the N a f i i membrane was predicted with an average error of 7 % as compared to an average error of 39% when the assumption of ideal solutions (that is, the binary seiectivity coefficients taken as unity) was used. While not highly accurate, this simple technique may be adequate for many applications.
Background A continuing area of study in ion exchange has been the development of continuous ion-exchange schemes in order to avoid the cyclic, intermittent operation of traditional packed column systems. One such process, termed Donnan dialysis (Wallace, 1967), uses countercurrent flow of the feed and regenerant streams in channels separated by an ion-exchange membrane. In recent studies (Lake and Melsheimer, 1978; Yazar et al., 1978) a mathematical model of mass transfer in Donnan dialysis has been developed for binary (two counterion) systems. This model utilized the Donnan equilibrium relation, written in terms of concentrations rather than activities, to represent the equilibrium between the solution and the membrane
* Amoco Research Center, Naperville, IL. 0196-4313/03/ 1022-0311$01.50/0
This implies L e assumption of ideal solution bt..avior for both phases, and thus an ionic selectivity of unity for the membrane. While this simplistic assumption gave acceptable results in binary exchange systems, ionic selectivity effects were expected to be of paramount importance in multicomponent systems. Investigations of ternary systems (Yazar et al., 1978) verified this expectation, leading to the requirement for reliable selectivity coefficient data for the membraneelectrolyte systems of interest. As no data were found in the literature for the membrane used in the dialyzer studies (Du Pont Ndion 120 perfluorosulfonic acid membrane), this investigation was undertaken to acquire the needed data. Another purpose of the study was to explore the feasibility of predicting ternary exchange 0 1983 American Chemical Soclety
312
Ind. Eng. Chem. Fundam., Vol. 22, No. 3, 1983
equilibrium from binary selectivity data. The equilibrium between an ion-exchange material in membrane or bead form and an electrolytic solution has been the subject of much investigation since the pioneering work of Donnan (1924). There are several aspects of this equilibrium, often partitioned (Crank and Park, 1968; Helfferich, 1962) into swelling equilibrium, electrolyte sorption equilibrium, and ion-exchange equilibrium. While these equilibria are interrelated through their thermodynamic basis, this study focuses on ion exchange. Various forms of equilibrium expressions may be used in expressing ion-exchange equilibria. Some early workers (Boyd et al., 1947; Kressman and Kitchener, 1949) applied equations corresponding to the Langmuir adsorption isotherm. The separation factor (Crank and Park, 1968; Helfferich, 1962) is an equivalent form. However, the separation factor does not explicitly reflect the effect of ionic valence, leading to very strong composition dependences when both ions are not of the same valence. Most efforts in this area have used some derivative of the Donnan equilibrium equation (Donnan, 1924), which can be expressed as
Note that K Bfor ~ this form is a thermodynamic equilibrium constant depending only on temperature if the activities are properly defined (Helfferich, 1962; Kressman and Kitchener, 1949). This thermodynamic equilibrium constant is seldom used in practice because of the difficulties faced in determining the ionic activities within the membrane phase. Replacing the activities with concentrations leads to the definition of the selectivity coefficient (Bauman and Eichhorn, 1947; Soldano et al., 1955; Tombalakian et al., 1967)
A number of investigators (e.g., Gregor and Bregman, 1951; Myers and Boyd, 1956; Reichenberg and McCauley, 1955) have found the selectivity sequence for alkali ions by strongly acidic cation exchangers to be: Li+ < Na+ < K+ < Rb+ < Cs+. This is the same as the order of decreasing hydrated radius of the ions. Thus, the affinity of the exchanger for the counterion having the smaller solvated radius in this sequence of similar ions has been attributed to the swelling equilibrium of the exchanger (Gregor and Bregman, 1951; Kressman and Kitchener, 1949; Helfferich, 1962). All of the above has been presented for binary (i.e., two counterion) exchange. For multicomponent exchange, the analysis becomes appreciably more involved because of the many possible modes of ion interaction. For ternary systems, triangular diagrams may be used to represent the equilibrium data. The ionic fractions in the solution phase can be plotted on the graph coordinates, while the exchanger phase composition is indicated by means of contour lines on the graph. Obviously, great amounts of data would be needed to produce such a graph at even one external solution total concentration. Klein and co-workers proposed an alternate method for the analysis of multicomponent ion exchange (Klein et al., 1967; Tondeur and Klein, 1967). “Pseudo-binary” selectivity coefficients were calculated for each ion pair from experimentally determined exchanger phase concentrations of the counterions. It was then assumed that these coefficients could be used to predict multicomponent ion-exchange equilibria at conditions near the experimental conditions at which they were obtained. Using the “pseudo-binary” approach for a ternary exchange equilibrium between an ion-exchangemembrane and a solution containing counterions “A”, “B”, and “C”, the following binary selectivity relationships can be written (4)
(3) Various composition units are used (e.g., molalities) and the value of the selectivity coefficient does depend on the composition units chosen. A “corrected” selectivity coefficient is sometimes used in which activities are retained in the solution phase while concentrations are used in the resin phase (Gregor and Bregman, 1951; Reichenberg et al., 1951; Subba Rao and David, 1957). The binary selectivity is a function of experimental conditions-ionic strength, ionic composition ( C B / C A ) , F d temperature, as well as the particular exchanger material. K B A data are generally reported as a function of the ionic fraction of “A” in the exchanger, %A. While no results have been reported for Ndion for the systems of interest in this work, numerous studies have been made with polystyrene-divinylbenzene resins with the same sulfonic acid active group. Reichenberg et al. (1951) examined the Na+-H+ system and found KHNa to decrease with increased ENa for highly cross-linked resins. Resins with low crosslinking showed a maximum for intermediate fNavalues. These results agree with those of numerous other investigators (e.g., Gregor and Bregman, 1951; Myers and Boyd, 1956) for exchanges between hydrogen and a univalent cation. For exchange between two univalent metallic cations it has generally been found (e.g., Soldano et al., 1955) that K B A decreases as the Z A values increase with “B” is the ion having the small hydrated radius. The same general trend was reported by Gregor et al. (1954) for the univalent-bivalent system Mg2+-K+.
and
where the subscript T indicates ternary data. Yazar et al. (1978) extended the “pseudo-binary” approach of Klein and co-workers for use in his dialyzer model by making the assumption that the presence of the other counterions does not appreciably affect the equilibrium relationships between 3-7pairs; i.e., the selectivity coefficients obtained from ternary exchange data would equal binary coefficients. The right-hand sides of eq 4, 5, and 6 then reduce to the familiar binary selectivity K A c , and K B ~ No . data were presented coefficients, KAB, to indicate to validity of this assumption. Dranoff and Lapidus (1957) investigated ternary exchanges between the Na+-H+-Ag+-Dowex 50 and the Cu2+-H+-Ag+-Dowex 50 systems and found that the data did not yield mass action equilibrium constants in agreement with those presented in the literature for the corresponding binary coefficients. However, a plot of %A/ (1 - a,) vs. X A j ( 1 - XC) for the A-B-C exchange data coincided with binary data plotted as f A vs. xA. Pieroni and Dranoff (1963) extended the examination of the Cu2+-H+-Na+-Dowex 50 system over a range of solution concentrations (0.01-0.1 N) to find this ternary exchange
Ind. Eng. Chem. Fundam., Vol. 22, No. 3, 1983
system can be successfully described by binary equilibrium data over this concentration range. The graphical presentation of ternary data as suggested by Dranoff and co-workers is complicated by the fact that bivalent-univalent exchange data is a strong function of solution concentration. I t also does not present binary equilibrium data in the form of a selectivity coefficient, the method that has been used by most investigators. Recent work by Soldatov and Bychkova (1970) and by Smith and Woodburn (1978) have used binary equilibrium data along with a phase equilibrium model (e.g., the Wilson model) to determine exchanger phase ionic activity coefficients and then use these to predict ternary exchange equilibrium. In this study, the pseudo-binary selectivity coefficient approach of Klein and co-workers was investigated, and the extension proposed by Yazar et al. was evaluated. By combining eq 4,5, and 6 with the following macroscopic electroneutrality restriction zACA
+ zBCB + ZCCC - X = o
(7)
equations can be written for the calculation of the exchanger phase concentrations of a ternary system. The resulting equations for the exchanger phase concentration of ion “A” are
8C A CA
=
CA
+ KABCB + KAcCc
(8)
for ZA = 1, ZB = 1, ZC = 1, Z N = -1, and CA
=
x 5
+
[(KAB)1/2C,+ (KAc)’/2c,]2 8C*
X
for zA = 2, Z B 7 1, zc =ZNI =, -1. Equations similar to (8) result for CB and Cc for an all-univalent exchange system. For a bivalent “A” ion, the equation for CB is CB
=
(10)
The equation for Cc is similar to (10). The analysis of Dranoff and associates was also applied to compare the binary and ternary equilibrium data.
Experimental Procedure Measurement of Membrane Properties. The ionexchange membrane used in all experiments of this investigation was Nafion 120, nominally 10 mils thick and 1200 equivalent weight. Various physical properties of the membrane including the water absorption as a percentage of dry polymer mass, the dimensional changes due to swelling, and the exchange capacity are necessary for the determination of ion-exchange equilibrium selectivities. Before any exchange measurements were made, these membrane properties were determined. Detailed procedures are available elsewhere (Manning, 1978). Binary Exchange Equilibrium. The binary exchange systems investigated were Na+-H+, K+-H+, Ca2+-H+, K+-Na+, K+-Ca2+,and Ca2+-Na+,with NO, as the co-ion in all cases. Binary selectivity coefficients were determined for external solution concentrations ranging from 0.016 to 1.4 M. The concentration ratio of the competing ions was varied in the range 0.01 to 100. All testa were performed
313
at room temperature (25 “C). External Ion Concentrations. The equilibrating solution was prepared to be the “A” to “B” concentration ratio and total ionic concentration specified at equilibrium. Typically, 400 mL of the equilibrating solution was used. Two membrane samples of approximately 1 g in dry mass were prepared, one placed in the “A” form and one in the “B” form. The two samples and solution were placed in a 500-mL plastic Erlenmeyer flask which was stoppered with a rubber stopper during equilibration. The samples were allowed to equilibrate for at least 3 h. The membrane samples were then separated from the solution, washed in deionized water, and wiped with a tissue to remove sorbed electrolytes. The concentrations of the two ionic species in the equilibrating solution were determined by the standard analytical techniques outlined below. Exchanger Phase Ion Concentrations. If both ions were metallic, both were replaced by three successive washings in 1.0 N HNOP The three washes were analyzed separately for the two metal ions and the results were combined to determine both exchanger phase ion concentrations at equilibrium. For an exchange between a metallic ion and the hydrogen ion, the experimental technique used depended on the relative amounts of each ion in the sample. If the metal ionic fraction was less than that of the hydrogen ion, the metallic ion was removed by washing with 1.0 N HNOBin the manner described above. The hydrogen ion concentration was determined by difference using this measured metallic ion concentration and the known ion-exchange capacity. If the metal ionic fraction was the greater of the two, a third ion in a concentrated nitrate solution containing its hydroxide at 0.01 molarity was used to replaced both the hydrogen and metal ions. Titration to a methyl orange end point then gave the hydrogen ion fraction. As the metal ion was also measured, both exchanger phase concentrations were directly measured in this case. Time Required for Equilibration. A time study was done to determine the length of time required to reach equilibrium. The Na+-Ca2+exchange system was studied and two membrane samples, one in the Na+ form and the other in the Ca2+form, were placed in solutions at the same external concentration. The samples were separated from the equilibrating solutions after 3 h, 6 h, 12 h, 24 h, 2 days, and 5 days. It was found that all the samples had the same internal composition, so 3 h was adequate to reach the equilibrium state. Ternary Exchange Equilibrium. Ternary equilibrium data were taken for the Na+-K+-H+, Na+-Ca2+-H+, and K+-Ca2+-H+ systems, again with NO3- as co-ion. Procedures very similar to those described above were used with ternary exchange systems. Three samples, one in each ionic form, were equilibrated with a solution of the three counterions at specified concentration ratios and a specified total solution concentration. All three ionic concentrations of the external solution were measured, and since all the ternary systems.considered contained middle to high ionic fractions of hydrogen, the exchanger phase metal ions were replaced with hydrogen ions by washing with 1.0 N HNO, as previously described. The hydrogen ion concentration in the membrane phase was calculated by using the capacity and the two measured metal ion concentrations. Analytical Techniques. The hydrogen ion concentrations of all binary and ternary systems in which hydrogen was one of the exchanging ions were determined in the external solutions by titration. Metallic ion concentrations of the external solutions and the removed
314
Ind. Eng. Chem. Fundam., Vol. 22, No. 3, 1983
EXTERNAL SOLUTION CONCENTRATION 0 0
A
0
+1
0 016 M 0040 M 040 M 13 M
X I
2a
I
o
0 00
02
8 04 - 0 6
zotI
EXTERNAL SOLUTION CONCENTRATION 3 0
0.022 M 0,20 M M
IO
1 08
10
*Na
Figure 1. Selectivity coefficient for Nat-Ht exchange as a function of exchanger sodium composition.
exchanger phases were measured by atomic absorption spectroscopy (AA). Titration. Sodium hydroxide solutions, restandardized each day before use against a potassium hydrogen phthalate solution, were used for titrations to a phenolphthalein end point. Atomic Absorption Spectroscopy. Linear absorption ranges for sodium, potassium, and calcium were determined before any actual sample analyses could be done by AA. High and low standards were chosen from these linear ranges for each ion. Samples containing only a single metal ion were diluted as necessary so that their concentrations were bracketed by the high and low standards established for that ion. The bracketing technique, coupled with operation in the linear absorption range, was found to be very effective in eliminating the effects of day-to-day changes in the equipment by allowing determinations on a relative basis. In cases in which more than one metal ion was present, significant interferences were observed. To cope with this problem, the smatrix matching" technique of Yazar et al. (1978) was used. Both the samples and the s t a n k & were doped with lo00 pg/mL of the interfering metal, resulting in interference errors of less than 2%. Despite the unavoidable operation at high absorption range, the linearity with concentration was preserved. Results Membrane Properties. The density of Nafion was determined to be within 0.190 of the 1.98 g/cm3 value reported by Grot et al. (1972). Two samples of the nominally 1200 equivalent weight Nafion 120 obtained separately were found to have ion-exchange capacities of 0.809 and 0.823 mequiv of H+/g of dry membrane, corresponding to equivalent weights of about 1240 and 1220, respectively. The water absorption of the membrane was found to deviate significantly from values obtained from a correlation reported by Grot et al. This correlation gave values exceeding the experimentally determined results by an average of 30% for membrane samples in the counterion forms of interest (H+, Na+, K+, ea2+)and for various external solution concentrations. The empirical constants of the correlation of Grot et al. were reevaluated from the data of this work to yield the following results
8070
-
EXTERNAL SOLUTION CONCENTRATICN
60.
50.
0
O040M
0
035 M
40. 0
I
E \ . , 08 00
02
04-
,
,
06
08
, 10
'Ca
Figure 3. Selectivity coefficient for CaZt-Ht exchange as a function of exchanger calcium composition.
where A is a function of the ionic content (H+ = 1.00, Na+ = 0.824, K+ = 0.505,Ca2+= 0.879). With this modified correlation the water absorption of the membrane samples of this study was fit within an average absolute error of 2.2%. Binary Exchange Data. Binary selectivity coefficients for the Na+-H+, Na+-K+, K+-H+, Na+-Ca2+,K+-Ca2+,and Ca2+-H+ exchange systems were calculated from experimentally measured concentrations. Figures 1 through 6 present the dependency of the selectivity coefficients on the ionic fraction of ion "A" within the exchanger phase at equilibrium. The variation in the membrane selectivity coefficients with the total ionic concentration of the external solution is also demonstrated in these figures. All six selectivity coefficient data seta were plotted on the same log scales to facilitate comparisons between the graphs. Each point on the curves of Figures 2 through 6 was determined from the concentration measurements of two separate samples. Since the experimental technique employed was to place two samples in the same container for equilibration, their external solution concentrations were identical. The exchanger phase concentrations of the two
Ind. Eng. Chem. Fundam., Vol. 22, No. 3, 1983 315
Table I. Comparison of Ternary and Binary Selectivity Coefficients no.
ternary binary ternary binary ternary binary
Calcium-Hydrogen-Sodium ( A - B G ) Exchange System 1 2.38 2.40 1.15 1.20 1.80 2.05
3.15 2.45 1.26 1.25 1.99 2.10 2 Calcium-Hydrogen-Potassium( A-BG) Exchange System 1 4.41 2.41 5.51 4.20 0.146 0.196 2 2.61 2.44 3.06 4.10 0.297 0.204 Potassium-Hydrogen-Sodium (A-B-C) Exchange System 1 3.67 4.20 1.17 1.20 3.15 2.60
-
20
0
EXTERNAL SOLUTION CONCENTRATION
-
10.
0'
0040 M
0'
020 M 092 M
A
,.TERNARY Ca-H-No
0.8. A K-H-No
09 0 E>
9
I
I
0.6
IX
0.4
BINARY
t
EXT CONC
0 A
0 00 00
EXTERNAL SOLUTION CONCENTRATION
02
06
0 4
O.04OM 0.40 M 13 M
OB
10
'NA 0.
50
0:
0040M 0 38 M
Figure 7. Binary and ternary (filed symbols) equilibrium data for Na+-H+.
40
IO
j0 0
0
020 M IO M
i
OB
10
BINARY
0.2
q , ,
A
,
,
,
06
08
IO
00
00
08
00
02
04
0 2
04
06 XK
Figure 8. Binary and ternary (filled symbols) equilibrium for
ca
Figure 5. Selectivity coefficient for Ca2+-Na+exchange aa a func-
K+-H+.
tion of exchanger calcium composition.
samples were determined separately, then averaged to obtain one internal concentration for each ion. The average exchanger phase concentrations were used to calculate the binary selectivity coefficient a t the specific equilibrium conditions set by the external solution. The points in Figure 1each represent the equilibration of only one membrane sample a t the specific experimental conditions, giving the appearance of a much larger volume of data for this binary system. The measured concentration data and the calculated results from these raw experimental data are available (Manning, 1978). Ternary Exchange Data. The ternary exchange systems studied in the investigation were the Ca2+-H+-Na+ the Ca2+-H+-K+, and the K+-H+-Na+ systems. T h i ternary system consisting of the three metal ions was not examined. All exchanges were carried out at 25 "C and at a total external solution concentration of approximately 0.04 M. Table I presents the results of the ternary experiments as "pseudo-binary" selectivity coefficients. In addition, Table I gives binary selectivities from Figures 1 through 6 at the corresponding equilibrium conditions. Figures 7 through 12 present the binary and ternary equilibrium data in the manner suggested by Dranoff and
l o 0
0
EXTERNA L SOLUTION CONCENTRATION
0 , 0027
YY2
0'
I
M
0.30 M
1.0
0.0
02
0.4
0.6
0.8
1.0
*K
Figure 6. Selectivity coefficient for K+-Ca*+exchange as a function of exchanger potassium composition.
316
Ind. Eng. Chem. Fundam., Vol. 22, No. 3, 1983
Table 11. Membrane Phase Counterion Concentrations for Ternary Exchange Systems
[ l , M E1 M [XI, MB 9
sample no. exptl
calcd
1 2
0.433 0.383
0.435 0.368
1 2
0.424 0.369
0.411 0.358
1
0.383
0.397
exptl calcd ideal exptl Calcium-Hydrogen-Sodium (A-B-C) Exchange System ideal
0.383 0.296
0.187 0.287
0.186 0.317
0.272 0.447
0.056 0.054
calcd
ideal
0.054 0.053
0.071 0.068
0.116 0.136
0.049 0.057
0.182
0.196
Calcium-Hydrogen-Potassium (A-B-C) Exchange System 0.394 0.328
0.141 0.267
0.186 0.268
0.287 0.406
0.134 0.115
Potassium-Hydrogen-Sodium ( A-B-C) Exchange System 0.142
0.591
0.562
0.805
0.168
06
u
IX
ozt/
TERNA R Y C o - H - NO BINARY E X0 T 0CONC 40MI
04
,II:-;
O
z
r
/
,
TERNARY
,
038 M
Co-H-K
00 00
02
04
06
08
00 0 0
I0
02
XCO
Figure
9.
04
06
08
10
’CA
Binary and ternary (filled symbols) equilibrium for
Ca2+-H+.
Figure 11. Binary and ternary (filled symbols) equilibrium for Ca’l+-Na+. IO,
081
Y
ix
00
02
04
06
08
10
00
XK
Figure 10. Binary and ternary (filled symbols) equilibrium for
K+-Na+. Lapidus (1957). In these plots, xA is merely the ionic equivalent fraction of ion “A” in the solution phase for an A-B binary exchange. For a ternary A-B-C exchange system, X A = x A / ( l - xc). Similar definitions follow for the exchanger phase ionic fraction, f k The ternary exchange data are distinguished by the use of filled symbols. Table I1 presents the experimentally measured counterion concentrations of the exchanger phase and also the concentrations determined by using binary selectivities. Counterion “B” was always the hydrogen ion and although its membrane phase concentration was never directly measured, the concentration values determined by the exchanger capacity are also tabulated for comparison with the calculated concentrations. It should be obvious that, had the ternary selectivity coefficients of Table I been used to calculate the exchanger phase ionic concentrations, the experimentally measured and calculated concentrations would have agreed exactly. The “ideal concentrations” obtained using selectivities of unity are also presented on Table 11. Discussion The water sorption values measured in this study of Nafion 120 ranged from 11 to 25 mass %, quite low in comparison to many other synthetic exchangers (Helffe-
02
04
06
08
IO
XK
Figure 12. Binary and ternary (filled symbols) equilibrium for K+-Ca2+.
rich, 1962; Reichenberg and McCauley, 1955; Soldano et al., 1955). One reason is its relatively low exchange capacity, 2.5 to 12 times lower than the capacities of common polystyrene-sulfonic acid membranes (Helfferich, 1962). Still, the low water sorption indicates a relatively rigid structure, as in highly cross-linked polystyrene resins. The sequence of the measured water sorption values obtained with different ionic forms corresponds to the sequence of the “coefficient A” values in eq 11: H+> Ca2+ > Na+ > K+. The potassium form of the membrane exhibits a considerably smaller extent of water sorption than the other ionic forms. The binary selectivities presented in Figures 1through 6 show, in general, relatively minor variation with either membrane phase composition or external solution concentration. Potassium (Figures 2 and 6) shows significant variations with composition, and calcium-hydrogen (Figure 3) may indicate some dependence but is obscured due to data scatter. Only potassium-hydrogen (Figure 2) exhibits a clear dependence on external solution concentration. The remaining systems can all be represented as constants with little compromise. Based on the values of the metal ion selectivities relative to hydrogen, the ionic preference sequence for Nafion 120
Ind. Eng. Chem. Fundam., Vol. 22, No. 3, 1983
is K+ > ea2+> Na+ > H+, with K+ and ea2+much more strongly preferred than Na+ and H+.The metal ion selectivities relative to each other validate this sequence, but with an anomalously high selectivity for K+ relative to ea2+. Mean values are KNaK= 2.7; KNaCa= 2.0; KcaK= 5.5 Inspection of the first two values would lead to the anticipation of KGKvalues near unity. Nafion 120 also shows much stronger preferences for potassium relative to hydrogen and sodium than literature values (Gregor and Bergman, 1951; Reichenberg and McCauley, 1955) for polystyrene-sulfonic acid membranes. The selectivity sequence agrees with the sequence for membrane water sorption in the pure electrolytes found in this study with the exception of Ca2+. That is, the ion with smallest hydrated radius (potassium) swells the membrane least and is most preferred, while the largest ion (hydrogen) swells the membrane most and is least preferred. This relationship between ionic selectivity and water sorption has been generally observed in other studies (e.g., Gregor and Bregman, 1951) for ions of the same valence. The ternary selectivities presented in Table I do deviate quite significantly from the binary values found at corresponding ionic ratios and total concentrations. Deviations are greatest when potassium is one of the ions involved. Note particularly the variation between the two samples presented for the calcium-hydrogen-potassium system with different ionic compositions in the external solution. Figures 7 through 12 clearly demonstrate that, for the three ternary systems of interest, it is possible to predict with a reasonable degree of accuracy the equilibrium distribution of the three ions from binary exchange data only. Figure 9, 11, and 12 demonstrate that binary exchange of univalent and bivalent counterions shows a strong dependence on solution concentration when presented in this graphical form. This dependence complicates the application of binary data fitted in this manner for use in the prediction of multicomponent ionic equilibria. However, the figures do indicate that the multicomponent interaction effects are not of severe consequence for prediction of multicomponent equilibria at relatively low ionic concentrations. In Table I1 the binary selectivities of Figures 1 through 6 were used to predict ternary exchanger phase compositions from known external conditions. The ternary compositions predicted by using binary selectivity data are in reasonable agreement with experimentally determined ternary values even where the binary and ternary selectivities show dramatic discrepancies. For the calciumhydrogen-potassium system, for example, metal ion concentrations in the membrane were predicted within 18% despite much larger deviations in the selectivities. The hydrogen ion concentration for this system is farther off, but it is also subject to the greatest experimental error since it is determined by difference from the capacity and the metal ion measurements. The other two systems showed significantly better correspondence between experimental and calculated membrane phase concentrations. The “ideal” concentrations shown in Table I1 illustrate the very poor agreement with experimental results which is obtained when the selectivities are simply taken as unity. In several cases the ideal predicted concentrations deviate by over 100% from the measured results. The enormous
317
improvement obtainable by use of the binary selectivity information is quite evident. Overall, the binary selectivities predict the exchanger phase composition with an average absolute error of 7%, as compared to 39% when no selectivity information is used. This accuracy is adequate for many applications.
Conclusions 1. The order of preference of Nafion 120 for the cations studied in this investigation is K+ > ea2+> Na+ > H+. Potassium is very strongly preferred by the membrane over any other ion. 2. The binary selectivities show only moderate dependence on experimental conditions in the range studied. 3. Binary selectivities may be successfully used to predict approximate ternary equilibrium compositions in the Nafion 120 exchanger even in cases in which the binary selectivities deviate substantially from ternary selectivities. Nomenclature A = ionic coefficient in eq 11 QA = activity of ion A, mol/L CA = concentration of ion A, mol/L E W = equivalent weight of the exchanger g/mequiv KBA = binary selectivity of ion A relative to B KBTA= pseudo-binary selectivity of ion A relative to B in ternary solution M = molarity, mol/L q A = concentration of ion A, mequiv/mL Q = total ionic concentration of the solution, mequiv/mL Q = capacity of the exchanger, mequiv/g of dry exchanger X = capacity of the swollen exchanger, equiv/L XA = equivalent ionic fraction of ion A %AA= valence of ion A KB = thermodynamic equilibrium constant for exchange of ions A and B overbar denotes membrane phase property Registry No. Na, 7440-23-5; K, 7440-09-7; Ca, 7440-70-2;
Nafion 120, 63346-31-6.
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Received for review June 11, 1982 Accepted March 2, 1983
This study was supported by National Science Foundation Grant ENG-08303.
