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Thermodynamic treatment and calorimetric study of H+Li+ ion exchange on α-titanium phosphate
O-96 J. Chem.
Thermodynamics
1985, 17, 63-68
Thermodynamic treatment and calorimetric study of H +/Li+ ion exchange on a-titanium phosphate C. G. GUARIDO, M. SUAREZ, J. R. GARCIA, and J. RODRIGUEZ
R. LLAVONA,
Departamento de Quimica Inorghnica, Farultad de Quimica, Universidad de Oviedo, C/Calve Sotelo s/n, Oviedo, Spain (Received 10 April
1984; in revised form 13 July 1984)
The thermodynamics of H+/Li+ ion exchange on a-Ti(HPO,),.H,O have been studied, and titration curves and exchange isotherms have been obtained at 298.15, 313.15, and 328.15( kO.1) K. The exchanger hydrolysis and the corrected isotherms have been calculated. The equilibrium constants, the standard molar Gibbs free energies, enthalpies, and entropies of the reactions have been all determined. The molar enthalpies of the exchange reaction have been measured calorimetrically. The thermodynamic and calorimetric results are compared.
1. Introduction E-Titanium phosphate Ti(HPO& . H,O, isomorphic with u-zirconium phosphate Zr(HPO& . HzO,(iy ‘1 is a layered inorganic exchanger with an interlayer distance of 0.76 nm. In X-ray diffraction the first reflexion of the crystals corresponds to the interlayer distance. During ion-exchange, the layers expand or contract and thus the study of the variation of this reflexion allows the reaction to be followed. In the H’/Na+ ion-exchange on ol-Ti(HPO,), * H,O, variations in the interlayer distance were observed and half-exchanged and fully-exchanged phases were detected.(3-6) Nevertheless, in the H+/Li+ ion-exchange, the interlayer distance was not modified over the entire range, though the retention of Li+ ions by the solid was observed by chemical analysis. Earlier papers on H+/Li+ exchange suggest that fully-exchanged phases Ti(LiPO,), -nH,O (n = 1,2) exist only with an interlayer distance of 0.76 nm,(‘**) but in a recent paper (‘I the bifunctionality of the exchanger has been demonstrated by the existence of half-exchanged and fully-exchanged phases. This paper is a contribution to the study of ion-exchange of alkali-metal cations on a-Ti(HPO,), . Hz0.(5*6*g~ lo) The thermodynamic functions of the exchange reactions: Ti(HPO&
. H,O(cr) + Li+(aq) + OH -(as) + (n - 2)H,O = TiHLi(PO,),
TiHLi(PO,),
* nH,O(cr) + Li+(aq) + OH-(aq)
0021-9614/85/010063+06
%02.00/O
+ (n’ - n - l)H,O = Ti(LiPO,),
*nH,O(cr),
(1)
* n’H,O(cr),
(2)
0 1985 Academic Press Inc. (London) Limited
64
C. G. GUARIDO
were calculated for H+/Li’ by application the molar enthalpy change was determined
ET
AL.
of the Gibbs-Helmholtz equation, and by direct calorimetric measurements.
2. Experimental All chemicals used were of reagent grade. a-Titanium phosphate was obtained as previously described. w LiOH solutions were standardized by titration against HCl(aq) which had been previously standardized against Na,CO,. The exchanger was equilibrated with the 0.1 mol. dmv3 (LiOH + LiCl) solution at 298.15, 313.15, and 328.15 K ( f 0.1 K) following the dynamic procedure described by Clearfield et al.“” The solid was present in the solution at approximately 2 g. dmv3 mass concentration; the equilibrium time was about 48 h. The isothermal calorimeter used was a Setaram Calvet Standard Model 1201, which had been previously calibrated. (lo) The solid a-titanium phosphate was introduced into the 0.1 mol. dmp3 (LiOH + LiCl) solutions at a mass concentration of 2 g*dmm3. The ion-exchange reaction occurred without shaking (static system). The working temperature was 298.15 K. The extent of the exchange was determined in each calorimetric measurement by analysis of the Li+ in solution. Measurements of pH were made with a Crison pH meter, Model 501, equipped with glass and saturated-calomel electrodes. The released phosphate groups were measured spectrophotometricallyt ’ *) using a Perkin Elmer, Model 200. The lithium ions in solution were determined by atomic absorption spectroscopy with a Perkin Elmer, Model 372. The diffractometer used was a Philips, Model PV 1050/23 (1 = 0.15418 nm).
3. Results and discussion Exchange isotherms, and titration and hydrolysis curves at 298.15 K, have been plotted in figure l(a) against the amount n(LiOH) of LiOH added divided by the mass m{u-Ti(HPO,), *H,O} of a-titanium phosphate. The results are similar at the three working temperatures. If in the course of the exchange only the substitution reaction takes place, a maximum uptake for a fixed amount of LiOH added should be reached and maintained for larger additions. Nevertheless, for additions in excess of 8 mmol of LiOH for 1 g of u-titanium phosphate, the experimental exchange capacity decreases. This fact and the detection of phosphate ions in solution suggest hydrolysis reactions.@ Taking into account the hydrolysis of the exchanger, the corrected exchange isotherms can be obtained, in which the extent of the exchange refers to the amount of non-hydrolyzed x-titanium phosphate (figure lb), it being assumed that Ti02 4nH,O does not act as a cation exchanger until the total saturation of a-Ti(HPO,), 1H,O is reached. The exchange capacity of TiO, * nH,O at the three working temperatures is almost constant (0.4Lii for each TiO, . nH,O), at pH values between 6.8 and 8.4. X-Ray patterns of samples obtained at 298.15 K at different degrees of saturation, show a constant value of the interlayer distance when
H+/Li+
ION EXCHANGE
0
2
4
ON a-TITANIUM
6
x
PHOSPHATE
IO
65
12
[n(LiOH)lm{a-Ti(HPO,)~.HzO}]/(mmol.g-’)
r
I
I 2
I 4
I 6
I 8
10
1
12
1
_; 1‘3
[n(LiOH)lm{cY-Ti(HP04)~~H~O}]/(mmol~g~’) FIGURE 1. At T = 298.15 K: (a), 0, titration curve; 0, exchange isotherm; and V, percentage hydrolysis 10% of the exchanger; (b), exchange isotherm corrected to take hydrolysis into account.
the solid is stored over H,O or treated at 368.15 K (figure 2a). In the heat treatment at 583.15 K (figure 2b), reflexions at 0.68, 0.74, and 0.76 nm are detected corresponding to the TiHLi(PO&, Ti(HPO&, and Ti(LiPO,), phases.(g’ Ion-exchange reactions on layered materials are usually not reversible” 3, and so it is not possible to assign true thermodynamic values to them. Nevertheless, one can obtain apparent thermodynamic values starting from the direct processes of substitution process occurs through the exchange.‘14T15) Since the H+/Li+ formation of half-exchanged and fully-exchanged crystalline phases, following a similar mechanism to that described by Suarez et a1.,‘@ from the expressions: K; = (x(Li+, 1, s)m(H+, 1)/@-I+, 1, s)m(Li+, l)}{f(H+, K’, = {x(Li+, 2, s)m(H+, 2)/x(H+, 2, s)m(Li+, 2)}(f(H+,
1)/f&i+, l), 2)/f(Li+, 2),
(3) (4)
66
C. G. GUARIDO
ET AL.
Angle, 20 FIG1 JRE 2. X-Ray patterns of some of the samples of partial substitution stabilized (a), at 368.15 K and 04, at 583.15 K.
where x is the mole fraction in the solid exchanger and m is the molality and f the activity coefficient in the solution, the apparent equilibrium constants K; and K; are calculated for every experimental point. The equilibrium constants are obtained by application of the Gaines and Thomas thermodynamic treatment. (16) For the first exchange stage:
logloKl =s(logloK’Ad{x(Li+, 1, s))-(n,-~,)log (5)
where a, is the activity of water in the solution. The integral is calculated by plotting log,,& against x(Li, 1, s) and determining the area under the curve. We consider the contribution of the water activity to log,&, to be negligible. K, is obtained by application of a similar treatment to the equation which represents the direct exchange reaction from 50 to 100 per cent completion. Plotting the equilibrium constants against l/T one obtains the value of AH: for both exchange stages. These values along with those for AC:, obtained from the K values, and AS& are given in table 1 for the apparent thermodynamic constants of H+/Li+ exchange with cr-Ti(HPO,), * H,O.
H+/Li+
ION EXCHANGE
ON a-TITANIUM
TABLE 1. Thermodynamic values for the H+/Li+
-log,,K Li+(l) Li +(2)
298.15 K
313.15 K
328.15 K
3.28 3.68
3.28 3.58
3.28 3.65
PHOSPHATE
67
exchange in a-Ti(HPO,),.H,O AH; kJ.mol-’ 0.00 -0.17
AC: kJ.mol-’
ASm J.K-‘.mol-’
18.70 21.00
- 62.72 -71.00
The calorimetric experiments (static system) are for exothermic processes giving rise to ballistic curves similar to those described for H+/Na+.(“) If there are no secondary reactions and some minor terms are neglected, the enthalpy variation can be separated into two processes: the exchange reactions and neutralization.“” Exact knowledge of the molar enthalpy of neutralization by our experimental measurements (55.90 kJ. mall ‘) makes possible the calculation of the exchange enthalpy in each calorimetric determination and positive values increasing with the amount of exchange are obtained (table 2). The results obtained in this paper (dynamic system) are those predicted by the model of ion-exchange generally accepted for such systems.‘i3) Thus, the absence of variation of enthalpy in both stages of exchange is attributed to the small size of the lithium ion which, when anhydrous or partially hydrated, can easily diffuse into the layers of the exchanger without distortions, in agreement with our X-ray diffraction patterns. The variation of entropy might correspond, by comparison with similar systems studied (W to the gaining of an Hz0 in each stage of the exchange. Phases of low stability, with stoichiometries corresponding to TiHLi(PO,), .2H,O and Ti(LiPO,), .3H,O are formed. These phases can be easily transformed into the respective monohydrate phases, which are detectable by X-ray diffraction. At relatively high temperatures anhydrous solids are obtained. The values of AH,?,, obtained from calorimetry correspond to an endothermic reaction. Since the application of the Gibbs-Helmholtz equation suggests a value of AH; near zero, an additional endothermic process (which is what we have really measured) must exist so that both measurements may be in agreement. In earlier papers@) an enthalpy corresponding to the ol-Ti(HPO,), 4H,O hydrolysis of (7 11 f 60) kJ . mol- i has been considered. From this value, the hydrolysis undergone by the exchanger so that the thermodynamic and calorimetric results concur, can be calculated. Good agreement is obtained when these results of hydrolysis and those experimentally reached by analysis of the released phosphates at 298.15 K, are compared.
TABLE
2. Exchange enthalpy of each calorimetric determination a-Ti(HPO& . H,O
x(Li+, s) AHx(kJ.mol-‘)
0.12 4.31
0.15 6.57
0.23 0.37 11.38 26.19
0.42 30.21
0.49 0.61 37.24 48.99
in the H+/Li+ 0.73 59.71
0.81 68.83
process on 0.86 73.05
0.98 76.61
68
C. G. GUARIDO
ET AL.
REFERENCES 1. Cleartield, A.; Nancollas, G. H.; Blessing, R. H. Ion Exchange and Solvenr Extraction, vol 5 Marinsky, J. A.; Marcus, Y.: editors. Marcel Dekker: New York. 1973. 2. Volkov, A. I.; Novikov, G. I.; Ivkovich, N. A. Khim. fiim. Teknol. (Minsk) 1976, 10, 46. 3. Alberti, G.; Costantino, U.; Luciani, M. L. Gazz. Chim. Ital. 1980, 110, 61. 4. Clearfield, A.; Frianeza, T. N. J. Inorg. Nucl. Chem. 1978,40, 1925. 5. Garcia, J. R.; SuLrez, M.; Rodriguez, J. Solvent Extraction and Ion Exchange 1984, 2. 289. 6. Suarez, M.; Garcia, J. R.; Rodriguez, J. J. Phys. Chem. 1984, 88, 159. 7. Takaguchi, K.; Tomita, I. J. Chromatogr. 1976, 118, 263. 8. Chernorukov, N. G.; Prokofeva, T. V. Zh. Fiz. Khim. 1977, 51, 1361. 9. Garcia, J. R.; Suirez, M.; Rodriguez, J. Solvent Extracrion and Ion Exchange 1984, 2, 275. 10. Suarez, M.; Garcia, J. R.; Rodriguez, J. J. Phys. Chem. 1984, 88, 157. Il. Clearfield, A.; Oskarsson, A.; Oskarsson, C. Ion Exchange and Membranes 1972, 1, 91. 12. Michelsen, 0. B. Anal. Chem. lM7, 29, 60. 13. Inorganic Ion Exchange Materials. Clearfield, A.: editor. CRC Press: Boca Raton, Florida. 1982. 14. Kullberg, L.; Cleartield, A. J. Phys. Chem. 1981, 85, 1585. 15. Clearfield, A.; Medina, A. S. J. Phys. Chem. 1971, 75, 3750. 16. Gaines, G. L.; Thomas, H. C. .I. Chem. Phys. 1953, 21, 714. 17. Clearfield, A.; Kullberg, L. H. J. Phys. Chem. 1974, 78, 152.
Thermodynamics
1985, 17, 63-68
Thermodynamic treatment and calorimetric study of H +/Li+ ion exchange on a-titanium phosphate C. G. GUARIDO, M. SUAREZ, J. R. GARCIA, and J. RODRIGUEZ
R. LLAVONA,
Departamento de Quimica Inorghnica, Farultad de Quimica, Universidad de Oviedo, C/Calve Sotelo s/n, Oviedo, Spain (Received 10 April
1984; in revised form 13 July 1984)
The thermodynamics of H+/Li+ ion exchange on a-Ti(HPO,),.H,O have been studied, and titration curves and exchange isotherms have been obtained at 298.15, 313.15, and 328.15( kO.1) K. The exchanger hydrolysis and the corrected isotherms have been calculated. The equilibrium constants, the standard molar Gibbs free energies, enthalpies, and entropies of the reactions have been all determined. The molar enthalpies of the exchange reaction have been measured calorimetrically. The thermodynamic and calorimetric results are compared.
1. Introduction E-Titanium phosphate Ti(HPO& . H,O, isomorphic with u-zirconium phosphate Zr(HPO& . HzO,(iy ‘1 is a layered inorganic exchanger with an interlayer distance of 0.76 nm. In X-ray diffraction the first reflexion of the crystals corresponds to the interlayer distance. During ion-exchange, the layers expand or contract and thus the study of the variation of this reflexion allows the reaction to be followed. In the H’/Na+ ion-exchange on ol-Ti(HPO,), * H,O, variations in the interlayer distance were observed and half-exchanged and fully-exchanged phases were detected.(3-6) Nevertheless, in the H+/Li+ ion-exchange, the interlayer distance was not modified over the entire range, though the retention of Li+ ions by the solid was observed by chemical analysis. Earlier papers on H+/Li+ exchange suggest that fully-exchanged phases Ti(LiPO,), -nH,O (n = 1,2) exist only with an interlayer distance of 0.76 nm,(‘**) but in a recent paper (‘I the bifunctionality of the exchanger has been demonstrated by the existence of half-exchanged and fully-exchanged phases. This paper is a contribution to the study of ion-exchange of alkali-metal cations on a-Ti(HPO,), . Hz0.(5*6*g~ lo) The thermodynamic functions of the exchange reactions: Ti(HPO&
. H,O(cr) + Li+(aq) + OH -(as) + (n - 2)H,O = TiHLi(PO,),
TiHLi(PO,),
* nH,O(cr) + Li+(aq) + OH-(aq)
0021-9614/85/010063+06
%02.00/O
+ (n’ - n - l)H,O = Ti(LiPO,),
*nH,O(cr),
(1)
* n’H,O(cr),
(2)
0 1985 Academic Press Inc. (London) Limited
64
C. G. GUARIDO
were calculated for H+/Li’ by application the molar enthalpy change was determined
ET
AL.
of the Gibbs-Helmholtz equation, and by direct calorimetric measurements.
2. Experimental All chemicals used were of reagent grade. a-Titanium phosphate was obtained as previously described. w LiOH solutions were standardized by titration against HCl(aq) which had been previously standardized against Na,CO,. The exchanger was equilibrated with the 0.1 mol. dmv3 (LiOH + LiCl) solution at 298.15, 313.15, and 328.15 K ( f 0.1 K) following the dynamic procedure described by Clearfield et al.“” The solid was present in the solution at approximately 2 g. dmv3 mass concentration; the equilibrium time was about 48 h. The isothermal calorimeter used was a Setaram Calvet Standard Model 1201, which had been previously calibrated. (lo) The solid a-titanium phosphate was introduced into the 0.1 mol. dmp3 (LiOH + LiCl) solutions at a mass concentration of 2 g*dmm3. The ion-exchange reaction occurred without shaking (static system). The working temperature was 298.15 K. The extent of the exchange was determined in each calorimetric measurement by analysis of the Li+ in solution. Measurements of pH were made with a Crison pH meter, Model 501, equipped with glass and saturated-calomel electrodes. The released phosphate groups were measured spectrophotometricallyt ’ *) using a Perkin Elmer, Model 200. The lithium ions in solution were determined by atomic absorption spectroscopy with a Perkin Elmer, Model 372. The diffractometer used was a Philips, Model PV 1050/23 (1 = 0.15418 nm).
3. Results and discussion Exchange isotherms, and titration and hydrolysis curves at 298.15 K, have been plotted in figure l(a) against the amount n(LiOH) of LiOH added divided by the mass m{u-Ti(HPO,), *H,O} of a-titanium phosphate. The results are similar at the three working temperatures. If in the course of the exchange only the substitution reaction takes place, a maximum uptake for a fixed amount of LiOH added should be reached and maintained for larger additions. Nevertheless, for additions in excess of 8 mmol of LiOH for 1 g of u-titanium phosphate, the experimental exchange capacity decreases. This fact and the detection of phosphate ions in solution suggest hydrolysis reactions.@ Taking into account the hydrolysis of the exchanger, the corrected exchange isotherms can be obtained, in which the extent of the exchange refers to the amount of non-hydrolyzed x-titanium phosphate (figure lb), it being assumed that Ti02 4nH,O does not act as a cation exchanger until the total saturation of a-Ti(HPO,), 1H,O is reached. The exchange capacity of TiO, * nH,O at the three working temperatures is almost constant (0.4Lii for each TiO, . nH,O), at pH values between 6.8 and 8.4. X-Ray patterns of samples obtained at 298.15 K at different degrees of saturation, show a constant value of the interlayer distance when
H+/Li+
ION EXCHANGE
0
2
4
ON a-TITANIUM
6
x
PHOSPHATE
IO
65
12
[n(LiOH)lm{a-Ti(HPO,)~.HzO}]/(mmol.g-’)
r
I
I 2
I 4
I 6
I 8
10
1
12
1
_; 1‘3
[n(LiOH)lm{cY-Ti(HP04)~~H~O}]/(mmol~g~’) FIGURE 1. At T = 298.15 K: (a), 0, titration curve; 0, exchange isotherm; and V, percentage hydrolysis 10% of the exchanger; (b), exchange isotherm corrected to take hydrolysis into account.
the solid is stored over H,O or treated at 368.15 K (figure 2a). In the heat treatment at 583.15 K (figure 2b), reflexions at 0.68, 0.74, and 0.76 nm are detected corresponding to the TiHLi(PO&, Ti(HPO&, and Ti(LiPO,), phases.(g’ Ion-exchange reactions on layered materials are usually not reversible” 3, and so it is not possible to assign true thermodynamic values to them. Nevertheless, one can obtain apparent thermodynamic values starting from the direct processes of substitution process occurs through the exchange.‘14T15) Since the H+/Li+ formation of half-exchanged and fully-exchanged crystalline phases, following a similar mechanism to that described by Suarez et a1.,‘@ from the expressions: K; = (x(Li+, 1, s)m(H+, 1)/@-I+, 1, s)m(Li+, l)}{f(H+, K’, = {x(Li+, 2, s)m(H+, 2)/x(H+, 2, s)m(Li+, 2)}(f(H+,
1)/f&i+, l), 2)/f(Li+, 2),
(3) (4)
66
C. G. GUARIDO
ET AL.
Angle, 20 FIG1 JRE 2. X-Ray patterns of some of the samples of partial substitution stabilized (a), at 368.15 K and 04, at 583.15 K.
where x is the mole fraction in the solid exchanger and m is the molality and f the activity coefficient in the solution, the apparent equilibrium constants K; and K; are calculated for every experimental point. The equilibrium constants are obtained by application of the Gaines and Thomas thermodynamic treatment. (16) For the first exchange stage:
logloKl =s(logloK’Ad{x(Li+, 1, s))-(n,-~,)log (5)
where a, is the activity of water in the solution. The integral is calculated by plotting log,,& against x(Li, 1, s) and determining the area under the curve. We consider the contribution of the water activity to log,&, to be negligible. K, is obtained by application of a similar treatment to the equation which represents the direct exchange reaction from 50 to 100 per cent completion. Plotting the equilibrium constants against l/T one obtains the value of AH: for both exchange stages. These values along with those for AC:, obtained from the K values, and AS& are given in table 1 for the apparent thermodynamic constants of H+/Li+ exchange with cr-Ti(HPO,), * H,O.
H+/Li+
ION EXCHANGE
ON a-TITANIUM
TABLE 1. Thermodynamic values for the H+/Li+
-log,,K Li+(l) Li +(2)
298.15 K
313.15 K
328.15 K
3.28 3.68
3.28 3.58
3.28 3.65
PHOSPHATE
67
exchange in a-Ti(HPO,),.H,O AH; kJ.mol-’ 0.00 -0.17
AC: kJ.mol-’
ASm J.K-‘.mol-’
18.70 21.00
- 62.72 -71.00
The calorimetric experiments (static system) are for exothermic processes giving rise to ballistic curves similar to those described for H+/Na+.(“) If there are no secondary reactions and some minor terms are neglected, the enthalpy variation can be separated into two processes: the exchange reactions and neutralization.“” Exact knowledge of the molar enthalpy of neutralization by our experimental measurements (55.90 kJ. mall ‘) makes possible the calculation of the exchange enthalpy in each calorimetric determination and positive values increasing with the amount of exchange are obtained (table 2). The results obtained in this paper (dynamic system) are those predicted by the model of ion-exchange generally accepted for such systems.‘i3) Thus, the absence of variation of enthalpy in both stages of exchange is attributed to the small size of the lithium ion which, when anhydrous or partially hydrated, can easily diffuse into the layers of the exchanger without distortions, in agreement with our X-ray diffraction patterns. The variation of entropy might correspond, by comparison with similar systems studied (W to the gaining of an Hz0 in each stage of the exchange. Phases of low stability, with stoichiometries corresponding to TiHLi(PO,), .2H,O and Ti(LiPO,), .3H,O are formed. These phases can be easily transformed into the respective monohydrate phases, which are detectable by X-ray diffraction. At relatively high temperatures anhydrous solids are obtained. The values of AH,?,, obtained from calorimetry correspond to an endothermic reaction. Since the application of the Gibbs-Helmholtz equation suggests a value of AH; near zero, an additional endothermic process (which is what we have really measured) must exist so that both measurements may be in agreement. In earlier papers@) an enthalpy corresponding to the ol-Ti(HPO,), 4H,O hydrolysis of (7 11 f 60) kJ . mol- i has been considered. From this value, the hydrolysis undergone by the exchanger so that the thermodynamic and calorimetric results concur, can be calculated. Good agreement is obtained when these results of hydrolysis and those experimentally reached by analysis of the released phosphates at 298.15 K, are compared.
TABLE
2. Exchange enthalpy of each calorimetric determination a-Ti(HPO& . H,O
x(Li+, s) AHx(kJ.mol-‘)
0.12 4.31
0.15 6.57
0.23 0.37 11.38 26.19
0.42 30.21
0.49 0.61 37.24 48.99
in the H+/Li+ 0.73 59.71
0.81 68.83
process on 0.86 73.05
0.98 76.61
68
C. G. GUARIDO
ET AL.
REFERENCES 1. Cleartield, A.; Nancollas, G. H.; Blessing, R. H. Ion Exchange and Solvenr Extraction, vol 5 Marinsky, J. A.; Marcus, Y.: editors. Marcel Dekker: New York. 1973. 2. Volkov, A. I.; Novikov, G. I.; Ivkovich, N. A. Khim. fiim. Teknol. (Minsk) 1976, 10, 46. 3. Alberti, G.; Costantino, U.; Luciani, M. L. Gazz. Chim. Ital. 1980, 110, 61. 4. Clearfield, A.; Frianeza, T. N. J. Inorg. Nucl. Chem. 1978,40, 1925. 5. Garcia, J. R.; SuLrez, M.; Rodriguez, J. Solvent Extraction and Ion Exchange 1984, 2. 289. 6. Suarez, M.; Garcia, J. R.; Rodriguez, J. J. Phys. Chem. 1984, 88, 159. 7. Takaguchi, K.; Tomita, I. J. Chromatogr. 1976, 118, 263. 8. Chernorukov, N. G.; Prokofeva, T. V. Zh. Fiz. Khim. 1977, 51, 1361. 9. Garcia, J. R.; Suirez, M.; Rodriguez, J. Solvent Extracrion and Ion Exchange 1984, 2, 275. 10. Suarez, M.; Garcia, J. R.; Rodriguez, J. J. Phys. Chem. 1984, 88, 157. Il. Clearfield, A.; Oskarsson, A.; Oskarsson, C. Ion Exchange and Membranes 1972, 1, 91. 12. Michelsen, 0. B. Anal. Chem. lM7, 29, 60. 13. Inorganic Ion Exchange Materials. Clearfield, A.: editor. CRC Press: Boca Raton, Florida. 1982. 14. Kullberg, L.; Cleartield, A. J. Phys. Chem. 1981, 85, 1585. 15. Clearfield, A.; Medina, A. S. J. Phys. Chem. 1971, 75, 3750. 16. Gaines, G. L.; Thomas, H. C. .I. Chem. Phys. 1953, 21, 714. 17. Clearfield, A.; Kullberg, L. H. J. Phys. Chem. 1974, 78, 152.