J. Phys. Chem. B 2001, 105, 4721-4726
4721
Estimation of Deprotonation Coefficients for Chelating Ion Exchange Resins. Comparison of Different Thermodynamic Model Raffaela Biesuz,† Andrei A. Zagorodni, and Mamoun Muhammed* Materials Chemistry DiVision, Royal Institute of Technology, SE-100 44 Stockholm, Sweden ReceiVed: August 2, 2000; In Final Form: February 23, 2001
The deprotonation of quinolic resin P-127 and iminodiacetic resin Amberlite IRC-718 has been studied. The process of salt transfer into the resin phase is considered to be an important contributor to the deprotonation process. Estimation of the salt transfer was based on the principle of equal activity of the salt in both phases at equilibrium. Two assumptions were made: sorbed alkali metal ions are not associated with functional groups, while all hydrogen ions are associated with functional groups. The associated hydrogen ions and functional groups do not contribute to the internal ionic strength value. Two thermodynamic models, describing the deprotonation of ion-exchange resin, were used and compared: the Gibbs-Donnan-based model of Bukata and Marinsky and the model proposed by Erik Ho¨gfeldt. Thermodynamic characteristics of the resins’ deprotonation are obtained using two different thermodynamic approaches. Ho¨gfeldt’s three-parameter model provides a better agreement with experimental data. The fitting of the data to Marinsky’s method can be improved by taking into account the influence of the resins’ macroporosity; however, this requires an additional empirical parameter to describe the resin.
1. Introduction Ion-exchange resins have been well-known materials since the 1950s. However, the thermodynamic equilibria taking place inside the resin phase has still not been fully investigated. There are no methods for the direct investigation of the resin phase. Sophisticated thermodynamic models have to be used in order to study elementary reactions inside the resin. The preparation of chelating ion exchangers with well-defined compositions has been reported earlier.1 An advantageous selectivity was observed to be exhibited by resins containing quinolic acid as the functional group attached to the Amberlite XAD-2 matrix. The chelating quinolic resin is a weak cation exchanger with dissociation properties sensitive to the salt concentration in the surrounding solution. In the present research, the deprotonation of the quinolic resin P-127 has been studied. The iminodiacetic resin Amberlite IRC-718 has been chosen to serve as a resin reference because of its well-defined properties. One of the objectives of this research was to determine the deprotonation characteristics of the resins studied. There are two main approaches to thermodynamic modeling of the ion exchange equilibria. The first is based on a detailed investigation of individual interactions. It requires a large amount of experimental work and encounters basic problems associated with direct investigation of the resin phase. The Gibbs-Donnanbased model2-4 of Bukata and Marinsky5 can be selected as the most successful approach. Different successful applications of the model were published including studies of protonation equilibria6-8 and the sorption of bivalent metal.8,9 The model describes independently the transfer of ions in the resin phase, protonation equilibria in the internal solution, and salt transfer * Corresponding author. Fax: +46-8-790 9072. E-mail:
[email protected]. † Present address: Dipartimento di Chimica Generale, via Taramelli 12, 27100 Pavia, Italy.
between two phases. The apparent protonation characteristics can be considered to be a cooperative effect of all these phenomena. The second approach considers the overall process as is. An equation describing the process is fitted to the experimental data. Thermodynamic characteristics are obtained from the results of the fitting. The best exploration of this approach was done in the three-parameter model proposed by Erik Ho¨gfeldt.10,11 2. Experimental Section 2.1. Resins, Reagents, and Solutions. Preparation of the P-127 resin was described earlier.1 The resin contains quinolic functional groups attached to the Amberlite XAD-2 matrix. Amberlite IRC-718 is a commercially available resin (Rohm & Haas) containing iminodiacetic functional groups. The resins, obtained in the sodium form, were placed in a glass column and converted to the hydrogen form by passing 3% HCl solution. The resins were washed with H2O. The washing efficiency was controlled by the Cl-ion test with AgNO3. The resin samples were air-dried, transferred into small bottles, and weighed prior to their storage. The samples used for water-content determination were weighed simultaneously. The water content was calculated from the weight loss of the resin sample after continuous drying at 105 °C. The dry weight of the resin was used for all calculations. All inorganic reagents were of analytical grade and used as received. All solutions were prepared using deionized water. 2.2. Titration of the Resins. A 50 mL aliquot of a standardized NaCl solution as an ionic medium was introduced in a thermostatic vessel. An exact amount of the resin in hydrogen form was added. The amount of the resin and the concentration of the ionic media were kept constant, while the acidity of the solution was varied by the addition of standardized carbonate-free sodium hydroxide. A small overpressure of
10.1021/jp0027703 CCC: $20.00 © 2001 American Chemical Society Published on Web 05/01/2001
4722 J. Phys. Chem. B, Vol. 105, No. 20, 2001
Biesuz et al.
nitrogen gas was applied to eliminate the possible presence of CO2 in the solution. Titration of the resins was performed using a computer system to control the addition of the titrant and the stirring. A minimum of 1.5 h was found to be the time needed for equilibrium to be reached. The equilibrium condition was considered to be attained when the drift of the glass electrode indication was no greater than 0.01 mV/min. The maximum time between two additions of base was fixed at 4 h. Each titration lasted approximately 48 h. The activity coefficient for Na was calculated by the standard Pitzer’s procedure.12 The pH was obtained through the concentration-based calibration of the glass electrode, according to the procedure developed by the Stockholm school.13,14 The first deprotonation step of both resins could not be examined because the measurement of pH values lower than 2 was not convenient or reliable at the chosen concentration levels of the ionic media. For comparison, the monomer analogues of IRC-718 and P-127 have log K3 ) 1.78 in 1 M NaClO4 and log K2 ) 1.9 in 1 M KNO3, respectively.15 2.3. Water Determination. A batch technique was used to evaluate the amount of water associated with the resin phase at each point of its neutralization. A relatively large quantity of the resin sample was used in order to reduce the error. A set of samples with different amounts of NaOH added was equilibrated, overnight, with the ionic medium selected. The solution’s pH was measured. The resin samples were collected on glass filters and centrifuged at 2000 rpm for 5 min. The samples were weighed and dried at 105 °C until the constant weight was achieved. The weight loss was used for the water content determination. The amount of water sorbed (gram of water per gram of dry resin) was calculated for each titration point from the experimental values by an interpolation procedure. 3. Results and Discussion 3.1. Calculation of Counterion Concentration in the Resin Phase. The titration process is considered to be neutralization of the hydrogen ion by the addition of base. The negative charge of the resin that results from the removal of hydrogen is compensated by the transfer of sodium ions into the resin phase. A certain amount of sodium chloride is also present in the internal solution of the resin. A direct measurement of the extra counterion (sodium in this case) transfer into the resin is difficult if possible. The transfer of salt (NaCl) can be estimated from the Donnan equilibrium, as shown below:
aNaaCl ) ajNaajCl
(1)
The members of this equation correspond to ion activities. The bar is used to indicate an association with the water of the resin phase. The equilibrium state is characterized by the equivalence of the sodium chloride activity in both phases, as written by eq 1. The following equations can be used to estimate the transfer of salt (m j s):
je + m j s)γ j Na ajNa ) (m
(2)
j sγ j Cl aCl ) m
(3)
aNaaCl ) ms2 γ((NaCl)2
(4)
where m j e is the molality of the sodium sorbed via ion exchange reaction (calculated per gram of water contained in the resin), m j s is the molality of the salt transferred, ms is the molality of the salt in the solution, γ j is the molal activity coefficient of an ion in the resin phase, and γ( is the mean molal activity
coefficient of the salt in the solution phase at ms. Equation 2 is written with the assumption that the sorbed sodium ions are not associated with resin functional groups. This assumption is based on the absence of any significant association between sodium and soluble analogues of the functional groups in solutions. The substitution of eqs 2-4 into eq 1 results in
m js )
-m je +
xmj e2 + 4ms2 γ((NaCl)2/(γj Naγj Cl) 2
(5)
j Cl) Assessment of the single ion activity coefficients (γ j Na and γ needed for this computation can be obtained through the use of an interactive approach presented in ref 16. The coefficients were calculated as follows:
γ j Na )
γ((NaCl)2 γ((KCl)
γ j Cl ) γ((KCl)
(6) (7)
The following assumptions have been made: γ jK ≈ γ j Cl ) γ((KCl) and γ j Na ) γNa at m j Na ) mNa.16 The data for KCl are used because the transport numbers of K+ and Cl- are nearly equal in KCl over a sizable concentration range.17 The literature values for γ((NaCl) and γ((KCl) at ionic strength (I)
je + m js hI ) m j Na ) m
(8)
were used for the calculation of the activity coefficients by eqs 6 and 7. Equation 8 was obtained using the assumptions that sorbed alkali metal ions are not associated with functional groups, while all hydrogen ions are associated with functional groups. The associated hydrogen ions and functional groups do not contribute to the internal ionic strength value. According to eq 8, the ionic strength in the resin phase depends on the amount of salt transferred. An iteration method was used for the calculation of m j s. The calculation algorithm is presented by Figure 1. Direct measurement of pm j Na
js + m j e) pm j Na ) -log(m
(9)
was performed by a standard method described in ref 4. The amount of sodium was determined by the ICP method (ARL 3520B) after extraction into HNO3. m j Na in eq 9 corresponds to the total Na molality in the resin phase (per gram of water contained in the resin phase). The results of the direct measurements and calculations are collected in Table 1. The good agreement was found. The amount of imbibed sodium (m j s) was calculated using the amount of H+ ions released:
ms ) mNa -
∆RH [H2O]
m js ) m j Na - [R h]
(10)
where ∆RH defines the number of hydrogen millimoles released in the solution (per gram of dry resin), [H2O] is the amount of water (gram) sorbed by 1 g of resin at equilibrium. It must be noted that the concentration of the deprotonated groups, [R h ], corresponds directly to the amount of hydrogen ions released. It also corresponds to the concentration of sodium ions that have replaced the H+ at the active sites. 3.2. Total Resin Capacity. Values of the total capacity (Q) defined as millimole of active sites per gram of dry resin, were obtained by plotting the quantity of sodium ions exchanged for hydrogen (m j e) against pH (Figure 2). Two acidic deprotonation
Deprotonation of Chelating Ion Exchange Resins
J. Phys. Chem. B, Vol. 105, No. 20, 2001 4723
Figure 1. Iteration procedure for the m j s calculation. ε ) 0.01 was selected.
TABLE 1: Amount of Sodium Sorbed in Different Experiments (mmol per g H2O Contained in the Resin) no. 1 2 3 4
resin
I(NaCl)
pH
pm j Na,exp
pm j Na,calc
IRC-718 IRC-718 IRC-718 P-127
0.05 0.5 0.5 0.5
2.88 2.68 9.10 4.10
1.44 0.52 -0.18 0.09
1.545 0.357 -0.281 0.124
steps are identified for IRC-718 resin (Figure 2b). They are equally spaced; the value obtained was 2.5 mmol of iminodiacetic groups/g of dry resin. The P-127 resin is characterized by only one acid deprotonation step. The capacity was found to be 1.2 mmol/g of dry resin. 3.3. Thermodynamic Models of the Ion Exchange Equilibria. Several approaches to the measurement of weak and chelating resins equilibrium constants have been reported in the literature.16,18-21 The main difficulty for thermodynamic modeling of such systems is related to the strong sensitivity of the equilibrium to the salt concentration in the aqueous solution. Two of the most successful models are considered below. 3.4. Marinsky’s Model. Marinsky proposed a model based on the Gibbs-Donnan theory. According to this approach, the cross-linked polyelectrolyte that constitutes the charged, threedimensional skeletal structure acts as a membrane permeable to the diffusing components of the surrounding solution. At an equilibrium state, the chemical potential of each of these components, e.g., salt, acid, and water, is the same in both phases. Hence, a transfer of these components, into or out of the resin phase, occurs when the equilibrium is disturbed by any change in the solution. The resin matrix is restrictive to the flow of water from the solution phase into the resin phase. The gel phase is considerably more concentrated in counterions and less concentrated in co-ions than the solution phase external
Figure 2. pH dependence of Na+ exchanged for P-127 (a) and IRC718 (b) resins. Open symbols correspond to 0.05 M ionic media; filled symbols correspond to 0.5 M ionic media. Three repetitions are performed for each experiment.
to it. The ion distribution between two phases may be described by the following activity ratio:
ajH ajNa ) aH aNa
(11)
The small contribution of the pressure difference (osmotic pressure) to the activity coefficients is neglected in eq 11. Ratio 11 is identifiable as the Donnan potential term. In a weak cation exchanger with a Na+ concentration level far exceeding that of the H+ ion, the Na+ ion acts as the Donnan potential-determining ion. This Donnan potential term is responsible for the sizable dependence of the measured dissociation constant on counterion concentration levels in the solution. Equation 11 can be rewritten as follows:
paH ) pajH - pajNa + paNa
(12)
The proton exchange reaction
RH ) R- + H+
(13)
can be described by the apparent dissociation constant
Kapp a )
aH[R h]
(14)
[HR]
which is strongly dependent on conditions of the experiment. This in turn can be rewritten as the Handerson-Hasselbach equation:
R pKapp a ) paH - log 1-R
(15)
4724 J. Phys. Chem. B, Vol. 105, No. 20, 2001
Biesuz et al.
where R is the degree of dissociation
[R h]
R)
[RH] + [R h]
)
m j e[H2O] Q
TABLE 2: Mean Values for the Resin Deprotonation Constants Calculated by Marinsky’s Model
(16)
resin P-127
R - pajNa + paNa 1-R
(17)
IRC-718
Hence, the relationship between the thermodynamic constant of the deprotonation (K h a) and Kapp a can be written as
jNa - paNa pK h a ) pKapp a + pa
(18)
titration
pK h a,1
1 2 1 2 3 1 2 3 1 2 3
4.62 4.72 4.36 4.29 4.20 4.52 4.36 4.53 3.86 3.89 3.88
0.5 M NaCl
for reaction 13. The substitution of eq 12 into eq 15 results in
Kapp jH - log a ) pa
media 0.05 M NaCla
0.05 M NaCl 0.5 M NaCl
pK h a,2
9.11 9.03 8.83 8.52
a
Titration 3 of P-127 in 0.05 M NaCl was not used for calculations because the equivalence point was not attained.
since
K ha )
ajHajR R ) ajH ajRH 1-R
(19)
for reaction 13. The sensitivity of Kapp a to the salt concentration level is explained by the fact that aH of the solution is measured when a weak acid resin is titrated, while it is the ajH of the resin phase that determines the K h a of the repeating acid unit. Equation 18 describes the relationship between experimentally measurable Kapp and the system-characterizing thermodynamic property a K h a. 3.5. Activity Coefficients. No methods have been developed for the direct measurement of activity coefficients in the resin phase. Various approaches to solve this problem have been applied. Szabadka and Inczedy have defined γ j R as the electrostatic free enthalpy of the polyion.18 They have shown that γ j RH and γ j R appear to cancel each other. This observation has been confirmed by ref 16 and therefore there is no need for their assessment. Other authors16-21 attempted to calculate activity coefficients by applying the specific interaction theory.22 There are difficulties encountered when determining the interaction coefficients of the charged groups fixed on the resin matrix. In this application of the Gibbs-Donnan approach, evaluation of the activity coefficients of the resin phase species (γ j RH and γ j R) has been avoided by assuming that the coefficients cancel each other.16,18 The activity coefficient of the Na ion in the resin phase has been estimated by eq 6. 3.6. Ho1 gfeldt’s Three-Parameter Model. The first variant of this model was presented in 197910 and since then several modifications and applications have been reported.11,19-21 The model is based on Guggenheim’s zero approximation. The ion exchange reaction
RH + Na+ ) RNa + H+
(20)
is considered. The coefficient characterizing equilibrium (20) can be written as follows:
R pK ˜ Na + log aNa (21) ˜ Na H ) - log pK H ) pH - log 1-R In a binary mixture of A and B, the number of AA, BB, and AB pairs are proportional to χA2, χB2, and 2χAχB, where χA and χB are stoichiometric mole fractions of A and B. According to the approach, any extensive thermodynamic property can be described by the following equation:
Y ) yAχA2 + yBχB2 + 2ymχAχB
(22)
where yA and yB correspond to the quantity Y for the pure forms
˜ Na and ym refers to the mixture. Y ) pK H in the case considered. The following expression can be obtained by combining eqs 21 and 22:
pK ˜ ) pK ˜ (1)R2 + pK ˜ (0)(1 - R)2 + pK ˜ mR(1 - R) (23) The thermodynamic equilibrium constant (KNa H ) for the exchange reaction 20 can be estimated by using
pKNa H )
∫01pK˜ NaH dR ) 31(pK˜ (0) + pK˜ (1) + pK˜ m)
(24)
In Ho¨gfeldt’s approach, an empirical equation is introduced at this point so that pK ˜ Na H is expressed as a function of R, instead 2 of R . Equation 23 can be rewritten as a polynomial equation:
pK ˜ ) a + bR + cR2
(25)
a ) pK ˜ (0)
(26)
b ) 2(pK ˜ m - pK ˜ (0))
(27)
˜ (1) - 2pK ˜m c ) pK ˜ (0) + pK
(28)
where
By multiple regression of eq 25 the values of a, b, and c can be obtained and the parameters pK ˜ (0), pK ˜ (1), and pK ˜ m can be easily calculated. The value of KNa H can be determined from the eq 24. The titration curve can thus be calculated with eqs 21 and 23. 3.7. Application of the Models. The experimental data were separately treated by the two models described above. The results of the calculations are reported in Tables 2 and 3. The F-test applied to the results did not show any significant difference between repeated titrations. Hence, the experimental points may be collected in one set (for each system) and recalculated to obtain the mean values of the model parameters. The recalculated results are shown in Table 4 for Marinsky’s model and in Table 5 for Ho¨gfeldt’s model. Figure 3 presents the fitting of the experimental data by the two models. Equations 15 and 18 are used for fitting by Marinsky’s model. The fitting of data to Ho¨gfeldt’s model is done by applying eqs 21 and 25. The standard deviation is shown in Table 6. Ho¨gfeldt’s model exhibits a good approximation of the experimental data. Marinsky’s model cannot be fitted satisfactorily with the experimental data. To explain this disagreement, the experimental values of pK h a were plotted versus R, as given in Figure 4. In the first instance, the pK h a resolved is not a unique function of R as expected. Instead pK h a increases linearly with R for the
Deprotonation of Chelating Ion Exchange Resins
J. Phys. Chem. B, Vol. 105, No. 20, 2001 4725
TABLE 3: Parameters Obtained by Least Square Fitting to Eq 24 (Ho1 gfeldt’s Method) resin
media
P-127
IRC-718, K1
IRC-718, K2
0.05 M NaCl titration 1 titration 2 0.5 M NaCl titration 1 titration 2 titration 3 0.05 M NaCl titration 1 titration 2 titration 3 0.5 M NaCl titration 1 titration 2 titration 3 titration 4 0.05 M NaCl titration 1 titration 2 titration 3 0.5 M NaCl titration 1 titration 2 titration 3
pK ˜ (0),
pK ˜ (1)
pK ˜m
pKNa H
2.90 2.79 3.79 3.23 3.04 3.86 3.44 3.79 3.87 4.12 4.55 2.62
5.92 5.65 5.19 4.95 4.55 6.60 5.36 5.76 4.51 5.04 3.56 2.82
4.06 4.08 3.68 4.15 4.23 1.87 2.76 1.91 2.83 2.24 2.71 3.69
4.29 4.17 4.22 4.12 3.94 4.11 3.85 3.82 3.74 3.80 3.61 3.04
9.31
10.45 8.57
9.44
8.72
8.94 9.40
9.02
8.50
8.43 9.58
8.84
TABLE 4: Recalculated Values for the Resins Deprotonation Constants (Gibbs-Donnan model) macroporosity is not taken into account resin P-127 IRC-718
media
pK h a,1
0.05 M NaCl 0.5 M NaCl 0.05 M NaCl 0.5 M NaCl
4.66 4.29 4.48 3.88
pK h a,2
9.09 8.65
macroporosity is taken into account pK h a,1
pK h a,2
3.73 3.86 4.47
9.09
Figure 3. Dependencies of pH on R fitted by two different models (continuous line, Ho¨gfeldt’s model; dashed line, Marinsky’s model)
TABLE 5: Recalculated Parameters Obtained by Least Square Fitting to Eq 24 (Ho1 gfeldt’s Method) resin P-127 IRC-718 K1 K2
media
pK ˜ (0),
pK ˜ (1)
pK ˜m
pKNa H
0.05 M NaCl 0.5 M NaCl
2.85 3.41
5.77 4.12
4.12 4.73
4.24 4.09
0.05 M NaCl 0.5 M NaCl 0.05 M NaCl 0.5 M NaCl
3.71 4.05 9.14 8.67
5.67 4.12 10.26 8.43
2.20 2.84 8.76 9.60
3.86 3.67 9.39 8.90
P-127 resin. The slope, in the presence of the more dilute salt solution (0.05 M NaCl), is somewhat larger than that obtained in the more concentrated solution (0.5 M NaCl). A similar sensitivity of pK h a to R was reported for the highly porous Sephadex CM-5023 and Amberlite IRC-50.24 It was attributed to the macroporosity of the gel.16 The macroporosity is, undoubtedly, the source of the variability of pK h a in the P-127 resin samples. Estimates of the water content of the resin samples, that are needed to evaluate ajNa, were obtained through
ajNa )
(
RQ [H2O]
)
+m js γ j Na
(29)
The obtained values are exaggerated by the presence of external solution trapped in the macrocavities. In earlier publications dealing with complication, the following approach was found. The dependence pK h a ) f(R) was assumed to be linear and the intercept of the ordinate axis at R ) 0 was considered to be identifiable as the pK h a value of the repeating monomer unit. The approach was considered to be correct, since the pK h a values resolved in this way agree with the literature values of simple weak acids that closely resembled the repeating monomer unit. In the present instance, however, the pK h a values determined by h a ) 3.86 such extrapolation (pK h a ) 3.73 in 0.05 M NaCl and pK in 0.5 M NaCl) are considerably smaller than the literature value
Figure 4. Fitting of experimental results by the Gibbs-Donnan model. Horizontal lines show the mean values of pK h a calculated; slopped lines take macroporosity into account.
4.76 reported for quinolic-2-carboxylic acid in 0.1 M NaNO3.15 This substance formed by inserting quinolic acid into the XAD-2 matrix is considered to resemble the repeating moiety of the P-127 product. This discrepancy can be attributed to the alteration of the acid unit at the time of the sorbent synthesis process. The results obtained with the IRC-718 resin are more consistent with the Gibbs-Donnan-based expectations. The pK ha values are invariant until an R value of 0.85 is reached. At high R values, pK h a deviates upward significantly. Taking into account a slope of pK h a ) f(R) cannot improve the fitting of the IRC718 experimental results (see Table 6). The values shown in Table 4 are found to characterize the dissociation of the iminodiacetic active sites considered to be repeated throughout the matrix of the IRC-718 resin. Only the larger of the two pK ha values is in reasonable agreement with the values reported for the resembling chelating molecule (2.57 and 9.17 in 0.5 M
4726 J. Phys. Chem. B, Vol. 105, No. 20, 2001
Biesuz et al.
TABLE 6: Standard Deviation for the Experimental pH Fitting by Two Modelsa Marinsky’s model macroporosity is not taken into account
macroporosity is taken into account
Ho¨gfeldt’s model
N - 1b
N-2
N-3
0.05 M NaCl 0.5 M NaCl
0.579 0.283
0.124 0.142
0.129 0.147
0.05 M NaCl 0.5 M NaCl
0.576 0.444
0.586 0.307
0.212
0.05 M NaCl 0.5 M NaCl
0.100 0.234
0.107 0.078
0.096
resin
media
degrees of freedom (n) P-127 IRC-718 first deprotonation step IRC-718 second deprotonation step a
The standard deviation was calculated as
σ)
x
Σ(pHi,exp - pHi,calc)2 n
where n is the number of degrees of freedom. b N is the number of experimental points.
NaClO415) and for another iminodiacetic resin (3.10 and 9.12 for Ligandex-I, Hungary7). The present examination of the resins with the three-parameter model shows that the model provides an acceptable fit for all of the data computed. It successfully replaces the experimental data with a few parameters. However, only one constant calculated by this method (pK h a,2 for IRC-718) perfectly agrees with the literature data. Certain similarities between the results obtained with the two models can be noted. The differences between the values given in Table 4 and Table 5 are smaller than those between any of these values and the characteristics of the monomeric analogues. 4. Conclusions Thermodynamic values of P-127 and IRC-718 resins deprotonation are obtained using two different thermodynamic approaches. Ho¨gfeldt’s three-parameter model has normally a better agreement with the experimental data. It demonstrates to be a very descriptive model. The fitting by Marinsky’s method can be improved by taking into account a slope of pK h a ) f(R). However, it results in the necessity for an additional empirical parameter for the resin characterization. The thermodynamic values provided by the two models are similar. The choice between the models depends on the information that is needed. Ho¨gfeldt’s three-parameter model can be usefully explored to describe the ion exchange performance. The Gibbs-Donnan model needs a much greater amount of experimental work. It is more informative but should be selected if the resin under consideration needs detailed physicochemical characterization (for example, the description of ion exchange equilibria in the presence of metal ions at trace level9).
Acknowledgment. We highly appreciate the comments of professor J. Marinsky and his kind attention to this work. Supporting Information Available: Experimentally determined amount of water in the resin phase and raw titration data are available free of charge via the Internet at http//pubs.acs.org. References and Notes (1) Moberg, C.; Weber, M.; Ho¨gberg, K.; Muhammed, M.; Nilsson, A. C. React. Polym. 1990, 12, 31. (2) Gregor, H. P. J. Am. Chem. Soc. 1951, 73, 642. (3) Gluechauf, E. Proc. R. Soc. London 1952, A214, 207. (4) Helfferich, F. Ion Exchange; McGraw-Hill: New York, 1962. (5) Bukata, S.; Marinsky, J. J. Phys. Chem. 1964, 68, 994. (6) Szabadka, O ¨ . Talanta 1982, 29, 177. (7) Szabadka, O ¨ . Talanta 1982, 29, 183. (8) Pesavento, M.; Biesuz, R.; Profumo, A.; Gallorini, M. Ann. Chem. 1993, 65, 2522. (9) Pesavento, M.; Biesuz, R. React. Polym. 1998, 88, 135. (10) Ho¨gfeldt, E. Acta Chem. Scand. 1979, A33, 557. (11) Ho¨gfeldt, E. React. Polym. 1989, 11, 199. (12) Pitzer, K. S. ActiVity Coefficients in Electrolyte Solutions; CRC Press: Boca Raton, FL, 1979; Vol. 1, p 157. (13) Gran, G. Acta Chem. Scand. 1950, 4, 559. (14) Gran, G. Analyst 1952, 77, 661. (15) Sille´n, L. G.; Martell, A. E. Stability Constants of Metal-Ions Complexes; The Chemical Society: London, 1971. (16) Marinsky, J.; Miyajima, T.; Muhammed, M.; Ho¨gfeldt, E. React. Polym. 1989, 11, 279. (17) Moore, W. J. Physical Chemistry, 5th ed.; Longmans: London, 1972. (18) Szabadka, O ¨ .; Inczedy, J. Acta Chim. Acad. Sci. Hung. 1980, 104, 55. (19) Ho¨gfeldt, E. J. Phys. Chem. 1988, 92, 6475. (20) Ho¨gfeldt, E.; Muraviev, D. React. Polym. 1988, 8, 97. (21) Ho¨gfeldt, E. React. Polym. 1988, 7, 81. (22) Ciavatta, L. Ann. Chim. 1980, 70, 551. (23) Merle, Y.; Marinsky, J. Talanta 1984, 31, 199. (24) Chatterjee, A.; Marinsky, J. J. Phys. Chem. 1963, 67, 41.
