Thermodynamics and dissociation constants of carboxylic acids at high ionic strength and temperature

Inorganica Chimica Acta 360 (2007) 3671–3680 www.elsevier.com/locate/ica

Thermodynamics and dissociation constants of carboxylic acids at high ionic strength and temperature P. Thakur, J.N. Mathur, R.C. Moore 1, G.R. Choppin

*

Department of Chemistry and Biochemistry, The Florida State University, Tallahassee, FL 32306-4390, USA Received 2 August 2006; accepted 22 January 2007 Available online 5 June 2007

Abstract Dissociation constants (pKa) of oxalic, iminodiacetic, citric, nitrilotriacetic, ethylenediaminetetraacetic, trans-1,2 diaminocyclohexanetetraacetic acid and diethylenetriaminepentaacetic acid have been determined potentiometrically using a glass electrode at an ionic strength of 6.60 m (NaClO4) and temperatures of 0–60 C. The constants of iminodiacetic, nitrilotriacetic and diethylenetriaminepentaacetic acid were measured at 25 C at ionic strengths from 0.30 to 6.60 m (NaClO4). The thermodynamic parameters for the dissociation of these carboxylic acids were derived from the temperature dependence of the dissociation constants. The Specific Ion Interaction Theory (SIT) and the Parabolic model successfully described the ionic strength dependencies of the pKa values. The variation of the pKa values at high ionic strengths as a function of the type and concentration of supporting electrolyte is discussed and compared with literature data.  2007 Elsevier B.V. All rights reserved. Keywords: Dissociation constants; Carboxylic acid; Aminopolycarboxylic acid SIT; Parabolic; Thermodynamics

1. Introduction Large volumes of high-level nuclear waste (HLW) from the cold war era are stored in tanks at US Department of Energy (DOE) sites. The tank solutions are highly alkaline with high concentration of salts. Some of the tanks have leaked, releasing radioactive contaminants. Some organic ligands (i.e., oxalate, citrate, NTA, EDTA, etc.) in the waste (from treatment and reprocessing of the wastes) have strong binding ability for some cationic radionuclides and their complexation can result in large releases of actinides to the surrounding environment [1,2]. To define the speciation and the related migration behavior of the actinides released into the environments, the thermodynamic data of actinide complexation by the specific ligands are necessary. Calculation of stability constants requires the *

Corresponding author. Fax: +1 850 6448281. E-mail address: [email protected] (G.R. Choppin). 1 Address: Sandia National Laboratories, Albuquerque, NM 871850779, USA. 0020-1693/$ - see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ica.2007.06.002

values of the acid dissociation constants, (pKa) of the ligand at the ionic strengths and temperatures of the systems. However, available data of the dissociation constants of some of ligands are limited to I 6 1.0 m and T = 25 C [3]. Values are available for solutions in high ionic strengths of NaCl or NaClO4 at 25 C for citric acid, oxalic acid and EDTA which were measured for use in performance assessment of the proposed nuclear waste repository in Gorleben, Germany [4] and the Waste Isolation Pilot Plant (WIPP) in the USA [5]. The present work measured the pKa values of IDA, NTA and DTPA at I = 0.3–6.60 m NaClO4 and 25 C and for Ox, IDA, Cit, EDTA CDTA and DTPA at I = 6.60 m (NaClO4) and temperatures of 0–60 C. These pKa values were measured by potentiometric titration. The thermodynamic parameters for the acidic dissociation were obtained from pKa measurements as a function of temperature. Such data is required for calculation of stability constants of the binary and the ternary complexation of Am3+ and Cm3+ with these ligands which are necessary to assess methods for safe and efficient management of the high-level actinide wastes.

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2. Experimental 2.1. Reagents Citric acid and nitrilotriacetic acid (Fluka, Puris), oxalic acid and disodium ethylenediaminetetraacetic acid (Fisher, ACS certified), diethylenetriaminepentaacetic acid (Sigma) and trans-1,2 diaminocyclohexanetetraacetic acid (Sigma– Aldrich ACS certified) were recrystallized from water or water/ethanol solutions. NaClO4 (Sigma–Aldrich ACS certified) stock solution was prepared in deionized water and filtered through 0.45 lm membranes. Deionized water (Barnstead Nanopure), purged with N2, was used to prepare the solutions. The stock solutions of the caboxylic acids were prepared by dissolving the required amounts of the acids in NaClO4 solutions of the desired ionic strength. To prepare the solutions of NTA and CDTA, measured volumes of standard carbonate-free NaOH solution was added dropwise to a suspension of a weighed amount of the reagent in water. NaOH titrant solutions at different ionic strengths were prepared by adding measured volumes of 50% (CO2 free) NaOH to a N2-saturated NaClO4 solution. The NaOH solutions were standardized by titration with potassium hydrogen phthalate. The HClO4 solutions at desired ionic strengths were prepared and standardized with standard NaOH. 2.2. Potentiometric titration The potentiometric titrations were conducted in a 30 mL jacketed cell controlled to ±0.1 C with an isotemp Model 910 constant temperature circulator system. The cell was capped with a jacketed lid to minimize condensation and volume loss during titration of the solution [6]. The titrant solution was delivered by a Metrohm Dosimat 665 motordriven piston burette. The titrations were performed under nitrogen gas that had been bubbled through solutions of 4 M NaOH to remove CO2 and of NaClO4 of the same ionic strength as the experimental solutions to saturate the gas with water vapor. The titrations were performed with stirring on a Corning model PC420 stirrer/hot plate. The system was interfaced to a computer that operated software prepared in the laboratory to control burette additions and to record the mV reading of the electrode. The general titration procedure has been adopted from Martell and Motekaitis [7]. 2.3. Measurements of pcH An Accumet 950 (Fisher Scientific) pH meter was used with a glass electrode (Corning semi-micro-combination) to measure the change in pH. The outer sleeve of the reference cell of the electrode was filled with saturated NaCl to minimize liquid junction potential effects. The electrode was calibrated by titration of a standardized strong acid with a standardized strong base, which provided a mV

versus pcH conversion equation. Aliquots of standardized perchloric acid solution and sodium perchlorate stock solution were added to deionized water to create 15.00 mL solutions of known concentrations. These solutions were typically 0.1000 M perchloric acid with an ionic strength between 0.30 and 6.60 m. The solutions were titrated by P10 titrand additions using addition sizes of 0.300 mL. The concentrations of the acid and the burette addition size were chosen so that approximately half the data points in the curve were in the acidic and half in the basic regions. The delay between the readings was P30 s to assure equilibrium. Standardization titrations were conducted at least after each third experimental titration. The titrand solutions, generally 15 mL, containing dissolved ligand (5 · 103 M citric acid, 2 · 103 M Na2EDTA and CDTA, 3 · 103–5 · 103 M NTA, 5 · 103 M IDA and 1 · 103 M DTPA), and a known amount of standard 0.1000 M HClO4 (for IDA, NTA, EDTA and the DTPA systems) were titrated with standardized NaOH (0.1000 M) at the same ionic strengths. 2.4. Calculation of the dissociation constants The computer program PSEQUAD [8] was used to calculate the acid dissociation constants from the titration data. At least five titrations of 80–100 data points per titration were done for each ligand. All pKa values and thermodynamic parameters are reported in molality. Conversions of molarity to molality were accomplished using the density of aqueous sodium perchlorate solutions as described in Ref. [9]. The protonation constants determined at various temperatures were used to calculate the thermodynamic parameters by the Van’t Hoff equation. The reported values of the thermodynamic parameters are rounded to the nearest kJ mol1 (enthalpy) and J K mol1 (entropy). The stepwise dissociation constants of the carboxylic acid, HnL have been calculated by the equation (charges omitted): pK ai ¼  log½H½Hni L=½Hni þ L

ð1Þ

3. Results and discussion The pKa values of IDA, NTA and DTPA measured at 25 C in solutions of ionic strengths ranging from 0.3 to 6.60 m (NaClO4) and those of Ox, IDA, Cit, NTA, EDTA, CDTA and DTPA at 0 to 60 C in an ionic strength of 6.60 m (NaClO4) along with literature data are listed in Tables 1 and 2, respectively. The general trends of pKai with increasing ionic strength are an initial decrease to a minimum between I = 0.5 and 2.0 m followed by increases with further increases in ionic strength, reflecting the increasing values of the activity coefficients with increased ionic strength. For Ox, the pKai values follow a linear relationship with temperature; pKa1 shows an increasing trend

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Table 1 pKa values of IDA, NTA and DTPA at 25 C in different concentrations of NaClO4 Ligands

NaClO4 (m)

pKa1

pKa2

IDA

0.304 0.511 1.03 2.18 3.44 4.92 6.60

2.67 ± 0.03 2.66 ± 0.03 2.62 ± 0.07 2.68 ± 0.08 2.72 ± 0.09 2.76 ± 0.08 2.82 ± 0.05

9.42 ± 0.03 9.32 ± 0.02 9.29 ± 0.08 9.49 ± 0.07 9.72 ± 0.07 9.76 ± 0.07 9.87 ± 0.03

NTA

0.304 0.511 1.03 2.18 3.44 4.92 6.60

1.85 ± 0.07 1.84 ± 0.05 1.82 ± 0.06 1.94 ± 0.05 2.03 ± 0.05 2.09 ± 0.05 2.14 ± 0.05

2.75 ± 0.01 2.66 ± 0.09 2.61 ± 0.06 2.53 ± 0.08 2.64 ± 0.07 2.69 ± 0.08 2.71 ± 0.08

9.44 ± 0.06 9.35 ± 0.02 9.28 ± 0.08 9.12 ± 0.03 9.33 ± 0.04 9.41 ± 0.02 9.56 ± 0.06

DTPA

0.304 0.511 1.03 2.18 3.44 4.92 6.60

2.18 ± 0.11 2.16 ± 0.09 2.14 ± 0.12 2.12 ± 0.11 2.21 ± 0.11 2.28 ± 0.08 2.32 ± 0.09

2.90 ± 0.09 2.79 ± 0.10 2.68 ± 0.09 2.64 ± 0.09 2.87 ± 0.07 2.92 ± 0.08 2.94 ± 0.07

4.20 ± 0.03 4.18 ± 0.02 4.15 ± 0.03 4.13 ± 0.09 4.22 ± 0.04 4.38 ± 0.06 4.41 ± 0.02

while pKa2 has a decreasing pattern. The agreement between our values of 25 C and I = 6.60 m and those of Moore and co-workers [10] in 5.0 m NaCl is good; however, our values are lower than those of Erten et al. [11] and Choppin and Chen [12] but somewhat higher than those of Kettle et al. [13]. For IDA, the values show a decreasing trend from I = 0.3 to 1.0 m, followed by an increase to I = 6.60 m, which is consistent with the usually observed trend of pKa with increased ionic strength. The pKa values increase with increased temperature. Within the experimental uncertainties, our values are in general agreement with critically selected values of IDA for I < 2.0 m3. The trend observed for pKa values of NTA show an initial decrease to a minimum at I = 2.08 m, then increase with increased ionic strength. Our pKa values of NTA agree well with the values reported in the critically selected database3. A linear relationship was observed for pKa values of NTA with temperature (Table 2). In Ref. [14] the author reported no differences of pKa values and the enthalpies of protonation (by calorimetry) for NTA, HEDTA, EDTA, CDTA and DTPA in KNO3 and NaClO4 as supporting electrolytes hence the pKa values of KNO3 and NaClO4 media were used interchangeably. By contrast, our values of NTA at I = 0.5 m (NaClO4) are consistently lower than the corresponding values in I = 0.5 m (KNO3). Similar to IDA and NTA, the pKa values of Cit show a relationship with temperature. The pKa value of Cit at 25 C and I = 6.60 m (NaClO4) are in good agreement with the values of Moore and co-workers [10] in 5.0 m (NaCl) whereas the constants reported by Erten and co-workers. [15] are generally higher with an average difference of ca. 0.35 log units for all three pKa values in 6.5 m (NaClO4)

pKa3

pKa4

pKa5

8.64 ± 0.04 8.53 ± 0.03 8.32 ± 0.04 8.28 ± 0.04 8.42 ± 0.06 8.58 ± 0.05 8.62 ± 0.04

9.87 ± 0.06 9.72 ± 0.02 9.52 ± 0.03 9.46 ± 0.05 9.58 ± 0.04. 9.83 ± 0.07 9.98 ± 0.08

and ca. 0.21 units for pKa1, pKa2 and ca. 0.14 log units for pKa3 in 5.0 m (NaCl). These deviations probably are related to the difficulty in calculating values for species with similar dissociation constants. We have not measured the pKa values of Cit in solutions of different ionic strength. The constants reported in NaClO4 (0.1–14.1 m) and NaCl (0.1–5.0 m) are consistent with the usually observed trend of pKa with increasing ionic strengths [15]. The pKa values of EDTA and CDTA increase with increased temperature from 0 to 60 C. The first and second pKa values of EDTA at 25 C and I = 6.60 m are in good agreement with the values of Moore and co-workers in 5.0 m (NaCl) [10], but our the pKa3 and pKa4 values are higher than the reference data. Ours values are also higher than those measured by Borkowski et al. [16] in 5.0 m (NaCl). For CDTA no such data are available in the literature for comparison. Our pKa1 and pKa2 values (which differ only slightly) have larger errors than those of pKa3 and pKa4 due to the greater difficulties in their measurement. All five pKa values of DTPA initially decrease to a minimum at I = 2.18 m, then increase to I = 6.60 m. The agreement between our values and those of the critically selected values for I 6 1.0 m is good. No such constants are reported in the critical values for DTPA at I > 1.0 m. With temperature, the pKa had increased values. The values listed in Tables 1 and 2 were not corrected for complexation with ions of the medium. At I = 6.60 m (NaClO4), the probability of complexation of the ligand by the Na+ [17] would result in a higher measured pKa. Since the interaction of trivalent lanthanides and actinides with carboxylates is primarily electrostatic, a direct proportionality is usually observed P between the log b (stability constant) and the pKa or pKa. The linear plot for Eu3+ in Fig. 1 allows estimation of values of the stability con-

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Table 2 pKa value of Ox, IDA, Cit, NTA, EDTA, CDTA and DTPA at various temperatures and ionic strengths Ligand Ox

Temp (0 C)

I (m) a

pKa1

pKa2

0 10 25 25 25 32 35 37 37 45 50 50 60

6.60 6.60a 6.60a 3.0a 5.0b 1.0d 6.60a 0.1c 0.3c 6.60a 5.0b 3.0b 6.60a

1.18 ± 0.12 1.20 ± 0.10 1.22 ± 0.09

1.27 ± 0.09 1.15 ± 0.08 0.97 ± 0.05 1.29 ± 0.12

4.07 ± 0.04 4.03 ± 0.05 3.99 ± 0.03 3.80 3.85 ± 0.02 3.68 3.92 ± 0.03 3.98 ± 0.02 3.98 ± 0.02 3.89 ± 0.05 3.67 ± 0.05 3.54 ± 0.03 3.87 ± 0.05

IDA

0 0.4 20 25 30 45 60

6.60 0.1d 1.0*,a 6.60 0.1e 6.60a 6.60a

2.72 ± 0.08 2.84 2.52 ± 0.01 2.82 ± 0.05 2.60, 2.54 2.86 ± 0.08 2.94 ± 0.06

9.22 ± 0.05 10.70 9.33 ± 0.01 9.87 ± 0.03 9.46, 9.12 9.98 ± 0.05 10.39 ± 0.05

Cit

0 5 20 25 25 25 30 37 45 60

6.60a 0.1g 4.00*,a 6.60a 3.00a 5.00b 0.1g 1.0c 6.60a 6.60a

2.82 ± 0.11 3.02 2.12 2.92 ± 0.05

0 15 20 20 20 25 25 35 37 40 45 60 0 0 0 5 5 10 10 20 25 30 30 30 37 45 60

NTA

EDTA

1.2 ± 0.2 1.12 1.24 ± 0.08 1.23 ± 0.06

pKa3

pKa4

pKa5

Ref. p.w p.w p.w [22] [10] [23] p.w [20] [20] p.w [13] p.w p.w [24] [25] p.w [26,27] p.w p.w

2.96 ± 0.07 2.94 3.06 ± 0.02 3.01 ± 0.08 3.06 ± 0.04

4.12 ± 0.09 4.50 3.41 4.28 ± 0.02 5.68 ± 0.05 4.32 ± 0.03 4.44 4.51 ± 0.08 4.36 ± 0.009 4.45 ± 0.08

5.08 ± 0.08 5.80 4.51 5.21 ± 0.02 7.16 ± 0.05 5.22 ± 0.04 5.82 6.07 ± 0.01 5.28 ± 0.01 5.35 ± 0.02

p.w [28] [29] p.w [30] [10] [28] [31] p.w p.w

6.60a 0.1d 0.1e 0.1f 1.0f 6.60a 3.0a 0.1d 1.0c 0.1d 6.60a 6.60a

2.07 ± 0.12

2.63 ± 0.09

1.75 ± 0.05

2.47 ± 0.02

1.7 2.14 ± 0.09 2.05 ± 0.02

2.4 2.71 ± 0.08 2.63 ± 0.05

1.95 ± 0.05

2.64 ± 0.03

2.18 ± 0.11 2.21 ± 0.12

2.78 ± 0.05 2.82 ± 0.09

9.01 ± 0.01 9.86 9.71 ± 0.02 9.87 9.67 9.56 ± 0.01 9.17 ± 0.04 9.62 9.70 ± 0.03 9.58 9.68 ± 0.01 9.91 ± 0.01

p.w [32] [33] [34] [34] p.w [35] [32] [31] [32] p.w p.w

6.60a 0.01e 0.05e 0.01e 0.05e 0.01e 0.05e 0.1d 6.60a 0.1d 0.01e 0.05e 1.0c 6.60a 6.60a

2.18 ± 0.05

2.54 ± 0.04

2.02 2.25 ± 0.12

2.66 2.64 ± 0.07

2.28 ± 0.08 2.30 ± 0.10

2.68 ± 0.06 2.72 ± 0.05

6.82 ± 0.04 6.41 6.37 6.35 6.27 6.30 6.20 6.21 7.18 ± 0.05 6.14 6.10 6.00 6.04 ± 0.02 7.51 ± 0.03 7.68 ± 0.08

8.92 ± 0.07 11.08 10.81 11.00 10.73 10.93 10.66 10.31 9.26 ± 0.04 10.12 10.64 10.37 10.10 ± 0.04 9.54 ± 0.04 10.06 ± 0.09

p.w [36] [36] [36] [36] [36] [36] [37] p.w [37] [36] [36] [31] p.w p.w

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Table 2 (continued) Ligand

Temp (0 C)

I (m)

pKa1

pKa2

pKa3

pKa4

CDTA

0 10 20 20 25 25 30 30 45 40 60

6.60a 1.0e 0.1d 1.0e 6.60a 0.5*,a 0.1d 1.0e 6.60a 0.1d 6.60a

3.07 ± 0.06 2.39 2.40 2.40 3.09 ± 0.05 2.38 ± 0.06

3.70 ± 0.09 3.22 3.55 3.22 3.73 ± 0.09 3.01 ± 0.06

2.42 3.15 ± 0.08

3.21 3.76 ± 0.08

3.22 ± 0.09

3.82 ± 0.09

6.59 ± 0.08 6.12 6.14 6.03 6.68 ± 0.07 6.51 ± 0.06 6.10 5.94 6.82 ± 0.06 6.07 7.05 ± 0.08

9.25 ± 0.06 12.54 11.70 12.26 10.25 ± 0.04 11.30 ± 0.07 11.52 12.01 10.52 ± 0.07 11.34 10.63 ± 0.08

0 10 10 20 20 25 30 30 40 45 60

a

2.21 ± 0.12 2.21

2.89 ± 0.08 2.48

2.27 1.80 2.32 ± 0.09 2.32

2.49 2.55 2.94 ± 0.08 2.50

2.35 ± 0.08 2.40 ± 0.12

2.98 ± 0.08 3.02 ± 0.08

4.21 ± 0.05 4.24 4.39 4.17 4.33 4.41 ± 0.07 4.10 4.30 4.27 4.49 ± 0.06 4.61 ± 0.08

8.24 ± 0.09 8.55 8.72 8.40 8.60 8.62 ± 0.09 8.26 8.46 8.37 8.81 ± 0.03 9.03 ± 0.11

DTPA

a b c d e f g *

6.60 1.0e 0.1d 1.0e 0.1d 6.60a 1.0e 0.1d 0.1d 6.60a 6.60a

pKa5

Ref. p.w [38,42] [37] [38,42] p.w [39] [37] [38,42] p.w [37] p.w

9.12 ± 0.08 10.33 10.63 10.15 10.58 9.98 ± 0.07 9.97 10.34 10.23 10.25 ± 0.04 10.42 ± 0.02

p.w [38,42] [37] [38,42] [37] p.w [38,42] [37] [37] p.w p.w

NaClO4. NaCl. Et4NI. KNO3. KCl. Me4NCl. NaNO3. Molar (M) scale.

stants of trivalent lanthanides and actinides with these carboxylates. The data points for Eu-Ox, -Cit, -NTA and -EDTA are experimental while those of Eu-IDA and -DTPA are estimated from the plot at I = 6.60 m. 3.1. Thermodynamic data The thermodynamic parameter for the reaction (Hi1 + L = HiL) are listed in Table 3. The thermodynamic 24 DTPA

Expt values Est. values

20

CDTA

log β101

16

EDTA NTA

12 IDA 8

Cit Ox 4 0

5

10

15

20

25

30

ΣpKa P Fig. 1. Correlation between ligand acidity constants, pKa and the stabi3+ lity constant, log b101, for Eu complexes at 25 C and I = 6.60 m (NaClO4).

parameters determined by the temperature coefficient method have larger experimental errors than those obtained by the calorimetric method. Measurements of the dissociation constants over a wide temperature range reduced the uncertainties in the measurements. Table 3 summarizes the thermodynamic parameters for the protonation of these carboxylic acids. Available data from calorimetric studies are included in Table 3. Comparison of the DH and DS values is rather difficult since, except for Ox, previous values refer to I 6 1.0 m. While comparing any two acids, it is not always definite whether DH, DS or both are the cause of differences in acid strength. For instance, the first and second protonation steps of EDTA and CDTA are accompanied by very similar enthalpy value and the differences in pKa1 and pKa2 of these acids are likely due to the different entropic contribution to DG. The DH of protonation of IDA, NTA, EDTA, CDTA and DTPA at I = 6.60 m are, in general, more exothermic than those reported at lower ionic strengths which is consistent with the observed trends of DH reported in the critically selected values [3]. With exception of Ox, the values of DH at I = 1.0 m are ca. 1–4 kJ mol1 more exothermic than the corresponding values in I = 0.1 m. For Ox, the values are nearly the same with less variance for ionic strength. The favorable enthalpy and entropic contributions observed in the protonation of these acids at I = 6.60 m are in line with the corresponding data at lower

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Table 3 Thermodynamics parameters for the protonation of Ox, IDA, NTA, EDTA, CDTA and DTPA at 25 C and in different ionic medium Ligand Ox

I (m) a

6.60 5.0b

0.00 IDA

6.60a 6.60a 1.0*,a 0.5a 0.1c

pKas

DH (kJ mol1)

DS (J K mol1)

method

Ref.

1 2 1 2 1 2

+3.27 ± 1.7 +6.20 ± 1.5 4.0 ± 1.2 +2.4 ± 3.3 +4.26 ± 0.21 +6.27 ± 0.21

13 ± 5 62 ± 8 34 ± 4 63 ± 11 38.46 102.82

T T T T C C

p.w p.w [13] [13] [40] [40]

1 2 2 1 2 1 2

6.01 ± 2.1 31.40 ± 6.2 35.61 ± 3.0 4.9 ± 1.0 38.0 ± 1.6 34.07

33 ± 7 85 ± 9 59 ± 6 32 ± 5 48 ± 6

T T C C C C

p.w p.w [41] [43] [43] [44]

Cit

6.60a 6.60a 6.60a 0.1a 0.1a 0.1a

1 2 3 1 2 3

7.20 ± 1.6 9.61 ± 2.4 7.95 ± 1.9 +1.93 ± 0.12 3.13 ± 0.12 4.52 ± 0.12

30 ± 6 51 ± 7 76 ± 9 116 ± 1 73 ± 1 42 ± 1

T T T C C C

p.w p.w p.w [30] [30] [30]

NTA

6.60a 6.60a 6.60a 0.5*,a 0.1c

1 2 3 3 3

4.33 ± 1.6 5.85 ± 1.5 25.08 ± 1.1 26.2 ± 0.2 19.56 ± 0.91

27 ± 5 33 ± 8 98 ± 6 102 ± 8 121 ± 6

T T T C T

p.w p.w p.w [14] [32]

EDTA

6.60a 6.60a 6.60a 6.60a 0.5*,c

1 2 3 4 3 4 3 4

3.78 ± 1.2 5.42 ± 1.5 25.59 ± 0.9 31.27 ± 1.8 22.7 ± 0.2 29.1 ± 0.2 19.89 ± 2.1 32.85 ± 7.8

31 ± 6 33 ± 7 52 ± 9 73 ± 11 44 ± 6 103 ± 8 51 ± 2 85 ± 6

T T T T C C T T

p.w p.w p.w p.w [14] [14] [37] [37]

1 2 3 4 1 2 3 4

4.16 ± 1.8 3.21 ± 2.1 12.45 ± 1.2 38.10 ± 1.5 1.7 ± 0.7 1.4 ± 0.3 10.7 ± 0.3 38.8 ± 0.3 +2.5 1.2 15.2 43.5 30.72 5.60

45 ± 8 61 ± 6 86 ± 8 68 ± 10 40 ± 4 58 ± 3 89 ± 5 86 ± 6 54 57 64 87 119 ± 7 98 ± 5

T T T T C C C C T T T T T T

p.w p.w p.w p.w [39] [39] [39] [39] [38,42] [38,42] [38,42] [38,42] [37] [37]

1 2 3 4 5 1 2 3 4 5 1 2 3 4

37.52 ± 2.8 22.12 ± 2.0 9.19 ± 1.5 3.77 ± 1.9 +5.45 ± 2.0 29.8 24.0 12.2 2.0 8.7 29.0 ± 0.5 24.9 ± 1.0 8.2 ± 0.3 4.8 ± 1.2

59 ± 13 86 ± 12 53 ± 10 43 ± 8 63 ± 10 93 79 39 54 73

T T T T T T T T

p.w p.w p.w p.w p.w [38,42] [38,42] [38,42] [38,42] [38,42] [41] [41] [41] [41]

0.1c CDTA

6.60a 6.60a 6.60a 6.60a 0.5*,a

1.0d

0.1c DTPA

6.60a 6.60a 6.60a 6.60a 1.0d

0.5*,a

T C C C C

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Table 3 (continued) Ligand

I (m)

pKas

DH (kJ mol1)

DS (J K mol1)

method

Ref.

0.1c

1 2 3

22.74 ± 0 20.31 ± 0 6.23 ± 0

123 ± 6 95 ± 10 61 ± 9

T T T

[34] [34] [34]

C, calorimetry; T, temperature dependence of potentiometric data. a NaClO4. b NaCl. c KNO3. d KCl. * Molar scale.

12

300 DTPA

250

10

CDTA

NaClO4, [p.w] NEt4I, [31]

8

200 150

pKai

ΣΔS

EDTA NTA

IDA

100

6

4

Ac

50

2

0 0

1

2

3

4

5

6

Number of carboxylates P Fig. 2. Correlation of DS of protonation with the number of carboxylate groups of ligands. The value for Ac from Ref. [46].

ionic strength [3].P Fig. 2 shows the relationship between the sum of entropy ( DS) of protonation of aminocarboxylic acids with the number of carboxylates groups. A linear plot indicates that the nitrogen of aminocarboxylates seem to play little or no role in the DS values. The deviation of the value for CDTA is likely due to the rigidity of the ligand structure. 3.2. SIT and Parabolic fit The experimental pKa values were modeled using SIT [18] and Parabolic models [19]. The literature data and those measured in this study were used in the model fitting. The fits of the model calculations to the experimental values of pKa based on the two models are shown in Fig. 3. The SIT model is generally valid to ionic strength 2–3 m; however, it was successfully used to describe the variation of pKa to 6.60 m (NaClO4). In the SIT model, the general equation describing the variation of dissociation constant with ionic strength (in molal units) takes the form [20]: p p pK ai ¼ pK 0ai  DZ 2 A I=ð1 þ aB IÞ þ Dei I ð2Þ where pK 0ai is the thermodynamic dissociation constant at I = 0.00. DZ2 is the difference between the squares of the

0 0

1

2

3

4

5

6

7

I, m Fig. 3. Plots of pKa fits of NTA with SIT model.

changes of the products and reactants multiplied by a stoichiometric coefficient. A is the Debye–Huckel constant (0.5091 at 25 C), and aB is an empirical parameter involving the mean distance of closest approach of ions from the Debye–Huckel limiting law (a value of 1.5 was used, as suggested by Scatchard [18]). Dei is the SIT parameter for species i and accounts for short range non-electrostatic interactions between ionic strength and other species in the system. p p Plotting pKai + 0.5091DZ2 I/(1 + 1.5 I) versus I results in a straight line with a slope of Dei and an intercept of pK 0ai . The results of the SIT calculations of our data and some literature data are presented in Table 4. The low correlation coefficients of pKa2 of IDA and DTPA and pKa1 of Ox, Cit and EDTA reflects the low precision of these dissociation constants rather than limitations of the SIT model as all plots are linear and no obvious curvature of the SIT plot is observed. The pKai values (Table 4) differ significantly in different ionic media. For the background electrolytes, pKai has the order NEt4I > NaClO4 > NaCl, which is consistent with the relative complexing properties of the cations and anions [21]. In contrast, alkali metal cations form weak complexes with carboxylates, resulting in lower apparent dissociation constants. Due to

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Table 4 Average SIT parameters of the ionic strength dependence of dissociation constants of carboxylic acid in different supporting electrolytes Acids

pK 0i

medium

DZ2

R2

Ref.

IDA (1) (2)

2.98 ± 0.02 10.01 ± 0.05

NaClO4 NaClO4

2 4

0.061 ± 0.004 0.142 ± 0.013

0.97 0.94

p.w p.w

Oxalic (1) (2) (2) (2)

1.23 ± 0.02 4.24 ± 0.02 4.34 ± 0.05 4.38 ± 0.03

NaCl NaCl NaClO4 NEt4I*

2 4 4 4

0.076 ± 0.001 0.12 ± 0.01 0.158 ± 0.008 0.69 ± 0.03

0.72 0.97 0.97

[10] [10] [12] [31]

NTA (1) (1) (2) (2) (3) (3)

2.17 ± 0.03 1.95 ± 0.03 3.34 ± 0.02 2.99 ± 0.02 10.33 ± 0.03 10.31 ± 0.04

NaClO4 NEt4I* NaClO4 NEt4I* NaClO4 NEt4I*

2 2 4 4 6 6

0.086 ± 0.009 0.4360 ± 0.057 0.073 ± 0.006 0.509 ± 0.036 0.129 ± 0.009 0.668 ± 0.076

0.95 0.95 0.97 0.98 0.98 0.96

p.w [31] p.w [31] p.w p.w

Citric (1) (1) (1) (2) (2) (2) (3) (3) (3)

3.16 ± 0.04 3.20 ± 0.10 3.10 ± 0.01 4.80 ± 0.02 4.88 ± 0.07 4.79 ± 0.03 6.29 ± 0.04 6.33 ± 0.03 6.44 ± 0.03

NaCl NaClO4 NEt4I* NaCl NaClO4 NEt4I* NaCl NaClO4 NEt4I*

2 2 2 4 4 4 6 6 6

0.06 ± 0.02 0.084 ± 0.007 0.39 ± 0.01 0.116 ± 0.006 0.113 ± 0.005 0.56 ± 0.03 0.10 ± 0.02 0.122 ± 0.002 0.92 ± 0.06

0.85 0.96 0.99 0.98 0.98 0.96 0.99 0.97

[10] [15] [31] [10] [15] [31] [10] [15] [31]

EDTA (1) (2) (3) (3) (4) (4)

2.36 ± 0.01 3.06 ± 0.04 6.88 ± 0.03 6.62 ± 0.03 10.19 ± 0.0 10.95 ± 0.05

NaCl NaCl NaCl NEt4I* NaCl NEt4I*

2 4 6 6 6 8

0.04 ± 0.02 0.10 ± 0.01 0.341 ± 0.004 0.76 ± 0.07 0.16 ± 0.02 0.89 ± 0.10

0.65 0.94 0.99 0.96 0.95 0.95

[10] [10] [10] [31] [10] [31]

DTPA (1) (2) (3) (4) (5)

2.48 ± 0.01 3.45 ± 0.05 5.18 ± 0.05 9.84 ± 0.03 11.36 ± 0.02

NaClO4 NaClO4 NaClO4 NaClO4 NaClO4

2 4 6 8 10

0.061 ± 0.004 0.095 ± 0.011 0.142 ± 0.013 0.153 ± 0.009 0.206 ± 0.006

0.98 0.93 0.96 0.98 0.99

p.w p.w p.w p.w p.w

De

* 37 C, SIT parameters have been adjusted to A = 0.523 according to Ref. [31].

significantly higher values of the specific ion interaction parameter, De, the SIT fits for Et4NI deviate from the NaClO4 curves in the Debye–Huckel limiting law region (Fig. 3). Due to the absence of density data, the values in NEt4I medium are those for molarity. Since the constants in Et4NI were measured at 37 C, the accuracy of SIT model with aB = 1.5 may be decreased and require adjustment to obtain better correlation with the experimental data, as has been done for the Debye–Huckel parameters (A = 0.523 at 37 C is used for constants measured in Et4NI medium) [21]. The pKa data at different ionic strengths were fitted to the Parabolic model, an extension of the SIT model, to cover higher ionic strengths, I > 2–3 m. The Parabolic model has the form: p p pK ai ¼ pK 0ai  DZ 2 A I=ð1 þ aB IÞ þ Dei I þ Ddi I 2 ð3Þ

It has been shown that the Parabolic model with two coefficients is satisfactory for ionic strengths to I = 14 m [19]. Although the Pitzer model [20] is more successful in calculating the interaction parameters, it requires a large number of parameters even in calculation of simpler systems, However, when the parameters are mutually compensating (one fitted curve gives more than one set of parameters with different selection of values of known parameters), the curve fitting is based on a polynomial form of the Pitzer formalism, which is comparable to the Parabolic model. The advantage of the Parabolic model is that it uses fewer unknown parameters than the theoretically based Pitzer model, and the fit can be obtained with less experimental data. Table 5 lists the pK 0ai values calculated by SIT, Parabolic and Pitzer model of the present and the literature data and Fig. 3 shows the fitting of pKai data of NTA with the SIT and Parabolic models.

P. Thakur et al. / Inorganica Chimica Acta 360 (2007) 3671–3680 Table 5 Regression results of pKai values by SIT, Parabolic and Pitzer models Acids

I* (m)

IDA (1) (2)

6.60a 6.60a

SIT

Parabolic

2.98 ± 0.09 10.01 ± 0.08

2.95 ± 0.02 9.89 ± 0.05

Pitzer

Ref. p.w p.w

Ox (1) (2) (1) (2)

14.1a 14.1a 5.0b 5.0b

1.63 ± 0.10 4.34 ± 0.05 1.23 ± 0.02 4.24 ± 0.02

1.69 ± 0.09 4.30 ± 0.04 1.39 ± 0.04 4.26 ± 0.03

1.42 4.28 1.38 4.25

[12] [12] [10] [10]

Cit (1) (2) (3)

14.1a 14.1a 14.1a

3.20 ± 0.10 4.88 ± 0.07 6.33 ± 0.10

3.15 ± 0.05 4.84 ± 0.03 6.32 ± 0.10

3.23 4.85 6.38

[45] [45] [45]

NTA (1) (2) (3)

6.60a 6.60a 6.60a

2.17 ± 0.03 3.34 ± 0.02 10.33 ± 0.03

2.10 ± 0.01 3.32 ± 0.01 10.33 ± 0.01

EDTA (1) (2) (3) (4)

5.0b 5.0b 5.0b 5.0b

2.36 ± 0.1 3.06 ± 0.04 6.88 ± 0.03 10.19 ± 0.09

2.50 ± 0.07 3.09 ± 0.07 6.82 ± 0.03 10.38 ± 0.03

DTPA (1) (2) (3) (4) (5)

6.60a 6.60a 6.60a 6.60a 6.60a

2.48 ± 0.01 3.45 ± 0.05 5.18 ± 0.05 9.84 ± 0.03 11.36 ± 0.02

2.46 ± 0.02 3.42 ± 0.06 5.10 ± 0.03 9.80 ± 0.04 11.34 ± 0.03

p.w p.w p.w 2.56 3.08 6.89 10.36

[10] [10] [10] [10] p.w p.w p.w p.w p.w

a

NaClO4. NaCl. * Ionic strength to which Parabolic model fits. b

4. Conclusion The pKa values of the carboxylic acids initially decrease to a minimum between I 6 1.0 and 2.0 m, followed by an increase to I = 6.60 m. The values, except for pKa1 of Ox, show a linear relationship with temperature. The enthalpies of protonation are more exothermic at high ionic strength. The SIT model for IDA, NTA and DTPA is satisfactory up to I = 6.60 m and may be useful in describing literature data on carboxylic acid dissociation in different ionic media. The Parabolic model with two coefficients correlate the variations in pKa with ionic strength better than the SIT models. The variation of pKa1 for Ox is more accurately described by the Pitzer than by the SIT and Parabolic model. Since the interactions of lanthanide and actinide cations with carboxylic acid are primarily ionic, the values of stability constants of these P cations with carboxylic acid can be estimated from the pKa. The reported acid constants are necessary in calculations of stability constants of metal ions. Acknowledgement This research was supported by a grant from the USDOE Environmental Management Science Program.

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