On-line Supplementary Material for Journal of Solution Chemistry
Studies of Size-Based Selectivity in Aqueous Ternary Complexes of Americium(III) or Lanthanide(III) Cations
Christina J. Leggett· Mark P. Jensen
C.J. Leggett· M.P. Jensen ()
Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, IL, USA
e-mail:
C.J. Leggett
Department of Nuclear Engineering, University of California, Berkeley, CA, USA
S1 Analysis of Tb SpectrofluorimetricData
Two approaches were used to analyze the spectrofluorimetric titrations of Tb(CDTA)– with Ox2–. In the first method, the change in the luminescence lifetime of the Tb species in solution was used. The average number of inner sphere water molecules of a Eu3+ or Tb3+ complex, , is related to the luminescence decay constants by
whereand are the luminescence decay constants of the complexes in H2O and D2O, respectively, in ms–1 and is an empirically determined constant. The values of (0.30) and ATb (4.2) have been previously reported by Horrocks and Sudnick, who also report the absolute uncertainty in determined by this method to be 0.5 water molecules[1]. Consequently, we used the number of inner sphere water molecules bound to Tb(CDTA)– and Tb(CDTA)(Ox)3–as a function of added oxalate concentration to calculate the equilibrium constant.
When Tb(CDTA)– and Tb(CDTA)(Ox)3– are the only significant Tb(III) containing species in solution, the average number of water molecules can be calculated using the equation
whereNTb(CDTA) and NTb(CDTA)(Ox) are the numbers of waters coordinated to Tb(CDTA)– and Tb(CDTA)(Ox)3–, respectively, and is the total concentration of terbium in a given solution. Using equation S1 and the measured, 0.79 ms–1, the number of residual water molecules bound to the binary Tb(CDTA)– complex, NTb(CDTA), was readily determined to be 2.07, as expected for octacoordinate terbium complexed by hexadentate CDTA. Introducing the equilibrium constant expression for K111 (Eq. 1) and realizing that [Tb(CDTA)–] + [Tb(CDTA)(Ox)3–] = , NTbCDTAOx and K111can be obtained from Eq. S2. The solver function in Excel was used to minimize the sum of the squared residuals between the observed and calculated number of water molecules by varyingNTbCDTAOx and K111.For each titration, eighteen datapoints corresponding to successive additions of 0.075 mol·L–1 oxalate were collected and used for fitting, giving NTbCDTAOx = 0.51 0.01 and log10K111 = 2.78 0.02.
In the second method, the intensity of emitted fluorescence at 544 nm was used to calculate the equilibrium constant according to the equation
where is the measured fluorescence intensity and the constants 1 and 2 are the operational molar fluorescence intensities of Tb(CDTA)– and Tb(CDTA)(Ox)3–, which are valid for a particular instrumental configuration. The value of 1, (2.48 0.03) × 103L·mol–1·cm–1, was determined from intensity measurements of known concentrations of Tb(CDTA)–. The terms 2 and K111 were then obtained by fitting to the experimental titration data in a manner similar to the luminescence lifetime measurements described above, giving values of2 = (4.24 0.08)× 103L·mol–1·cm–1and log10K111 = 2.75 0.02.
The uncertainties in the fitted parameters for both methods were estimated using the jackknife error method.[2]
S2 Determination of the Enthalpies of Protonation of CDTA
The enthalpies corresponding to the first three protonations of the CDTA4– ligand were measured at 1 mol·L–1 ionic strength using isothermal titration calorimetry. In a typical experiment, 0.9 mL of 0.001 mol·L–1 CDTA/1 mol·L–1 NaNO3 at pcH= 9.9 was titrated with 0.1 mL of 0.031 mol·L–1 HNO3/1 mol·L–1NaNO3 in 2 μL increments. Using the known pKa values[3], the pcH and changes in the amountsof H(CDTA)3–, H2(CDTA)2–, and H3(CDTA)– were readily calculated for each addition of acid. The total heat evolved from the beginning of the titration was calculated using the equation
whereΔHi is the enthalpy of protonation for HiCDTA(i–4) in kJ·mol–1, Δni is the change in the number of moles of HiCDTA(i–4)from the beginning of the titration, and Qcalc is the cumulative heat after each addition, after correction for the heat of dilution and the heat of water formation by the reaction H+ + OH–H2O. The Solver application in the program Excel was used to minimize the sum of the squared residuals between the calculated and measured cumulative heats by varying ΔHi. Four replicate titrations were used to determine the enthalpies. Figure S1 compares the calculated and measured heats from a representative titration.
Table S1 Thermodynamic data for protonation reactions of ligands used in this work
Ligand / Protonation reaction(s) / log10Ka / H(prot), kJ·mol–1bH5DTPA / H+ + DTPA5– HDTPA4–
H+ + HDTPA4– H2DTPA3–
H+ + H2DTPA3– H3DTPA2–
H+ + H3DTPA2– H4DTPA–
H+ + H4DTPA– H5DTPA / 9.98 0.08
8.29 0.04
4.15 0.03
2.6 0.1
2.1 0.2 / –33 0.4c
–18 0.4c
–6.3 0.4c
–1.3 0.8c
+2.1 0.8c
H2Ox / H+ + Ox2–HOx–
H+ + HOx– H2Ox / 3.57 0.04
1.07 0.07 / +3.2 0.3
+1.3
H2Mal / H+ + Mal2–HMal–
H+ + HMal– H2Mal / 5.08 0.06
2.58 0.02 / +2.0 0.04
–1.5 0.04
H2IDA / H+ + IDA2– HIDA–
H+ + HIDA– H2IDA
H+ + H2IDA H3IDA+ / 9.26 0.06
2.60 0.03
1.85 0.06 / –35.6 0.0
–4.2 0.8
–4.2 0.0
H4CDTA / H+ + CDTA4– HCDTA3–
H+ + HCDTA3– H2CDTA2–
H+ + H2CDTA2– H3CDTA–
H+ + H3CDTA–H4CDTA
H+ + H4CDTA H5CDTA+ / 9.22
5.84
3.21 0.04
2.42 0.01
1.6 0.1 / –25.6 0.3d
–12.4 0.4d
–8.6 2.4d
n/a
n/a
HMES / H+ + MES HMES / 6.194 0.008e / –4.35 0.07e
OH– / H+ + OH– H2O / 13.78 / –56.94
aAll stability constants are valid for 1 mol·L–1 ionic strength at 25 °C. Unless otherwise noted, data are taken from [3]
bUnless otherwise noted, all enthalpy values are valid for 1 mol·L–1 ionic strength at 25 °C and were obtained from [3]
cEnthalpy values valid for ionic strength = 0.1 mol·L–1 at 25 °C
dEnthalpy values measured in present work.
eValues taken from [4]
Table S2 Tabulation of calorimetric titration data for titration of Ln(CDTA)– with Ox2–
Ln(CDTA)– / Runsa / [Ln(CDTA)–]/mol·L–1 b / [Ox]/mol·L–1b / pcHfinal / Qmeas / cal / Qdil / cal / Qprot / cal / Qcorr / calNd(CDTA)– / 4 / 0.0100 / 0.0733 / 6.003 / 0.188 ± 0.004 / –0.017 ± 0.018 / 0.003 ± 0.001 / 0.202 ± 0.018
Sm(CDTA)– / 3 / 0.0100 / 0.0733 / 6.034 / 0.178 ± 0.001 / –0.017 ± 0.018 / 0.001 ± 0.001 / 0.194 ± 0.018
Tb(CDTA)– / 4 / 0.0100 / 0.0753 / 6.003 / 0.294 ± 0.008 / –0.017 ± 0.018 / 0.002± 0.002 / 0.312 ± 0.020
Ho(CDTA)– / 4 / 0.0101 / 0.0733 / 5.991 / 0.262 ± 0.008 / –0.017 ± 0.018 / 0.001 ± 0.001 / 0.278 ± 0.020
Er(CDTA)– / 4 / 0.0100 / 0.0733 / 5.991 / 0.312 ± 0.008 / –0.017 ± 0.018 / 0.001 ± 0.001 / 0.328 ± 0.020
aNumber of replicate titrations
bInitial analytical concentrations of titrant and titrand solutions used in titrations
Table S3 Tabulation of calorimetric titration data for titration of Ln(CDTA)– with Mal2–
Ln(CDTA)– / Runsa / [Ln(CDTA)–] / mol·L–1b / [Mal] / mol·L–1b / pcHfinal / Qmeas / cal / Qdil / cal / Qprot / cal / Qcorr / calNd(CDTA)– / 5 / 0.0402 / 0.502 / 5.965 / 0.035± 0.004 / –0.107± 0.008 / 0.062± 0.001 / 0.080± 0.009
Sm(CDTA)– / 3 / 0.0401 / 0.502 / 5.958 / –0.125± 0.016 / –0.107± 0.008 / 0.062± 0.001 / –0.080 ±0.018
Ho(CDTA)– / 3 / 0.00395 / 1.022 / 5.995 / –0.569 ± 0.006 / –0.472± 0.018 / 0.029± 0.001 / –0.126 ± 0.019
Er(CDTA)– / 4 / 0.0394 / 1.022 / 5.990 / –0.475 ± 0.009 / –0.472± 0.018 / 0.029± 0.001 / –0.032 ± 0.020
aNumber of replicate titrations
bInitial analytical concentrations of titrant and titrand solutions used in titrations
Table S4Tabulation of calorimetric titration data for titration of Ln(CDTA)– with IDA2–
Ln(CDTA)– / Runsa / [Ln(CDTA)–] / mol·L–1b / [IDA] / mol·L–1b / pcHfinal / Qmeas / cal / Qdil / cal / Qprot / cal / Qcorr / calNd(CDTA)– / 3 / 0.0103 / 1.499 / 6.716 / –1.137± 0.020 / –0.949± 0.010 / –0.464± 0.002 / 0.276± 0.022
Sm(CDTA)– / 4 / 0.0216 / 1.499 / 6.392 / –0.886± 0.012 / –0.949± 0.010 / –1.010± 0.010 / 1.073± 0.016
Ho(CDTA)– / 3 / 0.0101 / 1.499 / 6.742 / –0.794 ± 0.003 / –0.949± 0.010 / –0.391± 0.002 / 0.546 ± 0.011
Er(CDTA)– / 3 / 0.00999 / 1.499 / 6.802 / –0.756 ± 0.003 / –0.949± 0.010 / –0.300± 0.002 / 0.493 ± 0.011
aNumber of replicate titrations
bInitial analytical concentrations of titrant and titrand solutions used in titrations
Figure S1 Representative titration of 0.9 mL of 0.001 mol·L–1 CDTA/1 mol·L–1 NaNO3(initial pcH = 9.9) with 0.1 mL of 0.031 mol·L–1 HNO3/1 mol·L–1 NaNO3.The blue diamonds represent the cumulative heat after each 0.002 mL addition of titrant. The solid line shows the fit of the calculated heats obtained by varying ΔHito minimize the sum of the squared residuals
FigureS2 Normalized Sm(CDTA)– + Ox2– spectra. Left plot,titration of 10 mL of 0.01 mol·L–1Sm(CDTA)– with 0.075 mol·L–1 oxalate; right plot,molar absorptivities at selected wavelengths as a function of the total oxalate concentration.Wavelengths shown are indicated as follows: , 403.75 nm;, 404.1 nm;, 404.45 nm
FigureS3 Normalized Sm(CDTA)– +Mal2– spectra. Left plot,titration of 10 mL of 0.01 mol·L–1Sm(CDTA)– with 0.50 mol·L–1malonate; right plot,molar absorptivities at selected wavelengths as a function of the total malonate concentration. Spectra are not corrected for absorption of the free Mal2– ligand. Wavelengths shown are indicated as follows: ,403.75 nm;,404.25 nm;, 405 nm
FigureS4 Normalized Sm(CDTA)– + IDA2– spectra. Left plot,titration of 10 mL of 0.022 mol·L–1Sm(CDTA)– with 1.50 mol·L–1 IDA;right plot,molar absorptivities at selected wavelengths as a function of the total IDA concentration.Wavelengths shown are indicated as follows:, 404.9 nm;, 405.2 nm; ,405.5 nm
FigureS5 Normalized Ho(CDTA)– + Ox2– spectra. Left plot,titration of 10 mL of 0.01 mol·L–1Ho(CDTA)– with 0.073 mol·L–1 oxalate; right plot, molar absorptivities at selected wavelengths as a function of the total oxalate concentration. Wavelengths shown are indicated as follows: , 451.5 nm;, 453.5 nm;, 454.5 nm;*, 538 nm
FigureS6 Normalized Ho(CDTA)– +Mal2– spectra. Left plot,titration of 10 mL of 0.01 mol·L–1Ho(CDTA)– with 1.02 mol·L–1malonate; right plot,molar absorptivities at selected wavelengths as a function of the total malonate concentration. Wavelengths shown are indicated as follows: , 451.5 nm;, 453.5 nm;, 454.5 nm
FigureS7 Normalized Ho(CDTA)– + IDA2– spectra. Left plot,titration of 25 mL of 0.01 mol·L–1Ho(CDTA)– with 1.50 mol·L–1IDA;right plot,molar absorptivities at selected wavelengths as a function of the total IDA concentration. Wavelengths shown are indicated as follows: , 453.5 nm;,454.5 nm;*,539.75 nm
FigureS8 Normalized Er(CDTA)– + Ox2– spectra.Left plot,titration of 10 mL of 0.01 mol·L–1Er(CDTA)– with 0.073 mol·L–1 oxalate; right plot, molar absorptivities at selected wavelengths as a function of the total oxalate concentration. Wavelengths shown are indicated as follows: , 379.25 nm;, 518.75 nm;, 521 nm;, 525.25 nm
FigureS9 Normalized Er(CDTA)– +Mal2– spectra. Left plot,titration of 10 mL of 0.01 mol·L–1Er(CDTA)– with 0.50 mol·L–1malonate; right plot, molar absorptivities at selected wavelengths as a function of the total malonate concentration.Wavelengths shown are indicated as follows:*, 487 nm;, 518 nm;, 520.75 nm;, 525 nm
FigureS10 Normalized Er(CDTA)– + IDA2– spectra. Left plot, Titration of 10 mL of 0.01 mol·L–1Er(CDTA)– with 1.50 mol·L–1 IDA; right plot, molar absorptivities at selected wavelengths as a function of the total IDA concentration.Wavelengths shown are indicated as follows: , 379.2 nm;, 520 nm;, 522.4 nm;, 525.6 nm
Figure S11 Spectra of M(DTPA) and M(DTPA) + L2 solutions.Top plot, Nd(III) complexes;bottom plot, Er(III) complexes
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