Fabian
Böhm
a,
Vinay
Sharma
b,
Gerhard
Schwaab
*a and
Martina
Havenith
a
aDepartment of Physical Chemistry II, Ruhr-Universität Bochum, Germany. E-mail: gerhard.schwaab@rub.de; Fax: +49 234 321 4183; Tel: +49 234 322 4256
bInstitute of Chemistry, The Hebrew University, Jerusalem, Israel
First published on 1st July 2015
We have investigated the hydration dynamics of solvated iron(II) and iron(III) chloride. For this, THz/FIR absorption spectra of acidified aqueous FeCl2 and FeCl3 solutions have been measured in a frequency range of 30–350 cm−1 (≈1–10 THz). We observe a nonlinear concentration dependence of the absorption, which is attributed to the progressive formation of chloro-complexes of Fe(II) and Fe(III), respectively. By principal component analysis of the concentration dependent absorption spectra, we deduced the molar extinction spectra of the solvated species Fe2+ + 2Cl− and FeCl+ + Cl−, as well as FeCl2+ + 2Cl− and FeCl2+ + Cl−. In addition, we obtain ion association constants logKFeCl2 = −0.88(5) and log
KFeCl3 = −0.32(16) for the association of Fe2+ and Cl− to FeCl+ and the association of FeCl2+ and Cl− to FeCl2+, respectively. We performed a simultaneous fit of all the effective extinction spectra and their differences, including our previous results of solvated manganese(II) and nickel(II) chlorides and bromides. Thereby we were able to assign absorption peaks to vibrational modes of ion–water complexes. Furthermore, we were able to estimate a minimum number of affected water molecules, ranging from ca. 7 in the case of FeCl+ + Cl− to ca. 21 in the case of FeCl2+ + Cl−.
The hydration properties of transition metal ions have only recently been studied.11–13 The behaviour of ferrous (Fe2+) and ferric (Fe3+) iron in aqueous solution with respect to their tendency towards formation of distinct chloro-complexes are of special interest to the fields of iron metabolism and biological function,14,15 geochemical and hydrothermal studies,16,17 isotopic fractionation18 and chemistry of natural waters.19 In spite of a broad range of technical applications, simultaneous quantitative analysis of aqueous iron(II) and iron(III) at high concentrations still remains a challenge. Calorimetry,20 isotachophoresis,21 ion chromatography19,22 and spectrophotometry17,23–27 are restricted to the millimolar concentration range, since the formation of ion associates complicates data evaluation at higher concentrations.
While the masses of Fe2+ and Fe3+ are practically the same, the ionic radii of the ions differ considerably (0.92 Å for Fe2+ and 0.79 Å for Fe3+) due to the different charge states. Fe3+ has a much higher charge density, which causes substantially different hydration behavior compared to Fe2+. Besides the octahedral hexaaqua complex [Fe(H2O)6]2+, several chloro-complex species have been identified in acidic solutions of ferrous chloride, which are: octahedral monochloro-complex [Fe(H2O)5Cl]+, dichloro-complex [Fe(H2O)4Cl2], and tetrahedral tetrachloro-complex [FeCl4]2−.28 The latter species, however, is formed exclusively at very high chloride excess29 and/or high temperatures.28,30 Similarly, the complexes formed by ferric chloride are: octahedral hexaaqua complex [Fe(H2O)6]3+, monochloro-complex [Fe(H2O)5Cl]2+, dichloro-complex trans-[Fe(H2O)4Cl2]+, trichloro-complex [Fe(H2O)3Cl3] and tetrahedral tetrachloro-complex [FeCl4]−.17,31–41 Similarly to the ferrous salt, the highest order chloro-species is only found at high chloride excess and/or high temperatures.
So far, the equilibrium formation constant of the ferrous monochloro-complex at room temperature has been determined by spectrophotometry28,42 and potentiometry43 to be 0.69 kg mol−1, 0.43 kg mol−1 and 0.75 kg mol−1, respectively. The formation constant of the dichloro-complex has been determined spectrophotometrically to be 0.018 kg2 mol−2.28
In contrast to ferrous chloride, there have been many attempts to determine equilibrium constants for the formation of ferric chloro-complexes in aqueous phase using spectrophotometry17,26,32,33,44–49 and potentiometry.50,51 Most of them, however, did not include the concept of ion activity, and thus there is a clear divergence in the values of formation constants for solutions of different ionic strength. Only a handful of publications present an estimate of equilibrium constants at zero ionic strength, either by extrapolation32,33,44,51 or by introducing activity coefficients for the ions.17,26,49 While the values for the formation constant of the monochloro-complex at room temperature are in good agreement, ranging from 19.1 to 33.1 kg mol−1,17,44,49,51 there are large inconsistencies present for the formation constant of the dichloro-complexes ranging from 2 to 14 kg mol−1.17,26,33,44,49,51 The trichloro-complex formation constant is considerably smaller, ranging from 0.04 to 0.08 kg mol−1.17,26,33,44 Note that cumulative formation constants have been converted to stepwise formation constants.
Despite these previous efforts, several questions remain unresolved. For instance, are the aforementioned methods sensitive only to the formation of first shell complexes, or could other associates also play a role? Do the water molecules incorporated in ferrous and ferric complexes exhibit a different dynamic behaviour compared to bulk water molecules? Is water beyond the first hydration shell affected by the ions and ion associates as well?
In the present study, we investigate the hydration behavior of iron(II) and iron(III) chloride salts in aqueous phase, using THz/FIR Fourier transform spectroscopy. THz/FIR absorption spectroscopy has proven to be a powerful tool to analyse electrolyte solutions at high concentrations. Using this technique, we have determined the low frequency absorption characteristics of several alkaline,7 alkaline earth,8 transition metal52 and lanthanum halides53 as well as hydrochloric and hydrobromic acid.54 The obtained frequency dependent absorption spectra exhibit distinguished ion specific bands, which are not present in the spectrum of bulk water. The spectra of these solutions can be well described by a linear superposition of (a) the absorption of bulk water and (b) the absorption of hydrated anions and cations. In case of manganese(II), nickel(II) and lanthanum(III) chloride and bromide, as well as hydrochloric and hydrobromic acid, we have shown that the nonlinear concentration dependence of absorption can be attributed to the formation of ion pairs.52–54 Thorough analysis of the experimental data allowed us to extract the single ionic features as well as the ion pair absorption spectra.
Here we investigate the concentration dependent THz/FIR absorption of iron(II) and iron(III) chloride in water with respect to the formation of ion associates. Using principal component analysis (PCA) as an unbiased mathematical procedure in conjunction with a chemical equilibrium model, we are able to dissect the experimental spectra into the absorption features of the various ions and complex species. This enables us to extract information about the vibrational properties of the solvated ions and ion associates, as well as their dynamical hydration shells. This study provides a proof of principle for the applicability of THz/FIR spectroscopy as an analytical tool for the simultaneous determination of Fe(II) and Fe(III) chloride at concentrations up to the solubility limit.
Using Lambert–Beer's law, the frequency dependent absorption coefficient α() of an aqueous solution is expressed as
![]() | (1) |
The contribution of HCl to the absorption was determined in an independent measurement and subtracted from all subsequent measurements, assuming a weak interaction with the coexisting ions.
For further data evaluation, we subtract the expected absorption of water in the sample to get the effective ionic absorption αeffion:
![]() | (2) |
![]() | (3) |
It is important to mention here that any changes in solvation water absorption induced by the ions are inherent in the effective ionic extinction εeffion. We assume that the interaction between each ion and surrounding water molecules can be understood by taking into account two contributions.7 Since the absorption properties of water are modified in the vicinity of ions, subtraction of the bulk water absorption from the sample absorption results in a negative contribution with the line shape of the water spectrum. The hydrated ion, however, has additional low frequency modes which can be described in terms of rattling modes and/or vibrational modes of the ion–water complexes.7,8
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Fig. 1 THz/FIR absorption (A) and effective molar extinction spectra (B) of aqueous FeCl2 solutions at 20 °C, as obtained from FTIR absorption measurements. |
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Fig. 2 THz/FIR absorption (A) and effective molar extinction spectra (B) of aqueous FeCl3 solutions at 20 °C, as obtained from FTIR absorption measurements. |
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Fig. 3 First two principal components of FeCl2 (left) and FeCl3 (right). The insets show the associated scores as obtained from PCA. |
Although for both salts the results of the PCA are rather similar, the underlying mechanism seems to be different. Comparing different sets of association constants from literature (cf. Section 2) it becomes evident that in the case of FeCl2, the solvated ions and the first ion associate FeCl+ dominate over the whole concentration range, while in the case of FeCl3 the first and second associates, FeCl2+ and FeCl2+, dominate the solution's composition.
For the further evaluation of our data we make the assumption that next to Fe2+, FeCl+, FeCl2+, FeCl2+ and Cl− the contribution of other species to the observed absorption is negligible. Any changes in the concentration dependent absorption spectrum are attributed to a shift in the equilibrium:
![]() | (4) |
![]() | (5) |
![]() | (6) |
![]() | (7) |
Compound | β (0) | β (1) | C ϕ |
---|---|---|---|
FeCl2 | 0.339 ± 0.005 | 1.48 ± 0.06 | −0.019 ± 0.001 |
FeCl3 | 0.42 ± 0.01 | −0.028 ± 0.002 | 7.0 ± 0.4 |
The respective underlying models for the effective ionic absorption are the following:
![]() | (8) |
![]() | (9) |
We performed a fit of the scores of the first two principal components with KFeCl2 and KFeCl3, respectively, as parameters, as has been described before.52 Clearly the fitted lines match the scores quite well (see insets in Fig. 3, solid lines). The resulting values for the equilibrium constants are presented in Table 2.
In addition to the equilibrium constants, we were also able to deduce the molar extinction spectra of the different solvated species. The result is displayed in Fig. 4. Note that each of these spectra contains the anion contribution corresponding to the stoichiometry of the salt .
K (M−1) | log![]() |
|
---|---|---|
FeCl2 | 0.13(1) | −0.89(4) |
FeCl3 | 0.49(8) | −0.32(8) |
The extinction spectrum of Fe2+ + 2Cl− in Fig. 4A is dominated by one broad band at 150 cm−1 and the tail of a feature that peaks at >350 cm−1. The spectrum of FeCl+ + Cl− shows two resonances centered at 145 cm−1 and 230 cm−1, as well as a high frequency wing.
The extinction spectrum of FeCl2+ + 2Cl− in Fig. 4B displays two strong peaks at 190 cm−1 and 315 cm−1. The spectrum of FeCl2+ + Cl−, however, shows a clear resonance around 170 cm−1 and at least two overlapping spectral features between 250 cm−1 and 350 cm−1.
In the global fit, the anion and cation bands are modeled by a modified damped harmonic oscillator function:
![]() | (10) |
Here we extend the model to include the four spectra of FeCl2 and FeCl3. The inclusion of these in the global fit does not affect the previously determined parameters for the manganese and nickel bromide spectra significantly. Therefore the results of the bromide spectra are omitted here, and only the results for MnCl2 and NiCl2 are reported for comparison. The determined fit parameters are listed in Table 3.
We observe that several species have identical parameters, e.g. the linewidth of ionic bands, reducing the complexity of the fit. As an example for the various contributions to a fitting curve of one experimental spectrum, the spectrum of Fe2+ + 2Cl− is displayed in Fig. 5.
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Fig. 5 Top: Shown are the distinct contributions to the fit of the spectrum of Fe2+ + 2Cl−. Bottom: Hydration water spectrum (offset vertically for better display) and cation bands. nLF, nHF, WM, CM 1 and CM 2 are defined in the caption of Table 3. |
While trying to fit the spectra of the ion associates, it is possible that overlapping bands of anionic and cationic species cause an ambiguity in the assignment. Sharma et al. previously have overcome this challenge by including the difference spectra of each metal chloride and bromide into the fit, thereby uncoupling the anion from cation contributions.52 Since in the present work we lack the spectra of ferrous and ferric bromides for a direct comparison, we proceeded in an iterative approach: As a first step, we included only the spectrum of Fe2+ + 2Cl− into the fit of the manganese(II) and nickel(II) chloride and bromide spectra, thereby determining the Cl− mode. In a second step, this mode was then fixed in the spectra of FeCl+ + Cl−, FeCl2+ + 2Cl− and FeCl2+ + Cl− prior to inclusion of these spectra into the fit. After the global fit, the parameters of the chloride mode were fixed to the slightly changed new values. This was repeated iteratively until the change in the chloride fit parameters was smaller than the uncertainty. In Table 3, the fixed parameters are marked with an asterisk (*).
Here we performed a principal component analysis of our concentration dependent THz/FIR absorption spectra of FeCl2 and FeCl3 solutions, and fitted the scores with association constants KFeCl2 and KFeCl3, respectively, as fitting parameters. The logarithm of the determined parameters KFeCl2 and KFeCl3 is −0.89(4) and −0.32(8), respectively. These numbers are well below the values determined by other methods ranging from −0.37 to −0.12 in the case of FeCl228,42,43 and 0.32 to 1.16 in the case of FeCl3.17,26,33,44,49,51 This indicates that the THz/FIR absorption is especially sensitive to the formation of contact ion pairs, while the other methods might be more susceptible to solvent shared and solvent separated ion pairs.
By exchanging a water ligand by chloride, the reduced mass for the Θ vibration of the octahedral Fe2+ complex is increased to 43.27 g mol−1 (Cl− axial) or to 45.08 g mol−1 (Cl− equatorial). In absence of other effects, this increase would cause a red-shift of the Θ mode by ca. 4–6% or 6–9 cm−1. In good agreement with this, we observe a red-shift of 6 cm−1 to 142 cm−1.
Moving from Fe2+ to Fe3+, the reduced mass of the monochloro complex remains the same, while the bond strength increases due to the higher charge of the metal center. Accordingly, the Θ mode is blue-shifted by 12 cm−1 to 154 cm−1. Exchanging another water molecule (in trans-position) by Cl−, the reduced mass for the Θ vibration is increased to 45.68 g mol−1 (Cl− axial) or to 48.98 g mol−1 (Cl− equatorial). In absence of any other effect, this increase is expected to lead to a red-shift of 3–4% or 5–6 cm−1. In fact, we observe a much larger red-shift of 12 cm−1. We attribute this to a weakening of the bond strength by the partial charge compensation of the metal center by the negatively charged ligands.
For Fe2+ we fitted a small amplitude mode at fixed center frequency of 0 cm−1, which we attribute to a relaxational process.
We observe only one band which can be attributed to the chloride anion in the spectra of Mn2+ + 2Cl−, Fe2+ + 2Cl− and Ni2+ + 2Cl− at 184 cm−1, which is close to the chloride band around 190 cm−1 found for other salts.7,8 Due to the increased complexity of the spectra of FeCl+ + Cl−, FeCl2+ + 2Cl− and FeCl2+ + Cl−, we decided to fix the values of the anion band to the values deduced for Fe2+ + 2Cl− prior to the fit.
The linewidth of the modes attributed to the chloro-complexes of Fe2+ and Fe3+ varies. The first and third band of FeCl2+ have the same width as the free ion bands (231 cm−1), while the width of the second band of FeCl+ is slightly larger (248 cm−1). For all the other bands we observe a smaller width, ranging from 98 cm−1 to 205 cm−1. Distinct linewidths indicate that these modes are either connected to a different set of thermal bath states, or connected to the same bath, but with a different coupling parameter.
At this point, we can only speculate about the underlying molecular mechanism. We propose that the width of modes of solvated ions depends on the librational motions of the surrounding water molecules. These librations act as a random force causing line broadening. According to calculations by Vila Verde et al., water molecules between two ions (in case of a solvent-shared ion pair) or close to their point of contact (in case of a contact ion pair), are slowed down cooperatively.61 We therefore interpret the reduced linewidth as a consequence of inhibited librational motion of water close to the ion associates.
For the extinction spectra of Mn2+, Fe2+ and Ni2+ we can use the same fitting parameters for nhydration and nLF, while the effect on the librational mode of water (nHF) is slightly higher for Fe2+ compared to Mn2+ and Ni2+. nhydration is in the range of 14–15. In a previous study we found that HCl affects ca. 5 water molecules and attributed this effect mainly to the anion.54 If we transfer this result to the present study, a minimum number of 4–5 water molecules are affected by the metal ions Mn2+, Fe2+ and Ni2+, which is in good agreement with a value of six water molecules of an octahedral geometry.62
For the ion-associate FeCl+ + Cl−, the value obtained for the minimum number of affected water molecules is nhydration = 7.3, which is distinctly lower than for all other species. Assuming again a number of 5 water molecules affected by Cl−, the chloro-complex affects only a minimum number of 2–3 water molecules. This can only be explained if both the ferrous and chloride ions lose part of their influence on hydration water upon ion pairing.
For FeCl2+ + 2Cl− we obtain a lower limit of nhydration = 21.4 affected water molecules, with similar values for the high and low frequency components (nLF = 23.2 and nHF = 25.0). Subtracting the proposed effect of the anions, we deduce that 11–12 water molecules are affected by FeCl2+. This is surprisingly large, especially in comparison to FeCl+, in which the Cl− ligand loses most of its effect on water upon ion pairing. We speculate that this indicates an effect beyond the first hydration shell of Fe3+.
The minimum number of affected water molecules (nhydration = 16.9) as well as the low and high frequency components (nLF = 20.3 and nHF = 18.7) are smaller in the case of FeCl2+ + Cl− compared to FeCl2+ + 2Cl−. This can be explained by a compensation, or an effective shielding, of the positive charge of the central metal ion by the two axial chloride ligands.
Using Pitzer's equations58 and the complex formation constants KFeCl2 and KFeCl3, the distribution of different ions and ion complex species can be predicted for FeCl2 and FeCl3 solutions of any concentration and even for any mixture of both salts (cf. Section 5). For a given water concentration, the extinction spectrum of water and the extinction spectra of the different complex species displayed in Fig. 4 can be used to predict the total absorption spectrum of any solution of FeCl2 and/or FeCl3 according to the following equation:
αtot = cwaterεwater + cFe2+(εFe2+ + 2εCl−) + cFeCl+(εFeCl+ + εCl−) + cFeCl2+ (εFeCl2+ + 2εCl−) + cFeCl2+(εFeCl2+ + εCl−) | (11) |
The concentrations cx can be calculated as functions of density ρ and initial salt concentrations and
of a given solution. It is therefore possible to determine the composition of an unknown mixed solution of FeCl2 and FeCl3 by fitting eqn (11) to the experimental absorption spectrum, using
and
as fitting parameters.
We have tested this method for a quantitative analysis of five sample solutions containing FeCl2 and FeCl3 in concentration ratios of 1 M/0 M, 0.75 M/0.25 M, 0.5 M/0.5 M, 0.25 M/0.75 M and 0 M/1 M. Each solution was acidified with 1 M HCl to prevent hydroxide formation and oxidation. The absorption spectra of these solutions after subtraction of the HCl contribution are presented in Fig. 6. The real concentrations (known from sample preparation) and measured concentrations (obtained from fitting) of FeCl2 and FeCl3 are plotted in Fig. 7.
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Fig. 7 Comparison of concentrations as prepared and as spectroscopically retrieved of FeCl2 and FeCl3 in five mixed sample solutions. |
The logarithm of the formation constant of the ion pair FeCl+ determined this way is −0.89(4); the logarithm of the formation constant of the ion triplet FeCl2+ is −0.32(8). Both values are considerably lower than the values found in literature.17,26,28,33,42–44,49,51 However, we have to keep in mind that our measurements are susceptible mainly to the formation of contact ion pairs, while other methods might also be sensitive towards the formation of solvent separated or solvent shared ion pairs.
From the PCA of the FeCl2 spectra we extracted the molar extinction spectra of Fe2+ + 2Cl− and FeCl+ + Cl−; from the PCA of the FeCl3 spectra we extracted the molar extinction spectra of FeCl2+ + 2Cl− and FeCl2+ + Cl−. We performed a global fit of all the extinction spectra and their differences, including the previous results for manganese(II) and nickel(II) chlorides and bromides.52
For all cations we observe a peak centered around 150 cm−1, which we assign to the Θ vibration of the octahedral aqua- and chloro-complexes. This peak shifts for different cations, which can be explained by changes in reduced mass and bond strength of the complexes.
Mn2+ + 2Cl−, Ni2+ + 2Cl− and Fe2+ + 2Cl− affect approximately the same amount of water, with a minimum number of affected water molecules of 14–15. The ion pair FeCl+ + Cl− affects only half as much water, which we attribute to the charge compensation of the paired ions. The ion pair FeCl2+ + 2Cl−, on the other hand, affects a much larger number of water molecules (ca. 21), which is an indication for a hydration effect extending beyond the first hydration shell of Fe3+. Again, the minimum number of affected water molecules is reduced upon association of another chloride ion to ca. 17 in the case of FeCl2+ + Cl−.
Furthermore, our analysis could be used successfully for a quantitative determination of concentrations of FeCl2 and FeCl3 in mixed solutions of total salt concentration of 1 M with errors of less than 0.08 M. Thus we have provided a proof of principle that this technique can be used as an analytical tool for highly concentrated salt solutions.
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