Speciation of chromium aqua and chloro complexes in hydrochloric acid solutions at 298 K

The distribution of metal aqua and chloro complexes is fundamental information for analysis of a chemical reaction involving these complexes. The present study investigated the speciation and structures of chromium aqua and chloro complexes using the thermodynamic model fitting analysis of UV-vis/X-ray absorption spectra. The existence of a negatively charged species was examined by adsorbability of chromium species on a strong base anion exchanger. In the results, a planar square [CrIII(H2O)4]3+, a planar square or distorted tetrahedral [CrIIICl(H2O)3]2+, a trigonal bipyramidal [CrIIICl3(H2O)2]0, and a distorted octahedral [CrIIICl4(H2O)2]− were confirmed and the thermodynamic parameters of complexation reactions were quantitatively determined. Investigation of the evolution of speciation of chromium aqua and chloro complexes in a pH 1 solution suggested the existence of [CrIIICl2(H2O)m]+ (m = 2 or 3) during the hydration process, which diminished in the equilibrium state. The kinetic analysis deserves further investigation to understand the speciation process quantitatively.


Introduction
Metal aqua and chloro complexes play an important role in hydrometallurgical processes, especially involving the adsorption/ desorption process on/from ion exchangers, organic solvents, or ionic liquids. [1][2][3] The distribution of chloride complexes in brines is also signicant information in the geochemistry eld, used to simulate the ow of metal resources in the deep sea. 4 A metal aqua and chloro complex exhibits a beautiful transparent colour depending on the elements and the concentration of Cl in aqueous solutions. Changes in colour reect changes in the coordination number of Cl and/or the geometric conguration. The chemical properties of various beautiful colours have attracted many researchers and it is one of the key factors to consider when investigating metal aqua and chloro complexes. 5,6 Specically, absorption of electromagnetic radiation including light depends on electron orbitals of chemical species. Therefore, X-ray absorption spectra (XAS) as well as UV-vis absorption spectroscopy is employed to analyse chemical properties of species. 7 Raman spectroscopy besides electromagnetic radiation is also a useful technique. 8 Reactivity, such as hydrolysis, solubility, and so on can be used for understanding the thermodynamic properties. 9 The speciation of chromium aqua and chloro complexes in an equilibrium state has been investigated for over a century. [10][11][12][13][14][15][16][17][18][19][20][21] Table 1 shows a list of investigations. Most of the investigations were based on the reports by N. Bjerrum 10 or M. J. Bjerrum and J. Bjerrum,18 in which four chromium aqua and chloro complexes in an octahedral conguration were reported. The latter, M. J. Bjerrum 3 ] 0 . It is believed that all chromium aqua and chloro complexes take an octahedral conguration. [10][11][12][13][14][15][16][17][18][19][20][21] An octahedral conguration has to assume awkward geometric congurations, such as cis-[Cr III Cl 2 (H 2 O) 4 3 ] 0 are much lower than the rest of the chromium aqua and chloro complexes.
The existence of a negatively charged chromium aqua and chloro complex has not been reported. K. A. Kraus 1 reported that the adsorption of chromium species on anion exchangers was slight and the details were not clear, although adsorbability is important for hydrometallurgical processes involving purication, separation, and recovery. On the other hand, adsorption behaviour on cation exchangers has been investigated well and applied to separate chromium isotopes. [22][23][24] Every study dealing with chromium aqua and chloro complexes was based mainly on the distribution reported by M. J. Bjerrum and J. Bjerrum. 18 The authors investigated distributions of ferric, 6 cobaltous, 25 and cupric aqua and chloro complexes 26 in hydrochloric acid solutions using the thermodynamic model tting analysis they developed themselves. The tendencies of the distributions were in agreement with reported distributions, 18,22 but many differences were found in details. The differences in detail would affect the efficiency of hydrometallurgical processes and impair process improvement.
As regard to chromium aqua and chloro complexes, examination of the thermodynamic parameters in an equilibrium state is difficult since a long time is required for equilibration. 18,21 In addition, the literature has assumed that all chromium aqua and chloro complexes are in an octahedral conguration even though not only an octahedral conguration but also tetrahedral and trigonal bipyramidal congurations of other metal aqua and chloro complexes have been found. 6,25,26 Therefore, the proper geometric congurations of chromium aqua and chloro complexes should be re-investigated using a reliable analysis method.
The thermodynamic model tting analysis using series of UV-vis absorption spectra and XAS statistically extracts the best thermodynamic model out of the possible assumed models. The results are signicant in physical and chemical senses and more reliable than in previous reports.
In the present study, the thermodynamic model tting analysis was employed to examine the distribution and structures of chromium aqua and chloro complexes. Furthermore, a speciation mechanism of chromium aqua and chloro complexes in a diluted Cl solution was discussed using the properties determined in the present study.
2 Experimental procedure and data processing 2.1 Preparation of UV-vis/X-ray absorption spectra Sample solutions were prepared by dissolving reagent grade chemicals, CrCl 3 $6H 2 O and hydrochloric acid solution, purchased from FUJIFILM Wako Pure Chemical Corporation, into distilled and deionised water with resistivity greater than 180 kU m, puried by RFD260NC manufactured by Advantec Toyo Kaisha, Ltd.
Two series of solutions with different concentrations of Cr III species in an equilibrium state were prepared as listed in Table 2; one for UV-vis absorption spectra and the other for XAS measurement. The Cr III concentrations were adjusted in order to acquire spectra suitable for data analysis. The sample solutions had been maintained at 298 K in a thermostated water bath for 30 days until the UV-vis/X-ray absorption spectra were measured. The UV-vis absorption spectra were measured again aer being maintained at 298 K for 15 more days, i.e. 45 days in total, and it was conrmed that the two series of the UV-vis spectra measured 30 and 45 days aer preparation were equivalent. As a consequence, it was deduced that it took 30 days at least for Cr III aqua and chloro complexes to attain an equilibrium state at 298 K. In addition to chloride aqueous solutions, a dilute nitric acid solution dissolving 0.1 mol dm −3 -Cr III (NO 3 ) 3 .9H 2 O was prepared and its UV-vis absorption spectrum was measured in order to compare the difference in the absorption spectra with or without Cl − ions.
One more series of UV-vis absorption spectra was collected for qualitative analysis of speciation kinetics. CrCl 3 $6H 2 O was dissolved in a pH 1 solution at 0.1 mol dm −3 -Cr III and the spectrum measured with certain time intervals. In this measurement, the temperature was not maintained and ranged from 10°C to 25°C (night and day).
The two series of UV-vis absorption spectra, that is one for the equilibrium state and the other for the speciation kinetics, were collected using a V-770 Ultraviolet-visible spectrometer (JASCO Corporation) operating in the dual beam mode with a quartz cuvette with a path length of 10 mm. Dark and baseline corrections were made. UV-vis absorption spectra were collected at 298 K, and the three measurements were averaged. The spectra were recorded in the range from 364 nm to 922 nm in 2 nm increments and the abscissa was converted into wavenumber in the range from 10 860 cm −1 to 27 420 cm −1 in 60 cm −1 increments. The absorbance was interpolated using a cubic spline algorithm. 27 The Lambert-Beer law states that there is a linear relationship between the concentration of an absorbing solute, c, and the absorbance of a solution, a, when a light travels a distance of l. The product of the molar attenuation coefficient, 3, and the molarity of Cr III species, that is to say the quotient of the absorbance divided by the path length was employed for practical analysis, as shown in Fig. 1.
At the top of Fig. 1, the appearance of the series of sample solutions is displayed. Every spectrum has two characteristic absorption bands, which exhibit a red shi, and the colours of the solutions gradually change from dark bluish violet to dark green with the increase in the Cl molarity. However, no isosbestic point was observed. Therefore, the number of chromium aqua and chloro complexes greater than two were supposed. Fig. 2 shows X-ray absorption near edge structure (XANES) and extended X-ray absorption ne structure (EXAFS) spectra of chromium aqua and chloro complexes in hydrochloric acid solutions. XAS of the Cr K edge were collected using the transmission mode at BL-9C of Photon Factory with a ring energy of 2.5 GeV in Japan. A sample solution was lled up in a cell made from rigid vinyl chloride with a 20 mm-diameter window, and polyimide lm was pasted on as the window material. The path lengths of 0.5 mm or 1 mm were chosen corresponding to concentrations of salt as noted in Table 2. The incident X-rays were monochromatised by a silicon double crystal monochromator and the net planes were (111). The I 0 and I 1  ionisation chambers were lled with 70% He/30% N 2 and 25% Ar/75% N 2 , respectively.

Thermodynamic model tting analysis
An issue to be solved is an inverse problem, which draws an appropriate distribution of chromium aqua and chloro complexes in hydrochloric acid solutions from the series of UVvis/X-ray absorption spectra. An appropriate thermodynamic model was statistically determined by reproducibility of the UVvis absorption spectra. Eqn (1) can be represented as a matrix form of eqn (2).
where N is the number of signicant species,ñ and i are wavenumber and chemical species, and A ′ , C, and E are matrix forms of a ′ , c, and 3, respectively. The superscript of "tr" indicates transportation. Firstly, it should be determined how many chromium aqua and chloro complexes existed in hydrochloric acid solutions. The rst derivative test 6,25,28 was used for evaluation of the number of signicant species. When observing changes of smoothness in vectors in a unitary matrix decomposed by the singular value decomposition 29 of A ′ , a sudden change indicates a number of signicant species. The rst derivative test is the most useful and reliable index out of various empirical methods of principal component analysis. 30,31 At the beginning of the tting procedure, a distribution for a given set of thermodynamic parameters of C calc. was assessed using the EQBRM algorithm. 32 Substituting the assessed C calc. into eqn (2) derived E calc. by matrix division. E calc. would contain more distortion if the assessed C calc. was further from an appropriate distribution. A series of UV-vis spectra of A 0 calc: was re-composed by a matrix product of C tr calc. and E calc. and compared with the original spectra matrix of A ′ using R-factor dened as the following.
where a 0 ij and a 0 calc: ij denote the elements in the original A ′ and the assessed A 0 calc: , respectively. The tting parameters giving a minimum R-factor were the optimised thermodynamic parameters.
A thermodynamic model was based on formations of chromium chloro complexes and a dissociation of HCl. Formation reactions and constants of chromium chloro complexes were assumed as the following equations.
a ½Cr 3þ Â a ½Cl À n ¼ g ½Cr III Cln 3Àn m ½Cr III Cln 3Àn g ½Cr 3þ m ½Cr 3þ Â g ½Cl À m ½Cl À n ; (4b) where b n is a formation constant of [Cr III Cl n ] 3−n and a, g, and m are the activity, the activity coefficient, and the molality of the subscripted species, respectively. In addition, the dissociation reaction of HCl must be taken into account for assessment of the distribution of chromium chloro complexes.
Activity coefficients of charged aqueous species in hydrochloric acid solutions were estimated using the modied Debye-Hückel model 33 extended with the Pitzer model. 34 where g is the mean stoichiometric activity coefficient. A g and B g are the Debye-Hückel solvent parameters. I is the effective ionic strength and G g is the mole fraction to molality conversion factor. 33 z k is the charge of the aqueous species of k.å k is the distance of closest approach to k species, which mainly depends on the charge number of species. The values ofå k are assumed to be 4.0Å, 5.0Å, 9.0Å and 11.0Å for mono-, di-, tri-, and tetravalent species, respectively, referring to the reported values and the proton was the exception andå H + was 9.0Å. 35 Activity coefficients of neutral species were estimated using the Setchénow model. 36 The oxidation state of M is +n. The b terms in eqn (6) and (7) would be optimised to t the thermodynamic models to experimentally determined mean stoichiometric activity coefficients of H + summarised by Hamer and Wu 37 and Partanen et al. 34 Virtually complete dissociation is assumed when a mean stoichiometric activity coefficient is considered, therefore K d;½HCl 0 aq: was assumed 12, which was large enough so that the existence of HCl was negligible.
The tting result is demonstrated in Fig. 3 and the optimised b terms were as follows.
The modied Debye-Hückel model extended with the Pitzer model of eqn (6) with the optimised b terms reasonably represents the measured activity coefficient of H + , although the tted activity coefficient of H + deviates around the HCl molality of 1 mol kg −1 . The activity coefficient model should be improved so that the estimated curve approaches the observed activity coefficient.

Anion exchange behaviour of chromium species
The adsorbability of chromium chloro complexes on an anion exchanger was investigated. The adsorbability tells us whether a negatively charged complex exists or not in solvent. Concentrations of chromium and hydrochloric acid were set at 80 mg dm −3 and 11.6 mol dm −3 , respectively. DIAION SA10A© made by Mitsubishi Chemical Corporation is a strong basic anion exchange resin having quaternary ammonium groups, which was used as the adsorbent. Moisture adhering to the anion exchange resin was removed by centrifugation at 3000 rpm. for 10 min as a pre-treatment. 38 Fieen cm 3 of the sample solution and 5 cm 3 of resin were mixed in a ask and shaken horizontally at 100 rpm. for 10 min at 25°C. Chromium concentrations before and aer contact were analysed using a contrAA 600 atomic absorption spectrometer (Analytik Jena).

Structure analysis
The Lambert-Beer law can be applied to XAS as well as to UV-vis absorption spectra. The series of XAS of X and those of individual species of c were related as follows.
where C XAS is the distribution of chromium aqua and chloro complexes in the sample solutions for XAS measurement. Eqn (9) can be applied to both XANES and EXAFS spectra. It should be noted that C XAS must be expressed in mole fraction because XANES and EXAFS spectra are extracted from normalised XAS. XANES and EXAFS spectra of individual species were acquired using the following matrix division.
A theoretical model was tted to the individual EXAFS spectra in k-space (k = 3Å −1 to 11Å −1 ) using the Demeter 0.9.26 package. 39 The EXAFS spectrum of the assumed structure model was calculated using the FEFF programme bundled with the Demeter package. The best possible geometry congurations for each species were determined by the FEFF tting results. Representation of the resultant XANES spectra was attempted using the FDMNES code 40 and the geometry congurations examined by FEFF tting analysis.

Kinetic analysis of the chromium aqua and chloro complex speciation using model free analysis
A series of UV-vis absorption spectra of the evolution in speciation was decomposed using the multivariate curve resolutionalternative least square (MCR-ALS) technique developed by J. Jaumot et al. 41 The result is less signicant in a physical and chemical sense because the MCR-ALS is a model free analysis. Molar attenuation coefficients of individual components decomposed by the MCR-ALS were compared with those in Fig. 3 Representation of the mean stoichiometric activity coefficients of H + and Cl − . b terms in eqn (8) were fitted to the observed mean stoichiometric activity coefficient of H + summarised by Hamer and Wu. 37 The difference in g between H + and Cl − was caused by the Debye-Hückel term in eqn (8). equilibrium state investigated using the thermodynamic model tting analysis.
Considering the nature of absorbance and concentration, the following three constraints were applied to decomposition into molar attenuation coefficients and the distribution during every MCR-ALS iteration. 41 (1) Non-negativity: a molar attenuation coefficient and a concentration of species must be positive. A negative value is forced to be zero during iteration.
(2) Unimodality: it is assumed that a concentration prole as a function of time aer dissolution has one maximum, and monotonically decreases/increases on the le/right sides.
(3) Colosure: the total concentration of chromium species in the sample solution was xed at 0.10 mol dm −3 .
Besides MCR-ALS decomposition, a qualitative analysis was carried out. Principal spectra were intuitively extracted observing isosbestic points and changes in UV-vis absorption spectra during hydration. Compositions of possible species were assessed tting linear combinations of the extracted principal spectra.

Distribution and molar attenuation coefficients of chromium chloro complexes
The thermodynamic model tting analysis was applied to UVvis absorption spectra in order to obtain distribution and molar attenuation coefficients of individual chromium chloro complexes.
3.1.1 Building thermodynamic models. Possible combinations of coordination numbers of Cl ligands to Cr III atoms depend on the signicant number of complexes and minimum/ maximum coordination numbers.
The result of the rst derivative test 6,28 of the series of UV-vis absorption spectra in the equilibrium state shown in Fig. 1 is shown in Fig. 4. The changes in the smoothness are sudden when the number of components is four, and this indicates the number of signicant components, that is to say chromium chloro complexes.
The minimum coordination number of Cl ligands was supposed to be zero. The UV-vis absorption spectrum of the solution dissolving Cr(NO 3 ) 3 $9H 2 O at pH 2 was equivalent to that of the solution dissolving CrCl 3 $6H 2 O at pH 2, although the possible ligands were different; one was Cl − and the other was NO 3 − . Hence, it was deduced that the generated chromium complexes in the two solutions were equal and were chromium aqua complexes without Cl − or NO 3 − ligands.
The maximum Cl − coordination number was estimated to be six using the ionic radius. 42 The ionic radius ratio of r Cl −/r Cr 3+ was 167 pm/75.5 pm = 2.212 when six coordination was assumed. According to the so-sphere model, six coordination was possible because 1.366 < r Cl − /r Cr 3+ = 2.212 < 2.414. In contrast to six coordination, eight coordination was not possible because r Cl − /r Cr 3+ was outside the range. Thus, the maximum coordination number of Cl − was supposed to be six.
Thus, the possible combinations of the coordination numbers of Cl − ligands were the 20 combinations of four digits. The combinations had to include zero and the maximum had to be less than or equal to six. A combination is expressed as (n 1 n 2 n 3 n 4 ) in this paper, where n k (k = 1, ., 4) were the coordination numbers of Cl − which could be substituted to n of eqn (4). In practice, n 1 was always zero and three formation reactions and constants would be assumed for every thermodynamic model.
3.1.2 Speciation of chromium aqua and chloro complexes. Thermodynamic model tting analysis was conducted for every possible combination of the Cl − coordination numbers on the series of UV-vis absorption spectra. The R-factor as a function of the combinations of the coordination numbers of Cl − is plotted in Fig. 5. It was determined that the best possible thermodynamic model was the (0134) model and the thermodynamic parameters were optimised as listed in Table 3. The distribution and the molar attenuation coefficients assessed using the (0134) model are displayed in Fig. 6. The coordination numbers of H 2 O are noted in the chemical formulae, which will be determined later in Section 3.2.2. Fig. 4 The results of the first derivative test 6,28 of UV-vis absorption spectra shown in Fig. 1. The solid green and violet lines show the change in the slope when the number of components is four. Fig. 5 The results of the thermodynamic model fitting analysis. The solid green horizontal line indicates the minimum level of R-factor, which corresponds to that of the (0134) model. In Fig. 6(a) 2 ] − will be discussed in the next section.
The molar attenuation coefficients of every chromium aqua and chloro complex are similar in the two absorption bands, the intervals between the two absorption bands, and the red shis with the increase in the coordination number of Cl, while those of the ferric, cobaltous, and cupric aqua and chloro complexes are different as regards the characteristics of spectral features. 6,25,26 It is supposed that the absorption mechanism of the chromium aqua and chloro complexes in the UV-vis range is different from those of the other metal aqua and chloro complexes. Another analysis such as ab initio calculation is necessary in order to clarify the difference in the absorption mechanism.
The absorption bands are in good agreement with previous reports by Mønsted and Mønsted 14 and Díaz-Moreno et al., 20 although the assignment of chromium aqua and chloro complexes in the present study conicts with the previous reports. In the previous reports, sample solutions were prepared by dissolving specic crystals having characteristics equivalent to assigned species and ageing for a certain time.  3 ] 0 , respectively. Spectrum analysis using ab initio calculation is necessary for reliable assignment of a spectrum to a species and it deserves further investigation in the future.
3.1.3 Anion exchange behaviour of chromium species. The anion exchange behaviour of chromium species in an 11.6 mol dm −3 -HCl solution was investigated using the batch method. 38 Sample solutions taken in one hour and one, two, and four weeks aer preparation were used as the initial solutions. The chromium concentrations before and aer the adsorption tests are plotted at the top of Fig. 7. In addition, distribution coefficients, K D , are displayed at the bottom. K D was examined using the following equation.
where c init. Cr and c nal Cr are the chromium concentrations before and aer the adsorption test. The distribution coefficient of chromium species from a concentrated 10.9 mol dm −3 -Cl aqueous solution was assessed for comparison. In 10.9 mol dm −3 -Cl aqueous solution, a negatively charged [Cr III Cl 4 (H 2 -O) 2 ] − exists at 55 mol% as shown in Fig. 6(a). It was assumed that all [Cr III Cl 4 (H 2 O) 2 ] − was adsorbed on the resin for assessment.
As shown in Fig. 7, no adsorption was observed in the solution just aer preparation, and then the amount of adsorption slightly increased. However, the chromium concentrations in the nal solutions two and four weeks aer preparation were at the equivalent level. This means that an equilibrium state in a concentrated HCl solution was attained in two weeks. This implies that a chromium aqua and chloro complex in a concentrated HCl solution attains equilibrium faster than that in a diluted HCl solution.
The distribution coefficient determined by the batch experiment was less than that assessed from the distribution of Table 3 The logarithms of the formation constants for the chromium aqua and chloro complexes a

Formation reaction
The logarithm of the cumulative formation constant, log 10   chromium aqua and chloro complexes shown in Fig. 6(b). It is supposed that the difference was caused by competition between the negatively charged chromium chloro complex of [Cr III Cl 4 (H 2 O) 2 ] − and Cl − ion for adsorption on a functional group, especially in a concentrated chloride aqueous media. Furthermore, it is possible that 10 min was too short a time to attain a steady state. Thus, it was conrmed that the chromium species adsorbs on a strong basic anion exchange resin in an 11.6 mol dm −3 -HCl solution. It is deduced that a negatively charged chromium aqua and chloro complex is formed, although most literature has reported that the maximum coordination number of Cl − ligands to Cr III atom was three. 10-21 [Cr III Cl 3 (H 2 O) x ] 0 is a neutral species not adsorbed on anion exchanger. Adsorption of chromium species from a concentrated HCl solution ensures the (0134) model is a realistic model.

Analysis of X-ray absorption spectra
The EXAFS spectra of the individual species were acquired for the structure analysis. Dividing the series of the XANES and EXAFS spectra by the distribution of chromium chloro complexes in the sample solutions for XAFS measurement yielded the XANES and EXAFS spectra of the individual species. The distribution, the XANES, and the EXAFS spectra are shown in Fig. 8. 3.2.1 XANES spectra of individual chromium aqua and chloro complexes. The XANES spectra decomposed using eqn (9b) with that of a Cr 2 O 3 crystal are shown in Fig. 8(b). The XANES spectra of the individual species except [Cr III Cl 4 (H 2 O) 2 ] − were less distinguishable from each other and the intensities of the pre-edge peaks were comparable, too. This means that their orbital congurations were similar to each other.
The XANES spectrum of [Cr III Cl 4 (H 2 O) 2 ] − was hardly acceptable because it had a negative intensity around the pre-edge peak (at 5990 eV) and it was noisier than the others. In addition, the slope of [Cr III Cl 4 (H 2 O) 2 ] − around the absorption edge was steeper than the others including Cr 2 O 3 , which was fully oxidised to three. The steeper slope implies that [Cr III Cl 4 (H 2 O) 2 ] − was more oxidised than Cr 2 O 3 ; however that is impossible. This was for the same reason that the EXAFS spectrum of [Cr III Cl 4 (H 2 O) 2 ] − was not qualied enough. The stronger activity of Cl − would be necessary to acquire a better spectrum, but it was impossible under the conditions of the present study.
3.2.2 Structure analysis using EXAFS spectra. The structure analysis was conducted using the EXAFS spectra of the individual chromium aqua and chloro complexes shown in Fig. 8(c). The R-factor between the observed spectrum and the tted structure model, the difference of the absorption edge to the tted model of DE, and the Debye-Waller factor of s 2 were used as indices to evaluate the tting result. The three indices have their own recommended ranges. 43 R # 0:05; jDEj # 10; 0:002 # s 2 # 0:03: (11) It was judged that the model was inappropriate if any of the indices was outside the ranges. The thermodynamic model   Table 4 The results of FEFF fitting to the resultant EXAFS spectra of the individual chromium aqua and chloro complexes in hydrochloric acid solutions acquired in the transmission mode tting analysis in the present study could not deal with the H 2 O coordination; therefore determination of the coordination number of the H 2 O ligands was involved in the structure analysis. Various possible coordination geometries were assumed and tted to the obtained individual EXAFS spectra. Table 4 shows the results of the FEFF tting analysis when the (0134) model was assumed. Fig. 9 shows a visual representation of FEFF tting analysis of the best possible structures, that is to say a planar square of [Cr III 3 ] 2+ had four-fold coordination, although previous literature reported all chromium aqua and chloro complexes had six-fold coordination and an octahedral geometry conguration. [10][11][12][13][14][15][16][17][18][19][20][21] As for the chromium aqua complex without Cl ligands, the Rfactor of the planar square of [Cr III (H 2 O) 4 ] 3+ was the smallest and it was deduced that it was the best possible structure. Previous literature reported that the chromium aqua complex was in octahedral geometry having six H 2 O ligands. 11,12,[14][15][16][17][18][19][20] Fitting an octahedral [Cr III (H 2 O) 6 ] 3+ model to the EXAFS spectrum yielded an R-factor of 0.0922, which indicates the assumed theoretical model was inappropriate. The extracted signal of the chromium aqua complex was qualied enough to be analysed because the total fraction of [Cr III (H 2 O) 4 3 ] 2+ were less than the typical value dened by eqn (11). A Debye-Waller factor represents a displacement of a scatter atom from an average position. An energy surface yielded by ab initio calculation can show the rigidity or exibility in the position of a ligand. Therefore, an ab initio calculation is necessary for further evaluation. Moreover, a comparison in single point energies calculated by an ab initio technique species which geometry conguration is suitable to [ Fig. 10 is apparently considered to consist of two peaks. In other words, the two paths of Cr-O and Cr-Cl must be assumed to represent the maximum peak. Therefore, models of a planar square or tetrahedral [Cr III Cl 4 ] − were not appropriate.
However, the difference in absorption edge between the assumed model of the octahedral [Cr III Cl 4 (H 2 O) 2 ] − and the examined spectrum was greater than the recommended range dened by eqn (11). As shown in Fig. 8(b) and (c), the XANES and EXAFS spectra of [Cr III Cl 4 (H 2 O) 2 ] − were noisier than those of the other species. This is because the fraction of [Cr III Cl 4 (-H 2 O) 2 ] − in all examined solutions was 9 mol%, much smaller than the others from 27 mol% to 33 mol%. Therefore, the extracted EXAFS spectrum of [Cr III Cl 4 (H 2 O) 2 ] − was not fully qualied for structure analysis and the indices dened by eqn (11) should not be fully employed for evaluation. Fig. 11 shows the evolution of UV-vis absorption spectra of a pH 1 solution dissolving CrCl 3 $6H 2 O, which was collected in order to qualitatively analyse the development in speciation of chromium aqua and chloro complexes. The UV-vis absorption spectrum in an equilibrium state was deemed to be approximately equivalent to that of the 0.3 mol dm −1 -Cl sample solution out of the sample solutions for UV-vis measurement listed in Table 2, because the Cl molarity was 0.4 mol dm −1 originating from CrCl 3 $6H 2 O crystal and added HCl.

Speciation of chromium aqua and chloro complexes in pH 1 solution
A number of signicant components in speciation were evaluated using the rst derivative test. 6,28 The result of the rst derivative test is shown in Fig. 12 and it suggested four significant components.
The series of the UV-vis absorption spectra in the evolution was decomposed in two ways. One way was extraction of the principal spectra based on the isosbestic points. The evolution of the speciation was divided into three regions and isosbestic points were observed in each region, as shown in Fig. 11. Each region consisted of two components. The nal component in one region and the initial component in the subsequent region were considered equivalent. Every spectrum could be reconstructed by tting a linear combination of the two principal spectra. The other way was mathematical decomposition using the MCR-ALS technique. 41 The molar attenuation coefficients of the principal spectra decomposed by the MCR-ALS technique are shown in Fig. 13. The principal spectra extracted based on the isosbestic points were the spectra observed just aer preparation, at 15.9 ks, at 20.4 ks, and in an equilibrium state. These were equivalent to those of the initial, the second, the third, and the nal components acquired through the MCR-ALS analysis and are not displayed in Fig. 13.
The species development during the evolution to the equilibrium state is shown in Fig. 14. The developments were obtained by the MCR-ALS technique and linear combination tting of the principal spectra in each region. The R-factor, which is a mist between the observed and the tted UV-vis absorption spectra, is larger around the boundary between regions 1 and 2. This implies that the representation of the principal spectra and the species development would contain more distortion compared to region 3.
The kinetic model tting analysis deserves further investigation to understand the speciation mechanism in detail. An Fig. 11 The evolution of UV-vis absorption spectra of a pH 1 solution dissolving CrCl 3 $6H 2 O at room temperature. The evolution was divided into three regions and the spectra developed in regions 1, 2, and 3 in turn. The three bottom plots show details of the spectra in each region. Isosbestic points indicated by circles were observed in each plot. Fig. 12 The result of the first derivative test 6,28 of UV-vis absorption spectra shown in Fig. 11. The red and orange solid lines show the change in the slope when the number of components is four.
appropriate model would represent the evolution of the speciation as the thermodynamic model tting analysis represents the series of the UV-vis absorption spectra in equilibrium state. Fig. 14, four signicant species emerged and diminished in the order of the initial, the second, the third, and the nal components. The molar attenuation coefficients corresponding to the signicant species in the evolution of the speciation shown at the top of Fig. 13(a) were compared with the results of the thermodynamic model tting analysis shown at the bottom in order to assign the species. The plots on the le are arranged by experiment (a), and those at the right are arranged by species (b).

Estimation of possible species. As shown in
The absorption spectra of [Cr III (H 2 O) 4 ] 3+ and the nal component in the speciation in the pH 1 solution were equivalent. Furthermore, those of [Cr III Cl(H 2 O) 3 ] 2+ and the third component were also in good agreement. Therefore, the species of the aqua complex and the monochloro complex determined through the thermodynamic model tting analysis and the third and the nal components acquired through the qualitative analysis of the evolution of the speciation in pH 1 solution were identical.
It is interesting that the absorption bands of [Cr III Cl 3 (H 2 O) 2 ] 0 determined through the thermodynamic model tting analysis were equal to those of the initial component in the speciation in the pH 1 solution. On the other hand, their intensities were not equal. There is a possibility that the coordination number of Cl was three and that the geometry conguration including the coordination number of H 2 O ligands might be different. It is necessary to compare the structures between [Cr III Cl 3 (H 2 O) 2 ] 0 and the initial component in the evolution of the speciation in order to reveal any agreement or difference in structure between them. Fig. 14 Development of species fraction in the pH 1 solution dissolving CrCl 3 $6H 2 O at room temperature obtained by the decomposition of the series of the spectra depending on the time after preparation using the MCR-ALS technique (thick and closed symbols) and the linear combination fitting of the principal components in each region (thin and open symbols). Equilibrium was attained over 30 days, because the solution had not been maintained at a constant temperature and the room temperature had ranged from 10°C to 25°C (night and day). The R-factor indicates a misfit between the observed and the fitted absorption spectra. a distorted octahedron of [Cr III Cl 4 (H 2 O) 2 ] − . In addition, the thermodynamic parameters of the formation constants and the Setchénow coefficient of the neutral [Cr III Cl 3 (H 2 O) 2 ] 0 complex were successfully determined.
The distribution of chromium aqua and chloro complexes examined using the thermodynamic model tting analysis in Section 3.1.2 was validated by the success of the structure analysis, although the structure of [Cr III Cl 4 (H 2 O) 2 ] − was not rmly determined.
During the speciation development in pH 1 solution, the chromium aqua and chloro complex transformed in the following order.
[Cr III Cl 3  The chemical properties obtained in the present study are important information for hydrometallurgical processes, investigation, and so on, involving the chromium aqua and chloro complexes.

Conflicts of interest
There are no conicts of interest to declare.