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Determination of the Distribution of Cobalt-Chloro Complexes in Hydrochloric Acid Solutions at 298 K

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Abstract

Knowledge of the distribution of metal-chloro complexes in hydrochloric acid solutions is fundamental for understanding the anion-exchange reaction. Anion-exchange separation allows ultrahigh purification during hydrometallurgical processes. However, at present the exchange reactions are not understood in detail. A more sophisticated purification needs improvement of the anion-exchange separation process. The process is based upon anion-exchange reactions and the distribution of metal-chloro complexes. The present work deals with cobalt-chloro complexes which exhibit a beautiful deep blue color in a concentrated hydrochloric acid solution. The intensity of the absorption attributed to the deep blue color is so strong that it is hard to obtain meaningful results by factor analysis. Another absorption band was chosen to be used in factor analysis and the attempt was successful. The number of cobalt-chloro complexes in hydrochloric acid solutions was determined to be three, and the cumulative formation constants were fitted to absorption spectra decomposed by factor analysis. During the optimization of the cumulative formation constants, a modified Debye–Hückel model for estimation of the activity coefficients of \(\hbox {Cl}^{-}\) was used. It was found that there are three cobalt complexes \([\hbox {Co}^{\mathrm{II}}(\hbox {H}_{2}\hbox {O})_{6}]^{2+}\), \([\hbox {Co}^{\mathrm{II}}\hbox {Cl}(\hbox {H}_{2}\hbox {O})_{5}]^{+}\), and \([\hbox {Co}^{\mathrm{II}}\hbox {Cl}_{4}]^{2-}\), and the two cumulative formation constants were optimized such that \(\log _{10}\beta _{1} = -\,0.861\) and \(\log _{10}\beta _{4} = -\,7.40\). The geometries of the complexes are proposed by assignment of absorption bands using ligand field theory. A qualitative assessment of the relationship between the acquired distribution of cobalt-chloro complexes and the adsorption function of cobalt species from hydrochloric acid solutions to anion-exchange resin was made.

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Abbreviations

\(a_{\lambda }\) :

Absorbance at \(\lambda \) nm

\(\lambda \) :

Wavelength

\(l_{\text {path}}\) :

Path length in solution sample.

\(M_{i}\) :

Molarity of the subscripted species

\(\varepsilon _{i, \lambda }\) :

Molar attenuation coefficient of the subscripted species at \(\lambda \) nm

\({\mathbf {A}}\) :

Matrix of the total absorbance

\({\mathbf {C}}\) :

Matrix of the concentration profiles of species

\({\mathbf {E}}\) :

Matrix of the molar attenuation coefficients of species

\({\textit{RE}}\) :

Malinowski’s residual error function

\(\sigma \) :

Singular values of the concerned matrix

s :

Number of the singular values of the concerned matrix

\(m_{\text {row}}\) :

Number of rows in the concerned matrix

\(n_{\text {column}}\) :

Number of columns in the concerned matrix

n :

Coordination number

\(\beta _{n}\) :

Cumulative formation constants.

a :

Activity

\(\gamma \) :

Activity coefficient

m :

Molality of aqueous species

z :

Charge of aqueous species

\(\displaystyle {\bar{I} = \frac{1}{2}\sum _{i}m_{i}z_{i}}\) :

Effective ionic strength

\(m^{*}\) :

Sum of molalities of all solute species

\(\Gamma _{\gamma }\) :

Conversion factor from a mole fraction to molality

b :

Interaction parameters for salt

\({\mathring{a}}_{k}\) :

Distance of the closest approach for aqueous species k

\(\displaystyle {A_{\gamma } = \dfrac{e^{3}\sqrt{2\pi {}{\mathrm {N}}_{\mathrm {A}}\rho _{\mathrm{H}_{2}{\mathrm{O}}}}}{(\ln {}10)\sqrt{1000}\left( \varepsilon _{\mathrm{H}_{2}{\mathrm{O}}}{\mathrm {k}}T\right) ^{3/2}}}\) :

The Debye–Hückel limiting slope parameter

\(\displaystyle {B_{\gamma } = \sqrt{\dfrac{8\pi {}{\mathrm {N}}_{\mathrm {A}}\rho _{\mathrm{H}_{2}{\mathrm{O}}}e^{2}}{1000\varepsilon _{\mathrm{H}_{2}{\mathrm{O}}}{\mathrm {k}}T}}}\) :

The Debye–Hückel solvent parameter

\({\mathrm {N}}_{\mathrm {A}}\) :

The Avogadro constant

e :

The absolute electronic charge

\(\rho _{\mathrm{H}_{2}{\mathrm{O}}}\) :

Density of \(\hbox {H}_{2}\hbox {O}\)

\(\varepsilon _{\mathrm{H}_{2}{\mathrm{O}}}\) :

Dielectric constant of \(\hbox {H}_{2}\hbox {O}\)

\({\mathrm {k}}\) :

The Boltzmann constant

T :

The absolute temperature

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Acknowledgements

The author thanks Mr. Yuji Baba for his devotion to the experiments. This research was carried out as one of the projects of the Materiasls Science & Technology (MSTeC) Research Center at the Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University.

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  1. Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Katahira 2-1-1, Aoba, Sendai, 980-8577, Japan

    Masahito Uchikoshi

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Uchikoshi, M. Determination of the Distribution of Cobalt-Chloro Complexes in Hydrochloric Acid Solutions at 298 K. J Solution Chem 47, 2021–2038 (2018). https://doi.org/10.1007/s10953-018-0831-z

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