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UNIQUAC-ext-PDH* Framework for the Ionic Liquid Assisted Extraction of Gallium (III)

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Abstract

Ionic liquid (IL) assisted liquid–liquid-extraction (LLE) has been emerged as fascinating pathway to extract gallium (Ga(III)) from electronic waste. The computational investigation of LLE invokes the UNIQUAC model with extended Pitzer–Debye–Hückel (PDH*) framework to accommodate long range interactions due to the presence of ions. The combination of quantum chemical calculation and global optimization technique have been incorporated to estimate the model parameters. Herein, phosphonium and ammonium-based ILs having 26 tie-lines are used for sole Ga(III) extraction and 14 tie-lines for co-extraction. The sole Ga(III) extraction exhibits deviation between 0.5 and 0.8%, and co-extraction ranges from 0.85 to 1.5% and thus highlights the goodness of estimation.

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Abbreviations

\({\mu }_{i}^\text{ext}\) \(\text{J} \cdot \text{mol}^{-1}\) :

Chemical potential of extract phase

\({\mu }_{i}^\text{raf}\) \(\text{J} \cdot \text{mol}^{-1}\) :

Chemical potential of raffinate phase

\({\gamma }_{i}^\text{ext}\) :

Activity coefficient of component in extract phase

\({\gamma }_{i}^\text{raf}\) :

Activity coefficient of component in raffinate phase

λ:

Extract and raffinate phase molar holdup split

\({\gamma }_{i}^\text{comb}\) :

Combinatorial term

\({\gamma }_{i}^\text{res}\) :

Residual term

\({\gamma }_{i}^{\text{comb}(\infty )}\) :

Combinatorial term of the infinite dilution activity coefficient

\({\gamma }_{i}^{\text{res}(\infty )}\) :

Residual term of the infinite dilution activity coefficient

\({\phi }_{i}\) :

Volume fraction

\({\theta }_{i}\) :

Surface fraction

\({\psi }_{ji}\) :

Binary interaction parameter

\({\epsilon }_\text{IL}\) :

Approximate dielectric constant of IL

\({\epsilon }_{0}\) :

Dielectric constant value of vacuum

\(\overline{{\epsilon }_{s}}\) :

Dielectric constant value for solvent

\({\epsilon }_{i}\) :

Dielectric constant of components

E :

Extraction efficiency

D :

Distribution coefficient

i :

Components

\({f}_{i}^\text{ext}\) \(\text{mol} \cdot \text{Pa}^{-1} \cdot \text{m}^{-3}\) :

Fugacity of extract phase

\({f}_{i}^\text{raf}\) \(\text{mol} \cdot \text{Pa}^{-1} \cdot \text{m}^{-3}\) :

Fugacity of raffinate phase

\({x}_{i}^\text{ext}\) :

Mole fraction of extract phase

\({x}_{i}^\text{raf}\) :

Mole fraction of raffinate phase

L ext :

Molar holdup of extract stream

L raff :

Molar holdup of raffinate stream

L feed :

Molar holdup of feed mixture

K i :

Distribution coefficient

\(z\) :

Coordination number

\({r}_{i}{,q}_{i}\)  mol:

Structural parameters of component in UNIQUAC model

\({r}_\text{solvent}{, q}_\text{solvent}\)  mol:

Structural parameters of solvent in UNIQUAC model

\({Mw}_\text{IL}\) \(\text{g} \cdot \text{mol}^{-1}\) :

IL molecular weight

\(\overline{M _s}\) \(\text{g} \cdot \text{mol}^{-1}\) :

Solvent’s average molecular weight

\({M}_{i}\) \(\text{g} \cdot \text{mol}^{-1}\) :

Molecular weight of component

\({I}_{x}\) :

Ionic strength

\({z}_{i}\) :

Electrovalence value of component

\({A}_{\phi }\) :

Debye–Hückel parameter

\({r}_{+}\) Å:

Radius of cation

\({r}_{-}\) Å:

Radius of anion

\(k\) \(\text{J} \cdot \text{K}^{-1}\) :

Boltzmann constant

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

Avogadro’s number

\(e\)  C:

Electronic charge

\(T\)  K:

Temperature

\(\overline{{d }_{s}}\) \(\text{g} \cdot \text{L}^{-1}\) :

Average density of solvent

\({d}_{i}\) \(\text{g} \cdot \text{L}^{-1}\) :

Density of component

\(C_i\), \(\text{mol} \cdot \text{L}^{-1}\) :

Metal concentration in the aqueous phase before extraction

\(C_f\), \(\text{mol} \cdot \text{L}^{-1}\) :

Metal concentration on equilibrium after extraction performed

\(K_\text{ex-IP}\) :

Ion pair extraction constant

\(K_\text{ex-IE}\) :

Ion exchange extraction constant

\(\text{Ga}^{+3}_\text{w}\), \(\text{mol} \cdot \text{L}^{-1}\) :

Raffinate phase gallium(III) concentration

\(\text{Ga}^{+3}_\text{IL}\), \(\text{mol} \cdot \text{L}^{-1}\) :

Extract phase gallium(III) concentration

\([{C^+}]_\text{IL}\), \(\text{mol} \cdot \text{L}^{-1}\) :

Concentration of the IL’s cation

\([ {A^- }]_\text{IL}\), \(\text{mol} \cdot \text{L}^{-1}\) :

Concentration of IL’s anion

\(K_\text{sp}\) :

Solubility product

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Acknowledgements

The corresponding author, i.e., Dr. Debashis Kundu, had optimized the molecular structures, PCM calculation and generated the COSMO files while pursuing his Doctoral studies at the Department of Chemical Engineering, Indian Institute of Technology Guwahati under the guidance of Prof. Tamal Banerjee. Hence, the authors gracefully acknowledge the contribution of Prof. Tamal Banerjee (Department of Chemical Engineering, Indian Institute of Technology Guwahati) for mentoring Dr. Debashis Kundu to accomplish the geometry optimized structures (Gaussian 09) and COSMO files (Gaussian 03) of the respective compounds.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for profit sectors.

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Authors and Affiliations

  1. Department of Chemical Engineering, Institute of Chemical Technology Marathwada Campus, Jalna, Maharashtra, 431203, India

    Aradhana V. Thombre & Debashis Kundu

  2. Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India

    Debashis Kundu

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  1. Aradhana V. Thombre
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AVT: Computational Methodology, Formal analysis, Investigation, Data curation, Writing—original draft, Writing Revised Draft. DK: Conceptualization, Resources, Visualization, Supervision, Funding acquisition, Writing—review & editing.

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Correspondence to Debashis Kundu.

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Thombre, A.V., Kundu, D. UNIQUAC-ext-PDH* Framework for the Ionic Liquid Assisted Extraction of Gallium (III). J Solution Chem (2024). https://doi.org/10.1007/s10953-024-01365-9

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