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Electrochemical activity of various types of aqueous In(III) species at a mercury electrode

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Abstract

An interpretation framework is presented which provides a straightforward means to characterise the electrochemical reactivity of aqueous ions together with their various hydrolysed counterparts. Our novel approach bypasses the more laborious strategy of solving rigorously, for all relevant species, the complete set of Butler-Volmer equations coupled to diffusion differential equations. Specifically, we consider the spatial variable via a Koutecký-Koryta type of differentiation between nonlabile and labile zones adjacent to the electrode. The theory is illustrated by an assessment of the electrochemical reactivity of aqueous In(III) species based upon proper comparison between relevant time scales of the involved interfacial processes, i.e. diffusion, (de)protonation of inner-sphere water, dissociation/release of H2O and OH−, and electron transfer. The analysis reveals that whilst all In(III) species are labile on the experimental timescale with respect to (de)protonation and (de)hydration, there are large differences in the rates of electron transfer between \( \mathrm{In}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6^{3+} \) and the various hydroxy species. Specifically, in the case of \( \mathrm{In}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6^{3+} \), the rate of electron transfer is so slow that it replaces the traditional Eigen rate-limiting water release step in the overall passage from hydrated In3+ to its reduced metallic form; in contrast, the In(III) hydroxy species display electrochemically reversible behaviour.

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Abbreviations

a :

distance of closest approach of ions (m)

A :

electrode surface area (m2)

c i :

concentration of species i (mol m−3)

\( {c}_{\mathrm{In},\mathrm{t}}^{\ast } \) :

total concentration of In(III) in the bulk aqueous medium (mol m−3)

D :

diffusion coefficient (m2 s−1)

e :

elementary charge (1.6×10−19 C)

E d :

deposition potential (V)

E d,1/2 :

half-wave deposition potential (V)

E 1/2 :

half-wave potential (V)

E 0′ :

formal potential (V)

F :

Faraday’s constant (96,485 C mol−1)

HMDE:

hanging mercury drop electrode

I :

ionic strength (mol m−3)

\( {I}_{\mathrm{d}}^{\ast } \) :

limiting value of the deposition current (A)

I s :

stripping current (A)

J dif :

diffusion-controlled flux from the bulk medium to the electrode surface (mol m−2 s−1)

J kin :

kinetically controlled flux in the reaction layer (mol m−2 s−1)

k :

Boltzmann constant (1.38×10−23 J K−1)

k a :

association rate constant (m3 mol−1 s−1)

k d :

dissociation rate constant (s−1)

k 0 :

electron transfer rate constant (m s−1)

\( {k}_{\mathrm{eff}}^0\kern-0.4em \) :

effective electron transfer rate constant (m s−1)

KK:

Koutecký-Koryta

K os :

stability constant for an outer-sphere reactant pair (m3 mol−1)

k w :

inner-sphere dehydration rate constant of hydrated metal ions (s−1)

L:

ligand

ℒ:

lability parameter (dimensionless)

m In :

charge transport coefficient for In in aqueous solution

n :

number of electrons transferred in the electrochemical reaction

N Av :

Avogadro number (6.022×1023 mol−1)

OHP:

outer Helmholtz plane

R :

gas constant (8.314 J K−1 mol−1)

SCE:

saturated calomel electrode

SSCP:

stripping chronopotentiometry at scanned deposition potential

t d :

deposition time (s)

T :

temperature (K)

V :

electrode volume (m3)

y :

nF(Ed−E0′)/RT

z :

charge on an ion

α :

charge transfer coefficient

β :

1 – α

\( {\beta}_1^{\ast } \) :

stability constant for the reaction \( \mathrm{In}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6^{3+}\rightleftharpoons \mathrm{In}{\left({\mathrm{H}}_2\mathrm{O}\right)}_5{\left(\mathrm{OH}\right)}^{2+}+{\mathrm{H}}^{+} \)

\( {\beta}_2^{\ast } \) :

stability constant for the reaction \( \mathrm{In}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6^{3+}\rightleftharpoons \mathrm{In}{\left({\mathrm{H}}_2\mathrm{O}\right)}_4{\left(\mathrm{OH}\right)}_2^{+}+2{\mathrm{H}}^{+} \)

\( {\beta}_3^{\ast } \) :

stability constant for the reaction \( \mathrm{In}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6^{3+}\rightleftharpoons \mathrm{In}{\left({\mathrm{H}}_2\mathrm{O}\right)}_3{\left(\mathrm{OH}\right)}_3^0+3{\mathrm{H}}^{+} \)

δ :

thickness of the diffusion layer in solution at the electrode/medium interface (m)

εε 0 :

dielectric permittivity of the aqueous solution (7×10−10 F m−1 at 293 K)

θ :

exp(y)

θ α :

exp(−αy)

θ β :

exp(βy)

κ −1 :

Debye layer thickness (screening length) in the bulk electrolyte medium (m)

λ :

thickness of the generalized reaction layer at the electrode/medium interface (m)

μ :

thickness of the conventional association reaction layer at the electrode/medium interface (m)

τ :

SCP transition (stripping) time (s)

τ d :

characteristic time constant of the SCP deposition process (s)

ψ OHP :

potential at the outer Helmholtz plane (V)

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All data analysed during this study are included in this manuscript.

Funding

RMT conducted this research within the EnviroStress and EXPOSOME centers of excellence funded by Universiteit Antwerpen’s Bijzonder Onderzoeksfonds (BOF).

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Authors and Affiliations

  1. Systemic Physiological and Ecotoxicological Research (SPHERE), Department of Biology, Universiteit Antwerpen, Groenenborgerlaan 171, 2020, Antwerpen, Belgium

    Raewyn M. Town

  2. Physical Chemistry and Soft Matter, Wageningen University & Research, Stippeneng 4, 6708 WE, Wageningen, The Netherlands

    Raewyn M. Town & Herman P. van Leeuwen

  3. CNRS, Laboratoire Interdisciplinaire des Environnements Continentaux (LIEC), Université de Lorraine, F-54000, Nancy, France

    Jérôme F. L. Duval

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  1. Raewyn M. Town
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  2. Jérôme F. L. Duval
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Correspondence to Raewyn M. Town.

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Town, R.M., Duval, J.F.L. & van Leeuwen, H.P. Electrochemical activity of various types of aqueous In(III) species at a mercury electrode. J Solid State Electrochem 24, 2807–2818 (2020). https://doi.org/10.1007/s10008-020-04607-0

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