# Modelling the Effect of Solution Composition and Temperature on the Conductivity of Zinc Electrowinning Electrolytes

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}), H

_{2}SO

_{4}(150–200 g/dm

^{3}), Mn (0–8 g/dm

^{3}), Mg (0–4 g/dm

^{3}), and temperature, T (30–40 °C). These studies indicate that electrolyte conductivity increases with temperature and H

_{2}SO

_{4}concentration, whereas metal ions have negative effects on conductivity. In addition, the interaction effects of temperature and the concentrations of metal ions on solution conductivity were tested by comparing the performance of the linear model (Aalto-I) and interrelated models (Aalto-II and Aalto-III) to determine their significance in the electrowinning process. Statistical analysis shows that Aalto-I has the highest accuracy of all the models developed and investigated in this study. From the industrial validation, Aalto-I also demonstrates a high level of correlation in comparison to the other models presented in this study. Further comparison of model Aalto-I with the existing published models from previous studies shows that model Aalto-I substantially improves the accuracy of the zinc conductivity empirical model.

## 1. Introduction

_{2}SO

_{4}(150–200 g/dm

^{3}), Zn (50–70 g/dm

^{3}), Mn (4–8 g/dm

^{3}), and other impurities such as Mg and Ca. The main reactions during the electrowinning process are zinc deposition on the cathode (Equation (1)) and oxygen evolution on the anode (Equation (2)), although hydrogen evolution as an additional side reaction may also decrease the current efficiency at the cathode (Equation (3)).

^{0}is the standard potential of the reaction and SHE is the standard hydrogen electrode.

_{T}) can be outlined as in Equation (4):

_{cell}) is the sum of thermodynamical cell voltage (E

_{T}) and several overpotentials related to the cathodic and anodic reactions (E

_{η}), the ohmic drop of the electrolytes (E

_{ohmic}), and the resistance of the electric circuit (E

_{R}), Equation (5):

^{2}and typical current efficiencies of 89–92% [1]. Since the anodic reaction contributes more than 1.9 V of the total cell voltage [1], previous research has primarily focused on the development of new anode materials for reducing the oxygen evolution reaction (OER) overpotential [2,3,4,5,6,7,8,9,10]. Nevertheless, Pb-Ag alloys remain the most widely utilized anodes due to their low cost and favorable corrosion resistance properties in sulfuric acid media [11,12].

_{ohmic}and R

_{elec}are the ohmic drop and resistance, respectively. In addition, the electrolyte resistance, as a function of specific conductivity (κ) (as the inverse of specific resistivity (ρ)), can be written as Equation (7):

_{i}is the valence, D

_{i}is the diffusion coefficient and C

_{i}is the concentration (mol/dm

^{3}), F is the Faraday constant (96485 C/mol), R is the universal gas constant (8.314 J⋅K

^{−1}⋅mol

^{−1}), and T is the absolute temperature (K).

^{3}, and temperature T, is in °C.

_{2}SO

_{4}], and metal ion concentrations. Nevertheless, the previously published models have two major weaknesses: Firstly, the exclusion of minor impurities [15,16,17], and secondly, the utilization of a single coefficient value to represent zinc and other impurities [18,19]. Recent conductivity modelling studies in copper and silver electrolytes have demonstrated that every metal element ion present has an independent coefficient that can affect the electrolyte conductivity [20,21,22]. As a result, the main objective of this study is to develop an improved zinc electrolyte conductivity model, increasing prediction accuracy by taking into account the independent effects of metal impurities—such as Mn and Mg—along with the typical process parameters of zinc concentration, acidity, and temperature.

## 2. Materials and Methods

_{4}·7H

_{2}O, ≥99%, VWR Chemicals, Belgium), Magnesium sulfate (MgSO

_{4}·7H

_{2}O, ≥99.5%, Merck KGaA, Germany), Manganese sulfate (MnSO

_{4}·H

_{2}O, ≥99.5%, VWR Chemicals, Belgium), and sulfuric acid (H

_{2}SO

_{4}, 95–97%, Merck, Germany). All solutions were prepared with Millipore Milli-Q deionized water (≤2 μS/cm at 25 °C, EMD Millipore, Finland). The temperature of the electrolytes was controlled by a MGW Lauda MT/M3 circulating water bath (LAUDA, Lauda-Königshofen, Germany).

^{®}913 Cond conductivity meter (Knick Elektronische Messgeräte GmbH & Co. KG, Germany). Prior to measurement, the conductivity meter was calibrated in a standard reference solution (Reagecon, Ireland) with a conductivity of 12.88 mS/cm at 25 °C.

^{2}), accuracy of prediction (Q

^{2}), standard deviation of the response (SDY), residual standard deviation (RSD), validity, and reproducibility values. Based on these parameters, a good mathematical model is required to have values of Q

^{2}, with validity and reproducibility values higher than 0.5, 0.25, and 0.5, whilst the difference between Q

^{2}and R

^{2}should be <0.3 [23].

## 3. Results and Discussion

#### 3.1. Aalto Conductivity Models

^{3}, T is the temperature in °C, and κ is in mS/cm.

_{2}SO

_{4}with temperature. Nevertheless, the correlation of the minor concentrations of Mn and Mg to the temperature was deemed to be insignificant, and was thus excluded from the final model. For the pure, full-factorial model of Aalto-III, a strong correlation is observed between Zn and H

_{2}SO

_{4}. Furthermore, similar to the Aalto-II, valid interrelation of the minor concentrations was not observed either with other concentrations, or the temperature.

^{2}, Q

^{2}, validity, and conductivity. Nevertheless, from the comparison, Aalto-I has the highest values for all the statistical value requirements; in particular, the related validity value is superior to those of the other two models. As a result, Aalto-I was selected as the proposed conductivity model from this study.

_{2}SO

_{4}have a positive effect on conductivity, whereas the presence of metal ions (Zn, Mn, Mg) has a negative impact on solution conductivity. These findings are in agreement with earlier studies of Zn electrowinning conductivity [15,24,25,26], and are similar to the behavior found for Cu, Ni, and As, in copper electrowinning electrolytes [22].

#### 3.2. Comparison of Models with Synthetic Solutions

#### 3.3. Industrial Validation

#### 3.4. Model Utilization

_{ohmic}) during zinc electrowinning can be conducted by combining the equation of model Aalto-I with Equation (8), as shown in Equation (18). The sensitivity analysis result with the center point: 60 g/dm

^{3}Zn, 175 g/dm

^{3}H

_{2}SO

_{4}, 4 g/dm

^{3}Mn, 2 g/dm

^{3}Mg, at a temperature of 35 °C, is shown by Figure 7. The selected value varied by ±15%, and its effect on the conductivity was observed.

^{2}, l is in cm, concentrations are in g/cm

^{3}, and T is in °C.

_{2}SO

_{4}] and T lowered the E

_{ohmic}value, whereas an increase in the concentration of metal ions (in particular Zn) increased the level of ohmic drop. The variation from the defined H

_{2}SO

_{4}concentration (175 g/dm

^{3}H

_{2}SO

_{4}) has the most significant influence on E

_{ohmic}in the investigated parameter magnitude, while the effects of T and [Zn] are slightly lower. These findings suggest that increases in temperature, and/or acid concentration, can be considered to effectively decrease the electrolyte ohmic drop.

^{3}in order to produce the MnO

_{2}layer required for the corrosion protection of the Pb-Ag anodes [27,28,29]. However, the high concentration of Mg (11–12 g/dm

^{3}), besides causing the blockage of pipe systems [30,31,32] and difficulties in the mass-transfer process of zinc deposition [33], could also create extra electrolyte overpotential. From Aalto-I and Equation (18), approximately 15% of the electrolyte ohmic drop can be reduced by lowering the Mg concentration from 11.2 g/dm

^{3}to 2 g/dm

^{3}. Furthermore, the model Aalto-I results based on the published data of Zn electrorefining show a large deviation of the ohmic drop contribution to the cell potential, from the lowest at app. 6.1%—as discussed by We et al.—to more than double for the highest contribution to cell potential of 14.8% (outlined by Yanqing et al.) [13,18,34,35,36,37,38,39,40,41,42,43,44], as shown in Table 3.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic illustration of cells in the tank house, and the in situ conductivity measurements and sampling points.

**Figure 2.**Histogram of the specific conductivity measured from the synthetic zinc electrowinning solutions utilized in this study.

**Figure 3.**Scaled and centered coefficients of different contributory factors for constructed models Aalto-I, Aalto-II and Aalto-III.

**Figure 4.**Measured (synthetic Zn electrolyte) vs. predicted conductivity by models Aalto-I, II and III.

Parameters | Levels | Units |
---|---|---|

[Zn^{2+}
]
| 50, 60, 70 | g/dm^{3} |

[H_{2}SO_{4}
]
| 150, 175, 200 | g/dm^{3} |

[Mn^{2+}
]
| 0, 4, 8 | g/dm^{3} |

[Mg^{2+}
]
| 0, 2, 4 | g/dm^{3} |

T | 30, 35, 40 | °C |

Sample ID | Cell | Position | Composition (g/dm^{3}) | |||||
---|---|---|---|---|---|---|---|---|

Zn | H_{2}SO_{4} | Mg | Mn | Na | Ca | |||

1 | A | inlet | 52.8 | 189.6 | 11.8 | 7.3 | 2.3–2.5 | 0.4 |

2 | 1/3 | 49.4 | 192.2 | |||||

3 | 2/3 | 49.0 | 194.9 | |||||

4 | outlet | 50.3 | 192.2 | |||||

5 | B | inlet | 52.6 | 187.7 | 11.2 | 7.1 | ||

6 | 1/3 | 48.5 | 198.9 | |||||

7 | 2/3 | 48.5 | 193.2 | |||||

8 | outlet | 48.9 | 192.8 | |||||

9 | C | inlet | 54.3 | 191.0 | 11.2 | 7.2 | ||

10 | 1/3 | 47.2 | 194.1 | |||||

11 | 2/3 | 49.2 | 193.0 | |||||

12 | outlet | 50.1 | 193.7 | |||||

13 | D | inlet | 50.1 | 192.2 | 11.3 | 7.2 | ||

14 | 1/3 | 46.9 | 193.0 | |||||

15 | 2/3 | 49.4 | 195.3 | |||||

16 | outlet | 48.7 | 200.6 |

Parameters | Calculated E _{ohmic}(V) | E_{cell}(V) | Ref. | E_{ohmic}/E_{cell}(%) | ||||||
---|---|---|---|---|---|---|---|---|---|---|

[Zn] g/dm ^{3} | [H_{2}SO_{4}]g/dm ^{3} | T °C | Mn g/dm ^{3} | Mg g/dm ^{3} | l/ cm | j mA/cm ^{2} | ||||

60 | 180 | 38 | 8 | 0 | 2.0 | 50 | 0.21 | 2.898 | [34] | 7.4 |

55 | 155 | 40 | 0 | 0 | 2.5 | 40 | 0.21 | 2.89 | [35] | 7.4 |

55 | 150 | 40 | 0 | 0 | 3.0 | 40 | 0.26 | 2.91–2.98 | [36] | 8.7 |

50 | 150 | 35 | 5 | 0 | 2.0 | 50 | 0.23 | 3.22–3.8 | [37] | 6.1 |

50 | 210 | 45 | 4.6 | 12.2 | 3.8 | 40 | 0.31 | 3.21 | [18] | 9.6 |

62 | 190 | 38 | 0 | 0 | 2.5 | 50 | 0.25 | 2.91–2.99 | [38] | 8.4–8.6 |

58 | 160 | 38 | 0 | 0 | 2.5 | 50 | 0.27 | 3.03 | [39] | 9 |

55 | 165 | 38–42 | 3.5 | 15.87 | 3 | 50 | 0.42–0.44 | 3.0–3.25 | [40] | 12.8–14.8 |

48–52 | 170–190 | 35 | 0 | 0 | 3.5 | 58 | 0.39–0.44 | 3.45 | [41] | 11.3–12.4 |

65 | 150 | 35 | 5 | 0 | 3.5 | 50 | 0.44 | 3.15 | [42] | 14.1 |

50 | 150 | 38 | 3 | 0 | 3.0 | 50 | 0.33 | 3.28–3.31 | [43] | 10 |

50 | 160 | 35 | 2 | 0 | 3.0 | 50 | 0.33 | 2.66–2.82 | [44] | 11.6–12.3 |

61.5 | 171 | 38 | 5.2 | 5.31 | 2.5 | 50 | 0.30 | 3.00–3.05 | [13] | 10.0–10.1 |

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**MDPI and ACS Style**

Wang, Z.; Aji, A.T.; Wilson, B.P.; Jørstad, S.; Møll, M.; Lundström, M. Modelling the Effect of Solution Composition and Temperature on the Conductivity of Zinc Electrowinning Electrolytes. *Metals* **2021**, *11*, 1824.
https://doi.org/10.3390/met11111824

**AMA Style**

Wang Z, Aji AT, Wilson BP, Jørstad S, Møll M, Lundström M. Modelling the Effect of Solution Composition and Temperature on the Conductivity of Zinc Electrowinning Electrolytes. *Metals*. 2021; 11(11):1824.
https://doi.org/10.3390/met11111824

**Chicago/Turabian Style**

Wang, Zulin, Arif Tirto Aji, Benjamin Paul Wilson, Steinar Jørstad, Maria Møll, and Mari Lundström. 2021. "Modelling the Effect of Solution Composition and Temperature on the Conductivity of Zinc Electrowinning Electrolytes" *Metals* 11, no. 11: 1824.
https://doi.org/10.3390/met11111824