## 1 Introduction  
SO\({}_{2}\) in the atmosphere mainly comes from volcanic eruptions [1], burning fossil fuels in power plants [2], metal processing and smelting [3]. In the process of CO\({}_{2}\) capture and sequestration (CCS), SO\({}_{2}\) is also an impurity, and to sequester it with CO\({}_{2}\) in the deep saline aquifers can reduce the cost. Deep saline aquifers contain a variety of electrolyte ions (e.g., Na\({}^{+}\), K\({}^{+}\), Ca\({}^{+}\), Mg\({}^{2+}\), Cl\({}^{-}\), SO\({}_{4}^{2-}\)). Therefore, it is essential to study the solubility of single gases and mixed gases in multi-ion electrolyte solutions. The solubility model of CO\({}_{2}\) in multi-ion electrolyte solutions has been reported in our previous studies [4, 5], so this work focuses on the solubility model of SO\({}_{2}\) in multi-ion electrolyte solutions under different temperature-pressure (\(T\)-\(P\)) conditions. This research is of great practical significance for the co-storage of CO\({}_{2}\)-SO\({}_{2}\) gas mixtrelies in deep saline aquifers. Due to the strong corrosive potential of SO\({}_{2}\), experimental solubility data for SO\({}_{2}\) in multi-ion electrolyte solutions are difficult to collect, especially at high temperatures and pressures. Therefore, predictive SO\({}_{2}\) solubility models are desired. In recent decades, many scholars have developed thermodynamic models to predict SO\({}_{2}\) solubility in multi-ion electrolyte solutions (Table 1). [PERSON] et al. [6] applied the methods from [PERSON] [16; 17] and [PERSON] [18] to estimate activity coefficients, which can predict the solubility of SO\({}_{2}\) in Na\({}_{2}\)SO\({}_{4}\) or H\({}_{2}\)SO\({}_{4}\) solutions from 10\({}^{-4}\) to 0.1 bar at 298 K and 323 K. [PERSON] et al. [7] developed a phase equilibrium model to calculate SO\({}_{2}\) solubility in NaCl and NH\({}_{4}\)Cl aqueous solutions, from 313 to 393 K at total pressures up to 37 bar, which is capable of representing most of the experimental data within experimental uncertainties. [PERSON] et al. [8] adopted the extended Debye-Huckel theory [19] and the [PERSON] [20] ion-interaction model to evaluate the activity coefficients of ionic species, which can be used to predict the absorption equilibria of dilute SO\({}_{2}\) in seawater in the temperature range from 278.15 to 318.15 K with a pressure of up to 0.976 bar. [PERSON] [9] proposed a model for the solubility of SO\({}_{2}\) using Henry's Law in pure water with temperatures ranging between 293 and 333 K, with SO\({}_{2}\) partially pressurized up to 0.01 bar. [PERSON] et al. [10] developed a thermodynamic model with the [PERSON] activity coefficient theory and the [PERSON]'s approach from [PERSON] and [PERSON] [21], which can predict the SO\({}_{2}\) solubility in HCl, NaCl, HBr and NaBr electrolyte solutions. The applicable _P-T-m_ range is 298 K, 1.015 bar, 0-4.61 kg/mol. The developed thermodynamic model by [PERSON] et al. [10] is in good agreement with experimental data. [PERSON] et al. [11] developed a solubility model of SO\({}_{2}\) in pure water with a valid _T-P_ range of 298-313 K and 0.2-3.6 bar. The model is in good agreement with experimental data at lower pressures, but improvements are needed at higher pressures (\(p>\) 1.5 bar). [PERSON] et al. [12] adopted the PC-SAFT/PMSA and CPA EOS to evaluate SO\({}_{2}\) solubility in pure water and NaCl electrolyte solutions up to 393 K and 40 bar and 6 mol/kg. [PERSON] et al. [22] applied the SAFT1 model to estimate CO\({}_{2}\)-SO\({}_{2}\) solubility in pure water, covering a valid _T-P_ range of 303.15-373.15 K and 60-300 bar. [PERSON] et al. [13] developed an equilibrium model by the Pitzer and Sechenov approach, which provides a reliable prediction of SO\({}_{2}\) solubility in seawater and brine at 298 K and 323 K with molality of electrolytes up to 1 mol/kg. [PERSON] et al.