## 3 Results
### Carbonation  
After the precipitation process, the extra Ca(OH)\({}_{2}\) should be removed and the carbonation process introduced to both remove extra Ca(OH)\({}_{2}\) and neutralize the solution. Due to the fact that the appearance of CO\({}_{2}\) might promote the production of CaCO\({}_{3}\), which in turn might influence the final products of the carbonation process, the carbonation process was divided into 2 scenarios: with filtration and without filtration of the precipitates resulted from the precipitation process, respectively. In the filtration and carbonation scenario, the total calcium concentration (\(T_{Ca}\)) \(T_{Ca}\) = C\({}_{Ca^{2+}}\) + \(C_{CaOH+}\) + \(C_{CaSO4}\) = 33.122 mM, while the total sulfate concentration (\(T_{SO4}\)\({}^{2-}\)) \(T_{SO4}\)\({}^{2-}\) = \(C_{SO4}\)\({}^{2-}\) + \(C_{CaSO4}\) = 13.125 mM. Figure 6 shows the calculated species distributions of the carbonation process after filtration; as can be seen, the main precipitate when pH \(>\) 6 was CaCO\({}_{3}\) (Equation (12)), while in the pH range of 3-5 the main precipitate was CaSO\({}_{4}\)\(\cdot\)2H\({}_{2}\)O (Equation (43) from Table 1). As shown in Figure 6b, with the increase of pH the ratio of calcium in Ca\({}^{2+}\) ion form decreases and the ratio in CaCO\({}_{3}\) form increases, which was caused by the formation of CaCO\({}_{3}\) in the alkaline region (Equation (12)). As can be seen from Figure 6c, when the pH \(>\) 7, the dominant species is SO\({}_{4}\)\({}^{2-}\), because the dissociation of CaSO\({}_{4}\) (Equation (13)) and the dissociation of CaSO\({}_{4}\) were caused by the constant removal of Ca\({}^{2+}\) according to Equation (12). When the final pH is 7, the equilibrium species distributions are shown in Table 3; as can be seen, the equilibrium \(C_{[Ca^{2+}]}\) = 0.4509 mM, \(C_{[SO4^{2-}]}\) = 13.01 mM, and the main precipitate was CaCO\({}_{3}\)(s) (32.44 mM). \[\text{Ca}^{2+}\;+\;\text{CO}_{2}\;+\;2\text{OH}^{-}\;\leftrightarrow\;\text{ CaCO}_{3}(\text{s})\;+\;\text{H}_{2}\text{O} \tag{12}\]  
\[\text{CaSO}_{4}\;\leftrightarrow\;\text{Ca}^{2+}\;+\;\text{SO}_{4}\text{{}^{2-}} \tag{13}\]  
In the case of carbonation without filtration, the total calcium concentration is \(T_{\text{ca}}\) = 1.55 M, and the total sulfate concentration is \(T_{SO4^{2-}}\) = 1.53 M. As can be seen from Figure 7,  
Figure 6: Calculated species distributions of carbonation process with filtration at different pH: (**a**) with log concentration vs. pH; (**b**) with fraction of calcium vs. pH; and (**c**) with fraction of sulfate vs. pH. species were CaSO\({}_{4}\) 2H\({}_{2}\)O (pH: 2-5, Equation (9)), CaSO\({}_{4}\) 2H\({}_{2}\)O and CaCO\({}_{3}\) (pH: 5-13, Equations (9) and (12)), and Ca(OH)\({}_{2}\)(s) and CaCO\({}_{3}\) (pH: 13-14, Equations (11) and (12)), respectively. When pH is smaller than 2, a certain amount of CaSO\({}_{4}\) 2H\({}_{2}\)O would dissolve, as can be seen from Figure 7(b) (Equation (10)). The decrease of C\({}_{CaSO+2H2O}\) in pH 5-7 was mainly caused by the formation of CaCO\({}_{3}\) (Equation (12)), which leads to the dissolution of CaSO\({}_{4}\) 2H\({}_{2}\)O (Equation (14)), and simultaneously results in the increase of C\({}_{SO4^{2}}\)- in the same region. In other words, this decrease of C\({}_{CaSO+2H2O}\) in pH 5-7 resulted from the combination of CaSO\({}_{4}\) 2H\({}_{2}\)O dissolution reactions (Equation (14)) and carbonation reaction (Equation (12)). When pH is larger than 13, the fraction of CaSO\({}_{4}\) 2H\({}_{2}\)O further decreases to almost zero; this was caused by both the formation of CaCO\({}_{3}\) (Equation (12)), and most importantly, the formation of Ca(OH)\({}_{2}\)(s) (Equation (11)) at extremely high pH. The fraction of CaSO\({}_{4}\) 2H\({}_{2}\)O decreases with the increase of CO\({}_{2}\) concentrations, according to Figure 7b-d. To obtain a higher removal ratio of SO\({}_{4}\) 2-, 0.1 M CO\({}_{2}\) was chosen.