## 3 Results
### Precipitation
At the same time, if pH \(>\) 12, the ratio of CaSO\({}_{4}\)\(\cdot\)2H\({}_{2}\)O might also decrease because of the formation of Ca(OH)\({}_{2}\)(s) (Figure 4c) and SO\({}_{4}\)\({}^{2-}\) (Figure 4b), according to Equation (11). The final pH and composition of the mixture are shown in Table 3; as can be seen, the equilibrium pH of the mixture is 12.42 with C\({}_{\text{Ca}^{2+}}\) = 25.06 mM, C\({}_{\text{SO}_{4}\text{${}^{2-}$}}\) = 8.668 mM, and C\({}_{\text{Ca}\text{SO}\text{${}^{4}$}}\)\(\cdot\)2H\({}_{2}\)O = 1517 mM. Based on these data, the removal ratio of SO\({}_{4}\)\({}^{2-}\) can be calculated and shown in Table 3. Also, by comparing the data obtained from the precipitation process with the saturated CaCO\({}_{3}\) and CaSO\({}_{4}\) solution data, the result indicates that if CO\({}_{2}\) was introduced in the precipitation process, the removal efficiency of SO\({}_{4}\)\({}^{2-}\) might decrease. Therefore, ambient CO\({}_{2}\) should be avoided in the precipitation process to obtain a higher removal efficiency. Also, the theoretical results obtained in this model are very close to the experimental results of [PERSON] et al. [23]. \[\text{Ca(OH)}_{2}\text{(s) }+\text{ H}_{2}\text{SO}_{4} \leftrightarrow\text{ CaSO}_{4}\text{$\cdot$}2\text{H}_{2}\text{O (s)} \tag{9}\] \[\text{CaSO}_{4}\text{$\cdot$}2\text{H}_{2}\text{O (s) }+\text{ H}^{+} \leftrightarrow\text{ HSO}_{4}\text{${}^{-}$}+\text{ Ca}^{2+} +2\text{H}_{2}\text{O}\] (10) \[\text{CaSO}_{4}\text{$\cdot$}2\text{H}_{2}\text{O (s) }+2\text{OH}^{-} \leftrightarrow\text{ Ca(OH)}_{2}\text{(s) }+\text{ SO}_{4}\text{${}^{2-}$}+2\text{H}_{2}\text{O} \tag{11}\]  
Figure 4: Calculated species distributions of 1.53 M SO\({}_{4}\)\({}^{2-}\) reacting with 1.55 M Ca(OH)\({}_{2}\) at different pH: (**a**) with log concentration vs. pH; (**b**) with fraction of sulfate vs. pH; (**c**) with fraction of calcium vs. pH. Figure 5 shows the distributions of lead-related ions at different pH. As can be seen from Figure 5a, no precipitation was formed in the whole pH range due to the extremely low concentration of lead and the existence of SO42- (Table 3). [28] This might be in favor of the precipitation process due to the fact that lead is toxic, and according to this simulation, no lead was precipitated in the precipitation process with Ca(OH)2. Figure 5b shows the fraction of lead at different pH, based on which the distribution of lead can be divided into three regions: at low pH region (pH \(<\) 2), the main form of lead is Pd2+; at moderate pH region (2 \(<\) pH \(<\) 7), lead was mainly in the form of PbSO4 (Equation (52) from Table 1); at high pH region (pH \(>\) 7), lead forms a complex with OH- ions and forms four kinds of complexes with the increase of pH (Equations (48)-(51) from Table 1). Figure 5: Calculated species distributions of 8.67 mM SO42- reacting with 0.0145 mM Pb2+ at different pH: (**a**) with log concentration vs. pH; (**b**) with fraction of lead vs. pH. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Contents** & **Species** & **Concentrations (mM)** & **Removal Efficiency of SO42-/Pb2+** \\ \hline \multirow{6}{*}{1.55 M Ca(OH)2 + 1.53 M SO42- 2- \(\mathrm{SO}_{4}\)2- \